Talk:BPFK Section: Inexact Numbers
Will this work for fractional quantifiers?
piPA sumti == lo piPA si'e be sumti
When a sumti has a single referent (which may be a simple individual, a group, a set, etc.) then a fractional quantifier refers to a corresponding fraction of the referent. In particular, a fraction of a group or a set is a subgroup or subset whose cardinality is the corresponding fraction of the cardinality of the whole.
When a sumti has more than one referent (e.g. le ci plise) then a fractional quantifier refers to a fraction of one (which one is not specified) of the referents. Then {pimu le ci plise} is "half of one of the three apples. Then more generally we can define:
piPA sumti == lo piPA si'e be pa me sumti
which will also cover the case of a single referent.
We may then generalize to things like {repimu le ci plise} for "two and a half of the three apples".
mu'o mi'e xorxes
> Re: BPFK Section: Inexact Numbers > > Will this work for fractional quantifiers? > > piPA sumti == lo piPA si'e be sumti > > When a sumti has a single referent (which may > be a simple individual, a group, a set, etc.) > then a fractional quantifier refers to a > corresponding fraction of the referent. In > particular, a fraction of a group or a set is a > subgroup or subset whose cardinality is the > corresponding fraction of the cardinality of > the whole.
Yes, this seems the reasonable way to go — most useful and nearest tradition (I think many peopel have done it this way even when JCB was explicitly chopping objects in the set to pieces.)
> > When a sumti has more than one referent (e.g. > le ci plise) then a fractional quantifier > refers to a fraction of one (which one is not > specified) of the referents. Then {pimu le ci > plise} is "half of one of the three apples.
Well, this is still one referent due to Lojban's plural problem, so why not keep the same pattern (except now we know what we are taking the fraction of)? Consistency in the roles of these various items is a major virtue for me and for several other people who have voiced opinions. Partitive is again the most common usage — at least in English (which in this case gives no evidence of being peculiar).
> Then more generally we can define: > piPA sumti == lo piPA si'e be pa me > sumti > > which will also cover the case of a single > referent. > > We may then generalize to things like {repimu > le ci plise} for "two and a half of the three > apples".
This looks to be back at the first definition; why the divergence in the middle? Or have I missed something about that middle case (or the one enclosing it)?
pc: > > Re: BPFK Section: Inexact Numbers > > > > Will this work for fractional quantifiers? > > > > piPA sumti == lo piPA si'e be sumti > > > > When a sumti has a single referent (which may > > be a simple individual, a group, a set, etc.) > > then a fractional quantifier refers to a > > corresponding fraction of the referent. In > > particular, a fraction of a group or a set is a > > subgroup or subset whose cardinality is the > > corresponding fraction of the cardinality of > > the whole. > > Yes, this seems the reasonable way to go — most > useful and nearest tradition (I think many peopel > have done it this way even when JCB was > explicitly chopping objects in the set to > pieces.) > > > > > When a sumti has more than one referent (e.g. > > le ci plise) then a fractional quantifier > > refers to a fraction of one (which one is not > > specified) of the referents. Then {pimu le ci > > plise} is "half of one of the three apples. > > Well, this is still one referent due to Lojban's > plural problem, so why not keep the same pattern > (except now we know what we are taking the > fraction of)? Consistency in the roles of these > various items is a major virtue for me and for > several other people who have voiced opinions. > Partitive is again the most common usage — at > least in English (which in this case gives no > evidence of being peculiar). > > > Then more generally we can define: > > piPA sumti == lo piPA si'e be pa me > > sumti > > > > which will also cover the case of a single > > referent. > > > > We may then generalize to things like {repimu > > le ci plise} for "two and a half of the three > > apples". > > This looks to be back at the first definition; > why the divergence in the middle? Or have I > missed something about that middle case (or the > one enclosing it)?
I don't know, I can't figure it out from your comments.
The proposal gives a set of two apples for {pimu le'i vo plise}, a group of two apples for {pimu lei vo plise}, half an apple for {pimu le vo plise}, and three and a half apples for {cipimu le vo plise}.
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wrote: > > The proposal gives a set of two apples for > {pimu le'i vo plise}, > a group of two apples for {pimu lei vo plise}, > half an apple > for {pimu le vo plise}, and three and a half > apples > for {cipimu le vo plise}.
Good, so I did understand it. And now my question is "Why is the {le} case different from the others, chopping up one member of the group, when all the others chop the group / set / mass / whatever?" Why not two apples for half of four apples, rather than half of one apple (or -- considerably less plausibly than two but more than half of one — half of each of the four apples)?
pc: > Good, so I did understand it. And now my > question is "Why is the {le} case different from > the others, chopping up one member of the group, > when all the others chop the group / set / mass / > whatever?"
In the case of {le}, there is no group involved, just the individuals themselves.
The fractional always indicates a fraction of the referent: a fraction of a set of apples for {le'i plise}, a fraction of a group of apples for {lei plise}, a fraction of an individual apple for {le plise}.
> Why not two apples for half of four > apples, rather than half of one apple (or -- > considerably less plausibly than two but more > than half of one — half of each of the four > apples)?
So that we can have:
3.5 le vo plise = 3.5 of the 4 apples 3.0 le vo plise = 3.0 of the 4 apples 2.5 le vo plise = 2.5 of the 4 apples 2.0 le vo plise = 2.0 of the 4 apples 1.5 le vo plise = 1.5 of the 4 apples 1.0 le vo plise = 1.0 of the 4 apples 0.5 le vo plise = 0.5 of the 4 apples
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wrote:
> > pc: > > Good, so I did understand it. And now my > > question is "Why is the {le} case different > from > > the others, chopping up one member of the > group, > > when all the others chop the group / set / > mass / > > whatever?" > > In the case of {le}, there is no group > involved, just > the individuals themselves.
How did I miss the shift to plural quantification? If there are four apples then they can be the referents only if plural references are dealt with.., they are not in standard Lojban.
> The fractional always indicates a fraction of > the > referent: a fraction of a set of apples for > {le'i plise}, > a fraction of a group of apples for {lei > plise}, a fraction > of an individual apple for {le plise}.
But you just said the referent was the four apples, not some one of them. Please stick to one side of the issue or the other.
> > Why not two apples for half of four > > apples, rather than half of one apple (or -- > > considerably less plausibly than two but more > > than half of one — half of each of the four > > apples)? > > So that we can have: > > 3.5 le vo plise = 3.5 of the 4 apples > 3.0 le vo plise = 3.0 of the 4 apples > 2.5 le vo plise = 2.5 of the 4 apples > 2.0 le vo plise = 2.0 of the 4 apples > 1.5 le vo plise = 1.5 of the 4 apples > 1.0 le vo plise = 1.0 of the 4 apples > 0.5 le vo plise = 0.5 of the 4 apples > > mu'o mi'e xorxes
Ahah! It is not partitiveness that is the problem but whether {piPA} as Q1 is an absolute or a proportional number. The thrust from {le} and {le'i} is that it is proportional (as it also seems to be for Q2). But when we get to {le} (and{lo}?) it becomes absolute. I am afraid I don't yet see why; the objects referred to seem to be of the same sort.
pc: > How did I miss the shift to plural > quantification? If there are four apples then > they can be the referents only if plural > references are dealt with.., they are not in > standard Lojban.
I'm working under the definitions proposed in BPFK Section: gadri
> > The fractional always indicates a fraction of the > > referent: a fraction of a set of apples for {le'i plise}, > > a fraction of a group of apples for {lei plise}, a fraction > > of an individual apple for {le plise}. > > But you just said the referent was the four > apples, not some one of them.
Yes, that's why I said that when the sumti has more than one referent the fractional indicates a fraction of one of them, without specifying which one. So the general formula is:
piPA sumti = lo piPAse'i be lo pa me sumti "A piPA fraction of one of the sumti"
This works also when sumti has a single referent, in which case "one of the sumti" is the one referent.
> > 3.5 le vo plise = 3.5 of the 4 apples > > 3.0 le vo plise = 3.0 of the 4 apples > > 2.5 le vo plise = 2.5 of the 4 apples > > 2.0 le vo plise = 2.0 of the 4 apples > > 1.5 le vo plise = 1.5 of the 4 apples > > 1.0 le vo plise = 1.0 of the 4 apples > > 0.5 le vo plise = 0.5 of the 4 apples > > Ahah! It is not partitiveness that is the problem > but whether {piPA} as Q1 is an absolute or a > proportional number. The thrust from {le} and > {le'i} is that it is proportional (as it also > seems to be for Q2). But when we get to {le} > (and{lo}?) it becomes absolute. I am afraid I > don't yet see why; the objects referred to seem > to be of the same sort.
It is always a fraction of the referent. It is just that the referents of {lei plise} and {le'i plise} are groups and sets, whereas the referents of {le} are the apples.
Are you proposing that {pimu le vo plise} = {re le vo plise}? What would you then make of {repimu le vo plise}?
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wrote:
> > pc: > > How did I miss the shift to plural > > quantification? If there are four apples then > > they can be the referents only if plural > > references are dealt with.., they are not in > > standard Lojban. > > I'm working under the definitions proposed in > BPFK Section: gadri >
But those definition are inconsistent, vaaague, ambiguous, dubious and occasionally flat wrong. Why would you stick with them — aside from their being yours from various occasions. I am sure that you mean to fix them — indeed, I suppose that that is part of what these discussions are about. > > > The fractional always indicates a fraction > of the > > > referent: a fraction of a set of apples for > {le'i plise}, > > > a fraction of a group of apples for {lei > plise}, a fraction > > > of an individual apple for {le plise}. > > > > But you just said the referent was the four > > apples, not some one of them. > > Yes, that's why I said that when the sumti has > more than one referent > the fractional indicates a fraction of one of > them, without specifying > which one. So the general formula is: > > piPA sumti = lo piPAse'i be lo pa me > sumti > "A piPA fraction of one of the sumti"
You do realize that this specification is at variance with other parts of your "formal definitions" and they with other parts of what you say on htat page and elsewhere. (A part of what I mean by saying the above.) Can you use {me} with something that is not at least potentially a plurality, htat is, a set, group, or whatever?
> This works also when sumti has a single > referent, in which case > "one of the sumti" is the one referent. > > > > 3.5 le vo plise = 3.5 of the 4 apples > > > 3.0 le vo plise = 3.0 of the 4 apples > > > 2.5 le vo plise = 2.5 of the 4 apples > > > 2.0 le vo plise = 2.0 of the 4 apples > > > 1.5 le vo plise = 1.5 of the 4 apples > > > 1.0 le vo plise = 1.0 of the 4 apples > > > 0.5 le vo plise = 0.5 of the 4 apples > > > > Ahah! It is not partitiveness that is the > problem > > but whether {piPA} as Q1 is an absolute or a > > proportional number. The thrust from {le} > and > > {le'i} is that it is proportional (as it also > > seems to be for Q2). But when we get to {le} > > (and{lo}?) it becomes absolute. I am afraid > I > > don't yet see why; the objects referred to > seem > > to be of the same sort. > > It is always a fraction of the referent. It is > just that > the referents of {lei plise} and {le'i plise} > are groups and > sets, whereas the referents of {le} are the > apples.
As I keep pointing out: no it ain't — unless we have switched to plural quantification, in whihc case we would presumably get rid of the groups and sets elsewhere as well. And {le} would still be of the same sort as {lei}.
> Are you proposing that {pimu le vo plise} = {re > le vo plise}?
yes; at least as far as how many apples are involved. I suspect there are nuances that differ, though I don't know what they are (or will turn out to be, better).
> What would you then make of {repimu le vo > plise}? > Two and a half apples. I take it that the proportional reading of {piPA} only holds for fractions less that 1. They always are the size of the subgroup/set/whatever, however. I think your version would consequently have to be {nopimu lo vo plise}(the awkwardness corresponding to the rarity of its use).
I tried, by the way, to find an experssion in a real language which would have your suggested import and that was close to the structure of {pimu lo vo plise}. The closest I could get was a version in various languages of "a half of one of the apples" {pimu lo pa lo vo plise} or thereabouts. In English, which is more subject to these tricks than some, I could make a case for "a half from the four apples" but not a tight case. What does Spanish offer along this line -- or any other natural language (not of course a proof, but evidence surely)?
pc: > > piPA sumti = lo piPAse'i be lo pa me > > sumti > > "A piPA fraction of one of the sumti" > > You do realize that this specification is at > variance with other parts of your "formal > definitions"
No, I don't think it is. Which parts?
> Can you use > {me} with something that is not at least > potentially a plurality, htat is, a set, group, > or whatever?
Yes. {me sumti} is "x1 is/are among the sumti", so when sumti refers to a set, {me sumti} gives you "x1 is a set (of ...)". For example {me lo'i plise} means "x1 is a set of apples".
> > It is always a fraction of the referent. It is > > just that > > the referents of {lei plise} and {le'i plise} > > are groups and > > sets, whereas the referents of {le} are the > > apples. > > As I keep pointing out: no it ain't — unless we > have switched to plural quantification,
No, I only use singular quantification. I do use plural constants though. {le mu broda} is a constant with five referents. {ro le mu broda} is singular quantification over the referents of {le mu broda}:
ro le mu broda = ro da poi ke'a me le mu broda
> in whihc > case we would presumably get rid of the groups > and sets elsewhere as well.
As I said, I don't care either way. If it were my decision, I would get rid of all gadri but la/le/lo. This is not feasible, so I'm willing to go along with what the majority prefers for loi/lo'i etc., and that appears to be reified groups and sets. I can get those with {lo} too of course: {loi broda} = {lo gunma be lo broda}, and so on.
> I take it that the > proportional reading of {piPA} only holds for > fractions less that 1. They always are the size > of the subgroup/set/whatever, however. I think > your version would consequently have to be > {nopimu lo vo plise}(the awkwardness > corresponding to the rarity of its use).
OK, your view in this respect is not so different from mine, then. If you read the full page BPFK Section: Inexact Numbers
you will see that I use {pa fi'u re} for the proportional reading.
Our only disagreement (at least as far as this goes) is whether to make {pimu} equivalent to {pa fi'u re} (your choice) or to {nopimu} (my choice). Not a very big deal.
> In English, which is more subject to > these tricks than some, I could make a case for > "a half from the four apples" but not a tight > case. What does Spanish offer along this line -- > or any other natural language (not of course a > proof, but evidence surely)?
"Media de las cuatro manzanas", as opposed to "la mitad de las cuatro manzanas". The latter is ambiguous between two apples and four half-apples, just as "half of the four apples" in English.
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wrote:
> > pc: > > > Can you use > > {me} with something that is not at least > > potentially a plurality, htat is, a set, > group, > > or whatever? > > Yes. {me sumti} is "x1 is/are among the > sumti", > so when sumti refers to a set, {me > sumti} gives > you "x1 is a set (of ...)". For example {me > lo'i plise} > means "x1 is a set of apples".
I see that we are still reading {me} differently, much as I try to keep up with the shifting meanings of that expression. I would read {me lo'i broda} as "one broda," that is "one member of the set of broda," taking it to be the analog for sets of "among" for plurals (that is strictly, of course, inclusion, not membership but at least for singulars the difference is systematically ignored). Otherwise, {me lo'i broda} reduces to {lo'i broda} and the definitions that follow that form become circular and the whole expression useless.
> > > > It is always a fraction of the referent. It > is > > > just that > > > the referents of {lei plise} and {le'i > plise} > > > are groups and > > > sets, whereas the referents of {le} are the > > > apples. > > > > As I keep pointing out: no it ain't — unless > we > > have switched to plural quantification, > > No, I only use singular quantification. I do > use plural > constants though. {le mu broda} is a constant > with five > referents. {ro le mu broda} is singular > quantification > over the referents of {le mu broda}:
To say it again: if the quantification is singular, the constants can't be plural -- without a Hell of a lot of explanation of idioms that has not yet been supplied. Note also that the notion of a plural coinstant is a peculiar one unless you can guarantee that all the individuals covered by the "constant" always behave exactly the same. Otherwise, negation cannot pass freely through (one of the marks of a constant).
> ro le mu broda = ro da poi ke'a me le mu > broda
And what does that mean now that meanings are shifting all over the place? If — as appears to be the case — it means all the things that are groups of five specific brodas, then this is certainly an innovation and I would think a bad idea. We can do your intended meaning of the expression easily without that expression, but it is not clear how we can do the real meaning of the expression if we adopted your change. How do we say "all the five brodas" as opposed to "all fives of brodas" on your new version? And, by the way, didn't you once withdraw this change? Why the reversal yet again?
> > in whihc > > case we would presumably get rid of the > groups > > and sets elsewhere as well. > > As I said, I don't care either way. If it were > my decision, > I would get rid of all gadri but la/le/lo. This > is not > feasible, so I'm willing to go along with what > the majority > prefers for loi/lo'i etc., and that appears to > be reified > groups and sets. I can get those with {lo} too > of course: > {loi broda} = {lo gunma be lo broda}, and so > on.
Well, aside from the fact that we still lack a nailed down definition of {lo}, I suppose you can. My choice would be, as you know, to use plural definitions and use {loi} for collective predications, {lo} for distributive and {lo'i} for permanent collectives, but that is a proposal to be debated separately, not assumed in discussions of what proposal to use. As for doing something other than reified thigns for {loi} and {lo'i}; what choices do we have?
> > I take it that the > > proportional reading of {piPA} only holds for > > fractions less that 1. They always are the > size > > of the subgroup/set/whatever, however. I > think > > your version would consequently have to be > > {nopimu lo vo plise}(the awkwardness > > corresponding to the rarity of its use). > > OK, your view in this respect is not so > different from mine, > then. If you read the full page ((BPFK Section: > Inexact Numbers)) >
> you will see that I use {pa fi'u re} for the > proportional reading. > > Our only disagreement (at least as far as this > goes) is whether > to make {pimu} equivalent to {pa fi'u re} (your > choice) or > to {nopimu} (my choice). Not a very big deal.
My only arguments for doing thing that way are 1) that it makes Q1 uniform across the categories (but you somehow don't see {lo broda} as a group), 2)it is the "natural" reading and 3) it is hard to get it with the other reading (although splitting {pa fi'u re} from {pimu} would do it and I can hardly complain about it since I would split {pimu} from {nopimu}. As is true for most of these suggestion, either would work; the choices seem to be based on views about which are more Lojbanic or more convenient (including zipfean matters) or more natural. (I would throw in a check with the usages of logic but that is clearly nowadays a minor point.)So once we get the basic definitions straight, any of these possibilities (on this issue and others about quantifiers and relative clause and so on) will have a variety of solutions, any one of which will work and the choiuce will be on essentially aesthetic grounds. It is good to have these laid out now though we cannot really chose in the absence of clear treatment of the basic notions, {lo}, {le}, and — probably included — {la}.
> > In English, which is more subject to > > these tricks than some, I could make a case > for > > "a half from the four apples" but not a tight > > case. What does Spanish offer along this > line -- > > or any other natural language (not of course > a > > proof, but evidence surely)? > > "Media de las cuatro manzanas", as opposed to > "la mitad > de las cuatro manzanas". The latter is > ambiguous > between two apples and four half-apples, just > as > "half of the four apples" in English. > I took the first to be unambiguously in favoe of two apples — correct? Note that none of these gives *one* half apple. In a word, Spanish is pretty much like English (given the falling together to a large extent of "from" and "of").
pc: > I would read {me > lo'i broda} as "one broda," that is "one member > of the set of broda," taking it to be the analog > for sets of "among" for plurals (that is > strictly, of course, inclusion, not membership > but at least for singulars the difference is > systematically ignored).
OK, but that's not how I'm reading it.
I read {me sumti} as "x1 is/are among the referents of sumti" in all cases, even when the referent of sumti is a set.
> Otherwise, {me lo'i > broda} reduces to {lo'i broda} and the > definitions that follow that form become circular > and the whole expression useless.
{me lo'i broda} is a brivla, so it can't reduce to {lo'i broda}. I'm not sure which definitions you consider that become circular.
> > ro le mu broda = ro da poi ke'a me le mu > > broda > > And what does that mean now that meanings are > shifting all over the place? If — as appears to > be the case — it means all the things that are > groups of five specific brodas,
No, that's not what it means. It means "each of the things that are a referent of {le mu broda}, i.e. each of the five brodas. There are no groups involved here.
> My choice would be, as you know, to use
> plural definitions and use {loi} for collective
> predications, {lo} for distributive and {lo'i}
> for permanent collectives, but that is a proposal
> to be debated separately, not assumed in
> discussions of what proposal to use.
Yes, I understand that.
> As for doing > something other than reified thigns for {loi} and > {lo'i}; what choices do we have?
Those are the two basic choices, I think.
> > > In English, which is more subject to > > > these tricks than some, I could make a case > > for > > > "a half from the four apples" but not a tight > > > case. What does Spanish offer along this > > line -- > > > or any other natural language (not of course > > a > > > proof, but evidence surely)? > > > > "Media de las cuatro manzanas", as opposed to > > "la mitad > > de las cuatro manzanas". The latter is > > ambiguous > > between two apples and four half-apples, just > > as > > "half of the four apples" in English. > > > I took the first to be unambiguously in favoe of > two apples — correct?
No. "Media de las cuatro manzanas" is unambiguously "half (an apple) out of the four apples". "La mitad de las cuatro manzanas" is ambiguous between two other meanings, the same ones of "half of the four apples": i.e. two apples or four half-apples.
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wrote:
> > pc: > > I would read {me > > lo'i broda} as "one broda," that is "one > member > > of the set of broda," taking it to be the > analog > > for sets of "among" for plurals (that is > > strictly, of course, inclusion, not > membership > > but at least for singulars the difference is > > systematically ignored). > > OK, but that's not how I'm reading it. > > I read {me sumti} as "x1 is/are among the > referents of > sumti" in all cases, even when the referent > of sumti > is a set.
Then, if "sumti" refers to a set or group, {me "sumti"} is just {du "sumti"}, a much clearer claim, to say the least. And this is then completely general, since every sumti refers to an individual, in which case {me "sumti"} reduces to {du "sumti"} by default. So, what is the point of it? If, on the other hand, it refers to one of the things in an abstract individual, then it is quite useful. Of course, applied to a concrete individual it is more problematic, but probably should then reduce to identity.
> > Otherwise, {me lo'i > > broda} reduces to {lo'i broda} and the > > definitions that follow that form become > circular > > and the whole expression useless. > > {me lo'i broda} is a brivla, so it can't reduce > to {lo'i broda}. > I'm not sure which definitions you consider > that become > circular.
All the ones that run {lo me "sumti"} especially when defining "sumti" or one of its extensions. > > > > ro le mu broda = ro da poi ke'a me le mu > > > broda > > > > And what does that mean now that meanings are > > shifting all over the place? If — as > appears to > > be the case — it means all the things that > are > > groups of five specific brodas, > > No, that's not what it means. It means "each of > the things > that are a referent of {le mu broda}, i.e. each > of the > five brodas. There are no groups involved here.
Says you, but the evidence is against you: only individuals are allowed, not plurals; your own "formal definition" has {lo} "defined" as an individual (as it must, of course, until som other sense of predication has been defined. One of the advantages of plural quantification is that distributive and singular predication can be defined in terms of it but there has yet ot appear a defintion of collective predication in terms of singular or distributive.); and group interpetation is the historic Lojban position until a new one is explained and accepted. Your proposal — and remember it is not yet gospel -- fails on both counts so far.
> > My choice would be, as you know, to use > > plural definitions and use {loi} for > collective > > predications, {lo} for distributive and > {lo'i} > > for permanent collectives, but that is a > proposal > > to be debated separately, not assumed in > > discussions of what proposal to use. > > Yes, I understand that. > > > As for doing > > something other than reified thigns for {loi} > and > > {lo'i}; what choices do we have? > > Those are the two basic choices, I think.
I only gave one position, what is the other? I suppose you mean "plural constants" or at least plurals. How would that work exactly in terms of singulars — all we have to start with after all.
> > > > In English, which is more subject to > > > > these tricks than some, I could make a > case > > > for > > > > "a half from the four apples" but not a > tight > > > > case. What does Spanish offer along this > > > line -- > > > > or any other natural language (not of > course > > > a > > > > proof, but evidence surely)? > > > > > > "Media de las cuatro manzanas", as opposed > to > > > "la mitad > > > de las cuatro manzanas". The latter is > > > ambiguous > > > between two apples and four half-apples, > just > > > as > > > "half of the four apples" in English. > > > > > I took the first to be unambiguously in > favoe of > > two apples — correct? > > No. "Media de las cuatro manzanas" is > unambiguously "half > (an apple) out of the four apples". "La mitad > de las cuatro > manzanas" is ambiguous between two other > meanings, the same > ones of "half of the four apples": i.e. two > apples or > four half-apples.
I'll take your word for it, but then I will have to go back and reread some things from long ago. As for the "half of the four apples." it cannot mean in my idiolect four half apples, the nearest I can come to that-- after the example I gave before — "the halves of four apples" and even that is iffy. But in no case do we get to a half an apple.
pc: > Then, if "sumti" refers to a set or group, {me > "sumti"} is just {du "sumti"}, a much clearer > claim, to say the least.
Yes, whenever sumti has a single referent, {me} reduces to {du}, (There are some syntactical differences, but basically that's it.)
> And this is then > completely general, since every sumti > refers to an individual,
No. Some sumti refer to more than one individual. For example {le ci plise} refers to three individuals. In this case {me le ci plise} means "x1 is/are among the three apples", whereas {du le ci plise} gives "x1 are the three apples".
> > I'm not sure which definitions you consider > > that become circular. > > All the ones that run {lo me "sumti"} especially > when defining "sumti" or one of its extensions.
lo [PA] broda = zo'e noi ke'a broda [gi'e klani li PA lo se gradu be lo broda] loi [PA] broda = lo gunma be lo [PA] broda lo'i [PA] broda = lo selcmi be lo [PA] broda enai lo na broda PA sumti = PA da poi ke'a me sumti piPA sumti = lo piPA si'e be lo pa me sumti
I don't see any circularity.
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> pc: > > Then, if "sumti" refers to a set or group, > {me > > "sumti"} is just {du "sumti"}, a much clearer > > claim, to say the least. > > Yes, whenever sumti has a single referent, > {me} > reduces to {du}, (There are some syntactical > differences, > but basically that's it.) > > > And this is then > > completely general, since every sumti > > refers to an individual, > > No. Some sumti refer to more than one > individual. > For example {le ci plise} refers to three > individuals. > In this case {me le ci plise} means "x1 is/are > among > the three apples", whereas {du le ci plise} > gives > "x1 are the three apples".
How does that work, exactly. We have a given of single object predication. We nowwant to have plural predication. Presumably that is what the "formal definitions" will give us, if {lo} for example has several references. Well, the one trick we do have given for such cases is quantification (i.e., extended conjunctons and disjunctions of singular predications). The "definition" of {lo} is not obviously a quantification case and, indeed, you have fairly regularly denied that {lo} does involve quantifiers. So what is there? The form of the "definition" (ignoring cntent for the moment) is that of a singular predication, with nothing added to make the transition. If you want to say that {lo vo plise} has four referents, then you owe us an explanation (a real definition) of just how that works. To be sure, even if {lo vo plise} refers to a single set of four apples, we are owed an explanation of how that works, too. But that explanation (though not the one for {loi}) has been around for ever — except for occasional disputes about what quantifier is to be used when we say "Q of the members of the set." I admit that I cannot come up with any way of doing this (or for {loi} either) beyond the various suggestions I have made and you have rejected, but I am eager to see your proposal, however belatedly offered.
pc: > If you want to say > that {lo vo plise} has four referents, then you > owe us an explanation (a real definition) of just > how that works.
I don't think any further explanation I may give would ever satisfy you.
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> > pc: > > If you want to say > > that {lo vo plise} has four referents, then > you > > owe us an explanation (a real definition) of > just > > how that works. > > I don't think any further explanation I may > give would ever > satisfy you. >
Well, hard to say since you haven't ever really tried. I do know that the converse problem in plural logic — defining singular and distributive predication in terms of collective -- is fairly easy. But just what is the purpose of these various definitions you offer for {lo} and {le} in particular (and derivatively for the others)? They certainly fail as definitions and they are confusing and misleading as paraphrases (and also generally exxplaining the relatively clear by the markedly less clear). There is also the problem of the description (definition one) not matching the "formal definition" (assuming for the moment that the latter succeeds in saying something), leaving the student high and dry for any explanation at all — even without the plurality problem.
