Talk:bunches

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Posted by Anonymous on Mon 28 of Nov., 2005 04:49 GMT

> "-F" (and "F-") – distributive predication ("collective predication," > including personal predication for individuals, is the norm), > "F*" – "participates in Fing."

I suppose you would also need to distinguish "*F" from "F*", "participates in Fing" from "participates in being F-ed".

I think that would be the best way of marking distributivity. Marking it on the sumti is not very convenient because we sometimes want to use the same sumti filling a distributive place for one predicate and a collective one for another, or because it is cnvenient for anaphora to have as antecedent a sumti that is neutral with respect to distributivity.

Unfortunately, in Lojban this way of marking distributivity is complicated, because Lojban predicates don't normally have just two arguments, but they can have any number of arguments. So where does one put the mark?

Perhaps a practical solution would be to put the distributive mark as a selbri-tcita when it corresponds to the x1, and on the corresponding sumti in other cases. This is not the most elegant way of doing it, but because the x1 is the most likely sumti to be shared by more than one selbri, it would at least cover the most cases.

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Posted by pycyn on Mon 28 of Nov., 2005 04:49 GMT posts: 2388

> > "-F" (and "F-") – distributive predication > ("collective predication," > > including personal predication for > individuals, is the norm), > > "F*" – "participates in Fing." > > I suppose you would also need to distinguish > "*F" from "F*", > "participates in Fing" from "participates in > being F-ed".

Good point. If the second place is collective then there must be participation notion there as well. So, like dash, star goes more with the argument than the predicate (though sometimes with the predicate, apparently). Notation needs some work here.

> I think that would be the best way of marking > distributivity. Marking > it on the sumti is not very convenient because > we sometimes want > to use the same sumti filling a distributive > place for one predicate > and a collective one for another, or because it > is convenient for > anaphora to have as antecedent a sumti that is > neutral with respect > to distributivity.

Well, sometimes we also want a predicate taking one argument collectively and the other distributively at the same place. As I said, the notation needs some work here, lathough these are actualy problems for applications, not for the pure system, which lacks non-sentential conjunctions.

> Unfortunately, in Lojban this way of marking > distributivity is complicated, > because Lojban predicates don't normally have > just two arguments, but > they can have any number of arguments. So where > does one put the > mark?

With the argument generally - except in the cases noted. that is, after all how Lojban does it (with {lV} vs. {lVi}. But it lacks devices for the exception (and for the predication internal a description). I want to get the formalism right before I worry too much about any application to Lojban.

> Perhaps a practical solution would be to put > the distributive mark > as a selbri-tcita when it corresponds to the > x1, and on the corresponding > sumti in other cases. This is not the most > elegant way of doing it, but > because the x1 is the most likely sumti to be > shared by more than one > selbri, it would at least cover the most cases.

As noted, Lojban already covers most cases quite well. The remaining ones are going to take some novel device in any case. As far as I can see, some such device is going to be needed whatever happens with this notion (It appears to have to be UI or one of the other few "happen anywhere" groups.)

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Posted by Anonymous on Mon 28 of Nov., 2005 04:49 GMT

On 11/26/05, John E Clifford wrote: > So, like dash, star goes more with the > argument than the predicate (though sometimes > with the predicate, apparently). Notation needs > some work here.

I think one could say that it indicates the *manner* in which an argument fills a place. It is not a property of a sumti when not filling a place nor of a place when not being filled by a sumti.

Another interesting system, similar to bunches but different in one respect, is the system of kinds. Kinds, with the relation "subkind" for "in", share all the same thesis as bunches except for this one: "Every bunch breaks down completely into individuals". For kinds, it is not the case that every kind breaks down completely into ultimate kinds, where an ultimate kind is a kind that has only itself as a subkind, i.e. the equivalent of "individual" for bunches.

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Posted by pycyn on Mon 28 of Nov., 2005 04:49 GMT posts: 2388

> On 11/26/05, John E Clifford > wrote: > > So, like dash, star goes more with the > > argument than the predicate (though sometimes > > with the predicate, apparently). Notation > needs > > some work here. > > I think one could say that it indicates the > *manner* in which > an argument fills a place. It is not a property > of a sumti > when not filling a place nor of a place when > not being filled > by a sumti.

I'm not sure what the practical upshot of this is for either the theory or Lojban but it is essentially correct metaphysically. It seems to suggest the detached (UIish)marker, part of neither component. The fit of theory and Lojban is not very good at present. In Lojban the predication is neutral, with the differentiation being only in the gadri, with {lV} also be neutral except when differntiation is needed, when it becomes distributive just by not being {lVi}. In the thory the basic predication is collective; neutral is achieved by disjunction. But the bunch is the same whether predicated of distributively or collectively.

> Another interesting system, similar to bunches > but different in > one respect, is the system of kinds. Kinds, > with the relation > "subkind" for "in", share all the same thesis > as bunches except > for this one: "Every bunch breaks down > completely into individuals". > For kinds, it is not the case that every kind > breaks down completely > into ultimate kinds, where an ultimate kind is > a kind that has only > itself as a subkind, i.e. the equivalent of > "individual" for bunches.

I'm not sure that it will work out that there are kinds that do not break down into subkinds. The tendency to dichotomize is pretty strong after all. I can't think of a real case, anyhow. Of course, this does require in some cases, taking individuals as infima species (a hallowed practice).

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Posted by Anonymous on Mon 28 of Nov., 2005 04:49 GMT

On 11/27/05, John E Clifford wrote: > I'm not sure that it will work out that there are > kinds that do not break down into subkinds. The > tendency to dichotomize is pretty strong after > all. I can't think of a real case, anyhow.

I was thinking of special abstract things like the number seven. Any kind of seven is seven, at least from some point of view.

More normal kinds can be refined indefinitely: dogs > fat dogs > fat ugly dogs > fat ugly dogs that bark > fat ugly dogs