I do note a possible source for your confusion. Because of the way that {lo broda cu brode} is defined (Q of these broda are brode), it turns out that we cannot say directly that {lo broda} refers to a group {lo broda cu girzu} is only true if the member broda are themselves groups. We have to go to material mode: {la'e li lo broda li'u girzu}. It also occurs to me that the difference between a girzu and a gunma may be part of the problem. Though we can't say it officially, that this pretty much the difference between distributive and collective predication.
wrote:
> > pc: > > If you want to say > > that {lo vo plise} has four referents, then > you > > owe us an explanation (a real definition) of > just > > how that works. > > I don't think any further explanation I may > give would ever > satisfy you.
It occurs to me that, rather than being a seemly -- albeit misplaced — display of modesty, this is a claim that I set unreasonably high standards for explanations and definitions. I, of course, don't think I do; what I want is about what I expect from first semester logic students, who usually mange to do pretty well at meeting the guidelines. To spell it out (with modifications to apply to the present situation):
accuracy: saying clearly what is actually going on. If, as now, you are proposing changes (either new or precising previous vagueness or ambiguity) a clear statemtn of what the change is and some explanation of why a change is necessary and why this particular change is the way to go ("widespread usage" is not much help unless it also says why the users have chosen this deviance -- especially true when the usage is largely that of the proposer). But problems which do need to be met count for something.
clarity: at least avoiding vagueness and ambiguity, being as precise as possible and appropriate. An unemotional expression is often useful as well.
noncontroversial: if a change presupposes some other changes, they should be dealt with as well, so that each section begins pretty much from the basics (CLL in this case).
coherence: the various parts should fit together without internal contradiction or garden-pathing.
completeness: all the major aspects of the problem at issue are covered, reader extrapolation is kept to a minimum.
Objectively, the major proposal so far, for gadri, seems deficient in all of these respects except possibly the last — which is mitigated by the problems in other areas. But meeting these criteria does not seem to be too much to expect in a serious proposal in a serious project.
pc: > accuracy: saying clearly what is actually going > on. If, as now, you are proposing changes > (either new or precising previous vagueness or > ambiguity) a clear statemtn of what the change is > and some explanation of why a change is necessary > and why this particular change is the way to go > ("widespread usage" is not much help unless it > also says why the users have chosen this deviance > — especially true when the usage is largely that > of the proposer). But problems which do need to > be met count for something.
I don't think I'm proposing any changes here. This is what CLL says:
Each of these numbers, plus ro, may be prefixed with pi (the decimal point) in order to make a fractional form which represents part of a whole rather than some elements of a totality. piro therefore means the whole of:
8.8) mi citka piro lei nanba
I eat the-whole-of the-mass-of bread
Similarly, piso'a means almost the whole of; and so on down to piso'u, a tiny part of. These numbers are particularly appropriate with masses, which are usually measured rather than counted, as Example 8.8 shows.
I don't think what I'm proposing deviates from that.
> clarity: at least avoiding vagueness and > ambiguity, being as precise as possible and > appropriate. An unemotional expression is often > useful as well.
piPA sumti = lo piPA si'e be lo pa me sumti
seems clear enough to me. "A piPA fraction of one of the referents of sumti". When sumti has a single referent, this reduces to the CLL case: "A piPA fraction of the referent of sumti.
> noncontroversial: if a change presupposes some > other changes, they should be dealt with as well, > so that each section begins pretty much from the > basics (CLL in this case).
I wouldn't have thought this was going to be controversial. It is not even really a change, just a generalization of CLL.
> coherence: the various parts should fit together > without internal contradiction or garden-pathing.
All parts fit together as far as I can tell. You claim they don't, but you don't explain how they don't.
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wrote:
> > pc: > > accuracy: saying clearly what is actually > going > > on. If, as now, you are proposing changes > > (either new or precising previous vagueness > or > > ambiguity) a clear statemtn of what the > change is > > and some explanation of why a change is > necessary > > and why this particular change is the way to > go > > ("widespread usage" is not much help unless > it > > also says why the users have chosen this > deviance > > — especially true when the usage is largely > that > > of the proposer). But problems which do need > to > > be met count for something. > > I don't think I'm proposing any changes here.
Sorry, I was off thinking about the gadrii page not the actual topic of this thread. > This is what > CLL says: >
>> Each of these numbers, plus ro, may be > prefixed with pi (the decimal > point) in order to make a fractional form which > represents part of a whole > rather than some elements of a totality. > piro therefore means the whole > of: > > > 8.8) mi citka piro lei nanba > I eat the-whole-of the-mass-of bread > > Similarly, piso'a means almost the whole > of; and so on down to > piso'u, a tiny part of. These numbers > are particularly appropriate with > masses, which are usually measured rather than > counted, as Example 8.8 shows.
>> > I don't think what I'm proposing deviates from > that. > > > clarity: at least avoiding vagueness and > > ambiguity, being as precise as possible and > > appropriate. An unemotional expression is > often > > useful as well. > > piPA sumti = lo piPA si'e be lo pa me > sumti > > seems clear enough to me. "A piPA fraction of > one of the > referents of sumti". When sumti has a > single referent, > this reduces to the CLL case: "A piPA fraction > of the > referent of sumti.
I know that CLL says that {piPA lo broda} is 0.PA of one broda. This is, however, at variance with what it says elsewhere about fractional quantifiers and with practivcal considerations (what do we most want to say and what can be said appropriately otherwise). It is also at variance with what was (I thought) agreed on here earlier (much earlier, to be sure) ion response to the rather thorough muddle about quantified sumti in CLL, that fractionals gave fractions of the total size, not fractions of the members: external PA was to understood, then, as PA/ro. To be sure, this assumes that lo broda is a group, but then no one has yet even begun to say how it could be otherwise, given Lojban's defective plural structure. (Incidentally, even if {lo broda} were a plural, {pimu lo broda} would "naturally" be "half the men" not "a half of a man.")
> > noncontroversial: if a change presupposes > some > > other changes, they should be dealt with as > well, > > so that each section begins pretty much from > the > > basics (CLL in this case). > > I wouldn't have thought this was going to be > controversial. > It is not even really a change, just a > generalization of CLL.
Well, I suppose we could ask why this generalization rather than any of several others, including the earlier consensus. That section of CLL is a bit of a mess, after all, and many of the choices there are ill-advised from a practical point of view.
> > coherence: the various parts should fit > together > > without internal contradiction or > garden-pathing. > > All parts fit together as far as I can tell. > You claim they > don't, but you don't explain how they don't.
As noted, the claim was accidentlaly about something else that was on my mind at the time. This system seems to be coherent, if inefficient. I expect that we want to talk about half a group of (or several) broda far more often than about half a broda. The standard way to say half a broda otherwise is not much more complex that {pimu lo broda}, while, lacking this form, saying "half of the broda" seems rather harder -- certainly more so that its usefulnness suggests. But then, I am not all that confident about ewhat is possible by way of expressing these notions, so I have probably missed a correcting set.
wrote:
> > > noncontroversial: if a change presupposes > some > > other changes, they should be dealt with as > well, > > so that each section begins pretty much from > the > > basics (CLL in this case). > > I wouldn't have thought this was going to be > controversial. > It is not even really a change, just a > generalization of CLL. > Well, there is also the matter that, to get this to work as a generalization, you appear to have to take {PA1 loi PA2 broda} as "PA1 masses of PA2 broda each," a view that you proposed, backed off from and then presented as gospel. I should think that the fact that you backed off from it because of several protests makes it controversial.
pc: > --- Jorge Llambías wrote: > > This is what > > CLL says: > >
> >> > Each of these numbers, plus ro, may be > > prefixed with pi (the decimal > > point) in order to make a fractional form which > > represents part of a whole > > rather than some elements of a totality. > > piro therefore means the whole > > of: > > > > > > 8.8) mi citka piro lei nanba > > I eat the-whole-of the-mass-of bread > > > > Similarly, piso'a means almost the whole > > of; and so on down to > > piso'u, a tiny part of. These numbers > > are particularly appropriate with > > masses, which are usually measured rather than > > counted, as Example 8.8 shows.
> >> > I know that CLL says that {piPA lo broda} is 0.PA > of one broda.
Can you indicate where? All I could find about fractional quantifiers in CLL is what I quoted above.
> It is also at variance > with what was (I thought) agreed on here earlier > (much earlier, to be sure) ion response to the > rather thorough muddle about quantified sumti in > CLL, that fractionals gave fractions of the total > size, not fractions of the members: external PA > was to understood, then, as PA/ro.
I understand external PA as {PA fi'u ro}, i.e. PA out of all the referents of the sumti.
> I expect that we want to talk about half a group > of (or several) broda far more often than about > half a broda.
I expect so too. Both are easy to do with the proposed system.
> The standard way to say half a > broda otherwise is not much more complex that > {pimu lo broda}, while, lacking this form, saying > "half of the broda" seems rather harder -- > certainly more so that its usefulnness suggests.
{fi'u re lo broda}
This form also has the advantage that "a third of the broda" is {fi'u ci lo broda} rather than the somewhat stranger {pira'eci lo broda}, not to mention {fi'u ze} for "a seventh" instead of {pira'epavorebimuze}.
And there's also {muno ce'i lo broda}.
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wrote:
> > pc: > > --- Jorge Llambías wrote: > > > This is what > > > CLL says: > > >
> > >> > > Each of these numbers, plus ro, may be > > > prefixed with pi (the decimal > > > point) in order to make a fractional form > which > > > represents part of a whole > > > rather than some elements of a totality. > > > piro therefore means the whole > > > of: > > > > > > > > > 8.8) mi citka piro lei nanba > > > I eat the-whole-of the-mass-of bread > > > > > > Similarly, piso'a means almost the > whole > > > of; and so on down to > > > piso'u, a tiny part of. These > numbers > > > are particularly appropriate with > > > masses, which are usually measured rather > than > > > counted, as Example 8.8 shows.
> > >> > > > I know that CLL says that {piPA lo broda} is > 0.PA > > of one broda. > > Can you indicate where? All I could find about > fractional > quantifiers in CLL is what I quoted above.
Top of page 131, lines 4-5. I don't place much weight on it, of course.
> > It is also at variance > > with what was (I thought) agreed on here > earlier > > (much earlier, to be sure) ion response to > the > > rather thorough muddle about quantified sumti > in > > CLL, that fractionals gave fractions of the > total > > size, not fractions of the members: external > PA > > was to understood, then, as PA/ro. > > I understand external PA as {PA fi'u ro}, i.e. > PA out > of all the referents of the sumti.
But, but, but ... if they are fractional, why are the other fractions not fractional? I gather that you want to distinguish between {pimu}, {pa fi'u re} (and {mu fi'u pano}) and probably {nopimu}. this is legitimate, but does seem to need an explanation, since these are normally the same.
> > > I expect that we want to talk about half a > group > > of (or several) broda far more often than > about > > half a broda. > > I expect so too. Both are easy to do with the > proposed > system. > > > The standard way to say half a > > broda otherwise is not much more complex that > > {pimu lo broda}, while, lacking this form, > saying > > "half of the broda" seems rather harder -- > > certainly more so that its usefulnness > suggests. > > {fi'u re lo broda} > > This form also has the advantage that "a third > of the broda" > is {fi'u ci lo broda} rather than the somewhat > stranger > {pira'eci lo broda}, not to mention {fi'u ze} > for > "a seventh" instead of {pira'epavorebimuze}. > > And there's also {muno ce'i lo broda}.
Yes, of course most decimal expansions are messier than fractions, so we would generally use fractions for them, but not when the decimal expansion is shorter or maybe as short (I wonder if shorter actually happens). By parity of practical reasoning, if we want some sloppy decimal of an object surely we would use the fraction rather than the decimal there as well. Of course, since this is very uncommon, we can get by with long decimals in these cases. On the other hand, the suggested {(fraction) se'i} would always work and leave the simpler forms for the more common cases (basically the same argument as was made against using {PA1 lo PA2 broda} for PA1 examples of (groups of) PA2 objects. I find it pretty convincing, all things considered.
pc: > --- Jorge Llambías wrote: > > I understand external PA as {PA fi'u ro}, i.e. > > PA out of all the referents of the sumti. > > But, but, but ... if they are fractional, why are > the other fractions not fractional? I gather > that you want to distinguish between {pimu}, {pa > fi'u re} (and {mu fi'u pano}) and probably > {nopimu}.
I would say {nopimu} and {pimu} are the same, just as {pa fi'u re} is also {fi'u re}.
> this is legitimate, but does seem to > need an explanation, since these are normally the > same.
The need to differentiate arises from the reified groups and sets. With lo/le/la we refer to many things at once, with loi/lei/lai/lo'i/le'i/la'i we refer to a single thing (with many members). Then we need ways to talk about a number of things as a fraction of the total number of things on the one hand, and about a fraction of a (possibly membered) thing on the other.
Using the same expression for both would lead to unclear cases. For example, {pimu le selcmi} is half the set, i.e. a set with half of the members of le selcmi, whereas {pa fi'u re le selcmi} gives half of the sets. One out of every two of the sets. We can't conflate them.
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wrote:
> > pc: > > --- Jorge Llambías wrote: > > > I understand external PA as {PA fi'u ro}, > i.e. > > > PA out of all the referents of the sumti. > > > > But, but, but ... if they are fractional, why > are > > the other fractions not fractional? I gather > > that you want to distinguish between {pimu}, > {pa > > fi'u re} (and {mu fi'u pano}) and probably > > {nopimu}. > > I would say {nopimu} and {pimu} are the same, > just > as {pa fi'u re} is also {fi'u re}. > > > this is legitimate, but does seem to > > need an explanation, since these are normally > the > > same. > > The need to differentiate arises from the > reified > groups and sets. With lo/le/la we refer to many > things > at once, with loi/lei/lai/lo'i/le'i/la'i we > refer to > a single thing (with many members).
Of course, just here — on logical grounds as well as various parts of CLL — I disagree with you: {lo, le, la} introduce distributive groups as much as {loi le lai} introduce collective groups. The only way that {lo} for example could -- in CLL Lojban — stand fro a number of things is if it were a covert quantifier (or conjunction, of cours, for finite groups, {le} and {la} in particular) but it seems to me that you and others of your persuasion have regularly denied that {lo} expressions are quantifiers under the skin (note: quantifiers are still not strictly reference but near enough in this case to let pass). While one of your definitions for {lo} does sound a lot like a quantifier, the other (admittedly the poorer of the two) clearly is not. Of course, without the quantifiers or conjunctions, the predications with {lo} become mysterious (thought admittedly, with the quantifiers, outer quantifiers take some finagling). By the way, when I say "quantifier" I do not necessarily mean {su'o da} and the like: such variable binding expressions in Lojban may logically be more complex than "there is an x."
> Then we
> need ways
> to talk about a number of things as a fraction
> of the
> total number of things on the one hand, and
> about a
> fraction of a (possibly membered) thing on the
> other.
>
> Using the same expression for both would lead
> to
> unclear cases. For example, {pimu le selcmi} is
> half the set, i.e. a set with half of the
> members of
> le selcmi, whereas {pa fi'u re le selcmi} gives
> half of the sets. One out of every two of the
> sets.
> We can't conflate them.
Let's see. One of these assumes that {le selcmi} is a single set (a group with a single member) -- of something or other — and therefore that any fraction must be a fraction of that set (and presumably another set with that fraction of the cardinal of the set). The other assumes that {le selcmi} is (a group of) several sets and a fractional quantifier is therefore (a group of) that fraction of several sets. On your reasoning, if {le selcmi} were (a group of) several sets, {pimu le selcmi} would be half of one of these sets. Now, since this is {le} we presumably know how many sets are involved here and so no confusion would result from the ambiguity. With {lo}, where the size is in doubt, there would be a functioning ambiguity with at least the {pimu} case. And, of course, if le selcmi is single, what does {fi'u re lo selcmi} mean? As I said, it seems to me you need and want both of these modes of expression for both (all three or so?) cases. And that suggests that, to avoid ambiguity, the expressions for these various purposes cannot be the same — but not different form of the quantifier as such. As noted, I like the {piPA/ PA fu'i PA si'e} for pieces of an individual, {piPA / PA fui PA} for subwhatevers and quite explicit forms for a fraction of a member of the whatever involved {piPA /PA fu'i PA le pa lo ....}, which is about right for all the times we will use this.
pc: > Of course, just here — on logical grounds as > well as various parts of CLL — I disagree with > you: {lo, le, la} introduce distributive groups > as much as {loi le lai} introduce collective > groups.
OK, we disagree then.
> > Using the same expression for both would lead > > to > > unclear cases. For example, {pimu le selcmi} is > > half the set, i.e. a set with half of the > > members of > > le selcmi, whereas {pa fi'u re le selcmi} gives > > half of the sets. One out of every two of the > > sets. > > We can't conflate them. > > Let's see. One of these assumes that {le selcmi} > is a single set (a group with a single member) -- > of something or other — and therefore that any > fraction must be a fraction of that set (and > presumably another set with that fraction of the > cardinal of the set).
Right.
> The other assumes that {le > selcmi} is (a group of) several sets and a > fractional quantifier is therefore (a group of) > that fraction of several sets.
Minus the intervening groups, yes.
> On your > reasoning, if {le selcmi} were (a group of) > several sets, {pimu le selcmi} would be half of > one of these sets.
Right.
> Now, since this is {le} we > presumably know how many sets are involved here > and so no confusion would result from the > ambiguity.
No confusion results with the two different uses of {pimu} and {fi'ure}. Confusion does result if they are conflated.
> With {lo}, where the size is in > doubt, there would be a functioning ambiguity > with at least the {pimu} case.
If they were conflated, yes.
> And, of course, > if le selcmi is single, what does {fi'u re lo > selcmi} mean?
Nothing. "One in every two of the one thing I have in mind"? It's just nonsense.
> As I said, it seems to me you need and want both > of these modes of expression for both (all three > or so?) cases. And that suggests that, to avoid > ambiguity, the expressions for these various > purposes cannot be the same — but not different > form of the quantifier as such. As noted, I like > the {piPA/ PA fu'i PA si'e} for pieces of an > individual, {piPA / PA fui PA} for subwhatevers > and quite explicit forms for a fraction of a > member of the whatever involved {piPA /PA fu'i PA > le pa lo ....}, which is about right for all the > times we will use this.
The long forms are always available, of course.
The only reason I'm bothering with the piPA forms at all is to keep them CLL-compatible. {pimu} are not even the more relevant ones. {piso'i} and the like are the ones that need to be dealt with.
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wrote:
> > pc: > > > Now, since this is {le} we > > presumably know how many sets are involved > here > > and so no confusion would result from the > > ambiguity. > > No confusion results with the two different > uses of {pimu} > and {fi'ure}. Confusion does result if they are > conflated.
Given your interpretations, that is — which do not seem to me to be well motivated. The one which would create a problem here, {pimu le selcmi} meaning one half of one of the several sets, seems to me particularly unlikely. If I remember correctly, there was nothing with that meaning in any of the natural language cases. The closest was "the halves of the several sets," a possibility you (wisely) pass over.
> > With {lo}, where the size is in > > doubt, there would be a functioning ambiguity > > with at least the {pimu} case. > > If they were conflated, yes. > > > And, of course, > > if le selcmi is single, what does {fi'u re lo > > selcmi} mean? > > Nothing. "One in every two of the one thing I > have > in mind"? It's just nonsense.
But why not a set consisting of half of the set mentioned; this seems consistent with your other explanations — when it is otherwise forced on one.
> > As I said, it seems to me you need and want > both > > of these modes of expression for both (all > three > > or so?) cases. And that suggests that, to > avoid > > ambiguity, the expressions for these various > > purposes cannot be the same — but not > different > > form of the quantifier as such. As noted, I > like > > the {piPA/ PA fu'i PA si'e} for pieces of an > > individual, {piPA / PA fui PA} for > subwhatevers > > and quite explicit forms for a fraction of a > > member of the whatever involved {piPA /PA > fu'i PA > > le pa lo ....}, which is about right for all > the > > times we will use this. > > The long forms are always available, of course.
But what about the short (non-decimal) versions for pieces of s single thing. Why should a thrid of a person be longer and vaguer than a half? To use the fractional forms would require using the long forms, at least with {si'e}. OK, I revise my question: why allow the short forms for some cases of fractions of individuals; the long forms are more in accord with use.
>The only reason I'm bothering with the piPA > forms at all > is to keep them CLL-compatible. {pimu} are not > even the > more relevant ones. {piso'i} and the like are > the ones > that need to be dealt with. > Why are these more problematic — aside from the usual problems with {so'i} and the like, which have to be dealt with regardless of {pi}?
pc: > > > And, of course, > > > if le selcmi is single, what does {fi'u re lo > > > selcmi} mean? > > > > Nothing. "One in every two of the one thing I > > have in mind"? It's just nonsense. > > But why not a set consisting of half of the set > mentioned; this seems consistent with your other > explanations — when it is otherwise forced on > one.
None of the forms change with the meaning of "broda". {piPA le broda} is always about fractions of broda, and {fi'u PA le broda} is always about a number of brodas, whatever broda is.
> > The long forms are always available, of course. > > But what about the short (non-decimal) versions > for pieces of s single thing. Why should a thrid > of a person be longer and vaguer than a half? To > use the fractional forms would require using the > long forms, at least with {si'e}. OK, I revise > my question: why allow the short forms for some > cases of fractions of individuals; the long forms > are more in accord with use.
I wouldn't mind forbidding those forms, I don't really use them. What I don't want is to give different meanings to {piPA lo broda} depending on the meaning of "broda". The generalization to pieces for brodas that don't have members is the natural one, and also follows from the natural interpretation of things like {3.5 lo broda}.
> >The only reason I'm bothering with the piPA > > forms at all > > is to keep them CLL-compatible. {pimu} are not > > even the > > more relevant ones. {piso'i} and the like are > > the ones > > that need to be dealt with. > > > Why are these more problematic — aside from the > usual problems with {so'i} and the like, which > have to be dealt with regardless of {pi}?
They are not problematic, they are just explicitly covered in CLL.
piso'i lei broda = a large fraction of the broda so'i le broda = many of the broda
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wrote:
> > pc: > > > > And, of course, > > > > if le selcmi is single, what does {fi'u > re lo > > > > selcmi} mean? > > > > > > Nothing. "One in every two of the one thing > I > > > have in mind"? It's just nonsense. > > > > But why not a set consisting of half of the > set > > mentioned; this seems consistent with your > other > > explanations — when it is otherwise forced > on > > one. > > None of the forms change with the meaning of > "broda". > {piPA le broda} is always about fractions of > broda, > and {fi'u PA le broda} is always about a number > of > brodas, whatever broda is.
Exactly. Is not half a broda a number of broda -- the number required if {lo broda} is a single thing? > > > > The long forms are always available, of > course. > > > > But what about the short (non-decimal) > versions > > for pieces of s single thing. Why should a > thrid > > of a person be longer and vaguer than a half? > To > > use the fractional forms would require using > the > > long forms, at least with {si'e}. OK, I > revise > > my question: why allow the short forms for > some > > cases of fractions of individuals; the long > forms > > are more in accord with use. > > I wouldn't mind forbidding those forms, I don't > really > use them. What I don't want is to give > different meanings > to {piPA lo broda} depending on the meaning of > "broda". > The generalization to pieces for brodas that > don't have > members is the natural one, and also follows > from the > natural interpretation of things like {3.5 lo > broda}.
But apparently you do give different meaning depending on the nature of brodas. Otherwisse I simply cannot understand some of your examples -- same form, different readings.
> > >The only reason I'm bothering with the piPA > > > forms at all > > > is to keep them CLL-compatible. {pimu} are > not > > > even the > > > more relevant ones. {piso'i} and the like > are > > > the ones > > > that need to be dealt with. > > > > > Why are these more problematic — aside from > the > > usual problems with {so'i} and the like, > which > > have to be dealt with regardless of {pi}? > > They are not problematic, they are just > explicitly covered > in CLL. > > piso'i lei broda = a large fraction of the > broda > so'i le broda = many of the broda > That is, the two mean virtually the same thing in reality, however different they are in form. And {piso'i le broda} would be? Or {so'i lei broda} for that matter. It starts to look as though these {pi} with nonnumeric quantifiers are just redundant. Is that why you decided to give them a new use (or why the creatorss of Lojban did -- to the extent that they did)?
pc: > But apparently you do give different meaning > depending on the nature of brodas.
PA sumti is "PA referents of sumti". Always. piPA sumti is "a piPA fraction of one referent of sumti". Always.
Those work for any form of sumti, {lo broda}, {lo'i broda}, etc, and for broda that mean "is an apple" or "is a set". So the meaning of the construction is independent of the nature of brodas.
> > piso'i lei broda = a large fraction of the > > broda > > so'i le broda = many of the broda > > > That is, the two mean virtually the same thing in > reality, however different they are in form.
The first one is collective, the second one distributive.
> And > {piso'i le broda} would be?
A large fraction of one of the referents of {le broda}.
If {broda} means "is a set of apples", then {piso'i le selcmi be lo plise} means "a large subset of the set of apples.
If {broda} means "is an apple", then {piso'i le plise} means "a large fraction of the apple".
> Or {so'i lei broda} > for that matter.
{so'i lei broda} would be meaningless, because {lei broda} has a single referent, so there cannot be many of them doing anything.
> It starts to look as though > these {pi} with nonnumeric quantifiers are just > redundant.
I think they are. I wouldn't want to define them if they weren't already there.
> Is that why you decided to give them > a new use (or why the creatorss of Lojban did -- > to the extent that they did)?
You should ask them. I'm just defining them in accordance with CLL.
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wrote:
> > pc: > > But apparently you do give different meaning > > depending on the nature of brodas. > > PA sumti is "PA referents of sumti". > Always. > piPA sumti is "a piPA fraction of one > referent of sumti". Always. > > Those work for any form of sumti, {lo broda}, > {lo'i broda}, etc, > and for broda that mean "is an apple" or "is a > set". So the meaning > of the construction is independent of the > nature of brodas.
So, {me lo broda} means "is a referent of {lo broda}" and what we disagree about then is what a referent of {lo broda} might be> I say that the only referent of {lo broda} is a group of broda and you say — against the odds — that it is one or several broda. Thus, I come up with a smaller group of broda (as in English) and you come up with a fraction of one broda (as in no known laguage, apparently). So, yes, your position is coherent, just very strange, at leas in this case. What, by the way, happened to {me} meaning "is an instance / example of," which talked about lo broda, not {lo broda}?
> > > piso'i lei broda = a large fraction of the > > > broda > > > so'i le broda = many of the broda > > > > > That is, the two mean virtually the same > thing in > > reality, however different they are in form. > > The first one is collective, the second one > distributive.
Well, yes, but they are about the same group (or the same many broda, as you wpould have it); the distributive / collective differentce only comes into play at the predication level.
> > And
> > {piso'i le broda} would be?
>
> A large fraction of one of the referents of {le
> broda}.
>
> If {broda} means "is a set of apples", then
> {piso'i le selcmi be lo plise} means "a large
> subset of the set
> of apples.
>
> If {broda} means "is an apple", then {piso'i le
> plise} means
> "a large fraction of the apple".
>
> > Or {so'i lei broda}
> > for that matter.
>
> {so'i lei broda} would be meaningless, because
> {lei broda} has
> a single referent, so there cannot be many of
> them doing anything.
So, {so'i le pa broda} is also nonsensefor the same reason, but {piso'i lei ro broda} would also be nonsense again for that reason. this still seems very odd to me, "unnatural" as it were -- certainly in comparison with the old consensus . And, of course, with your second definition (which in this case is the clearer one).
> > It starts to look as though > > these {pi} with nonnumeric quantifiers are > just > > redundant. > > I think they are. I wouldn't want to define > them if they weren't > already there.
How would you replace them, since by you they do have non-redundant uses: how do {piso'i le broda} without {piso'i}? I take using {fu'i} somehow as a cheat.
> > Is that why you decided to give them > > a new use (or why the creatorss of Lojban did > -- > > to the extent that they did)? > > You should ask them. I'm just defining them in > accordance with CLL.
Well, given the muddle in that section of CLL, it would be hard to avoid this for some part. Or, for that matter, to do something that *is* in accord with the whole of the section. Still, the general thrust of that section — as worked out later by you and & — seems very different from what you offer. And far more sensible.
pc: > So, {me lo broda} means "is a referent of {lo > broda}" and what we disagree about then is what a > referent of {lo broda} might be>
That appears to be the situation, yes.
> I say that the > only referent of {lo broda} is a group of broda > and you say — against the odds — that it is one > or several broda.
Against what odds?
> Thus, I come up with a smaller > group of broda (as in English) and you come up > with a fraction of one broda (as in no known > laguage, apparently).
I agree excluding the parentheticals.
> So, yes, your position is > coherent, just very strange, at leas in this > case. What, by the way, happened to {me} meaning > "is an instance / example of," which talked about > lo broda, not {lo broda}?
That will work for lo/loi/lo'i, but not for le/la/lei/lai/le'i/la'i. Identifying {me} with McKay's "Among" gives a definition that works in all cases.
There is no need to talk about {lo broda}, we can just say: {me ko'a} = "x1 is/are among ko'a". When ko'a is an apple or several apples, x1 is an apple or several apples, when ko'a is a set, x1 is a set.
> So, {so'i le pa broda} is also nonsensefor the > same reason,
Right.
> but {piso'i lei ro broda} would also > be nonsense again for that reason.
No, that one is meaningful:
piso'i lei ro broda (= piso'i lo gunma be le ro broda)
"A large fraction of the group that consists of all the brodas".
> > > It starts to look as though > > > these {pi} with nonnumeric quantifiers are just > > > redundant. > > > > I think they are. I wouldn't want to define > > them if they weren't > > already there. > > How would you replace them, since by you they do > have non-redundant uses: how do {piso'i le broda} > without {piso'i}? I take using {fu'i} somehow as > a cheat.
I would have lo/le/la as the only gadri. I would say {lo so'i le broda} for "many of the broda" when not taken distributively.
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wrote:
> > pc: > > So, {me lo broda} means "is a referent of {lo > > broda}" and what we disagree about then is > what a > > referent of {lo broda} might be> > > That appears to be the situation, yes. > > > I say that the > > only referent of {lo broda} is a group of > broda > > and you say — against the odds — that it is > one > > or several broda. > > Against what odds? I break in here to apologize for being stupid: I have been uncomfortable with this presentation for a long time but have not been able to find the root source of the problem, so have picked away half-heartedly at the individual oddities. The new definition of {me}, in terms of reference, finally clicked to show me a more fundamental underlying problem. Reference is a function; that is, each sucessful referring expression refers to exactly one thing (on a given occasion, yada yada all the pragmatic stuff). It is variance from this principle that seems to me now to underlie all the difficulties with this raft of proposals. Since so many of the are explicitly about reference, I have to asume that xorxes is using "refer" in some nonstandard way. Two possibilities occur to me so far. 1) He is using plural semantics (already nonstandard) at least occasionally. Or 2), he means by "'sumti' refers to a" something like "a is one of the things whose behavior we have to check in order to determine the truth of a sentence containing 'sumti'." Since xorxes is as familiar witrh plural reference theory as I am, I assume this is not what is happening, leaving — until some better suggestion comes along — 2. I skimmed CLL and did not find any uses of "reference" or "refer" that fit this pattern, but I did find some cases of "mean" and "meaning" which might be the source of the problem. In any case, working with this new assumption, I am going back over the previously troubling positions to see whether they now work. As you might expect, I have not yet found one that didn't; xorxes stuff tends to cohere. And, since in the case of sets, anyhow, the ordinary referent is the only thing one has has to consider, the generalization about what the various quantifiers quantify works pretty well. The {loi/lei/lai} case is problematic, since it could be argued that we do have to consider the behavior of each member of the group to determine truth. But it could also be argued that we consider each member only insofar as it is a member of the group and contributes to the whole, thus making the group in this case (unlike the {lo/le/la} case, the correct unit for evaluation. I still don't quite get half an apple, but a bunch of apple halves is looking more resonable (for coherence, not for usefulness).
> > Thus, I come up with a smaller
> > group of broda (as in English) and you come
> up
> > with a fraction of one broda (as in no known
> > laguage, apparently).
>
> I agree excluding the parentheticals.
>
> > So, yes, your position is
> > coherent, just very strange, at leas in this
> > case. What, by the way, happened to {me}
> meaning
> > "is an instance / example of," which talked
> about
> > lo broda, not {lo broda}?
>
> That will work for lo/loi/lo'i, but not for
> le/la/lei/lai/le'i/la'i. Identifying {me} with
> McKay's "Among" gives a definition that works
> in
> all cases.
Except, of course, that "among" is about plurality and here we have groups and sets and what not. To be sure, the crucial relation in each of these cases is formally the same as "among," but is not the same relation (nor is the one for groups the same as that for sets) so this reduction does not quite work. Unless we really are going over to plurals after all, in which case the groups at least drop out.
> There is no need to talk about {lo broda},
> we can just say: {me ko'a} = "x1 is/are among
> ko'a".
> When ko'a is an apple or several apples, x1 is
> an
> apple or several apples, when ko'a is a set, x1
> is
> a set.
This is new and opaque. {ko'a} doesn't "refer" (or refer, for that matter) to anything until it has been assigned somehow, so how does it come to "refer" an apple or a bunch of apples. I suppose this is contextual. And, of course, {me ko'a}, even with {ko'a} "referring" to apples does not do away with the need for {lo plise} or any other {lo} expression. And certainly not in a way that distinguishes {lo} from {le}.
The subsequent stuff about fractions of the "referents" of various expressions I witrhdraw from, since my remarks were based on reference not "reference."
> > So, {so'i le pa broda} is also nonsensefor > the > > same reason, > > Right. > > > but {piso'i lei ro broda} would also > > be nonsense again for that reason. > > No, that one is meaningful: > > piso'i lei ro broda > (= piso'i lo gunma be le ro broda) > > "A large fraction of the group that consists of > all the brodas". > > > > > It starts to look as though > > > > these {pi} with nonnumeric quantifiers > are just > > > > redundant. > > > > > > I think they are. I wouldn't want to define > > > them if they weren't > > > already there. > > > > How would you replace them, since by you they > do > > have non-redundant uses: how do {piso'i le > broda} > > without {piso'i}? I take using {fu'i} > somehow as > > a cheat. > > I would have lo/le/la as the only gadri. > I would say {lo so'i le broda} for "many of the > broda" when > not taken distributively. > How do we know nondistributively? We could do this, assuming we had some other way of showing wen predication was distributive and when not and assuming that we never wanted sets (except under the rubric {le selcmi be}) This is getting formally very close to plurals again (or, rather, still) when the groups disappear.
Ahah! I just got it: unquantified descriptions (or at least {lo}) are inherently collective, but external quantifiers (at least numerical ones)are inherently distributive. so, {so'i} distributes and allows for a non-fractional quantification, and then {lo} collects the result again. This would work, but seems unduly complex, requiring a quantifier for every distributive use (and they do seem to be the most common). So, I suspect I have missed something. And, of course, we don't have plurality logic going yet (I think). On the whole it still seems that leaving distributive as (linguistically — though not logically) fundamental and then marking collectives somehow is going to be most efficient — if we are going to introduce these notions at all (which, if we do, why not go to plural logic altogether, since then at least we are up front about what is going on, which is mightily unclear now).
pc: > Since so many of > the are explicitly about reference, I have to > asume that xorxes is using "refer" in some > nonstandard way. Two possibilities occur to me > so far. 1) He is using plural semantics (already > nonstandard) at least occasionally.
Yes. I take every unquantified sumti as a plural constant, i.e. a constant with one or more referents.
> Ahah! I just got it: unquantified descriptions > (or at least {lo}) are inherently collective, but > external quantifiers (at least numerical ones)are > inherently distributive.
Right.
> On the > whole it still seems that leaving distributive as > (linguistically — though not logically) > fundamental and then marking collectives somehow > is going to be most efficient — if we are going > to introduce these notions at all (which, if we > do, why not go to plural logic altogether, since > then at least we are up front about what is going > on, which is mightily unclear now).
>From my part, you are welcome to offer an alternative system.
The system I propose consists of lo/le/la and non-fractional quantifiers. That's all we need.
Sets, masses, typicals and fractional quantifiers are bells and whistles as far as I'm concerned, added for back compatibility with CLL but really not a relevant part of the system. I think they have been added in a fairly systematic way given those constrains. I can certainly imagine more elegant functions for them, but they wouldn't agree with CLL. If you suggest something else and there is support for the idea, I'll be happy to go along with it.
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> > pc: > > Since so many of > > the are explicitly about reference, I have to > > asume that xorxes is using "refer" in some > > nonstandard way. Two possibilities occur to > me > > so far. 1) He is using plural semantics > (already > > nonstandard) at least occasionally. > > Yes. I take every unquantified sumti as a > plural constant, > i.e. a constant with one or more referents.
Well, we've been over this before. If you are going to make reference sometimes a relation rather than a function, it becomes one all of the time. That is, variables become plural, too. I suppose that it does happen that as a matter of fact variables are always assigned on a single referent but that can't be built into the system (and, indeed, would result in no variable be usable to generalize on one of the plural terms).
The "constant" continues to worry me — what do you mean by that expression. It cannot be negation transparency of course, because that doesn't work in one direction or the other. I suppose it just means that the expression refers to the same thing(s) wherever it occurs (yada yada) as opposed to a variable which can refer to different thing in various occurrences. Ao it is not very surprising after all,since this was always assumed (descriptions stick).
> > From my part, you are welcome to offer an > alternative system. > > The system I propose consists of lo/le/la and > non-fractional > quantifiers. That's all we need. > > Sets, masses, typicals and fractional > quantifiers are bells > and whistles as far as I'm concerned, added for > back compatibility > with CLL but really not a relevant part of the > system. I think they > have been added in a fairly systematic way > given those constrains. > I can certainly imagine more elegant functions > for them, but they > wouldn't agree with CLL. If you suggest > something else and there > is support for the idea, I'll be happy to go > along with it. > Well, I did offer a version of my own a while back (with fractionals as far as I can remember) and with collective {loi lei lai}. You objected that some of the things that I had for descriptors you had for quantifier expressions (and I think I had my quantifier expressions wrong from my point of view, too) but otherwise did not comment on the project as a whole. I think it was internally consistent, however, once the quantifiers are corrected to read, for example, {(su'o) da broda} = [ex:Fx Ex:Fx][ay:Fy Ay:Fy]y among x (I assumed plural quantifiers, to be sure -- I could redo it in terms of groups, which would be formally identical, though a bit wordier). It also seemed to agree with CLL pretty much — except for universally accepted changes, like allowing unlabelled {lo} to be something other than all the brodas or whatever. I haven't implemented the notion that collective predication is alone basic, but it should run smoothly, with individual and distributive predication being definable (real definitions). Failing that, I think the problem of indication type of predication is the single most complex one — that is, finding a sensible method within the context of the language: we could solve the problem by just putting a word for C or D at each place, but that gets to be way too long. I like the idea of not having fractional quantifiers at all but using (I suppose you intend) longer expressions involving {se'i} and the like.
pc: > --- Jorge Llambías wrote: > > I take every unquantified sumti as a > > plural constant, > > i.e. a constant with one or more referents. > > Well, we've been over this before. If you are > going to make reference sometimes a relation > rather than a function, it becomes one all of the > time. That is, variables become plural, too.
Let {da'oi}, {de'oi}, {di'oi} be plural variables. Let {su'oi} be the existential plural quantifier.
(Note: I am not proposing to actually make these part of the language, I am just using them as stepping stones in the definitions.)
Now define {su'o da zo'u da broda} as:
su'oi da'oi poi naku su'oi de'oi naku zo'u ganai de'oi me da'oi gi da'oi me de'oi zo'u da'oi broda
So we have da defined as a singular variable with the
singular quantifier {su'o}. The rest of the numeric
quantifiers can be defined in terms of {su'o}.
> I > suppose that it does happen that as a matter of > fact variables are always assigned on a single > referent but that can't be built into the system
Why can't it be built into the system?
> (and, indeed, would result in no variable be > usable to generalize on one of the plural terms).
Right, da, de, di as defined above can only generalize on the special cases where the plural constant happens to have a single referent.
> The "constant" continues to worry me — what do > you mean by that expression. It cannot be > negation transparency of course, because that > doesn't work in one direction or the other.
Yes, I do mean negation transparency. I take these to be materially equivalent:
naku lo rozgu cu xunre lo rozgu naku cu xunre
"It is not the case that roses are red." "As for roses, it is not the case that they are red."
> Well, I did offer a version of my own a while
> back (with fractionals as far as I can remember)
> and with collective {loi lei lai}. You objected
> that some of the things that I had for
> descriptors you had for quantifier expressions
> (and I think I had my quantifier expressions
> wrong from my point of view, too) but otherwise
> did not comment on the project as a whole. I
> think it was internally consistent, however, once
> the quantifiers are corrected to read, for
> example, {(su'o) da broda} = [ex:Fx Ex:Fx][ay:Fy Ay:Fy]y
> among x (I assumed plural quantifiers, to be sure
> — I could redo it in terms of groups, which
> would be formally identical, though a bit
> wordier).
It would be easier if you put everything in a wiki page, which you can update with any corrections and improvements as you make them.
> It also seemed to agree with CLL pretty > much — except for universally accepted changes, > like allowing unlabelled {lo} to be something > other than all the brodas or whatever.
I really can't tell from what you say here. If you have alternative definitions, it would be nice to have them all together, preferrably in a page where they are easier to find later for consultation and where you can fix inevitable typos and mistakes. The crucial step however will be that somone else take a look at it, not just myself.
mu'o mi'e xorxes
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wrote:
> > pc: > > --- Jorge Llambías wrote: > > > I take every unquantified sumti as a > > > plural constant, > > > i.e. a constant with one or more referents. > > > > Well, we've been over this before. If you > are > > going to make reference sometimes a relation > > rather than a function, it becomes one all of > the > > time. That is, variables become plural, too. > > > Let {da'oi}, {de'oi}, {di'oi} be plural > variables. > Let {su'oi} be the existential plural > quantifier. > > (Note: I am not proposing to actually make > these part of > the language, I am just using them as stepping > stones in > the definitions.) > > Now define {su'o da zo'u da broda} as: > > su'oi da'oi poi naku su'oi de'oi naku zo'u > ganai de'oi me da'oi gi da'oi me de'oi zo'u > da'oi broda
Well, OK, though I think that using restricted quantifiers along with plurals makes the whole tidier (and, of course, I want my universals to be importing — but that is easy to work either way, especially if we start with importing ones. In fact your device is just the right one to use in that case.)
> So we have da defined as a singular variable > with the > singular quantifier {su'o}. The rest of the > numeric > quantifiers can be defined in terms of {su'o}. > > > I > > suppose that it does happen that as a matter > of > > fact variables are always assigned on a > single > > referent but that can't be built into the > system > > Why can't it be built into the system?
Well, it could be — but the system in which it works is the plural one. We can't strat with the singular and then allow that some variables havve more than one referent. And, of course, once we have the plurals, the point of keeping separate singulars is mostly lost. If they are enforced singulars, then again we have it that ordinary variable cannot generalize plural objects, so almost everything is just done twice: "There is x or there are i such that x F or iD-F" and so on.
> > (and, indeed, would result in no variable be > > usable to generalize on one of the plural > terms). > > Right, da, de, di as defined above can only > generalize > on the special cases where the plural constant > happens > to have a single referent. > > > The "constant" continues to worry me — what > do > > you mean by that expression. It cannot be > > negation transparency of course, because that > > doesn't work in one direction or the other. > > Yes, I do mean negation transparency. I take > these > to be materially equivalent: > > naku lo rozgu cu xunre > lo rozgu naku cu xunre > > "It is not the case that roses are red." > "As for roses, it is not the case that they are > red."
I know you do and I am still waiting for an explanation of how this is going to work. The first means that is false that some (particular, I would think) roses are red — all of them. That could be because there are no roses or because there are no roses picked out by the expression or because there are but not all of them are are red — but some of them might be. The second says that there are roses picked out by the expression and all of them are non-red. Note that only one subcase covered by the first is covered by the second, hardly an equivalence.
> > Well, I did offer a version of my own a while
> > back (with fractionals as far as I can
> remember)
> > and with collective {loi lei lai}. You
> objected
> > that some of the things that I had for
> > descriptors you had for quantifier
> expressions
> > (and I think I had my quantifier expressions
> > wrong from my point of view, too) but
> otherwise
> > did not comment on the project as a whole. I
> > think it was internally consistent, however,
> once
> > the quantifiers are corrected to read, for
> > example, {(su'o) da broda} = [ex:Fx Ex:Fx][ay:Fy Ay:Fy]y
> > among x (I assumed plural quantifiers, to be
> sure
> > — I could redo it in terms of groups, which
> > would be formally identical, though a bit
> > wordier).
>
> It would be easier if you put everything in a
> wiki page,
> which you can update with any corrections and
> improvements as you make them.
I would not put up a wiki page — which has a habit of being permanent — until I was reasonably confident of what I had. And, of course, I would not put up my page without criticizing your — which means that der Gruppenfuehrer will erase my page immediately he notices it (he has threatened this several times and has usually followed through on his threats). So there is not much of a point to that exercise.
> > It also seemed to agree with CLL pretty
> > much — except for universally accepted
> changes,
> > like allowing unlabelled {lo} to be something
> > other than all the brodas or whatever.
>
> I really can't tell from what you say here. If
> you have
> alternative definitions, it would be nice to
> have them
> all together, preferrably in a page where they
> are easier
> to find later for consultation and where you
> can fix
> inevitable typos and mistakes. The crucial step
> however
> will be that somone else take a look at it, not
> just
> myself.
Well, it is back in the archives of the gadri thread somewhere. I can try to fish it out, but -- on the basis of the response the last time -- I doubt that anyone but you will look at it.
pc: > > Yes, I do mean negation transparency. I take > > these to be materially equivalent: > > > > naku lo rozgu cu xunre > > lo rozgu naku cu xunre > > > > "It is not the case that roses are red." > > "As for roses, it is not the case that they are > > red." > > I know you do and I am still waiting for an > explanation of how this is going to work.
I don't know what kind of further explanation you expect. Why wouldn't it work?
> The > first means that is false that some (particular, > I would think) roses are red — all of them. > That could be because there are no roses or > because there are no roses picked out by the > expression or because there are but not all of > them are are red — but some of them might be. > The second says that there are roses picked out > by the expression and all of them are non-red. > Note that only one subcase covered by the first > is covered by the second, hardly an equivalence.
That's the case if you take {lo rozgu} to be {ro lo rozgu}, a quantified term. But I don't. For me it's a constant that refers to roses.
> I would not put up a wiki page — which has a > habit of being permanent — until I was > reasonably confident of what I had.
Wiki pages are modifiable, and if you want to erase the whole thing at some point you can.
> And, of > course, I would not put up my page without > criticizing your — which means that der > Gruppenfuehrer will erase my page immediately he > notices it
I doubt that very much. You are very welcome to criticize mine all you please.
>(he has threatened this several times > and has usually followed through on his threats).
Most of his complaints as I remember have been about form rather than content, things like excessive quoting and such. I doubt very much he would censor anything you write about the language.
> So there is not much of a point to that exercise.
OK, but don't expect me to keep all your proposals with their variations in mind if there isn't a place where I can check what they were with reasonable accessibility.
> Well, it is back in the archives of the gadri > thread somewhere. I can try to fish it out, but > — on the basis of the response the last time -- > I doubt that anyone but you will look at it.
And if you find it and just post it here, it will be lost when we need to check again next month. A wiki page is much more convenient for this, because then you can just direct me to go look there. And if someone else suddenly became interested, now or three months from now, they wouldn't have to wade through hundreds of posts to find it.
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wrote:
> > pc: > > > Yes, I do mean negation transparency. I > take > > > these to be materially equivalent: > > > > > > naku lo rozgu cu xunre > > > lo rozgu naku cu xunre > > > > > > "It is not the case that roses are red." > > > "As for roses, it is not the case that they > are > > > red." > > > > I know you do and I am still waiting for an > > explanation of how this is going to work. > > I don't know what kind of further explanation > you > expect. Why wouldn't it work? > > > The > > first means that is false that some > (particular, > > I would think) roses are red — all of them. > > That could be because there are no roses or > > because there are no roses picked out by the > > expression or because there are but not all > of > > them are are red — but some of them might > be. > > The second says that there are roses picked > out > > by the expression and all of them are > non-red. > > Note that only one subcase covered by the > first > > is covered by the second, hardly an > equivalence. > > That's the case if you take {lo rozgu} to be > {ro lo rozgu}, a quantified term. But I don't. > For me it's a constant that refers to roses.
Reference is to particulars. Now, if you want generality, you have two choices — one not officially available in Lojban. You can use quantifiers — and whichever one you pick will generate the problems mentioned above — or you can use some modal notion like "generally" or "usually" or "typically." Lojban doesn't have those but clearly needs them. As modal notions they do take one out of the real world into idealized ones of some sort — but then, in that world, {lo rozgu} picks out some roses, all of which or some of which are or are not red and on that hinges the truth about {lo rozgu}. I note in passing that your second definition of {lo} makes it not only particular roses but specific ones, "the obvious ones in the context" (assuming that {zo'e} is meaningful and a referring expression in a definition context). Your first definition (otherwise generally better) contains the unexplained "generic reference," for which I cannot find a plausible interpretation still after all these years (quantifiers or reference to a genus or species having both been rejected). The basic problem is that a claim, to be meaningful, has to have some way of verifying it, at least in principle. How would you verify {lo rozgu cu xunre}? If nom particular roses are relevant then it seems impossible to do, if some are then the question is how many of them are needed to show the claim true (or how are they distributed, which is an only slightly more complex case). You can say that quantifiers don't count, but in the real world they almost always do.
> > I would not put up a wiki page — which has a > > habit of being permanent — until I was > > reasonably confident of what I had. > > Wiki pages are modifiable, and if you want to > erase the > whole thing at some point you can.
Obviously true, but the iorignals tend to get saved and used later.
> > And, of > > course, I would not put up my page without > > criticizing your — which means that der > > Gruppenfuehrer will erase my page immediately > he > > notices it > > I doubt that very much. You are very welcome to > criticize > mine all you please.
I have been explicitly told not too on pain of being excluded from all sites under dGF's control -- which, alas, is virtually everything having to do with Lojban.
> >(he has threatened this several times > > and has usually followed through on his > threats). > > Most of his complaints as I remember have been > about form > rather than content, things like excessive > quoting and such. > I doubt very much he would censor anything you > write about > the language.
As I said....
> > So there is not much of a point to that > exercise. > > OK, but don't expect me to keep all your > proposals with > their variations in mind if there isn't a place > where I > can check what they were with reasonable > accessibility. > > > Well, it is back in the archives of the gadri > > thread somewhere. I can try to fish it out, > but > > — on the basis of the response the last time > -- > > I doubt that anyone but you will look at it. > > And if you find it and just post it here, it > will be lost > when we need to check again next month. A wiki > page is much > more convenient for this, because then you can > just direct > me to go look there. And if someone else > suddenly became > interested, now or three months from now, they > wouldn't > have to wade through hundreds of posts to find > it.
I think that was the point of the mythical elephant, but I'll see what I can do.
pc: > Reference is to particulars.
OK, but what counts as a particular is left to ontology. No need for us to dictate what is or what is not a thing. And I certainly don't want things to be fixed once for any and all contexts.
> Now, if you want > generality, you have two choices — one not > officially available in Lojban. You can use > quantifiers — and whichever one you pick will > generate the problems mentioned above
I don't use quantifiers for unquantified terms.
> — or you > can use some modal notion like "generally" or > "usually" or "typically."
Which need not always be made explicit. Context can determine whether you are speaking in general terms or not.
> Lojban doesn't have > those but clearly needs them.
{ta'e} and {na'o} would seem to be for something of that sort. But I agree this area needs more clarification, if not necessarily more words.
> As modal notions > they do take one out of the real world into > idealized ones of some sort — but then, in that > world, {lo rozgu} picks out some roses, all of > which or some of which are or are not red and on > that hinges the truth about {lo rozgu}. I note > in passing that your second definition of {lo} > makes it not only particular roses but specific > ones, "the obvious ones in the context" (assuming > that {zo'e} is meaningful and a referring > expression in a definition context).
The obvious ones in some context might be roses in general.
> Your first > definition (otherwise generally better) contains > the unexplained "generic reference," for which I > cannot find a plausible interpretation still > after all these years (quantifiers or reference > to a genus or species having both been rejected).
Maybe your ontology is too restrictive.
> The basic problem is that a claim, to be > meaningful, has to have some way of verifying it, > at least in principle.
Is that a claim? If so, how do I verify it?
> How would you verify {lo rozgu cu xunre}?
In what context?
> If nom particular roses are > relevant then it seems impossible to do, if some > are then the question is how many of them are > needed to show the claim true (or how are they > distributed, which is an only slightly more > complex case). You can say that quantifiers > don't count, but in the real world they almost > always do.
When quantifiers are important, they should be made explicit.
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wrote:
> > pc: > > Reference is to particulars. > > OK, but what counts as a particular is left to > ontology. No need for us to dictate what is or > what > is not a thing. And I certainly don't want > things to > be fixed once for any and all contexts. True enough. but we have some givens in Lojban and if you want some more you ought to introduce them explicitly (and definitionally, if possible). I have trouble imagining what is left out here.
> > Now, if you want
> > generality, you have two choices — one not
> > officially available in Lojban. You can use
> > quantifiers — and whichever one you pick
> will
> > generate the problems mentioned above
>
> I don't use quantifiers for unquantified terms.
But what terms are quantified is a matter of interpretation. {lo} descriptions are not quantified as such, but at least one plausible interpretation of them is that they involve an underlying quantifier — or several.
> > — or you > > can use some modal notion like "generally" or > > "usually" or "typically." > > Which need not always be made explicit. Context > can > determine whether you are speaking in general > terms > or not. Very true, but, if you are going to claim that something is meant generally, you should make sure the context does determine that. {lo rozgu cu xunre} without context is particular, not general — almost exactly what your second definition has it be.
> > Lojban doesn't have > > those but clearly needs them. > > {ta'e} and {na'o} would seem to be for > something of > that sort. But I agree this area needs more > clarification, > if not necessarily more words.
Yes, it has some items in the area, but none really clearly spelled out. I recall taht someone used {na'o} in an attempt to explain {lo'e}, which seems right. {ta'e}, as "habitually", looks like it belongs, with {ka'e} as "able to," as a brivla not a modal. Nothing looks like "generally" or "usually" really. But they are relatively easy to add.
> > As modal notions > > they do take one out of the real world into > > idealized ones of some sort — but then, in > that > > world, {lo rozgu} picks out some roses, all > of > > which or some of which are or are not red and > on > > that hinges the truth about {lo rozgu}. I > note > > in passing that your second definition of > {lo} > > makes it not only particular roses but > specific > > ones, "the obvious ones in the context" > (assuming > > that {zo'e} is meaningful and a referring > > expression in a definition context). > > The obvious ones in some context might be roses > in general.
But those aren't ones in any context. Roses in general are just (like typical roses) about the general situation with particular roses in each.
> > Your first
> > definition (otherwise generally better)
> contains
> > the unexplained "generic reference," for
> which I
> > cannot find a plausible interpretation still
> > after all these years (quantifiers or
> reference
> > to a genus or species having both been
> rejected).
>
> Maybe your ontology is too restrictive.
Maybe. How would you expand it — keeping with things , not with mere forms of words.
> > The basic problem is that a claim, to be > > meaningful, has to have some way of verifying > it, > > at least in principle. > > Is that a claim? If so, how do I verify it?
It is definitional. It is also a matter of practical concern: if something is claimed and you are concerned about whether it is true or not, you have to have a way of finding out — at least in principle.
> > How would you verify {lo rozgu cu xunre}? > > In what context?
I assume that you mean it here as a general claim about roses. You apparently mean something by it other than that there are red roses (which is easy to verify), but it is not clear what more.
> > If nom particular roses are > > relevant then it seems impossible to do, if > some > > are then the question is how many of them are > > needed to show the claim true (or how are > they > > distributed, which is an only slightly more > > complex case). You can say that quantifiers > > don't count, but in the real world they > almost > > always do. > > When quantifiers are important, they should be > made > explicit.
Very likely true, but since they always are and it is often clear what ones are involved, we leave them out whenever possible. The conflicts between logic and language are inherent in spoken Lojban. However, in explaining Lojban, we try to do justice to both. Your line of chat so far helps with neither.
pc: > > I don't use quantifiers for unquantified terms. > > But what terms are quantified is a matter of > interpretation.
If the term has a PA in front, it is quantified. If the term does not have a PA in front it is not. That's all the interpretation that's required, the way I see it.
> {lo rozgu > cu xunre} without context is particular, not > general — almost exactly what your second > definition has it be.
I tend to take any out of the blue sentence as general. I'm not sure why you say it has to be otherwise.
> > The obvious ones in some context might be roses > > in general. > > But those aren't ones in any context. Roses in > general are just (like typical roses) about the > general situation with particular roses in each.
That's your take on things, we are obviously not going to agree about that.
> > Maybe your ontology is too restrictive. > > Maybe. How would you expand it — keeping with > things , not with mere forms of words.
Roses are things. We've been here, I suspect we won't be getting anywhere this time either.
> > > How would you verify {lo rozgu cu xunre}? > > In what context? > > I assume that you mean it here as a general claim > about roses. You apparently mean something by it > other than that there are red roses (which is > easy to verify), but it is not clear what more.
"Roses are red" in English does not just mean that there are red roses.
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wrote:
> > pc: > > > I don't use quantifiers for unquantified > terms. > > > > But what terms are quantified is a matter of > > interpretation. > > If the term has a PA in front, it is > quantified. > If the term does not have a PA in front it is > not. > That's all the interpretation that's required, > the > way I see it.
Well, in CLL at least (and matchingly in the real world) every description, whether explicitly quantified or not involves at least one quantifier. On the other hand, on one way of matching up with McKay's system, most quantifiers on descriptions would not actually be quantifiers at all, but predicates: "is Q in number" or "is the Q of." The logical language idea was to put as much logic as possible as overtly as possible -- subject to the requirements of a spoken language. From these came the use of descriptors in place of overt quantifiers (there is precedent for this in logic, of course).
> . > > {lo rozgu > > cu xunre} without context is particular, not > > general — almost exactly what your second > > definition has it be. > > I tend to take any out of the blue sentence as > general. > I'm not sure why you say it has to be > otherwise.
I don't say it has to be otherwise. I just take sentences out of the blue to be about particular events. So, when you seem to say it has to be otherwise, I beg to disagree.
> > > The obvious ones in some context might be > roses > > > in general. > > > > But those aren't ones in any context. Roses > in > > general are just (like typical roses) about > the > > general situation with particular roses in > each. > > That's your take on things, we are obviously > not going > to agree about that.
I am trying to understand what you want instead, but every time I try something that might work for one of your ideas, if fails on another sometimes batting back and forth like a shuttlecock in a hot game: it is not quantifiers nor species nor properties (with interpetation rules). That about exhausts my supply of possible meanings for things like "generic reference" or "roses in general (but not general remarks about various real roses)." I tend to think about this point that this is just feel-good words that do not — and cannot — have any concrete meaning behind them. I am probably wrong about this, but the evidence to the contrary has never been forthcoming.
> > > Maybe your ontology is too restrictive.
> >
> > Maybe. How would you expand it — keeping
> with
> > things , not with mere forms of words.
>
> Roses are things. We've been here, I suspect we
> won't be getting
> anywhere this time either.
Roses are indeed things, particular concrete things, that we want to say general things about. You seem to want some other kind of roses altogether, general roses about which we say particular things, e.g., that they are red. I would see that claim as one about ordinary roses in a not well worked out, but fairly well understood, modality: "generally." The not well worked out part has to do with how many roses we have to examine to determine whether the claim is true (not that it will be a fixed number — and distribution will count as well). Nothing else will matter. But I don't know where to find a general rose nor what to do with it. If examining it or them will give me the same information as examining a number of roses, then, while they are a convenient shortcut, they are really unnecessary. If they give different information, then they are irrelevant, since they don't tell me about ordinary roses.
> > > > How would you verify {lo rozgu cu xunre}? > > > > In what context? > > > > I assume that you mean it here as a general > claim > > about roses. You apparently mean something > by it > > other than that there are red roses (which is > > easy to verify), but it is not clear what > more. > > "Roses are red" in English does not just mean > that > there are red roses. > Well, it means very different things in different contexts, but the broad outline is something along the line that a plurality of rose (or, more likely, a plurality of rose cultivar) blossoms are in the red line (red, pink, orange, yellow, whites off in these directions). So we whip out our Jackson & Perkins or the Rosarian registry and check. Sometimes, of course, the English sentence just means that some roses are — in response to a clueless person who believes that roses come only in colors other than red. Sometimes it means (a case that Lojban can handle) that the typicla (or even stereotypical) rose is red. And so on. Lojban would presumably like to have different means of exressing each of these different claims. To be sure, it probably also wants one that is not so determinate, and maybe {lo rozgu cu xunre} is that — but that doesn't mean that it does not have rules for figuring out whether it is true or not (the first part of the rule may well be to divide its various senses if it is ambiguous or look toward precising if it is vague). But {lo rozgu cu xunre} is not limited to taht use; it does perfectly well as the beginning of a story about a totally particular event — a date, say.
pc: > Well, in CLL at least (and matchingly in the real > world) every description, whether explicitly > quantified or not involves at least one > quantifier.
In CLL, yes. CLL does not allow constant terms (in theory), every term according to CLL is quantified, even names. That is the important difference between the proposed definitions and CLL. (I don't understand what you mean by "and matchingly in the real world". Reference, description, quantification are all theoretical constructs.)
> Roses are indeed things, particular concrete > things, that we want to say general things about.
Yes. And sometimes we may want to say particular things about them too. For example:
- Tell me something about roses. - Roses? My grandmother loved them. She used to buy them from the flowershop at the corner.
> You seem to want some other kind of roses > altogether, general roses about which we say > particular things, e.g., that they are red.
Roses in general are not general roses, whatever these are. So no, I don't want to speak of any particular kind of roses when I speak of roses in general.
> I would see that claim as one about ordinary > roses in a not well worked out, but fairly well > understood, modality: "generally." The not well > worked out part has to do with how many roses we > have to examine to determine whether the claim is > true (not that it will be a fixed number — and > distribution will count as well).
Do you propose that as a general strategy for {lo broda}, or as an explanation of English generics that we can't replicate in Lojban?
> > "Roses are red" in English does not just mean > > that > > there are red roses. > > > Well, it means very different things in different > contexts, but the broad outline is something > along the line that a plurality of rose (or, more > likely, a plurality of rose cultivar) blossoms > are in the red line (red, pink, orange, yellow, > whites off in these directions). So we whip out > our Jackson & Perkins or the Rosarian registry > and check. Sometimes, of course, the English > sentence just means that some roses are — in > response to a clueless person who believes that > roses come only in colors other than red. > Sometimes it means (a case that Lojban can > handle) that the typicla (or even stereotypical) > rose is red. And so on. Lojban would presumably > like to have different means of exressing each of > these different claims. To be sure, it probably > also wants one that is not so determinate, and > maybe {lo rozgu cu xunre} is that — but that > doesn't mean that it does not have rules for > figuring out whether it is true or not (the first > part of the rule may well be to divide its > various senses if it is ambiguous or look toward > precising if it is vague). But {lo rozgu cu > xunre} is not limited to taht use; it does > perfectly well as the beginning of a story about > a totally particular event — a date, say.
It certainly does. It all depends on the context.
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wrote:
> > pc: > > Well, in CLL at least (and matchingly in the > real > > world) every description, whether explicitly > > quantified or not involves at least one > > quantifier. > > In CLL, yes. CLL does not allow constant terms > (in theory), > every term according to CLL is quantified, even > names. That is > the important difference between the proposed > definitions and CLL. > (I don't understand what you mean by "and > matchingly > in the real world". Reference, description, > quantification > are all theoretical constructs.)
Well, yes and no. The point is that in the real world things come singly and each or several of them do something to accomplish what we say happens. What we say may be vague in a variety of ways, but what happens is not. But however vague our talk may be, it has to hook up with what happens in some way and thus has to take account of the fact that every event involves some number of things. Whatever we say is then going to reflect this some how, at the risk of not saying anything about the world or saying impossible things.
> > Roses are indeed things, particular concrete > > things, that we want to say general things > about. > > Yes. And sometimes we may want to say > particular things > about them too. For example: > > - Tell me something about roses. > - Roses? My grandmother loved them. She used to > buy > them from the flowershop at the corner.
Of course, but how do we do this in Lojban if we are allowed only general things. The roses your grandmother loved were particular roses, scented, thorny, and the liek, not generic roses -- whatever those are. hey were not identified, perhaps (though some may have been) and she may even have been indifferent to whihc roses they were, but they were particular ones each time she bought some.
> > You seem to want some other kind of roses > > altogether, general roses about which we say > > particular things, e.g., that they are red. > > Roses in general are not general roses, > whatever these > are. So no, I don't want to speak of any > particular > kind of roses when I speak of roses in general.
I think you mean any specific roses. Every rose is particular, but specificity is about our language not about the roses. We can identify a rose only as a rose, without getting specific, and then we take it as a type, or we can stop short of even that and just say general things about roses. But it is still ordinary roses we are talking aobut; we are just talking aboout them in a general way. This has nothing to do with reference; it is bout context frames perhaps, within which identification is abrogated.
> > I would see that claim as one about ordinary > > roses in a not well worked out, but fairly > well > > understood, modality: "generally." The not > well > > worked out part has to do with how many roses > we > > have to examine to determine whether the > claim is > > true (not that it will be a fixed number -- > and > > distribution will count as well). > > Do you propose that as a general strategy for > {lo broda}, > or as an explanation of English generics that > we can't > replicate in Lojban?
Well, as you know, I think {lo broda} is just a quantified expression (not equivalent to {su'o da}, howver, which is more complex) and that takes care of generality or particularity depending on context and usage. For general contexts, the quantifiers involved tend to be pretty vague (typically more than "most" and less than "all") with details coming in from further context. But what the cointexts fills in is how we go about answering the question "is this claim true?" Will a not even very random sample do or is more research needed, where is the cost/benefit break in research — and in confirming or denying, for that matter.
> > > "Roses are red" in English does not just > mean > > > that > > > there are red roses. > > > > > Well, it means very different things in > different > > contexts, but the broad outline is something > > along the line that a plurality of rose (or, > more > > likely, a plurality of rose cultivar) > blossoms > > are in the red line (red, pink, orange, > yellow, > > whites off in these directions). So we whip > out > > our Jackson & Perkins or the Rosarian > registry > > and check. Sometimes, of course, the English > > sentence just means that some roses are — in > > response to a clueless person who believes > that > > roses come only in colors other than red. > > Sometimes it means (a case that Lojban can > > handle) that the typicla (or even > stereotypical) > > rose is red. And so on. Lojban would > presumably > > like to have different means of exressing > each of > > these different claims. To be sure, it > probably > > also wants one that is not so determinate, > and > > maybe {lo rozgu cu xunre} is that — but > that > > doesn't mean that it does not have rules for > > figuring out whether it is true or not (the > first > > part of the rule may well be to divide its > > various senses if it is ambiguous or look > toward > > precising if it is vague). But {lo rozgu cu > > xunre} is not limited to taht use; it does > > perfectly well as the beginning of a story > about > > a totally particular event — a date, say. > > It certainly does. It all depends on the > context.
If you agree to that, then you will concede that your first definition (second too but for different reasons) is just wrong. {lo} is not generic in the sense you seem to want, though it can be used in that way (there is as you know an argument that quantifier expression are better for this purpose than descriptions because they are less likely to be drawn into merely local application). It can be used in any number of ways. At most these ways share the feature of being inspecific, just what we would expect from the usual contrast with the specific {le} — a contrast omitted in your second definition and misstated in the first. It does seem to me that you will be hard pressed -- as indeed you have been — to account for actual generalizing usage in terms of other usage (your "formal definitions") and, indeed, in saying much more about it even in English than to point to typical English cases which some particular Lojban parallels. Starting by locating the generalizing in the form of the description seems a particularly bad start, since that is not where it is (although, of course, {le} is not a good descriptor to use in gneralizing sentences).
pc: > The point is that in the real > world things come singly and each or several of > them do something to accomplish what we say > happens. What we say may be vague in a variety > of ways, but what happens is not. But however > vague our talk may be, it has to hook up with > what happens in some way and thus has to take > account of the fact that every event involves > some number of things. Whatever we say is then > going to reflect this some how, at the risk of > not saying anything about the world or saying > impossible things.
That's all metaphysics, it is not something one needs to believe in order to speak Lojban, or English for that matter. What counts as a thing is not dictated by the language, need not be context independent, and need not be specified in the description of the language.
> Well, as you know, I think {lo broda} is just a
> quantified expression (not equivalent to {su'o
> da}, howver, which is more complex) and that
> takes care of generality or particularity
> depending on context and usage. For general
> contexts, the quantifiers involved tend to be
> pretty vague (typically more than "most" and less
> than "all") with details coming in from further
> context. But what the cointexts fills in is how
> we go about answering the question "is this claim
> true?" Will a not even very random sample do or
> is more research needed, where is the
> cost/benefit break in research — and in
> confirming or denying, for that matter.
I can't tell from that how your take would differ from mine. If {lo broda} always has a context dependent and very complex quantifier, your interpretation may in effect very well end up agreeing with my interpretation in all cases. We would need example sentences that we would interpret differently in a given context to decide.
> > > But {lo rozgu cu > > > xunre} is not limited to taht use; it does > > > perfectly well as the beginning of a story > > about > > > a totally particular event — a date, say. > > > > It certainly does. It all depends on the > > context. > > If you agree to that, then you will concede that > your first definition (second too but for > different reasons) is just wrong. {lo} is not > generic in the sense you seem to want, though it > can be used in that way
What wording would you suggest for the definition? Would you be happy with it if I remove the "generically"?
> At most these ways share the feature of > being inspecific, just what we would expect from > the usual contrast with the specific {le} — a > contrast omitted in your second definition and > misstated in the first.
The specificity is included in that definition by requiring the {skicu} relationship to hold between the speaker, the audience and the thing in question. The speaker has to have the thing in mind in order to describe it to the audience. I'm sure the definition can be improved, but I don't think it's hopeless.
mu'o mi'e xorxes
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wrote:
> > pc: > > The point is that in the real > > world things come singly and each or several > of > > them do something to accomplish what we say > > happens. What we say may be vague in a > variety > > of ways, but what happens is not. But > however > > vague our talk may be, it has to hook up with > > what happens in some way and thus has to take > > account of the fact that every event involves > > some number of things. Whatever we say is > then > > going to reflect this some how, at the risk > of > > not saying anything about the world or saying > > impossible things. > > That's all metaphysics, it is not something one > needs > to believe in order to speak Lojban, or English > for > that matter. What counts as a thing is not > dictated by > the language, need not be context independent, > and need > not be specified in the description of the > language. > Well, I would deny that it is strictly metaphysics, but even if it is it has to be dealt with in our speech. To be sure, what counts as a thing is to some extent governed by our language (that is, after all, the Sapir-Whorf hypothesis that Loglan was designed to examine — and did a remarkably bad job of doing, given its inherent metaphysics). What we pick out of the world as things to talk about is, of course, largely dependent on context — in cluding the language used — but it helps if it is there is some sense to pick.
> > Well, as you know, I think {lo broda} is just > a > > quantified expression (not equivalent to > {su'o > > da}, howver, which is more complex) and that > > takes care of generality or particularity > > depending on context and usage. For general > > contexts, the quantifiers involved tend to be > > pretty vague (typically more than "most" and > less > > than "all") with details coming in from > further > > context. But what the cointexts fills in is > how > > we go about answering the question "is this > claim > > true?" Will a not even very random sample do > or > > is more research needed, where is the > > cost/benefit break in research — and in > > confirming or denying, for that matter. > > I can't tell from that how your take would > differ from mine. > If {lo broda} always has a context dependent > and very complex > quantifier, your interpretation may in effect > very well end > up agreeing with my interpretation in all > cases. We would > need example sentences that we would interpret > differently > in a given context to decide.
Metaphysics aside, I would expect that we end up at about the same place. After all, we are both reasonably careful observers of what goes on. But the metaphysics — or at least the logic -- is important for understanding at least and there is where we generally disagree. BTW, in working out a hard case, I suddenly saw where your idea that descriptions are constants came from (in my terms, that is). For a number of purposes it is handy if quantifiers (all importing, not quite by the way)carried "namely riders" which limit the scope of the quantifiers strictly speaking but provide a way to continue the reference outside the scope. I think this goes back to Partee's paper of donkey years ago, but I can't check. And building it in in such a way as to come out right under negations is a nice technical problem.
> > > > But {lo rozgu cu > > > > xunre} is not limited to taht use; it > does > > > > perfectly well as the beginning of a > story > > > about > > > > a totally particular event — a date, > say. > > > > > > It certainly does. It all depends on the > > > context. > > > > If you agree to that, then you will concede > that > > your first definition (second too but for > > different reasons) is just wrong. {lo} is not > > generic in the sense you seem to want, though > it > > can be used in that way > > What wording would you suggest for the > definition? > Would you be happy with it if I remove the > "generically"?
Well, that would help> I suggest "nonspecifically" except that that needs defining, too, even though it has a standard one for this context somewhere. This will make the contrast with {le} clear and open the way to the right variety of uses.
> > At most these ways share the feature of > > being inspecific, just what we would expect > from > > the usual contrast with the specific {le} -- > a > > contrast omitted in your second definition > and > > misstated in the first. > > The specificity is included in that definition > by requiring > the {skicu} relationship to hold between the > speaker, the > audience and the thing in question. The speaker > has to have > the thing in mind in order to describe it to > the audience. > I'm sure the definition can be improved, but I > don't think > it's hopeless. > No definition is hopeless as long as we have erasers. I am not at all sure that specificity is inherent in the {skicu} relation. After all, when one says {_lo_ broda} one is describing the thing as a broda but it is still nonspecific. Specificity seems to be a matter of whether the object is already in the context in some way; {le} serves to bring those particulars of the context into focus; {lo} to bring them into the context altogether. That is not all the two do, of course, but it seems to be a significant part of the whole. (I am not sure just how the internal context and the external interact. We can sometimes bring the external into the internal without introduction and at other times seem to need a introduction. Focus may be important here as well.)
On Tue, Sep 21, 2004 at 06:16:02AM -0700, Jorge Llamb?as wrote: > I would say {nopimu} and {pimu} are the same, just > as {pa fi'u re} is also {fi'u re}.
Sanity check. Are you saying that {pa fi'u re} is different as an outer quantifier than {pi mu}?
Are you saying that {pi mu broda} means half of one broda, while {pa fi'u re broda} means half of all brodas?
If so, why? I thought it was concluded a while ago that outer quantifiers that don't somehow resolve to an integer don't make sense. (As in, you can't really say you have 0.5 apples, when what you have is a single half-apple, because you could also have two half-apples that are different from one apple.)
-- Rob Speer
> Sanity check. Are you saying that {pa fi'u re} is different as an outer > quantifier than {pi mu}?
Right. The proposed definitions are:
PA1 fi'u PA2 sumti = PA1 out of every PA2 of the referents of sumti.
piPA sumti = A piPA fraction of one of the referents of sumti.
> Are you saying that {pi mu broda} means half of one broda, while {pa fi'u re > broda} means half of all brodas?
"One out of every two brodas", yes.
> If so, why?
To be consistent with other definitions.
We want masses to be things: {loi broda} = {lo gunma be lo broda}
We want {piso'i loi broda} to be "a lot of brodas".
>I thought it was concluded a while ago that outer quantifiers > that > don't somehow resolve to an integer don't make sense. (As in, you can't > really > say you have 0.5 apples, when what you have is a single half-apple, because > you could also have two half-apples that are different from one apple.)
piPA quantifiers, as can be seen from the definition, are not true quantifiers. They are a shorthand for a description.
piPA sumti = lo piPA si'e be pa me sumti
(The same is true for inner quantifiers, which are also part of a description.)
I am not especially committed to this definition of piPA quantifiers. If we want to identify {pimu} with {pa fi'u re} as quantifiers, then we must:
1) Drop CLL's interpretation of piPA's with masses and sets,
or
2) Drop the idea that masses and sets are possible values of da,
or
3) Drop the interpretation of {PA1fi'uPA2} as PA1 out of every PA2,
or
4) Find some other definitions that are consistent with all of that.
Any suggestions?
mu'o mi'e xorxes
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On Sat, Oct 02, 2004 at 10:56:20AM -0700, Jorge Llamb?as wrote: > > --- Rob Speer wrote: > > Sanity check. Are you saying that {pa fi'u re} is different as an outer > > quantifier than {pi mu}? > > Right. The proposed definitions are: > > PA1 fi'u PA2 sumti = PA1 out of every PA2 of the referents of sumti. > > piPA sumti = A piPA fraction of one of the referents of sumti. > > > Are you saying that {pi mu broda} means half of one broda, while {pa fi'u re > > broda} means half of all brodas? > > "One out of every two brodas", yes. > > > If so, why? > > To be consistent with other definitions. > > We want masses to be things: {loi broda} = {lo gunma be lo broda} > > We want {piso'i loi broda} to be "a lot of brodas".
First of all, how is that different from "so'i lo broda"?
Anyway, I consider "piso'i" to be a non-integer quantifier, for a value around maybe 0.4, so I would read this the same way I would read a fraction.
If "pimu lo broda" is "0.5 brodas", then "piso'i lo broda" should be "a sizable fraction of a broda", which is not what you want.
Can you cite an example where the "0.5 brodas" reading is necessary and makes sense? I can't imagine anything you can actually have 0.5 of, besides a unit of measure, and Lojban already deals with units of measure differently.
-- Rob Speer
> > We want {piso'i loi broda} to be "a lot of brodas". > > First of all, how is that different from "so'i lo broda"?
{piso'i loi broda} is collective, {so'i lo broda} distributive.
If you want an even more clearcut example, consider {pimu le'i broda} which is meant to be a new set with half of the members of le'i broda.
> Anyway, I consider "piso'i" to be a non-integer quantifier, for a value > around maybe 0.4, so I would read this the same way I would read a fraction.
I'm defining all piPA the same way, whether it's {piso'i} or {pivo}.
> If "pimu lo broda" is "0.5 brodas", then "piso'i lo broda" should be "a > sizable > fraction of a broda", which is not what you want.
Yes, that's how it is now being defined.
> Can you cite an example where the "0.5 brodas" reading is necessary and makes > sense?
The example in CLL is:
mi citka piro lei nanba I eat the-whole-of the-mass-of bread
CLL also says: "Smaller quantifiers are possible for sets, and refer to subsets. Thus pimu le'i nanmu is a subset of the set of men I have in mind; we don't know precisely which elements make up this subset, but it must have half the size of the full set. This is the best way to say half of the men; saying pimu le nanmu would give us a half-portion of one of them instead! Of course, the result of pimu le'i nanmu is still a set; if you need to refer to the individuals of the subset, you must say so (see lu'a in Section 10)."
> I can't imagine anything you can actually have 0.5 of, besides a unit > of > measure, and Lojban already deals with units of measure differently.
As I said, I don't think {piPA} is a true quantifier. It is simply a shorthand for a description: {lo piPA si'e be lo pa me...}.
mu'o mi'e xorxes
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Well, the obvious and natural solution does not fit any of these choices exactly: recognize that {lo}, {le} and {la} refer to groups (or whatever; the terms keep shifting here) as well as {loi}, {lei} and {lai} do. Then we get the natural result: external quantifiers refer to subgroups of the indicated size, whether absolute, proportional to the size of indicated group, or relative to the (usually implicit) state of affairs used for comparison. The internal quantifiers do the same for the whole of broda, whatever that may be. This has been the practical understanding of these quantifiers for about as many years as reinterpretation to get around problems with CLL's muddle about plurals has been allowed.
wrote:
> > --- Rob Speer wrote: > > Sanity check. Are you saying that {pa fi'u > re} is different as an outer > > quantifier than {pi mu}? > > Right. The proposed definitions are: > > PA1 fi'u PA2 sumti = PA1 out of every PA2 > of the referents of sumti. > > piPA sumti = A piPA fraction of one of the > referents of sumti. > > > Are you saying that {pi mu broda} means half > of one broda, while {pa fi'u re > > broda} means half of all brodas? > > "One out of every two brodas", yes. > > > If so, why? > > To be consistent with other definitions. > > We want masses to be things: {loi broda} = {lo > gunma be lo broda} > > We want {piso'i loi broda} to be "a lot of > brodas". > > >I thought it was concluded a while ago that > outer quantifiers > > that > > don't somehow resolve to an integer don't > make sense. (As in, you can't > > really > > say you have 0.5 apples, when what you have > is a single half-apple, because > > you could also have two half-apples that are > different from one apple.) > > piPA quantifiers, as can be seen from the > definition, are not true > quantifiers. They are a shorthand for a > description. > > piPA sumti = lo piPA si'e be pa me > sumti > > (The same is true for inner quantifiers, which > are also part of a > description.) > > I am not especially committed to this > definition of piPA quantifiers. > If we want to identify {pimu} with {pa fi'u re} > as quantifiers, then > we must: > > 1) Drop CLL's interpretation of piPA's with > masses and sets, > > or > > 2) Drop the idea that masses and sets are > possible values of da, > > or > > 3) Drop the interpretation of {PA1fi'uPA2} as > PA1 out of every PA2, > > or > > 4) Find some other definitions that are > consistent with all of that. > > Any suggestions? > > mu'o mi'e xorxes > > > > > '''''''''''''''''''''''''''''''''''''___ > Do you Yahoo!? > Declare Yourself - Register online to vote > today! > http://vote.yahoo.com > > >
pc: > Well, the obvious and natural solution does not > fit any of these choices exactly: recognize that > {lo}, {le} and {la} refer to groups (or whatever; > the terms keep shifting here) as well as {loi}, > {lei} and {lai} do. Then we get the natural > result: external quantifiers refer to subgroups > of the indicated size, whether absolute, > proportional to the size of indicated group, or > relative to the (usually implicit) state of > affairs used for comparison.
Let's say we do that. Then we'd have:
1- PA lo plise = PA da poi ke'a plise
2- PA lo'i plise = lo selcmi be PA da poi ke'a plise
But what do we do with {PA lo selcmi be lo plise}? We have two choices:
3a- PA lo selcmi be lo plise = PA da poi ke'a selcmi be lo plise
3b- PA lo selcmi be lo plise = lo selcmi be PA da poi ke'a plise
3a is the obvious first choice: in {PA lo broda}, PA should always count the number of brodas, so in {PA lo selcmi} PA should count sets. But, if we go with that, what happens when {ko'a} is given a set as referent? Does a quantifier quantify over sets or over members of the set? Do we have to remember how ko'a was assigned to a set?
ko'a goi lo selcmi be lo broda .... PA ko'a: PA counts sets.
ko'a goi lo'i broda ... PA ko'a: PA counts brodas
So it would not be the case that lo'i broda cu du lo selcmi be lo broda.
If we choose 3b instead, then what PA in {PA lo broda} counts will depend on what broda is. Normally it will count brodas, but if broda have members, it counts the members. This is very unsatisfying.
So these three are not all compatible:
1) In {PA lo broda}, PA always counts brodas.
2) In {PA lo'i broda}, PA counts brodas.
3) lo'i broda cu du lo selcmi be lo broda
If we want a consistent interpretation we must give up one of those three. For me, the easiest to give up is (2).
We can also, of course, adopt an inconsistent interpretation. In practice quantifiers on {lo'i} are hardly ever used, or not at all, so adopting an inconsistent interpretation won't cause much trouble.
mu'o mi'e xorxes
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Jorge Llamb?as scripsit:
> If we want to identify {pimu} with {pa fi'u re} as quantifiers, then > we must: > > 1) Drop CLL's interpretation of piPA's with masses and sets, > 2) Drop the idea that masses and sets are possible values of da, > 3) Drop the interpretation of {PA1fi'uPA2} as PA1 out of every PA2, > 4) Find some other definitions that are consistent with all of that.
I choose 3; I see no reason why pa fi'u re should have special semantics. Mathematically, li pa fi'u re du li pimu li pa fe'i re, and all three (with vei-ve'o brackets in the last case) should mean the same thing as sumti quantifiers.
-- He played King Lear as though John Cowan someone had played the ace. http://www.ccil.org/~cowan --Eugene Field http://www.reutershealth.com
> Jorge Llamb?as scripsit: > > > If we want to identify {pimu} with {pa fi'u re} as quantifiers, then > > we must: > > > > 1) Drop CLL's interpretation of piPA's with masses and sets, > > 2) Drop the idea that masses and sets are possible values of da, > > 3) Drop the interpretation of {PA1fi'uPA2} as PA1 out of every PA2, > > 4) Find some other definitions that are consistent with all of that. > > I choose 3; I see no reason why pa fi'u re should have special > semantics.
Then we are left with no way of saying "PA1 out of every PA2". (This is kind of an idiom in English, it does not literally mean "for every group of PA2 members, PA1 of the members are ..." It's more like "we can divide the total number in groups of PA2 such that PA1 out of every group are ...".)
> Mathematically, li pa fi'u re du li pimu li pa fe'i re, > and all three (with vei-ve'o brackets in the last case) should mean > the same thing as sumti quantifiers.
We can postulate that, or we can postulate that the different forms (that undisputably represent the same number) are used to represent different quantifiers.
We have a similar issue with {ce'i}. {munoce'i lo plise} could be "50% of an apple" or "50% of apples". In the proposal I make {ce'i} equivalent to {fi'u panono}, so {PA ce'i} is "PA out of every 100".
mu'o mi'e xorxes
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I am puzzled by xorxes use of {da poi} as an expansion of {lo}, since that position is one he has frequently rejected and is also incompatible with his three (so far)different explications of {lo}. To be sure, it would make a kind of sense if we had plural quantification, but xorxes also rejects this. Still, given this, does the point he is trying to make hold water? The following things are incompatible, we are told: 1> in {PA lo broda}, PA counts broda 2> in {PA lo'i broda}, PA counts broda 3> lo'i broda = lo selcmi be lo broda
xorxes' attempted solution is give up two, in favor of generalizing 1 to encompass the case of 3. Presumably, no one would give up 2. But what about 3? A the heart of 3 is the question of just what {lo'i broda} means. xorxes has it meaning (subject to difference in basic interpretation, particularly what {da poi} means) a group of sets of broda. By parallelism, then, {lo broda} would mean a (distributive) group of (distributive)groups of broda and {loi broda} would be a distributive group of collective groups of broda. The o would indicate an unspecified (distributive) group and the -, i or 'i what sort of structure was being grouped: d-group, c-group, or set. But, in fact, each of these marks indicates directly a certain structure of brodas, not of structures of brodas. {lo broda} is an unspecified d-group of brodas, {loi broda} an unspecified c-group of brodas, and {lo'i} broda an unspecified set of brodas. Thus, equaton three does not hold. If we use quantifed variables in xorxes' pattern, then we have {lo broda} ={da poi girzu be fi lo'i broda} (this would get into circularity — as these definitions often do — but these are not ultimate definitions, so we will pass over the problem for the moment) {loi broda} = {da poi gunma be loi broda} (another circularity, but the list of members seems to be a collective argument) {lo'i broda} = {da poi selcmi be loi broda} So {PA l broda} always counts broda in a consistent way: the indicated constituents of the structure, to be sure, here referred to via yet another structure.
Somewhat closer to thta ctual situation (there are problems, but they do not affect the generality here) {lo broda cu brode} = [Ex: x group & [ay: y in x Ay: y in x] y broda] x d-brode
{loi broda cu brode} = [Ex: x group & [ay: y in x Ay: y in x] x broda] y c-brode
{lo'i broda cu brode} =
[Ex: x set & [ay: y member x Ay: y member x] y broda]x brode (in
fact i-brode, the degenerate case of collective
predication where the collective has only one
member. Distributive predication of a group is
just the i-predication of everything in the
group.)
In the case where broda takes c-predication, the
quantifier phrase gets simplified to [ex: x group
& x c-broda Ex: x group
& x c-broda] to which the set case adds [Ey: y
set & [az: z in x Az: z in x]z member y & [aw: w member y Aw: w member y] w
in x]
wrote:
> > pc: > > Well, the obvious and natural solution does > not > > fit any of these choices exactly: recognize > that > > {lo}, {le} and {la} refer to groups (or > whatever; > > the terms keep shifting here) as well as > {loi}, > > {lei} and {lai} do. Then we get the natural > > result: external quantifiers refer to > subgroups > > of the indicated size, whether absolute, > > proportional to the size of indicated group, > or > > relative to the (usually implicit) state of > > affairs used for comparison. > > Let's say we do that. Then we'd have: > > 1- PA lo plise = PA da poi ke'a plise > > 2- PA lo'i plise = lo selcmi be PA da poi ke'a > plise > > But what do we do with {PA lo selcmi be lo > plise}? > We have two choices: > > 3a- PA lo selcmi be lo plise = PA da poi ke'a > selcmi be lo plise > > 3b- PA lo selcmi be lo plise = lo selcmi be PA > da poi ke'a plise > > 3a is the obvious first choice: in {PA lo > broda}, PA should always > count the number of brodas, so in {PA lo > selcmi} PA should count sets. > But, if we go with that, what happens when > {ko'a} is given a set > as referent? Does a quantifier quantify over > sets or over members of > the set? Do we have to remember how ko'a > was assigned to a set? > > ko'a goi lo selcmi be lo broda > ... > PA ko'a: PA counts sets. > > ko'a goi lo'i broda > .. > PA ko'a: PA counts brodas > > So it would not be the case that lo'i broda cu > du lo selcmi be lo broda. > > If we choose 3b instead, then what PA in {PA lo > broda} counts will > depend on what broda is. Normally it will count > brodas, but if broda > have members, it counts the members. This is > very unsatisfying. > > So these three are not all compatible: > > 1) In {PA lo broda}, PA always counts brodas. > > 2) In {PA lo'i broda}, PA counts brodas. > > 3) lo'i broda cu du lo selcmi be lo broda > > If we want a consistent interpretation we must > give up one of > those three. For me, the easiest to give up is > (2). > > We can also, of course, adopt an inconsistent > interpretation. In > practice quantifiers on {lo'i} are hardly ever > used, or not at all, > so adopting an inconsistent interpretation > won't cause much trouble. > > mu'o mi'e xorxes > > > > > > '''''''''''''''''''''''''''''''''''''''''''__ > Do you Yahoo!? > New and Improved Yahoo! Mail - Send 10MB > messages! > http://promotions.yahoo.com/new_mail > > >
pc: > I am puzzled by xorxes use of {da poi} as an > expansion of {lo}, since that position is one he > has frequently rejected
Perhaps this will solve the puzzle:
PA sumti = PA da poi ke'a me sumti
Then:
PA lo broda = PA da poi ke'a me lo broda = PA da poi ke'a broda
.... > The following things are > incompatible, we are told: > 1> in {PA lo broda}, PA counts broda > 2> in {PA lo'i broda}, PA counts broda > 3> lo'i broda = lo selcmi be lo broda > > xorxes' attempted solution is give up two, in > favor of generalizing 1 to encompass the case of > 3. Presumably, no one would give up 2.
No one else, you mean?
> But what > about 3? A the heart of 3 is the question of > just what {lo'i broda} means.
Yes.
.... > {lo broda} is an unspecified d-group of brodas, > {loi broda} an unspecified c-group of brodas, and > {lo'i} broda an unspecified set of brodas. > Thus, equaton three does not hold.
OK. So in your system, {ko'a goi lo'i broda} assigns a different referent to {ko'a} than {ko'a goi lo selcmi be lo broda}. In other words, you would have {lo'i broda} be a set in a metalanguage sense, not a set in the normal sense.
> So {PA l broda} always counts broda in a > consistent way: the indicated constituents of the > structure, to be sure, here referred to via yet > another structure.
That's one way of defining things. It has its drawbacks though. Suppose we use {cuxna be lo'i karda}, "chooses from a set of cards". We now have that {lo'i karda} and {lo te cuxna} have different referents. The second refers to sets, whereas the first would refer to cards via a certain structure. So {mu lo te cuxna} are five sets of cards (to choose cards from each), whereas {mu lo'i karda} would be just one (sub)set of five cards.
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wrote:
> > pc: > > I am puzzled by xorxes use of {da poi} as an > > expansion of {lo}, since that position is one > he > > has frequently rejected > > Perhaps this will solve the puzzle: > > PA sumti = PA da poi ke'a me sumti > > Then: > > PA lo broda = PA da poi ke'a me lo broda > = PA da poi ke'a broda
I see, it is the PA that merits a quantifier, not the {lo}. I would get rid of the quantifiers for quantifiers, but that is another issue.
> > ... > > The following things are > > incompatible, we are told: > > 1> in {PA lo broda}, PA counts broda > > 2> in {PA lo'i broda}, PA counts broda > > 3> lo'i broda = lo selcmi be lo broda > > > > xorxes' attempted solution is give up two, in > > favor of generalizing 1 to encompass the case > of > > 3. Presumably, no one would give up 2. > > No one else, you mean?
Oops, I meant 1. > > > But what > > about 3? A the heart of 3 is the question of > > just what {lo'i broda} means. > > Yes. > > ... > > {lo broda} is an unspecified d-group of > brodas, > > {loi broda} an unspecified c-group of brodas, > and > > {lo'i} broda an unspecified set of brodas. > > Thus, equaton three does not hold. > > OK. So in your system, {ko'a goi lo'i broda} > assigns a different > referent to {ko'a} than {ko'a goi lo selcmi be > lo broda}. In other > words, you would have {lo'i broda} be a set in > a metalanguage sense, > not a set in the normal sense.
I don't get the difference you claim is involved. A set of broda is an abstract structure which has brodas as members. This is the normal sense, so far as I can see, and is my sense. What is a metalanguage set?
> > So {PA l broda} always counts broda in a > > consistent way: the indicated constituents of > the > > structure, to be sure, here referred to via > yet > > another structure. > > That's one way of defining things. It has its > drawbacks though. > Suppose we use {cuxna be lo'i karda}, "chooses > from a set of cards". > We now have that {lo'i karda} and {lo te cuxna} > have different > referents. The second refers to sets, whereas > the first would refer > to cards via a certain structure.
I don't follow this at all. Both of them, in the instant case, can refer to the set of cards. {lo te cuxna} need not, however (and in this case probably does not, {le} being more appropriate). {lo te cuxna} refers to (a group of)some number things from which choices can be made, {lo'i karda} refers to one such thing, an unspecified set of cards. >So {mu lo te > cuxna} are five sets > of cards (to choose cards from each), whereas > {mu lo'i karda} would > be just one (sub)set of five cards.
Quite true, and thus, of course, {lo te cuxna} does not mean {lo'i karda}, which is, as you say, only pa lo te cuxna. Given that the choice is to be made from lo'i karda, then one would hope that {le te cuxna} would refer to that set as well (or, rather, to the group of which that set is the only component). But it is a different description and, therefore, behaves differently under various modifications. "One of the things from which choices may be made" is not the same as "one of the things which may be chosen."
pc: > --- Jorge Llambías wrote: > > PA lo broda = PA da poi ke'a me lo broda > > = PA da poi ke'a broda > > I see, it is the PA that merits a quantifier, not > the {lo}. I would get rid of the quantifiers for > quantifiers, but that is another issue.
Quantifiers for quantifiers?
> > OK. So in your system, {ko'a goi lo'i broda} > > assigns a different > > referent to {ko'a} than {ko'a goi lo selcmi be > > lo broda}. In other > > words, you would have {lo'i broda} be a set in > > a metalanguage sense, > > not a set in the normal sense. > > I don't get the difference you claim is involved. > A set of broda is an abstract structure which > has brodas as members. This is the normal sense, > so far as I can see, and is my sense. What is a > metalanguage set?
I meant that when you use {lo'i broda} you are talking about brodas, and the set talk only enters into it when you explain what you are saying about the brodas, whereas when you use {lo selcmi} you are actually talking about a set, for example when explaining what {lo'i broda} means one would talk about sets.
However, I am not sure how tenable that is. If I use your exansions on:
lo'i plise cu du lo selcmi be lo plise
I get:
[Ex: x is a set & [[Ay: y is a member of x] y plise] [Ez: z is a group & [[Aw: w in z] w selcmi be lo plise] x = z
which seems true enough, unless being "a set" whose members are all plise is not the same as being "selcmi be lo plise".
> {lo te cuxna} refers to (a group of)some number
> things from which choices can be made, {lo'i
> karda} refers to one such thing, an unspecified
> set of cards.
Consider {lo pa te cuxna} vs. {lo'i karda} then. Or {le pa te cuxna} vs. {le'i karda}.
{ko'a goi le pa te cuxna} and {ko'a goi le'i karda} would seem to assign the same referent to {ko'a}, the one set of choices, the one set of cards. But a quantifier on {le'i karda} gets you a subset, whereas a quantifier on {le pa te cuxna} does not. So to know how a quantifier acts on {ko'a} you need to know not only the referent assigned to {ko'a} (the same in both cases) but also the expression used to assign that referent to {ko'a}.
> "One of the things > from which choices may be made" is not the same > as "one of the things which may be chosen."
Right, those are:
pa le te cuxna "One of the things from which choices may be made."
pa le (ka'e) se cuxna "One of the things which may be chosen."
I don't think we disagree about those. But in your system:
le'i karda = le te cuxna
and:
pa le'i karda =/= pa le te cuxna
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wrote:
> > pc: > > --- Jorge Llambías wrote: > > > PA lo broda = PA da poi ke'a me lo broda > > > = PA da poi ke'a broda > > > > I see, it is the PA that merits a quantifier, > not > > the {lo}. I would get rid of the quantifiers > for > > quantifiers, but that is another issue. > > Quantifiers for quantifiers?
Yes; although Lojban is based syntactically on formal logic, there is only an occasional correlation between the two in regard particular categories. For example, as you know, I would replace quantifiers in descriptions by redicates in most cases and by quite different quantifiers in the rest. > > > > OK. So in your system, {ko'a goi lo'i > broda} > > > assigns a different > > > referent to {ko'a} than {ko'a goi lo selcmi > be > > > lo broda}. In other > > > words, you would have {lo'i broda} be a set > in > > > a metalanguage sense, > > > not a set in the normal sense. > > > > I don't get the difference you claim is > involved. > > A set of broda is an abstract structure > which > > has brodas as members. This is the normal > sense, > > so far as I can see, and is my sense. What > is a > > metalanguage set? > > I meant that when you use {lo'i broda} you are > talking > about brodas, and the set talk only enters into > it when > you explain what you are saying about the > brodas, whereas > when you use {lo selcmi} you are actually > talking about a > set, for example when explaining what {lo'i > broda} means > one would talk about sets. > Well, {lo'i broda} refers to a set, but a set of broda, to be sure. I still don't get the point. {mu lo'i broda} is also a set of broda, one that contains five of them, all of which were in the original referent of {lo'i broda}. {lo selcmi} on the other hand refers to a group of sets — no indication of what they are sets of. So when I talk about the content of the referents in one case I talk about brodas, in the other sets. What is odd here?
> However, I am not sure how tenable that is. If > I use your > exansions on: > > lo'i plise cu du lo selcmi be lo plise
But, as you will note, I deny the equation, even when there is only one set in the group. To be sure, it is difficult to separate a singleton group and its one member, since they have so many properties in common, yet they are ontologically distinct.
> I get: > > [Ex: x is a set & [[Ay: y is a member of x] y > plise] > [Ez: z is a group & [[Aw: w in z] w selcmi be > lo plise] x = z > > which seems true enough, unless being "a set" > whose members > are all plise is not the same as being "selcmi > be lo plise". > That is finde, but {lo selcmi be lo plise} refers to a group, not a set.
refers to (a group of)some > number > > things from which choices can be made, {lo'i > > karda} refers to one such thing, an > unspecified > > set of cards. > > Consider {lo pa te cuxna} vs. {lo'i karda} > then. > Or {le pa te cuxna} vs. {le'i karda}. > > {ko'a goi le pa te cuxna} and {ko'a goi le'i > karda} > would seem to assign the same referent to > {ko'a}, > the one set of choices, the one set of cards. > But a quantifier on {le'i karda} gets you a > subset, > whereas a quantifier on {le pa te cuxna} does > not. > So to know how a quantifier acts on {ko'a} you > need > to know not only the referent assigned to > {ko'a} > (the same in both cases) but also the > expression > used to assign that referent to {ko'a}.
Well, the one assigns a *group* of sources of choices, the other a *set* of cards. So they are not the same referent.
> > "One of the things > > from which choices may be made" is not the > same > > as "one of the things which may be chosen." > > Right, those are: > > pa le te cuxna > "One of the things from which choices may be > made." > > pa le (ka'e) se cuxna > "One of the things which may be chosen." > > I don't think we disagree about those. But in > your system: > > le'i karda = le te cuxna
NO. See above.
> and: > > pa le'i karda =/= pa le te cuxna > a fortiori
I agree that groups are messy creatures at the bottom end. "Being in" a group shares features of both membership and inclusion, so that singleton groups are hard to tell from their members — and for most purposes the difference can be ignored. Yet the difference is there. This is one place, by the way, where plural quantification is clearer than groups. Your comments would have more force if applied to that situation, although several cards taken collectively, say, would still be different from the set with exactly them as members. But in that case, we should probably not use sets at all and {le karda} and {le te cuxna} would in this context be the same — and selections from them would be cards (though you would have to know the whole contexts to know this).
pc: > > > I would get rid of the quantifiers for > > > quantifiers, but that is another issue. > > > > Quantifiers for quantifiers? > > Yes; although Lojban is based syntactically on > formal logic, there is only an occasional > correlation between the two in regard particular > categories. For example, as you know, I would > replace quantifiers in descriptions by redicates > in most cases and by quite different quantifiers > in the rest.
I can't really say I know that. You have said things like that, but I'm not sure whether you consider them to be practical definitions for lojban or whether you intend them as material for LoCCan3. In any case, it is hard to judge without having the full story spelled out. For example, would you keep {su'o}, {ro}, {no} as true quantifiers, or would these too turn into descriptions?
> To be > sure, it is difficult to separate a singleton > group and its one member, since they have so many > properties in common, yet they are ontologically > distinct.
So in your lojban you would have no way of referring to an individual card. The closest you could get is the singleton group that contains it, {le pa karda}.
{le'i karda} is an individual set of cards. {le pa te cuxna} is a group containing the individual set of cards. {le pa karda} is a group containing a single card.
So we can refer directly to a single set of cards, {le'i karda}, but there is no way to refer directly to a single card.
> This is one place, by the way, where plural > quantification is clearer than groups. Your > comments would have more force if applied to that > situation, although several cards taken > collectively, say, would still be different from > the set with exactly them as members. But in > that case, we should probably not use sets at all > and {le karda} and {le te cuxna} would in this > context be the same — and selections from them > would be cards (though you would have to know the > whole contexts to know this).
Exactly. That's why I don't use sets, they don't add anything.
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wrote:
> > pc: > > > > I would get rid of the quantifiers for > > > > quantifiers, but that is another issue. > > > > > > Quantifiers for quantifiers? > > > > Yes; although Lojban is based syntactically > on > > formal logic, there is only an occasional > > correlation between the two in regard > particular > > categories. For example, as you know, I > would > > replace quantifiers in descriptions by > predicates > > in most cases and by quite different > quantifiers > > in the rest. > > I can't really say I know that. You have said > things > like that, but I'm not sure whether you > consider them > to be practical definitions for lojban or > whether you > intend them as material for LoCCan3. In any > case, it is > hard to judge without having the full story > spelled out. > For example, would you keep {su'o}, {ro}, {no} > as true > quantifiers, or would these too turn into > descriptions?
Not descriptions, predicates: "is Q in number," "is Q of," "is Q for/to/that." {no} stays a quantifier, a special case, since groups (or pluralities) assume there are some things involved. And {su'o} can largely be ignored, wrapped up in the general framework.
> > > To be > > sure, it is difficult to separate a singleton > > group and its one member, since they have so > many > > properties in common, yet they are > ontologically > > distinct. > > So in your lojban you would have no way of > referring to > an individual card. The closest you could get > is the singleton > group that contains it, {le pa karda}.
Or {ko'a} or {pa da poi} appropriately introduced. But basically right.
> {le'i karda} is an individual set of cards. > {le pa te cuxna} is a group containing the > individual set of cards. > {le pa karda} is a group containing a single > card. > > So we can refer directly to a single set of > cards, {le'i karda}, > but there is no way to refer directly to a > single card. Yup — with the exceptions above. Now you are beginning to see what is attractive about plural quantification, which does refer to cards (and not to groups).
> > This is one place, by the way, where plural > > quantification is clearer than groups. Your > > comments would have more force if applied to > that > > situation, although several cards taken > > collectively, say, would still be different > from > > the set with exactly them as members. But in > > that case, we should probably not use sets at > all > > and {le karda} and {le te cuxna} would in > this > > context be the same — and selections from > them > > would be cards (though you would have to know > the > > whole contexts to know this). > > Exactly. That's why I don't use sets, they > don't add > anything.
Well, they always add sets, but we have little real use for those except in set theory (so the set former could be move way over into MEX space, probably). Most of the real work is done — or could be — by groups, pretty much as it is done just by several things taken plurally (usually collectively for the kinds of things sets are called on for now) with plural quantification. It does seem to me that you want plural quantification — or rather the naturalness that it gives you — without actually using plural quantification. Come on over!
pc: > > So in your lojban you would have no way of > > referring to > > an individual card. The closest you could get > > is the singleton > > group that contains it, {le pa karda}. .... > > So we can refer directly to a single set of > > cards, {le'i karda}, > > but there is no way to refer directly to a > > single card. > Yup — with the exceptions above. Now you are > beginning to see what is attractive about plural > quantification, which does refer to cards (and > not to groups).
Beginning to see? Are you serious? It is you who was arguing for groups. In my scheme groups and sets (loi and lo'i) are marginal enities, they are there only for backwards compatibility. {lo broda} is a plural constant. It refers to brodas, not to groups of brodas.
> > That's why I don't use sets, they > > don't add > > anything. > > Well, they always add sets, but we have little > real use for those except in set theory (so the > set former could be move way over into MEX space, > probably).
In the gi'uste, many gismu places (such as the x3 of cuxna) are reserved for sets.
> Most of the real work is done — or > could be — by groups, pretty much as it is done > just by several things taken plurally (usually > collectively for the kinds of things sets are > called on for now) with plural quantification.
Yes.
> It does seem to me that you want plural > quantification — or rather the naturalness that > it gives you — without actually using plural > quantification.
All I need are plural constants. Singular (distributive) quantification, over the referents of those plural constants, is useful to have for when it's needed.
> Come on over!
Where?
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wrote:
> > pc: > > > So in your lojban you would have no way of > > > referring to > > > an individual card. The closest you could > get > > > is the singleton > > > group that contains it, {le pa karda}. > ... > > > So we can refer directly to a single set of > > > cards, {le'i karda}, > > > but there is no way to refer directly to a > > > single card. > > Yup — with the exceptions above. Now you > are > > beginning to see what is attractive about > plural > > quantification, which does refer to cards > (and > > not to groups). > > Beginning to see? Are you serious? It is you > who was > arguing for groups. In my scheme groups and > sets > (loi and lo'i) are marginal enities, they are > there > only for backwards compatibility. {lo broda} is > a > plural constant. It refers to brodas, not to > groups > of brodas.
Reread several dozen notes about the inherent
incompatibility of this notion with Lojban as now
constituted. I am not sure what you think you
have (a plural constant is problematic in its own
way — see earlier again) but what you say
fluctuates back and forth between plural
quantification and groups (which I talk about
only because they are needed for current Lojban;
my preference has been for plural quantification
since a workable form became available).
> > > That's why I don't use sets, they > > > don't add > > > anything. > > > > Well, they always add sets, but we have > little > > real use for those except in set theory (so > the > > set former could be move way over into MEX > space, > > probably). > > In the gi'uste, many gismu places (such as the > x3 of > cuxna) are reserved for sets.
Well, the lists wou;d have to be revised to deal with the distributive - collective contrast anyhow; chaning those places from sets to plurality would be a minor matter, lamost a a case for universal search and replace.
> > Most of the real work is done — or > > could be — by groups, pretty much as it is > done > > just by several things taken plurally > (usually > > collectively for the kinds of things sets are > > called on for now) with plural > quantification. > > Yes. > > > It does seem to me that you want plural > > quantification — or rather the naturalness > that > > it gives you — without actually using plural > > quantification. > > All I need are plural constants. Singular > (distributive) > quantification, over the referents of those > plural constants, > is useful to have for when it's needed. > > > Come on over! > > Where?
To an intellecctually responsible theory that gives you what your scattered wish list would provide if it were feasible.
pc: > what you say > fluctuates back and forth between plural > quantification and groups
I use singular (i.e. distributive) quantification for outer quantifiers (ignoring piPA here, as I don't think they are properly quantifiers):
PA sumti = PA da poi ke'a me sumti
where {me sumti} means "x1 is/are among sumti", and PA are the ordinary quantifiers with singular variables.
Inner quantifiers are similar in many respects to plural quantification, but I suspect not quite the same thing. Groups are very marginal in my system, they can be totally avoided by using the predicate {gunma} instead of the "mass" gadri. So I use neither plural quantification nor groups really.
> > > Come on over! > > > > Where? > > To an intellecctually responsible theory that > gives you what your scattered wish list would > provide if it were feasible.
Let me know when you have worked it out and I'll be more than happy to take a look.
The bit you were presenting until recently, where {lo'i broda} and {lo pa selcmi be lo broda} have different referents, is not something I would want.
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A new set of eyes looked over my files and told me that I had been oblivious to the fact that you were talking about at least four different things, taking them all to be about one — or at most two. I confess that even with that information — which does make sense of a few things — I am often not sure just which of these things you are talking about. I was also told that I have been talking about at least as many different things and not clearly distinguishing them. Indeed, looking back over what I have said, I am often not sure now — and probably was not when I wrote them — which I am talking about. The most important case pointed out to me was that my attacks (at least the main one) on the notion of plural constants was misguided, since it was about a {lo} which was in collective predication, a part of your ideal system, not a distributive one, part of current Lojban or your reconstruction of that in one of your proposals. The logical objections to plural constants does indeed not apply to collective cases (and I agree that these are the basic cases), although there are similar practical problems with particular predicates (and the mirror image problems with others). The problems with the distributive cases disappear because these are now explicitly quantified and so can be dealt with in that way. You have also dealt with the "no broda" problem of negated descriptions by moving to a gappy or many-valued truth system (not clear which). The problems with pluralities too large or too small remain and I don't yet see how you will avoid them, but they are relatively minor and apply only to some predicates, not all. As for your comments this time, I take it that your claim to do without groups is more than a bit disingenuous. I agree that you do not talk about groups but you still seem to use them: if {lo broda} is at any way related to {ro broda} or {su'o broda} — or {ro da poi broda} and {su'o da poi broda}, then the logic of the situation still requires that it be a single thing, whether it is called a group or a mass or a plurality or whatever. And, as a collective, it is less open to the easy confusion between group and members. You have solved the core of that by getting down to member only by quantifiers. I didn't realize that I had said that {lo'i broda} had a different referent from {da poi selcmi be lo broda} (I assume that this has a built in namely-rider so that it has a referent at all), only different from {lo selcmi be lo broda}, unless you are identifying them as well, which seems against something you said elsewhere, presumably on another topic altogether. As for the rest of group theory, what can I add? I have developed it far beyond what I thought I would need, since my point was to get rid of groups altogether and move to plural quantification — explicitly so called.
wrote:
> > pc: > > what you say > > fluctuates back and forth between plural > > quantification and groups > > I use singular (i.e. distributive) > quantification for > outer quantifiers (ignoring piPA here, as I > don't think they > are properly quantifiers): > > PA sumti = PA da poi ke'a me sumti > > where {me sumti} means "x1 is/are among > sumti", > and PA are the ordinary quantifiers with > singular variables. > > Inner quantifiers are similar in many respects > to plural > quantification, but I suspect not quite the > same thing. > Groups are very marginal in my system, they can > be totally > avoided by using the predicate {gunma} instead > of the > "mass" gadri. So I use neither plural > quantification nor > groups really. > > > > > Come on over! > > > > > > Where? > > > > To an intellecctually responsible theory that > > gives you what your scattered wish list would > > provide if it were feasible. > > Let me know when you have worked it out and > I'll be more > than happy to take a look. > > The bit you were presenting until recently, > where {lo'i broda} > and {lo pa selcmi be lo broda} have different > referents, is > not something I would want. > > > >
pc: > You have also dealt with the "no broda" problem > of negated descriptions by moving to a gappy or > many-valued truth system (not clear which).
How does logic deal with constants that have no referents? Can there evn be such a thing? Can you really evaluate F(a) if 'a' does not refer? I would have thought that a constant refers by definition.
I think our approaches don't really differ in the truth system. It's rather that I take {lo broda} to be a constant, and therefore it must necessarily refer in order to be meaningful, whereas you don't take it to be a constant, and so for you the expression can have meaning (and thus can be part of a claim) even when there is nothing that brodas.
> As for your comments this time, I take it that > your claim to do without groups is more than a > bit disingenuous. I agree that you do not talk > about groups but you still seem to use them: if > {lo broda} is at any way related to {ro broda} or > {su'o broda} — or {ro da poi broda} and {su'o > da poi broda}, then the logic of the situation > still requires that it be a single thing, whether > it is called a group or a mass or a plurality or > whatever.
I don't see why. When {lo broda} has many referents, lo broda are many things. {PA lo broda} is a quantification over those things: {PA da poi ke'a me lo broda}. There is no recourse here to a single thing that contains them. How does the logic require that I introduce a group?
Of course, you can talk about the set of those things, or the group of those things, but {lo broda} does not refer to that, it refers to the things themselves.
> I didn't realize that I had said that {lo'i > broda} had a different referent from {da poi > selcmi be lo broda} (I assume that this has a > built in namely-rider so that it has a referent > at all), only different from {lo selcmi be lo > broda}, unless you are identifying them as well, > which seems against something you said elsewhere, > presumably on another topic altogether.
Not sure what you mean. What I said was:
> > The bit you were presenting until recently, > > where {lo'i broda} > > and {lo pa selcmi be lo broda} have different > > referents, is > > not something I would want.
mu'o mi'e xorxes
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wrote:
> > pc: > > You have also dealt with the "no broda" > problem > > of negated descriptions by moving to a gappy > or > > many-valued truth system (not clear which). > > How does logic deal with constants that have no > > referents? Can there evn be such a thing? Can > you > really evaluate F(a) if 'a' does not refer? I > would > have thought that a constant refers by > definition.
Yes, in logic a constant has a referent by definition (except, of course, logics that explicitly make allowances — free logics and the like). But, whether or not {lo broda} ends up being a constant, it starts as a description, and that can be unmet: {lo pavyseljirna} has no referent but is perfectly acceptable in other ways in the language — or do you just shiift to another domain when such expressions occur, even without other indications of the shift? There are also accidental shifts, given that there are brodas and brodes you might expect there to be {lo broda poi brode}, but there may not be. Grammar is pretty free from facts, but truth is not.
> I think our approaches don't really differ in > the > truth system. It's rather that I take {lo > broda} > to be a constant, and therefore it must > necessarily > refer in order to be meaningful, whereas you > don't > take it to be a constant, and so for you the > expression can have meaning (and thus can be > part > of a claim) even when there is nothing that > brodas.
OK (aside from the part about cit being a constant — that still gives problems), you use a gappy or many-valued truth system, with the extra piece of space being "meaningless" (and deopping out of the overall valuation if the result vcan be otherwise determined?)
> > As for your comments this time, I take it > that > > your claim to do without groups is more than > a > > bit disingenuous. I agree that you do not > talk > > about groups but you still seem to use them: > if > > {lo broda} is at any way related to {ro > broda} or > > {su'o broda} — or {ro da poi broda} and > {su'o > > da poi broda}, then the logic of the > situation > > still requires that it be a single thing, > whether > > it is called a group or a mass or a plurality > or > > whatever. > > I don't see why. When {lo broda} has many > referents, > lo broda are many things. {PA lo broda} is a > quantification > over those things: {PA da poi ke'a me lo > broda}. There is > no recourse here to a single thing that > contains them. > How does the logic require that I introduce a > group?
If {lo broda} had many referents, it would be many things, but, given the underlying logic of Lojban, it cannot have many referents. The quantifier — distributive predication — problem does indeed disappear, as I said. The problem is with the original {lo broda}.
> Of course, you can talk about the set of those
> things, or
> the group of those things, but {lo broda} does
> not refer
> to that, it refers to the things themselves.
No, inevitably (so far as I cansee and assuming I understand your claim this time) it refers to their collection, however described.
> > I didn't realize that I had said that {lo'i > > broda} had a different referent from {da poi > > selcmi be lo broda} (I assume that this has a > > built in namely-rider so that it has a > referent > > at all), only different from {lo selcmi be lo > > broda}, unless you are identifying them as > well, > > which seems against something you said > elsewhere, > > presumably on another topic altogether. > > Not sure what you mean. What I said was: > > > > The bit you were presenting until recently, > > > where {lo'i broda} > > > and {lo pa selcmi be lo broda} have > different > > > referents, is > > > not something I would want. > And I repeat, where did I say that as opposed to saying that {lo'i broda} and {lo selcmi be lo broda} have different referents? I can't find it.
pc: > But, whether or not {lo broda} ends up > being a constant, it starts as a description, and > that can be unmet: {lo pavyseljirna} has no > referent but is perfectly acceptable in other > ways in the language — or do you just shiift to > another domain when such expressions occur, even > without other indications of the shift?
I think {lo pavyseljirna} usually does have a referent, and so for example {lo pavyseljirna cu se ranmi} is true.
> There are > also accidental shifts, given that there are > brodas and brodes you might expect there to be > {lo broda poi brode}, but there may not be.
In that case, you wouldn't be talking about anything when you use {lo broda poi brode}. A {ki'a} or {na'i} reaction might be appropriate. But I think in such cases there will at least be a postulated referent, which is something referrable.
> Grammar is pretty free from facts, but truth is > not.
Lojban grammar certainly allows the construction of meaningless bridi (as does any human language, I suppose).
> OK (aside from the part about cit being a
> constant — that still gives problems), you use a
> gappy or many-valued truth system, with the extra
> piece of space being "meaningless" (and deopping
> out of the overall valuation if the result vcan
> be otherwise determined?)
I don't understand the question. Could you give an example?
> If {lo broda} had many referents, it would be > many things, but, given the underlying logic of > Lojban, it cannot have many referents.
I guess "the underlying logic of Lojban" is something accessible to you but not to me, so it is pointless to argue that point.
> > > I didn't realize that I had said that {lo'i
> > > broda} had a different referent from {da poi
> > > selcmi be lo broda} (I assume that this has a
> > > built in namely-rider so that it has a
> > referent
> > > at all), only different from {lo selcmi be lo
> > > broda}, unless you are identifying them as
> > well,
> > > which seems against something you said
> > elsewhere,
> > > presumably on another topic altogether.
> >
> > Not sure what you mean. What I said was:
> >
> > > > The bit you were presenting until recently,
> > > > where {lo'i broda}
> > > > and {lo pa selcmi be lo broda} have
> > different
> > > > referents, is
> > > > not something I would want.
> >
> And I repeat, where did I say that as opposed to
> saying that {lo'i broda} and {lo selcmi be lo
> broda} have different referents? I can't find it.
You may be reading {lo pa selcmi} as {da poi selcmi}, that's the only explanation I can think of to explain this exchange.
Anyway, how's this:
(1) mi cuxna fi ko'a goi lo'i karda I choose from a set of cards.
(2) mi cuxna fi ko'e goi lo selcmi be lo karda I choose from a set of cards. (Ontologically different one from before, even if in the end it consists of the same cards.)
(3) ko'a na du ko'e
Therefore:
(4) mi cuxna fi su'o re da I choose from at least two sets.
I disagree with (3), of course, so for me (4) does not follow from (1) and (2).
mu'o mi'e xorxes
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wrote:
> > pc: > > But, whether or not {lo broda} ends up > > being a constant, it starts as a description, > and > > that can be unmet: {lo pavyseljirna} has no > > referent but is perfectly acceptable in other > > ways in the language — or do you just shiift > to > > another domain when such expressions occur, > even > > without other indications of the shift? > > I think {lo pavyseljirna} usually does have a > referent, > and so for example {lo pavyseljirna cu se > ranmi} is true.
This is one of the ungoing paradoxes — if the sentence is true, then {lo pavyseljirna} has no referent and so the sentence is not true, whether false or meaningless. The only consistent way I know to handle it in the present context is to say (reasonably, though messily) that {1ranmi} is an intensional context, taking us to an alternate situation in which there are unicorns. Personally, I would rather insist that {1 ranmi} only makes sense when it is filled (extensionally) with an intensional object, either a property or a situation. Since the appropriate object is usually clear from the context it is usually enough to mention an crucial part of it in a {tu'a} phrase. But that would take a lot of rewriting of definitions and so seems — at least unti we get a definition tidying project going (as we might for eexample in taking on plural qunatification). So, I leave the paradox for now; it rarely causes much trouble.
> > There are > > also accidental shifts, given that there are > > brodas and brodes you might expect there to > be > > {lo broda poi brode}, but there may not be. > > In that case, you wouldn't be talking about > anything when > you use {lo broda poi brode}. A {ki'a} or > {na'i} reaction > might be appropriate. But I think in such cases > there will > at least be a postulated referent, which is > something > referrable.
Whoa!. OK, there is another way to deal with this, namely allowing for the outer domain -- possible objects and perhaps even impossible ones. I prefer to shift to alternate situations, clearly marked. Of course, the whole may be in an alternate situation already, as when we are reasoning under hypothesis, in which case the situation outside the hypothesis is not relevant and so there is not problem (assuming that the hypothesis supplies the actually missing things).
> > Grammar is pretty free from facts, but truth
> is
> > not.
>
> Lojban grammar certainly allows the
> construction of meaningless
> bridi (as does any human language, I suppose).
Yup, though as noted, I like the ones that look OK but mess up just about whether some set is non-null to be false rather than meaningless. I like to save {nai} for clear cases of presupposition failure and I read "no broda" cases as failure of an implication instead. Either way will work, however. I wonder if {ki'a} is appropriate here — thi is less confusion -- or even inability to determine a referent — and more just saying somehting that appears wrong. The correct reponse seems to me to be "But there aren't any unicorns" or whatever.
> > > OK (aside from the part about it being a > > constant — that still gives problems), you > use a > > gappy or many-valued truth system, with the > extra > > piece of space being "meaningless" (and > deopping > > out of the overall valuation if the result > can > > be otherwise determined?) > > I don't understand the question. Could you give > an example?
Which kind of built in meaningless do you favor? If, for example, if one component of a disjunction is meaningless and the other true, is the whole true or meaningless (and corresponding things for other connectives)
> > > If {lo broda} had many referents, it would be > > many things, but, given the underlying logic > of > > Lojban, it cannot have many referents. > > I guess "the underlying logic of Lojban" is > something > accessible to you but not to me, so it is > pointless to argue > that point.
It seems to be quite out in the open; it is singular logic. Reference is a function (part of the general conditions for singluar logic -- maybe definitional) and therefore (this is definitional) each referring expression can have only one referent (with variations about whether it can have none). Of course, since {lo broda} is a deescription (apparently), not a logical constant, its reference is not found directly by that function but by some calculations. (I don't think {lo broda} really is a description, but on my workup it would be even further from directly assigned reference.) The calculations do not introduce something different from the one expression - one referent rule of of direct reference. Indeed, they could not, since then such expressiions could never justify true particular generalization nor be justifeied by true universals — not a desirable situation in a logical language.
> > > > > I didn't realize that I had said that > {lo'i > > > > broda} had a different referent from {da > poi > > > > selcmi be lo broda} (I assume that this > has a > > > > built in namely-rider so that it has a > > > referent > > > > at all), only different from {lo selcmi > be lo > > > > broda}, unless you are identifying them > as > > > well, > > > > which seems against something you said > > > elsewhere, > > > > presumably on another topic altogether. > > > > > > Not sure what you mean. What I said was: > > > > > > > > The bit you were presenting until > recently, > > > > > where {lo'i broda} > > > > > and {lo pa selcmi be lo broda} have > > > different > > > > > referents, is > > > > > not something I would want. > > > > > And I repeat, where did I say that as opposed > to > > saying that {lo'i broda} and {lo selcmi be lo > > broda} have different referents? I can't > find it. > > You may be reading {lo pa selcmi} as {da poi > selcmi}, that's > the only explanation I can think of to explain > this exchange.
I'm not but I never denied the equation which
- you* offered and charged me with denying. Have
I missed something here?
> Anyway, how's this: > > (1) mi cuxna fi ko'a goi lo'i karda > I choose from a set of cards. > > (2) mi cuxna fi ko'e goi lo selcmi be lo karda > I choose from a set of cards. > (Ontologically different one from > before, even if in the end it consists of > the same cards.) > > (3) ko'a na du ko'e > > Therefore: > > (4) mi cuxna fi su'o re da > I choose from at least two sets. > > I disagree with (3), of course, so for me (4) > does not follow from (1) > and (2).
Well, I would of course say that 2 is a bad translation and is presumably false in the present context. I agree that 4 does not follow and I do hold that 3 is true. I do not know how {da poi selcmi be lo broda} snuck into this, so drop all that.
pc: > --- Jorge Llambías wrote: > > I think {lo pavyseljirna} usually does have a > > referent, > > and so for example {lo pavyseljirna cu se > > ranmi} is true. > > This is one of the ungoing paradoxes — if the > sentence is true, then {lo pavyseljirna} has no > referent and so the sentence is not true, whether > false or meaningless.
For me, from the sentence being true it doesn't follow that {lo pavyseljyrna} has no referent, so no paradox arises. In other words, I don't take {no da se ranmi} as true by definition. To be is to be the value of a variable, not necessarily the same as to exist in the actual world.
> The only consistent way I > know to handle it in the present context is to > say (reasonably, though messily) that {1ranmi} is > an intensional context, taking us to an alternate > situation in which there are unicorns.
I used {2ranmi}, the subject of the myth. Myths can have both real and unreal subjects.
> I wonder if {ki'a} > is appropriate here — thi is less confusion -- > or even inability to determine a referent — and > more just saying somehting that appears wrong. > The correct reponse seems to me to be "But there > aren't any unicorns" or whatever.
It will depend on the context. They may be using the word in a manner I'm not familiar with, so what appears like nonsense to me may be perfectly meaningful to them. Depending on the context, it may be more reasonable to assume that they are confused (in which case {na'i} would be more appropriate) or that I am the one confused, in which case {ki'a} is better.
> Which kind of built in meaningless do you favor?
> If, for example, if one component of a
> disjunction is meaningless and the other true, is
> the whole true or meaningless (and corresponding
> things for other connectives)
If someone says what appears to be "[stuff] and [nonsense]", I will take it that they are claiming both the stuff and the nonsense. The default assumption would be that they meant something by what I take to be nonsense, so its meaning would be +definite -specific for me, using Cowan's terminology. The truth value of true and unknown is unknown, false and unknown is false, true or unknown is true, and false or unknown is unknown.
> > I guess "the underlying logic of Lojban" is > > something > > accessible to you but not to me, so it is > > pointless to argue > > that point. > > It seems to be quite out in the open; it is > singular logic. Reference is a function (part of > the general conditions for singluar logic -- > maybe definitional) and therefore (this is > definitional) each referring expression can have > only one referent (with variations about whether > it can have none).
We are obviously working under different definitions.
> > > > > I didn't realize that I had said that > > {lo'i > > > > > broda} had a different referent from {da > > poi > > > > > selcmi be lo broda} (I assume that this > > has a > > > > > built in namely-rider so that it has a > > > > referent > > > > > at all), only different from {lo selcmi > > be lo > > > > > broda}, unless you are identifying them > > as > > > > well, > > > > > which seems against something you said > > > > elsewhere, > > > > > presumably on another topic altogether. > > > > > > > > Not sure what you mean. What I said was: > > > > > > > > > > The bit you were presenting until > > recently, > > > > > > where {lo'i broda} > > > > > > and {lo pa selcmi be lo broda} have > > > > different > > > > > > referents, is > > > > > > not something I would want. > > > > > > > And I repeat, where did I say that as opposed > > to > > > saying that {lo'i broda} and {lo selcmi be lo > > > broda} have different referents? I can't > > find it. > > > > You may be reading {lo pa selcmi} as {da poi > > selcmi}, that's > > the only explanation I can think of to explain > > this exchange. > > I'm not but I never denied the equation which > *you* offered and charged me with denying. Have > I missed something here?
It appears to me that you have:
xorxes: I don't want {lo'i broda} and {lo pa selcmi be lo broda} to have different referents, which is what you propose.
pc: I never said {lo'i broda} and {da poi selcmi be lo broda} are different, only that {lo'i broda} and {lo selcmi be lo broda} are different.
xorxes: Huh?
pc: Where did I say that as opposed to saying that {lo'i broda} and {lo selcmi be lo broda} have different referents?
xorxes: Are you reading my {lo pa selcmi} as {da poi selcmi}?
pc: I'm not but I never denied the equation which
- you* offered and charged me with denying. Have
I missed something here?
xorxes: Yes. I never charged you with denying the equation
that you charge me with charging you with denying. 
> > Anyway, how's this:
> >
> > (1) mi cuxna fi ko'a goi lo'i karda
> > I choose from a set of cards.
> >
> > (2) mi cuxna fi ko'e goi lo selcmi be lo karda
> > I choose from a set of cards.
> > (Ontologically different one from
> > before, even if in the end it consists of
> > the same cards.)
> >
> > (3) ko'a na du ko'e
> >
> > Therefore:
> >
> > (4) mi cuxna fi su'o re da
> > I choose from at least two sets.
> >
> > I disagree with (3), of course, so for me (4)
> > does not follow from (1)
> > and (2).
>
> Well, I would of course say that 2 is a bad
> translation and is presumably false in the
> present context. I agree that 4 does not follow
> and I do hold that 3 is true.
> I do not know how {da poi selcmi be lo broda}
> snuck into this, so drop all that.
(I never mentioned {da poi selcmi be lo broda}.)
If you disagree with (3), what would be a correct use of {lo pa selcmi be lo broda}?
More generally, if a thing and the singleton group of that thing count as two things, and given that they share most properties, can we conclude that if something does something, then at least two things do it?
(a) ko'a goi lo'i ro broda cu selcmi ro lo ro broda (b) ko'e goi lo pa selcmi be ro lo ro broda cu selcmi ro lo ro broda (c) ko'a na du ko'e Therefore: (d) su'o re da selcmi ro lo ro broda
At least two things are the set of all broda?
mu'o mi'e xorxes
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wrote:
> > pc: > > --- Jorge Llambías wrote: > > > I think {lo pavyseljirna} usually does have > a > > > referent, > > > and so for example {lo pavyseljirna cu se > > > ranmi} is true. > > > > This is one of the ungoing paradoxes — if > the > > sentence is true, then {lo pavyseljirna} has > no > > referent and so the sentence is not true, > whether > > false or meaningless. > > For me, from the sentence being true it doesn't > follow > that {lo pavyseljyrna} has no referent, so no > paradox > arises. In other words, I don't take {no da se > ranmi} > as true by definition. To be is to be the value > of a > variable, not necessarily the same as to exist > in the > actual world.
OK. So you allow at least some members of the outer domain into the range of variables. That works, too. But it would be a good idea towarn people of it, since it is not the presumed situation.
> > The only consistent way I > > know to handle it in the present context is > to > > say (reasonably, though messily) that > {1ranmi} is > > an intensional context, taking us to an > alternate > > situation in which there are unicorns. > > I used {2ranmi}, the subject of the myth. Myths > can > have both real and unreal subjects.
Sorry, autopilot. This argument usually starts with {xanri} and I went there automatically. OK, so {2 ranmi} is intensional, if we don't have the outer domain in the range.
> > I wonder if {ki'a} > > is appropriate here — thi is less confusion > -- > > or even inability to determine a referent -- > and > > more just saying somehting that appears > wrong. > > The correct reponse seems to me to be "But > there > > aren't any unicorns" or whatever. > > It will depend on the context. They may be > using > the word in a manner I'm not familiar with, so > what > appears like nonsense to me may be perfectly > meaningful > to them. Depending on the context, it may be > more > reasonable to assume that they are confused (in > which > case {na'i} would be more appropriate) or that > I am > the one confused, in which case {ki'a} is > better. > > > > Which kind of built in meaningless do you > favor? > > If, for example, if one component of a > > disjunction is meaningless and the other > true, is > > the whole true or meaningless (and > corresponding > > things for other connectives) > > If someone says what appears to be "[stuff] > and > [nonsense]", I will take it that they are > claiming > both the stuff and the nonsense. The default > assumption > would be that they meant something by what I > take to be > nonsense, so its meaning would be +definite > -specific > for me, using Cowan's terminology. The truth > value > of true and unknown is unknown, false and > unknown is false, > true or unknown is true, and false or unknown > is unknown.
Thanx. This is a classic supervaluation or Lukasiewicz three-valued logic, depending on whether you want a third truth value or the possibility of a claim having no truth value.
> > > > I guess "the underlying logic of Lojban" is > > > something > > > accessible to you but not to me, so it is > > > pointless to argue > > > that point. > > > > It seems to be quite out in the open; it is > > singular logic. Reference is a function > (part of > > the general conditions for singluar logic -- > > maybe definitional) and therefore (this is > > definitional) each referring expression can > have > > only one referent (with variations about > whether > > it can have none). > > We are obviously working under different > definitions.
That is a useful hypothesis. What is your definition — or at least a characterization that covers these cases?
> > > > > > I didn't realize that I had said that > > > {lo'i > > > > > > broda} had a different referent from > {da > > > poi > > > > > > selcmi be lo broda} (I assume that > this > > > has a > > > > > > built in namely-rider so that it has > a > > > > > referent > > > > > > at all), only different from {lo > selcmi > > > be lo > > > > > > broda}, unless you are identifying > them > > > as > > > > > well, > > > > > > which seems against something you > said > > > > > elsewhere, > > > > > > presumably on another topic > altogether. > > > > > > > > > > Not sure what you mean. What I said > was: > > > > > > > > > > > > The bit you were presenting until > > > recently, > > > > > > > where {lo'i broda} > > > > > > > and {lo pa selcmi be lo broda} have > > > > > different > > > > > > > referents, is > > > > > > > not something I would want. > > > > > > > > > And I repeat, where did I say that as > opposed > > > to > > > > saying that {lo'i broda} and {lo selcmi > be lo > > > > broda} have different referents? I can't > > > find it. > > > > > > You may be reading {lo pa selcmi} as {da > poi > > > selcmi}, that's > > > the only explanation I can think of to > explain > > > this exchange. > > > > I'm not but I never denied the equation which > > *you* offered and charged me with denying. > Have > > I missed something here? > > It appears to me that you have: > > xorxes: I don't want {lo'i broda} and {lo pa > selcmi > be lo broda} to have different > referents, > which is what you propose. > > pc: I never said {lo'i broda} and {da poi > selcmi be lo > broda} are different, only that {lo'i > broda} and > {lo selcmi be lo broda} are different. > > xorxes: Huh? > > pc: Where did I say that as opposed to saying > that > {lo'i broda} and {lo selcmi be lo broda} > have > different referents? > > xorxes: Are you reading my {lo pa selcmi} as > {da poi selcmi}? > > pc: I'm not but I never denied the equation > which > *you* offered and charged me with denying. > Have > I missed something here? > > As I said, I have no idea how that came about. Brain fart seems to weak an explanation.
But back to the original point, whether {lo'i broda} has the same referent as {lo selcmi be lo broda}, consider {pa lo'i broda} refers to a set containing exactly one broda, a member of {lo'i broda} in fact, or to that one broda itself. {pa lo selcmi be lo bbroda} refers to one set of broda, which set may be of any size. Similarly, {lo'i pa broda} is a set containing exactly one broda, {lo pa selcmi be lo broda} is a single set of broda, which set may be of any size. There may be circumstances where the two expressions refer to the same thing or at least where bridi involving their interchange come to the same result, but it does not appear to be the general situation and is certainly not guaranteed.
pc: > OK. So you allow at least some members of the > outer domain into the range of variables. That > works, too. But it would be a good idea towarn > people of it, since it is not the presumed > situation.
I would have said strict restriction to the inner domain was the exceptional case, so that's the one that would need warning when context is not enough. (The warning would consist of a {poi zasti} or similar.)
> > We are obviously working under different > > definitions. > > That is a useful hypothesis. What is your > definition — or at least a characterization that > covers these cases?
I gave it many times already: Every unquantified sumti is a plural constant. Outer quantifiers on a sumti quantify over the referents of the constant: PA sumti = PA da poi ke'a me sumti.
If you absolutely require plural variables and quantifiers in order to have plural constants, then introduce {da'oi}, {de'oi}, {di'oi} as plural variables, and {su'oi} as the plural existential quantifier (that one should be enough), and we can define the singular variables and quantifiers in terms of them.
> But back to the original point, whether {lo'i > broda} has the same referent as {lo selcmi be lo > broda}, consider > {pa lo'i broda} refers to a set containing > exactly one broda, a member of {lo'i broda} in > fact, or to that one broda itself.
I know that's how you want to define it, and that's what I don't like. I want the meaning of {PA sumti} to depend only on the referents of sumti, not on its form.
> {pa lo selcmi be lo bbroda} refers to one set of > broda, which set may be of any size.
I don't think quantifiers quite refer, but I think we basically agree on the meaning of that one. I want {pa lo'i broda} to have this meaning too.
> Similarly, > {lo'i pa broda} is a set containing exactly one > broda,
No problem with that.
> {lo pa selcmi be lo broda} is a single set of > broda, which set may be of any size.
No problem with that.
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wrote:
> > pc: > > OK. So you allow at least some members of > the > > outer domain into the range of variables. > That > > works, too. But it would be a good idea > towarn > > people of it, since it is not the presumed > > situation. > > I would have said strict restriction to the > inner > domain was the exceptional case, so that's the > one that would need warning when context is not > enough. (The warning would consist of a {poi > zasti} > or similar.)
Well, of course, strict restriction to the inner domain is just what "To be is to be the value of a variable" means, despite the obvious reasonable extention to the outer domain; "a exists" is defined as "Ex x = a." Whether that is the usual case with natural languages is highly problematic. In the best cases the evidence is mixed and subject to both possible interpretations — implicit context shifting or outer domains.
> > > We are obviously working under different > > > definitions. > > > > That is a useful hypothesis. What is your > > definition — or at least a characterization > that > > covers these cases? > > I gave it many times already: Every > unquantified sumti > is a plural constant. Outer quantifiers on a > sumti > quantify over the referents of the constant: > PA sumti = PA da poi ke'a me sumti. > > If you absolutely require plural variables and > quantifiers in order to have plural constants, > then > introduce {da'oi}, {de'oi}, {di'oi} as plural > variables, and {su'oi} as the plural > existential > quantifier (that one should be enough), and we > can > define the singular variables and quantifiers > in > terms of them.
If we can define singular quantifiers in terms of plural (as we can), shouldn't the plural quantifiers be given the basic forms and the others the more remote ones. Generally, it would seem that variables function better as plural than as singular, especially given that {lo} and the like are instances of them (and are not, we hope, sets or groups). The "constant" part remains a problem, of course.
> > But back to the original point, whether {lo'i > > broda} has the same referent as {lo selcmi be > lo > > broda}, consider > > {pa lo'i broda} refers to a set containing > > exactly one broda, a member of {lo'i broda} > in > > fact, or to that one broda itself. > > I know that's how you want to define it, and > that's > what I don't like. I want the meaning of {PA > sumti} > to depend only on the referents of sumti, > not on > its form.
And how does this not? The referent of {lo'i broda} is a set of broda and what is among it is either some broda or some set of broda (just what {me} means with sets is somewhat obscure, since it is "defined" for other types of entities. The referent(s) of {lo selcmi be lo broda} is (a group of) several sets of broda, what is among them (or it) is (a group of)several sets of broda -- size indefinite.
> > {pa lo selcmi be lo bbroda} refers to one set > of > > broda, which set may be of any size. > I don't think quantifiers quite refer, but I > think > we basically agree on the meaning of that one.
Odd, I thought I was copying your usage, but let us agree that that is just loose usage and we know what we mean here (though if the going gets rouggh we may have to go back ans spell it out a bit more).
> I want > {pa lo'i broda} to have this meaning too.
But that would be most strange and the result of depending on the expression in the {lo} case. Or at least so it appears to me. Perhaps this is one of those cases of not clearly marked (or not carefully observed) differences in what we are talking about. I think I am talking about current Lojban (your usage possibly excepted), are you talking about your ideal system? (If so it seems to me monstrously inefficient, but that is another discussion).
> > Similarly, > > {lo'i pa broda} is a set containing exactly > one > > broda, > > No problem with that. > > > {lo pa selcmi be lo broda} is a single set of > > broda, which set may be of any size. > > No problem with that. >
Why isn't this a serious objection to your claim of the identity of the two encircling phrases? Does merely specifying how many satisfiers of the predicate are involved completely change the nature of the referring expression? Why?
pc: > Well, of course, strict restriction to the inner > domain is just what "To be is to be the value of > a variable" means, despite the obvious reasonable > extention to the outer domain; "a exists" is > defined as "Ex x = a."
For me, {abu zasti} and {su'o da zo'u da du abu} are quite different.
> If we can define singular quantifiers in terms of > plural (as we can), shouldn't the plural > quantifiers be given the basic forms and the > others the more remote ones.
If the singular ones are the ones used more frequently, then they should get the short forms. In any case, this question is not one of logical consistency but one of convenience.
> Generally, it would > seem that variables function better as plural > than as singular, especially given that {lo} and > the like are instances of them (and are not, we > hope, sets or groups). The "constant" part > remains a problem, of course.
What other things, besides constants, can instantiate variables in logic?
> > I want the meaning of {PA > > sumti} > > to depend only on the referents of sumti, > > not on > > its form. > > And how does this not? The referent of {lo'i > broda} is a set of broda and what is among it is > either some broda or some set of broda (just what > {me} means with sets is somewhat obscure, since > it is "defined" for other types of entities.
Well, that's the point. In my definitions it is no more obscure than any other broda, {lo'i [PA] broda} is just {lo selcmi be lo [PA] broda}. It is not a special case.
> Perhaps this is > one of those cases of not clearly marked (or not > carefully observed) differences in what we are > talking about. I think I am talking about > current Lojban (your usage possibly excepted), > are you talking about your ideal system?
I am talking about the proposed definitions, yes.
> (If so > it seems to me monstrously inefficient, but that > is another discussion).
And to me it seems wonderfully efficient. How do we test efficiency? With examples?
> > > Similarly,
> > > {lo'i pa broda} is a set containing exactly
> > one
> > > broda,
> >
> > No problem with that.
> >
> > > {lo pa selcmi be lo broda} is a single set of
> > > broda, which set may be of any size.
> >
> > No problem with that.
> >
>
> Why isn't this a serious objection to your claim
> of the identity of the two encircling phrases?
Why should it be? {lo'i broda} = {lo brode} does not of course entail {broda} = {brode}.
> Does merely specifying how many satisfiers of the > predicate are involved completely change the > nature of the referring expression? Why?
By definition:
{lo'i PA broda} = {lo selcmi be lo PA broda}.
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wrote:
> > pc: > > Well, of course, strict restriction to the > inner > > domain is just what "To be is to be the value > of > > a variable" means, despite the obvious > reasonable > > extention to the outer domain; "a exists" is > > defined as "Ex x = a." > > For me, {abu zasti} and {su'o da zo'u da du > abu} > are quite different.
Of course, since you allow at least parts of the outer domain in the range. No problems in the long run. Part of the prejudice against this is an old philosophical claim that usually comes out as "Existence is not a predicate," to which the stock reply is "'Exists' sure is." The Lesniewskian approach (parts of which lie behind much of the plural logic and/or group theory) is that every well formed sumti is "in the domain" ("has a referent", I suppose this means). this has the advantage of doing away with intensional contexts but the disadvantage of having to ask all the time about whether something is real or not. We could collapse {da poi zasti} sdown to a single simple form — and probably should if this approach become general. Lojban has rejected this idea several times however.
> > If we can define singular quantifiers in > terms of > > plural (as we can), shouldn't the plural > > quantifiers be given the basic forms and the > > others the more remote ones. > > If the singular ones are the ones used more > frequently, > then they should get the short forms. In any > case, this > question is not one of logical consistency but > one of > convenience.
True;I am just thinking like a system constructor here.
> > Generally, it would > > seem that variables function better as plural > > than as singular, especially given that {lo} > and > > the like are instances of them (and are not, > we > > hope, sets or groups). The "constant" part > > remains a problem, of course. > > What other things, besides constants, can > instantiate > variables in logic?
Descriptions, which at least in logic are not constants (in the sense I think you mean by that).
> > > I want the meaning of {PA > > > sumti} > > > to depend only on the referents of > sumti, > > > not on > > > its form. > > > > And how does this not? The referent of {lo'i > > broda} is a set of broda and what is among it > is > > either some broda or some set of broda (just > what > > {me} means with sets is somewhat obscure, > since > > it is "defined" for other types of entities. > > Well, that's the point. In my definitions it is > no > more obscure than any other broda, {lo'i [PA] > broda} > is just {lo selcmi be lo [PA] broda}. It is > not > a special case.
But I thought the issue was about {PA lo'i broda}
and {PA lo broda}; we seem to agree on the inner
quantifiers — though I think that counts against
your identification.
> > Perhaps this is > > one of those cases of not clearly marked (or > not > > carefully observed) differences in what we > are > > talking about. I think I am talking about > > current Lojban (your usage possibly > excepted), > > are you talking about your ideal system? > > I am talking about the proposed definitions, > yes.
Well, the definition set where this is proposed is so defective from the get-go that I have never seen any reason to take it seriously. However, this proposal can be separated from its context and be proposed for a more adequate base. In that case, it seems to me t0o give the results that you find objectionable, {pa lo selcmi be lo broda} is a set of some of broda of some size, {pa lo'i broda} is a one-memberd set of broda or a single broda (depending on what that base is).
> > (If so > > it seems to me monstrously inefficient, but > that > > is another discussion). > > And to me it seems wonderfully efficient. How > do we > test efficiency? With examples?
Well, I suppose we look to see how often we need the various expressions and which one fits best with this ditribution. To be sure, a consistent pattern running though the whole gadri set (ignoring the typicals and the like) would count for something as well.
> > > > > Similarly, > > > > {lo'i pa broda} is a set containing > exactly > > > one > > > > broda, > > > > > > No problem with that. > > > > > > > {lo pa selcmi be lo broda} is a single > set of > > > > broda, which set may be of any size. > > > > > > No problem with that. > > > > > > > Why isn't this a serious objection to your > claim > > of the identity of the two encircling > phrases? > > Why should it be? {lo'i broda} = {lo brode} > does > not of course entail {broda} = {brode}.
I don't get the point of this. Yes, a set of brodas is typically not itself a broda, but no one suggested they were; the question was about the whole phrases.
> > Does merely specifying how many satisfiers of > the > > predicate are involved completely change the > > nature of the referring expression? Why? > > By definition: > > {lo'i PA broda} = {lo selcmi be lo PA broda}. > That is, of course, your definition. Since its appropriateness is ultimately the point at issue, citing it as an explanation is mere question begging.
Oh, yes. Not only may {lo selcmi be lo broda} refer to more than one set — and so not be identical to the referent of {lo'i broda}, which is one set, but also, while {lo'i broda} contains only broda, the set(s) among lo selcmi be lo broda may have other things in them as well -- may indeed be preponderantly non-brodas.
pc: > > > > I want the meaning of {PA > > > > sumti} > > > > to depend only on the referents of > > sumti, > > > > not on > > > > its form. > > > > > > And how does this not? The referent of {lo'i > > > broda} is a set of broda and what is among it > > is > > > either some broda or some set of broda (just > > what > > > {me} means with sets is somewhat obscure, > > since > > > it is "defined" for other types of entities. > > > > Well, that's the point. In my definitions it is > > no > > more obscure than any other broda, {lo'i [PA] > > broda} > > is just {lo selcmi be lo [PA] broda}. It is > > not > > a special case. > > > But I thought the issue was about {PA lo'i broda} > and {PA lo broda}; we seem to agree on the inner > quantifiers — though I think that counts against > your identification.
{PA lo broda} and {PA lo'i broda} are both examples of PA sumti. I don't need to give a special rule for each. I don't need to give a special rule for {me lo'i broda} either, because that's just {me lo pa selcmi be ...}.
> > > Does merely specifying how many satisfiers of > > the > > > predicate are involved completely change the > > > nature of the referring expression? Why? > > > > By definition: > > > > {lo'i PA broda} = {lo selcmi be lo PA broda}. > > > That is, of course, your definition. Since its > appropriateness is ultimately the point at issue, > citing it as an explanation is mere question begging.
Then I'm afraid I don't understand what type of reasons you are after.
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pc: > Oh, yes. Not only may {lo selcmi be lo broda} > refer to more than one set — and so not be > identical to the referent of {lo'i broda}, which > is one set, but also, while {lo'i broda} contains > only broda, the set(s) among lo selcmi be lo > broda may have other things in them as well -- > may indeed be preponderantly non-brodas.
That's already contemplated. The actual definition I have on the proposal page is:
lo selcmi be ro lo [PA] broda e no lo na me lo [PA] broda
Ideally we should have a brivla meaning "x1 is the set of x2", where x2 are all and only the members of x1, then the definition would be simpler. I suppose nothing really stops us from defining {selcmi} that way, since it doesn't really have to mean exactly {se cmima}.
In the case of {loi} we do have the desired brivla, that's why {loi PA broda} can be simply {lo gunma be lo PA broda}.
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wrote:
> > pc: > > > > > I want the meaning of {PA > > > > > sumti} > > > > > to depend only on the referents of > > > sumti, > > > > > not on > > > > > its form. > > > > > > > > And how does this not? The referent of > {lo'i > > > > broda} is a set of broda and what is > among it > > > is > > > > either some broda or some set of broda > (just > > > what > > > > {me} means with sets is somewhat obscure, > > > since > > > > it is "defined" for other types of > entities. > > > > > > Well, that's the point. In my definitions > it is > > > no > > > more obscure than any other broda, {lo'i > [PA] > > > broda} > > > is just {lo selcmi be lo [PA] broda}. It > is > > > not > > > a special case. > > > > > > But I thought the issue was about {PA lo'i > broda} > > and {PA lo broda}; we seem to agree on the > inner > > quantifiers — though I think that counts > against > > your identification. > > {PA lo broda} and {PA lo'i broda} are both > examples > of PA sumti. I don't need to give a special > > rule for each. I don't need to give a special > rule > for {me lo'i broda} either, because that's just > > {me lo pa selcmi be ...}.
Well, that is what is in dispute ultimately, so saying it yet again does not further the discussion. As for the rest, your remarks suggest that you either think {pa lo'i broda} is some unspecified set of brodas, like {pa lo selcmi be lo broda} or you think that {pa lo selcmi be lo broda} is a one-membered subset or is one broda, like {pa lo'i broda}. Either way you violate your uniformity rule and need special, either for {lo'i} among the gadri or {selcmi} among predicates.
> > > > > Does merely specifying how many > satisfiers of > > > the > > > > predicate are involved completely change > the > > > > nature of the referring expression? Why? > > > > > > By definition: > > > > > > {lo'i PA broda} = {lo selcmi be lo PA > broda}. > > > > > That is, of course, your definition. Since > its > > appropriateness is ultimately the point at > issue, > > citing it as an explanation is mere question > begging. > > Then I'm afraid I don't understand what type of > reasons > you are after. > Actually, I don't think there can be a good reason for the identification, so I don't really expect you to provide one. What I have been presenting is (now five) reasons not to accept the identification, to see if you can knock any of them down.
> > pc: > > Oh, yes. Not only may {lo selcmi be lo > broda} > > refer to more than one set — and so not be > > identical to the referent of {lo'i broda}, > which > > is one set, but also, while {lo'i broda} > contains > > only broda, the set(s) among lo selcmi be lo > > broda may have other things in them as well > -- > > may indeed be preponderantly non-brodas. > > That's already contemplated. The actual > definition I have on > the proposal page is: > > lo selcmi be ro lo [PA] broda e no lo na me lo > [PA] broda > > Ideally we should have a brivla meaning "x1 is > the set of x2", > where x2 are all and only the members of x1, > then the definition > would be simpler. I suppose nothing really > stops us from defining > {selcmi} that way, since it doesn't really have > to mean exactly > {se cmima}. > > In the case of {loi} we do have the desired > brivla, that's why > {loi PA broda} can be simply {lo gunma be lo PA > broda}.
OK, that knocks down one, four to go. Essentially the same objections apply to this latest definition as well: the first is PA brodas (collectively), the second is some collections of PA brodas — maybe but not necessarily only one -- and that one may or may not be the one picked out {loi broda}.
You are welcome to use {selcmi} in that way -- once you advertise it. In that case, x2 is presumably {loi broda}, not {lo} (or, of course, {lo} in your ideal sense if you are point shifting again.
pc: > As for the rest, your remarks suggest > that you either think {pa lo'i broda} is some > unspecified set of brodas, like {pa lo selcmi be > lo broda}
Not exactly, but along those lines, yes.
Strictly speaking, {pa sumti} is a quantified term, so it does not refer to anything, so it is not some unspecified thing. What the quantifier does is tell us that (exactly) one thing from those that are referents of the sumti satisfies the selbri for which it is an argument. I know you already know that, please don't take it as lecturing. I'm just writing it down mainly to clarify for myself.
> or you think that {pa lo selcmi be lo > broda} is a one-membered subset or is one broda, > like {pa lo'i broda}.
No, I do not think that. I think that outer quantifiers are always true quantifiers. That would not count as a true quantifier.
> Either way you violate > your uniformity rule and need special, either for > {lo'i} among the gadri or {selcmi} among > predicates.
Could you please elaborate. In both cases, the referent of the sumti is a set, and {pa} quantifies over those referents. (They are a special case in that the sumti happen to have a single referent to start with, so quantification is not very interesting, but that's not a violation of the general rule.)
> Actually, I don't think there can be a good > reason for the identification, so I don't really > expect you to provide one. What I have been > presenting is (now five) reasons not to accept > the identification, to see if you can knock any > of them down.
Could you make a succint list of the remaining reasons? I think I lost truck, sorry.
> Essentially the same objections apply to this > latest definition as well: the first is PA brodas > (collectively), the second is some collections of > PA brodas — maybe but not necessarily only one > — and that one may or may not be the one picked > out {loi broda}.
"x1 is the set of x2" gives a function: for a given x2 there is one and only one x1 that satisfies, so {lo'i} as a contraction of {lo selcmi be lo} is well defined.
> You are welcome to use {selcmi} in that way -- > once you advertise it. In that case, x2 is > presumably {loi broda}, not {lo} (or, of course, > {lo} in your ideal sense if you are point > shifting again.
Point shifting? It's plural {lo}, as always.
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wrote:
> > pc: > > As for the rest, your remarks suggest > > that you either think {pa lo'i broda} is some > > unspecified set of brodas, like {pa lo selcmi > be > > lo broda} > > Not exactly, but along those lines, yes. > > Strictly speaking, {pa sumti} is a > quantified term, > so it does not refer to anything, so it is not > some > unspecified thing. What the quantifier does is > tell us > that (exactly) one thing from those that are > referents of > the sumti satisfies the selbri for which it is > an argument. > I know you already know that, please don't take > it as > lecturing. I'm just writing it down mainly to > clarify > for myself.
Good. So, in place of "refer to" we can use "is satisfied by" or some such locution.
> > or you think that {pa lo selcmi be lo > > broda} is a one-membered subset or is one > broda, > > like {pa lo'i broda}. > > No, I do not think that. I think that outer > quantifiers > are always true quantifiers. That would not > count as a true > quantifier.
So, what satisfies {pa lo'i broda}? It can't mean "one of the things that satisfy {lo'i broda}", since that would always just be {lo'i broda} again — and {re lo'i broda} would always be meaningless. Or do you think that {lo'i broda} is as inherently plural as {lo broda}, rather than being absolutely singular?
> > Either way you violate > > your uniformity rule and need special, either > for > > {lo'i} among the gadri or {selcmi} among > > predicates. > > Could you please elaborate. In both cases, the > referent of the > sumti is a set, and {pa} quantifies over those > referents. No, in one case the referent is a set, in the other it is (a group of) some number of sets, maybe but not certainly one.
>(They > are a special case in that the sumti happen to > have a single > referent to start with, so quantification is > not very > interesting, but that's not a violation of the > general rule.)
Well, only {lo'i broda} is guaranteed a single referent (unless you mean the group — which I doubt you do). Does this also mean that {PA lo'i broda} is always uninteresting? If not meaningless?
But the point. If {pa lo selcmi be lo broda} is like {pa lo'i broda}, either a set with a single member or a single broda, then in this case (only? — well, maybe for {gunma} too), the count is not by the satisfiers but by their content. If {pa lo'i broda} is, like {lo selcmi be lo broda} a set of unspecified size, then it breaks the pattern of the gadri of giving a structure of the same sort with a defined number of members -- or that number of members standing alone. > > > Actually, I don't think there can be a good > > reason for the identification, so I don't > really > > expect you to provide one. What I have been > > presenting is (now five) reasons not to > accept > > the identification, to see if you can knock > any > > of them down. > > Could you make a succint list of the remaining > reasons? I think I lost truck, sorry.
the two sides have different numbers of referents; even if they have the same number there is no necessity that they be the same referents; they count by different units; there partitives are different.
> > Essentially the same objections apply to this > > latest definition as well: the first is PA > brodas > > (collectively), the second is some > collections of > > PA brodas — maybe but not necessarily only > one > > — and that one may or may not be the one > picked > > out {loi broda}. > > "x1 is the set of x2" gives a function: for a > given > x2 there is one and only one x1 that satisfies, > so > {lo'i} as a contraction of {lo selcmi be lo} is > well > defined.
Not if "is a set of" is {selcmi} as presently defined. If you want a new definition, then aannounce it beforehand. Incidentally, you don't need the complex, what you want is just {lu'i lo broda} — without any problems. It works slightly better with {gunma}, which gives the whole list.
> > You are welcome to use {selcmi} in that way > -- > > once you advertise it. In that case, x2 is > > presumably {loi broda}, not {lo} (or, of > course, > > {lo} in your ideal sense if you are point > > shifting again. > > Point shifting? It's plural {lo}, as always. > Well, always since when: it is not in your proposed definitions, for example. But I meant whether you were using {lo} for collective rather than distributive gfoups.
pc: > So, what satisfies {pa lo'i broda}?
{pa lo'i broda cu brode} says that of the referents of {lo'i broda}, however many it has, exactly one of them satisfies brode.
I don't understand the question "what satisfies {pa lo'i broda}?" because quantified terms are not predicates that can be satisfied.
> It can't > mean "one of the things that satisfy {lo'i > broda}", since that would always just be {lo'i > broda} again — and {re lo'i broda} would always > be meaningless. Or do you think that {lo'i > broda} is as inherently plural as {lo broda}, > rather than being absolutely singular?
Yes, that's what I think.
> >(They > > are a special case in that the sumti happen to > > have a single > > referent to start with, so quantification is > > not very > > interesting, but that's not a violation of the > > general rule.) > > Well, only {lo'i broda} is guaranteed a single > referent (unless you mean the group — which I > doubt you do). Does this also mean that {PA lo'i > broda} is always uninteresting? If not > meaningless?
When {lo'i broda} has a single referent, {PA lo'i broda} is meaningful but uninteresting, just as {PA lo selcmi be lo broda} is when {lo selcmi be lo broda} has a single referent.
> > Could you make a succint list of the remaining
> > reasons? I think I lost truck, sorry.
Hmm, "track" and "truck" are homonyms for me
> the two sides have different numbers of > referents;
I admit many referents for {lo'i broda} in general. {lo'i ro broda} has a single referent, but so does {lo selcmi be lo ro broda}.
> even if they have the same number > there is no necessity that they be the same > referents;
I don't get this. In a given context, they will be the same referents: namely the set or sets in question.
> they count by different units;
They are both sets, I don't understand what you mean by them counting by different units.
> there > partitives are different.
If the partitives are the {piPA} quantifiers, then they are the same:
piPA lo'i broda = lo piPAsi'e be lo pa lo'i broda
piPA lo selcmi be lo broda = lo piPAsi'e be lo pa lo selcmi be lo broda
> Incidentally, you don't > need the complex, what you want is just {lu'i lo > broda} — without any problems.
That works too, but as a definition it would be circular, because I'm defining {lu'i sumti} as {lo'i me sumti}.
If we define {lo'i broda} as {lu'i lo broda} we would have to define {lu'i sumti} as {lo selcmi be sumti}, with {selcmi} meaning "x2 are the members of x1", or as {lo se cmima be ro me sumti e no lo na me sumti}.
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wrote:
> > pc: > > So, what satisfies {pa lo'i broda}? > > {pa lo'i broda cu brode} says that of the > referents > of {lo'i broda}, however many it has, exactly > one of > them satisfies brode. > > I don't understand the question "what satisfies > > {pa lo'i broda}?" because quantified terms are > not > predicates that can be satisfied.
I was using "satisfies" as a substitute for "refers to" appropriate to quantifiers. Would you prefer "justifies" or some such thing?
> > It can't
> > mean "one of the things that satisfy {lo'i
> > broda}", since that would always just be
> {lo'i
> > broda} again — and {re lo'i broda} would
> always
> > be meaningless. Or do you think that {lo'i
> > broda} is as inherently plural as {lo broda},
> > rather than being absolutely singular?
>
> Yes, that's what I think.
Well, that is an innovation that I had not noticed you announced. I would oppose it on practical and historical grounds: we rarely need more than one set (indeed, of course, we rarely need any sets at all) so the extras are superfluous. And, of course, {lo'i broda} started life as the set of all broda and then was moved to *a* set of broda at the same time as {loi} and {lo} were moved to local cases.
> > >(They
> > > are a special case in that the sumti happen
> to
> > > have a single
> > > referent to start with, so quantification
> is
> > > not very
> > > interesting, but that's not a violation of
> the
> > > general rule.)
> >
> > Well, only {lo'i broda} is guaranteed a
> single
> > referent (unless you mean the group — which
> I
> > doubt you do). Does this also mean that {PA
> lo'i
> > broda} is always uninteresting? If not
> > meaningless?
>
> When {lo'i broda} has a single referent, {PA
> lo'i broda}
> is meaningful but uninteresting, just as
> {PA lo selcmi be lo broda} is when {lo selcmi
> be lo broda}
> has a single referent.
>
>
> > > Could you make a succint list of the
> remaining
> > > reasons? I think I lost truck, sorry.
>
> Hmm, "track" and "truck" are homonyms for me
>
> > the two sides have different numbers of
> > referents;
>
> I admit many referents for {lo'i broda} in
> general.
> {lo'i ro broda} has a single referent, but so
> does
> {lo selcmi be lo ro broda}.
>
> > even if they have the same number
> > there is no necessity that they be the same
> > referents;
>
> I don't get this. In a given context, they will
> be the same
> referents: namely the set or sets in question.
I gather that {lo'i broda} is a distributive group of sets for you. This makes for even more practical problems, since most of the things we want to say about sets — size, inclusion, and members — cannot be said of lo'i broda.
The point at this place is that {lo'i broda} and {lo selcmi be lo broda}, being different descriptions are not compelled to be the same set(s) — any more than two occurrences of {su'o da poi broda} need to be the same broda(s). This is why we have {lu'i} and the like — get the set that corresponds to the group or the group to the set or the members to whatever. This does not happen automatically. (Actually, CLL does not require that the set and the group be the same things arranged in different structures but only subsets or subgroups of the original. I have never seen a discussion of these critters but assume that this has shifted in a practical way to "the". Given that {lo} gives a distributive groups and {loi} a collective, these qualifiers would be the way to shift types of predication while still dealing with the same individuals. Of course, you do that differently, so that will not impress you.)
> > they count by different units; > > They are both sets, I don't understand what you > mean by > them counting by different units.
In the current system — not in your ideal one (and I really don't think you marked that shift at all) — {lo'i pa broda} is a set(or even sets) containing exactly a single broda, while {lo pa selcmi be lo broda} is a single set of broda of indeterminate size.
> > there > > partitives are different. > > If the partitives are the {piPA} quantifiers, > then they > are the same: > > piPA lo'i broda > = lo piPAsi'e be lo pa lo'i broda > > piPA lo selcmi be lo broda > = lo piPAsi'e be lo pa lo selcmi be lo broda
We'll leave what the hell happens with {piPA} for another day — we've been around it enough and it is not relevant here. What I mean is that {pa lo'i broda} is in current Lojban either (because of the uncertainty about {me} with a single set) a subset with a single member or that single member itself. {pa lo selcmi be lo broda} is a set of broda of indeterminate size. Never the same thing, except by pure chance.
> > Incidentally, you don't > > need the complex, what you want is just {lu'i > lo > > broda} — without any problems. > > That works too, but as a definition it would be > circular, > because I'm defining {lu'i sumti} as {lo'i > me sumti}. > > If we define {lo'i broda} as {lu'i lo broda} we > would > have to define {lu'i sumti} as {lo selcmi > be sumti}, > with {selcmi} meaning "x2 are the members of > x1", or > as {lo se cmima be ro me sumti e no lo na > me sumti}.
Sorry, I am still going on the current sense of these expression, under which the the identifications you propose do not make sense.
pc: > I gather that {lo'i broda} is a distributive > group of sets for you.
I know it is pointless to say this again, but anyway: no, it is not a group for me. It is a set or several sets of broda, not a group of sets.
> The point at this place is that {lo'i broda} and > {lo selcmi be lo broda}, being different > descriptions are not compelled to be the same > set(s) — any more than two occurrences of {su'o > da poi broda} need to be the same broda(s).
Of course not. All it means is that you can replace one expression with the other in a given context and get the same meaning. Neither expression is compelled to be anything without a context.
> In the current system — not in your ideal one > (and I really don't think you marked that shift > at all) — {lo'i pa broda} is a set(or even sets) > containing exactly a single broda, while {lo pa > selcmi be lo broda} is a single set of broda of > indeterminate size.
Right, and I don't propose to equate those.
If you look carefully at the definition, I equate {lo'i pa broda} with {lo selcmi be lo pa broda}, not with {lo pa selcmi be lo broda}. {lo'i} = {lo selcmi be lo}.
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wrote:
> > pc: > > I gather that {lo'i broda} is a distributive > > group of sets for you. > > I know it is pointless to say this again, but > anyway: no, it is not a group for me. It is a > set or > several sets of broda, not a group of sets.
Sorry, it is hard to talk in English about things working together without giving them a collective label. I had your point (though I disagree with it in both respects) and will try to be more careful when tlking to you in the future.
> > The point at this place is that {lo'i broda} > and > > {lo selcmi be lo broda}, being different > > descriptions are not compelled to be the same > > > set(s) — any more than two occurrences of > {su'o > > da poi broda} need to be the same broda(s). > > Of course not. All it means is that you can > replace > one expression with the other in a given > context > and get the same meaning. Neither expression is > > compelled to be anything without a context.
Sorry, but if they are identical they have to be the same sets and there is nothing to compel them to be so, even in a single context.
> > In the current system — not in your ideal > one > > (and I really don't think you marked that > shift > > at all) — {lo'i pa broda} is a set(or even > sets) > > containing exactly a single broda, while {lo > pa > > selcmi be lo broda} is a single set of broda > of > > indeterminate size. > > Right, and I don't propose to equate those.
Why should mentioning the size of a set change the whole nature? It seems that internal quantifiers are non-restrictive relative clauses.
> If you look carefully at the definition, I > equate > {lo'i pa broda} with {lo selcmi be lo pa > broda}, > not with {lo pa selcmi be lo broda}. > {lo'i} = {lo selcmi be lo}. > Well, I give up trying to make something consistent and useful out of xorlan. If it becomes Lojban eventually, that ought to hasten the need for LoCCan3 (strictly 4 in that case), though LLG has not yet shown much of the political aura that seems to be needed along with the aesthetic ones to start up another offspring. One last question, so that I can understand whatever it is that I am dropping — against the day when it will come up again somewhere else. You regularly say that {loi broda} is one or several broda taken collectively, yet, by the definition you have been using here, {lo gunma be lo broda}, it is in fact several several-brodas-taken-collectively (see why "group" is so handy, even if it has no ontological status?) taken distributively. So each of these several-brodas has to fill the predicate involved. What you seem to have been talking about in various places here is {pa loi broda}, a single several-brodas taken collectively. Which is right?
pc: > > > I gather that {lo'i broda} is a distributive > > > group of sets for you. > > > > I know it is pointless to say this again, but > > anyway: no, it is not a group for me. It is a > > set or > > several sets of broda, not a group of sets. > > Sorry, it is hard to talk in English about things > working together without giving them a collective > label. I had your point (though I disagree with > it in both respects) and will try to be more > careful when tlking to you in the future.
I wouldn't even mention it if one of your objections wasn't precisely centered on the distinction between sets and a group of sets.
> > > The point at this place is that {lo'i broda} > > and > > > {lo selcmi be lo broda}, being different > > > descriptions are not compelled to be the same > > > set(s) — any more than two occurrences of > > {su'o > > > da poi broda} need to be the same broda(s). > > > > Of course not. All it means is that you can > > replace > > one expression with the other in a given > > context > > and get the same meaning. Neither expression is > > compelled to be anything without a context. > > Sorry, but if they are identical they have to be > the same sets and there is nothing to compel them > to be so, even in a single context.
Would you give an example of how you think {lo selcmi be lo broda} should be used? In the example I gave:
1- mi cuxna fi ko'a goi lo'i karda 2- mi cuxna fi ko'e goi lo selcmi be lo karda 3a- ko'a du ko'e 3b- ko'a na du ko'e 4- mi cuxna fi su'o re da
4 does not follow from 1, 2, 3a, but it does follow from 1, 2, 3b. You said you find that 2 would be incorrect usage but I don't understand what your objection to it is.
I'm proposing that {lo'i broda} and {lo selcmi be lo broda} be equal by definition. Is the above an example where you would want them to make a distinction? If so, what's the distinction? If not, could you provide an example that shows the distinction?
> > > In the current system — not in your ideal one > > > (and I really don't think you marked that shift > > > at all) — {lo'i pa broda} is a set(or even sets) > > > containing exactly a single broda, while {lo pa > > > selcmi be lo broda} is a single set of broda of > > > indeterminate size. > > > > Right, and I don't propose to equate those. > > Why should mentioning the size of a set change > the whole nature? It seems that internal > quantifiers are non-restrictive relative clauses.
Mentioning the size of the set does not change the whole nature. It is perfectly doable in both cases: {lo'i mu karda} = a set/sets of five cards. {lo selcmi be lo mu karda} = a set/sets of five cards.
No change of nature. {lo'i} is just shorthand for {lo selcmi be lo} = "the set of those that really are" (that happens to be the definition of {lo'i} given in the ma'oste).
> You regularly say that {loi broda} is one or > several broda taken collectively, yet, by the > definition you have been using here, {lo gunma be > lo broda}, it is in fact several > several-brodas-taken-collectively (see why > "group" is so handy, even if it has no > ontological status?) taken distributively.
{lo broda} are not necessarily taken distributively. {lo} is silent about distributivity. Outer quantifiers are always distributive. {lo gunma be lo broda} is a group/groups of broda. {loi broda} is also (as currently proposed) a group/groups of broda.
At one point, I had {loi broda} being just {lo broda} but with the additional constraint of non-distributivity. ({lo} was even then silent about distributivity.)
John Cowan said that he preferred reified groups/masses, Robin supported this move. You objected somewhat but then sort of retracted the objection (as far as I could tell). Nobody else gave an opinion. Given that I don't have a preference one way or the other, I changed the definition of {loi}, from:
loi [PA] broda cu brode = lo [PA] broda cu kansi'u lo ka ce'u brode
to:
loi [PA] broda = lo gunma be lo [PA] broda
The latter has {loi} more parallel to {lo'i}, the former had it more parallel to {lo}.
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wrote:
> > pc: > > > > I gather that {lo'i broda} is a > distributive > > > > group of sets for you. > > > > > > I know it is pointless to say this again, > but > > > anyway: no, it is not a group for me. It is > a > > > set or > > > several sets of broda, not a group of sets. > > > > Sorry, it is hard to talk in English about > things > > working together without giving them a > collective > > label. I had your point (though I disagree > with > > it in both respects) and will try to be more > > careful when tlking to you in the future. > > I wouldn't even mention it if one of your > objections > wasn't precisely centered on the distinction > between > sets and a group of sets.
It works as well with several sets as with groups
of sets, since that is not the point.
> > > > The point at this place is that {lo'i > broda} > > > and > > > > {lo selcmi be lo broda}, being different > > > > descriptions are not compelled to be the > same > > > > set(s) — any more than two occurrences > of > > > {su'o > > > > da poi broda} need to be the same > broda(s). > > > > > > Of course not. All it means is that you can > > > replace > > > one expression with the other in a given > > > context > > > and get the same meaning. Neither > expression is > > > compelled to be anything without a context. > > > > Sorry, but if they are identical they have to > be > > the same sets and there is nothing to compel > them > > to be so, even in a single context. > > Would you give an example of how you think {lo > selcmi > be lo broda} should be used? In the example I > gave: > > 1- mi cuxna fi ko'a goi lo'i karda > 2- mi cuxna fi ko'e goi lo selcmi be lo karda > 3a- ko'a du ko'e > 3b- ko'a na du ko'e > 4- mi cuxna fi su'o re da > > 4 does not follow from 1, 2, 3a, but it does > follow > from 1, 2, 3b. You said you find that 2 would > be incorrect > usage but I don't understand what your > objection to it is. > > I'm proposing that {lo'i broda} and {lo selcmi > be lo broda} > be equal by definition. Is the above an example > where you > would want them to make a distinction? If so, > what's the > distinction? If not, could you provide an > example that shows > the distinction?
Well, I said I was not interested in improving xorlan now that it is clear that is what we are talking about. Given that definition of {loi}, I would be hard pressed to answer. But of course it was the propriety of that definition
- in**Lojban*** that was the issue here.
> > > > In the current system — not in your > ideal one > > > > (and I really don't think you marked that > shift > > > > at all) — {lo'i pa broda} is a set(or > even sets) > > > > containing exactly a single broda, while > {lo pa > > > > selcmi be lo broda} is a single set of > broda of > > > > indeterminate size. > > > > > > Right, and I don't propose to equate those. > > > > Why should mentioning the size of a set > change > > the whole nature? It seems that internal > > quantifiers are non-restrictive relative > clauses. > > Mentioning the size of the set does not change > the > whole nature. It is perfectly doable in both > cases: > {lo'i mu karda} = a set/sets of five cards. > {lo selcmi be lo mu karda} = a set/sets of five > cards. > > No change of nature. {lo'i} is just shorthand > for > {lo selcmi be lo} = "the set of those that > really are" > (that happens to be the definition of {lo'i} > given in > the ma'oste).
Sorry I forgot that you are talking about xorlan,
with that strange defeinition, not about Lojban,
which I was foolishly continuiing to discuss.
> > You regularly say that {loi broda} is one or
> > several broda taken collectively, yet, by the
> > definition you have been using here, {lo
> gunma be
> > lo broda}, it is in fact several
> > several-brodas-taken-collectively (see why
> > "group" is so handy, even if it has no
> > ontological status?) taken distributively.
>
> {lo broda} are not necessarily taken
> distributively.
> {lo} is silent about distributivity.
> Outer quantifiers are always distributive.
> {lo gunma be lo broda} is a group/groups of
> broda.
> {loi broda} is also (as currently proposed) a
> group/groups
> of broda.
I guess that means that your earlier remarks about the referent of {loi broda} being brodas taken collectively was either a slip or a facon de parler (which I should, I suppose, have understoood as such). You always really meant not some number of broda but some number of some number of brodas, the latter at least taken collectively. OK, ypou said it oddly, but if that is the way you have defined it in xorlan, so be it. I have no objections to that and, while I think to do so would be stupid, I have no real objection to adopting that as the official Lojban (now strictly 2) position. I do think that all these changes should be mentioned in your summary of the effects of adopting your various proposals, which change virtually all the descriptors, and are generally not backward compatible unless our only samples are xorlan disguised as Lojban over the years.
> At one point, I had {loi broda} being just {lo > broda} > but with the additional constraint of > non-distributivity. > ({lo} was even then silent about > distributivity.) > > John Cowan said that he preferred reified > groups/masses, > Robin supported this move. You objected > somewhat but then > sort of retracted the objection (as far as I > could tell).
I preferred (and still prefer) plural quantification. Groups are essential, however, if we are to continue singular quantification. The differences are minor, but technically significant.
> Nobody else gave an opinion. Given that I don't > have a > preference one way or the other, I changed the > definition > of {loi}, from: > > loi [PA] broda cu brode = lo [PA] broda cu > kansi'u > lo ka ce'u brode > > to: > > loi [PA] broda = lo gunma be lo [PA] broda
This is an improvement since it was unclear that {kansi'u} really did the job, while {gunma} at least clearly does that one. The other xorlan peculiarities remain.
> The latter has {loi} more parallel to {lo'i}, > the former > had it more parallel to {lo}. > Mainly because the definitions of {lo} are so screwed up.
End of this discussion, since it has apparently been a cross-purposes — talking about different languages — from the get-go.
pc: > --- Jorge Llambías wrote: > > {lo'i} is just shorthand for > > {lo selcmi be lo} = "the set of those that really are" > > (that happens to be the definition of {lo'i} given in > > the ma'oste). > > Sorry I forgot that you are talking about xorlan, > with that strange defeinition, not about Lojban, > which I was foolishly continuiing to discuss.
That is hardly a strange definition, as it is a straight translation of the English definition in the ma'oste. The ma'oste has:
lo: the one(s) that really is(are)... lo'i: the set of those that really are...
so the first and most natural stab at a Lojban definition of {lo'i} is {lo selcmi be lo}. We can then argue whether we want {lo'i} to have additonal more subtle properties. For my part, I don't even see the point of having {lo'i} there in the first place, so I'm willing to consider any definition. You say {lo selcmi be lo} doesn't work, but you have not offered an alternative, nor any example where one expression could not be substituted for the other.
> I do think that all > these changes should be mentioned in your summary > of the effects of adopting your various > proposals, which change virtually all the > descriptors, and are generally not backward > compatible unless our only samples are xorlan > disguised as Lojban over the years.
My definitions for la/le'i/la'i/lei/lai/lo'e/le'e are, as far as I can tell, totally compatible with CLL.
{loi}/{lo'i} differ in the interpretation of the inner quantifier, which is no longer required to be the number of all the brodas that exist in the world. A consequence of that is that {lo'i broda} is no longer unique, as it can be any set of brodas and not necessarily the unique set of all brodas.
{le} differs in the interpretation of the outer quantifier, which is no longer taken to always be there. In practice this makes very little difference because {le} was mostly used with singular referents. (In theory {la} also would differ in the same way, but the default outer quantifier for {la} was taken even less seriously than the one for {le}). Also, the idea of plural reference was not explicitly present in CLL, at least not in any formalized way.
{lo} is really the only significant difference, as I propose {lo broda} to have referents and CLL simply defines it as a quantifier expression. Also the inner quantifier interpretation changes as with lo'i/loi. The definition in the ma'oste "the one(s) that really is(are)..." is closer to the proposed definition than to CLL's.
> End of this discussion, since it has apparently > been a cross-purposes — talking about different > languages — from the get-go.
Since we are on the discussion section for "Inexact Numbers" we should really be addressing quantifiers here.
The proposed definition for outer (true) quantifiers is:
PA sumti = PA da poi ke'a me sumti
which makes no reference to gadri. It works generally for all sumti, independently of gadri. All that it requires is that sumti has referents.
The proposed definition for {piPA} outer things is:
piPA sumti = lo piPA si'e be pa lo me sumti
Again this is meant to work generally for any sumti, independently of its form, all that is required is that sumti has referents. This definition does use {lo}, but I don't think this use of {lo} has caused any problems here. All the arguments have been about what counts as a referent of sumti for particular forms of sumti.
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wrote:
> > pc: > > --- Jorge Llambías wrote: > > > {lo'i} is just shorthand for > > > {lo selcmi be lo} = "the set of those that > really are" > > > (that happens to be the definition of > {lo'i} given in > > > the ma'oste). > > > > Sorry I forgot that you are talking about > xorlan, > > with that strange defeinition, not about > Lojban, > > which I was foolishly continuiing to discuss. > > That is hardly a strange definition, as it is a > straight > translation of the English definition in the > ma'oste. > The ma'oste has: > > lo: the one(s) that really is(are)... > lo'i: the set of those that really are...
But notice "the set" singular.
> so the first and most natural stab at a Lojban > definition > of {lo'i} is {lo selcmi be lo}. We can then > argue whether > we want {lo'i} to have additonal more subtle > properties.
Uniqueness is hardly subtle.
> For my part, I don't even see the point of > having {lo'i} > there in the first place, so I'm willing to > consider any > definition. You say {lo selcmi be lo} doesn't > work, but > you have not offered an alternative, nor any > example where > one expression could not be substituted for the > other.
Actually, I have offered a good number in the process of talking about *Lojban,* all of which assumed that {lo'i broda} was singular (a rare thing in Lojban). I am not concerned with how you develop xorlan nor even whether Lojbban becomes xorlan, just with getting a practically workable and coherent system. xorlan may be such, but the evidence so far is not encouraging.
> > > I do think that all > > these changes should be mentioned in your > summary > > of the effects of adopting your various > > proposals, which change virtually all the > > descriptors, and are generally not backward > > compatible unless our only samples are xorlan > > disguised as Lojban over the years. > > My definitions for > la/le'i/la'i/lei/lai/lo'e/le'e are, > as far as I can tell, totally compatible with > CLL. > {loi}/{lo'i} differ in the interpretation of > the inner > quantifier, which is no longer required to be > the > number of all the brodas that exist in the > world.
Thgis has been the general consensus for at least five years, but still needs to be mentioned officially.
A > consequence of that is that {lo'i broda} is no > longer > unique, as it can be any set of brodas and not > necessarily > the unique set of all brodas.
But it is a single set, contrary to your definition.
> {le} differs in the interpretation of the outer > quantifier, > which is no longer taken to always be there. In > practice > this makes very little difference because {le} > was mostly > used with singular referents. (In theory {la} > also would > differ in the same way, but the default outer > quantifier > for {la} was taken even less seriously than the > one > for {le}). Also, the idea of plural reference > was not > explicitly present in CLL, at least not in any > formalized > way. > For the obvious reason (though admittedly not actually used) that plural reference is incompatible with the rest of Lojban, only group/set reference can perform plurality duty.
> {lo} is really the only significant difference, > as I propose > {lo broda} to have referents and CLL simply > defines it > as a quantifier expression. Also the inner > quantifier > interpretation changes as with lo'i/loi. The > definition in > the ma'oste "the one(s) that really is(are)..." > is closer to > the proposed definition than to CLL's.
Which definition is it that has these properties? Neither of the appears to at forty third reading. Notice what an enormous change this is -- from a quantifier expression to something you ca,, a constant (whatever that may be — your explanation in the note does not describe and real thing).
> > End of this discussion, since it has > apparently > > been a cross-purposes — talking about > different > > languages — from the get-go. > > Since we are on the discussion section for > "Inexact Numbers" > we should really be addressing quantifiers > here. > > The proposed definition for outer (true) > quantifiers is: > > PA sumti = PA da poi ke'a me sumti > > which makes no reference to gadri. It works > generally > for all sumti, independently of gadri. All that > it requires is > that sumti has referents.
Well, there is the problem of what {me} means when applied to a single object with several members, but since you have none of those directly in your earlier "definitions" this does not arise.
> > The proposed definition for {piPA} outer things > is: > > piPA sumti = lo piPA si'e be pa lo me > sumti > > Again this is meant to work generally for any > sumti, > independently of its form, all that is required > is that > sumti has referents. This definition does > use {lo}, > but I don't think this use of {lo} has caused > any problems > here. All the arguments have been about what > counts as > a referent of sumti for particular forms of > sumti.
This probably works, even though it is rarely what one needs as far as I can see. The problem with {lo} is, in this case as in others is that it allows several referents when what is wanted is just one unspecified one. That is, I suppose, that there is a {pa} missing somewhere in all of these (I would not dare guess where given how weird all of this seems to me).
pc: > --- Jorge Llambías wrote: > > Since we are on the discussion section for > > "Inexact Numbers" > > we should really be addressing quantifiers > > here. > > > > The proposed definition for outer (true) > > quantifiers is: > > > > PA sumti = PA da poi ke'a me sumti > > > > which makes no reference to gadri. It works > > generally > > for all sumti, independently of gadri. All that > > it requires is > > that sumti has referents. > > Well, there is the problem of what {me} means > when applied to a single object with several > members,
It gets the single object itself. {me} always gets just the referents of the sumti, whether they are things with members, things whose members have members, things whose members' members have members or things without members at all.
> but since you have none of those > directly in your earlier "definitions" this does > not arise.
I do have things with members in my definitions of {loi} and {lo'i}, both gunma and selcmi have members, but {me} with them does not get to their members.
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Re: BPFK Section: Inexact Numbers
Will this work for fractional quantifiers?
piPA sumti == lo piPA si'e be sumti
When a sumti has a single referent (which may be a simple individual, a group, a set, etc.) then a fractional quantifier refers to a corresponding fraction of the referent. In particular, a fraction of a group or a set is a subgroup or subset whose cardinality is the corresponding fraction of the cardinality of the whole.
When a sumti has more than one referent (e.g. le ci plise) then a fractional quantifier refers to a fraction of one (which one is not specified) of the referents. Then {pimu le ci plise} is "half of one of the three apples. Then more generally we can define:
piPA sumti == lo piPA si'e be pa me sumti
which will also cover the case of a single referent.
We may then generalize to things like {repimu le ci plise} for "two and a half of the three apples".
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It seems to me that for ji'i to be useful, it needs to scope to the right; that is "pa ji'i re no no" is 1000 + ji'i re 100s + ji'i no 10s
+ ji'i no 1s
I haven't read your proposal well enough to tell if this is already
the case, but wanted to mention it.
-Robin
> Re: BPFK Section: Inexact Numbers > It seems to me that for ji'i to be useful, it needs to scope to the > right; that is "pa ji'i re no no" is 1000 + ji'i re 100s + ji'i no 10s > + ji'i no 1s > > I haven't read your proposal well enough to tell if this is already > the case, but wanted to mention it.
In my proposal, ji'i does scope to the right, but it cannot appear between the digits of a number.
When two quantifiers with a range operator (su'o, su'e, za'u, me'i, ji'i) appear one next to the other, they indicate a number in the common range. For example:
za'u ci me'i so more than three less than 9
su'o ci su'e so between three and nine
ji'i ci ji'i vo around three or four
When there is no common range, the union of ranges is used instead:
za'u vo me'i vo more than four less than four other than four
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On Fri, Feb 11, 2005 at 11:57:58AM -0800, Jorge Llamb?as wrote: > > --- [email protected] wrote: > > Re: BPFK Section: Inexact Numbers It seems to me that for ji'i > > to be useful, it needs to scope to the right; that is "pa ji'i > > re no no" is 1000 + ji'i re 100s + ji'i no 10s + ji'i no 1s > > > > I haven't read your proposal well enough to tell if this is > > already the case, but wanted to mention it. > > In my proposal, ji'i does scope to the right, but it cannot appear > between the digits of a number.
I consider this a Serious Problem.
> When two quantifiers with a range operator (su'o, su'e, za'u, > me'i, ji'i) appear one next to the other, they indicate a number > in the common range. For example: > > za'u ci me'i so > more than three less than 9 > > su'o ci su'e so > between three and nine > > ji'i ci ji'i vo > around three or four
That's neat and useful, but I consider losing usages like the one I gave a rather drastic price to pay.
-Robin
> On Fri, Feb 11, 2005 at 11:57:58AM -0800, Jorge Llamb?as wrote: > > > > When two quantifiers with a range operator (su'o, su'e, za'u, > > me'i, ji'i) appear one next to the other, they indicate a number > > in the common range. For example: > > > > za'u ci me'i so > > more than three less than 9 > > > > su'o ci su'e so > > between three and nine > > > > ji'i ci ji'i vo > > around three or four > > That's neat and useful, but I consider losing usages like the one I > gave a rather drastic price to pay.
There aren't that many scientific papers published in Lojban yet, and I doubt anything else requires the level of precision that inner number ji'i provides. Even for those cases ji'i is much worse than the more usual convention of +/- uncertainty/error.
Anyway, my proposal is meant for use with quantifiers, and the digit precision convention is more suited for measurements, so there is little chance of conflict there.
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On Fri, Feb 11, 2005 at 01:29:57PM -0800, Jorge Llamb?as wrote: > > That's neat and useful, but I consider losing usages like the > > one I gave a rather drastic price to pay. > > There aren't that many scientific papers published in Lojban yet, > and I doubt anything else requires the level of precision that > inner number ji'i provides.
I want to use constructs like this in English all the time.
> Even for those cases ji'i is much worse than the more usual > convention of +/- uncertainty/error.
I'm not talking about scientific levels of precision here.
> Anyway, my proposal is meant for use with quantifiers, and the > digit precision convention is more suited for measurements, so > there is little chance of conflict there.
If you expect it to be used different ways in different contexts, the proposal should say so.
-Robin
The titel is a bit misleading as it applies at most to the last three cases; the oters are perfectly objective. As often noted, the last three need a place (s0mehow) to talk about purposes (at which point they become less subjective). Once that desideratum is found, we also need a quantifier(?) "so many" for results rather than purposes and [prbably a comparative form, "as many as" (but at least the last of these can be cobbled together fairly naturally out of existing elements). While "too few" is probably the same (as near as makes no never-mind) to "less than enough," "too many" is not the same as "more than enough." "Too many" has negative connotations (at least, there may also be objective bits) while "more than enough" is positive — where "enough" is just barely sqeaking by.
pc: > Re: BPFK Section: Subjective Numbers > The titel is a bit misleading as it applies at most to the last three cases; > the oters are perfectly objective.
Yes. CLL calls some of them "indefinite numbers" and others "inexact numbers". I can't change the title though.
> As often noted, the last three need a place (s0mehow) to talk about purposes > (at which point they become less subjective).
Yes, that might be a new cmavo in NOI. (Or, I wouldn't mind recycling {voi} for this.)
> Once that desideratum is > found, we also need a quantifier(?) "so many" for results rather than > purposes and [prbably a comparative form, "as many as" (but at least the last > of these can be cobbled together fairly naturally out of existing elements).
I wonder if {xokau} plus the new NOI might work for "so many... that". Hmmm... This needs more thinking.
> While "too few" is probably the same (as near as makes no never-mind) to > "less than enough," "too many" is not the same as "more than enough." "Too > many" has negative connotations (at least, there may also be objective bits) > while "more than enough" is positive — where "enough" is just barely > sqeaking by.
I prefer "the right number" as a gloss for {rau}. Then "too few" is "less than the right number" and "too many" is "more than the right number". This means that I'm defining {rau} as bounded both from below and from above: {rau} is more than too few AND less than too many. "Enough" is more properly {su'orau}, "at least the right number". The reason is that this seems to be how the so'V series works too, as well as numbers in general {ci gerku} is exactly three dogs, not at least three dogs. Also, there is an example in CLL, {raumoi} in line, that doesn't really work with "at least the right number", because the right number is clearly bounded from above in that case.
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On Fri, Aug 06, 2004 at 04:16:08PM -0700, Jorge Llamb?as wrote: > pc: > > Re: BPFK Section: Subjective Numbers The titel is a bit misleading > > as it applies at most to the last three cases; the oters are > > perfectly objective. > > Yes. CLL calls some of them "indefinite numbers" and others "inexact > numbers". I can't change the title though.
But I can.
-Robin
> > > Re: BPFK Section: Subjective Numbers The titel is a bit misleading > > > as it applies at most to the last three cases; the oters are > > > perfectly objective. > > > > Yes. CLL calls some of them "indefinite numbers" and others "inexact > > numbers". I can't change the title though. > > But I can.
Something like "quantifiers" might be better. They can be used as other-than-quantifiers too, but that's their main function.
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On the other hand, "quantifier" has an established use that is broader than these case, so maybe sticking with "subjective" or "inexact" or "relative" will do.
Jorge Llambías wrote:
> > > Re: BPFK Section: Subjective Numbers The titel is a bit misleading > > > as it applies at most to the last three cases; the oters are > > > perfectly objective. > > > > Yes. CLL calls some of them "indefinite numbers" and others "inexact > > numbers". I can't change the title though. > > But I can.
Something like "quantifiers" might be better. They can be used as other-than-quantifiers too, but that's their main function.
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Re: BPFK Section: Subjective Numbers The titel is a bit misleading as it applies at most to the last three cases; the oters are perfectly objective. As often noted, the last three need a place (s0mehow) to talk about purposes (at which point they become less subjective). Once that desideratum is found, we also need a quantifier(?) "so many" for results rather than purposes and [prbably a comparative form, "as many as" (but at least the last of these can be cobbled together fairly naturally out of existing elements). While "too few" is probably the same (as near as makes no never-mind) to "less than enough," "too many" is not the same as "more than enough." "Too many" has negative connotations (at least, there may also be objective bits) while "more than enough" is positive — where "enough" is just barely sqeaking by.
The notion of a significant number is a brilliant addition. But "most" ought to be "more than half" (and perhaps in a different section — with "all of" and "some of," say), not just "all but several." These numbers are significantly more subjective than the "subjective" ones. Note that most of these are class-relative: there aren't many tigers but many of the ones there are are in zoos. A (weak) argument for restricted quantification.
pc: > The notion of a significant number is a brilliant addition. But "most" ought > to be "more than half" (and perhaps in a different section — with "all of" > and "some of," say), not just "all but several."
But we can't yank {so'e} out of the so'V series just like that. We can give {so'e} the meaning it inherits as part of the gradiated series and when we really mean literally "most" we can use {za'upimu}, which is not that much longer, and it makes it clear what is meant.
> These numbers are significantly more subjective than the "subjective" ones. > Note that most of these are class-relative:
For example, do you really mean "most" literally there, or will {so'e} as part of the so'V gradation do? I don't think you went to the trouble of counting those that are class relative and compare with the total. And even if you did, your purpose was probably not to say that more than half are class-relative, was it?
> there aren't many tigers but many > of the ones there are are in zoos. A (weak) argument for restricted > quantification.
Yes, I think the fact that they are defined as a gradation between no and ro makes them of the proportional sort of quantifiers.
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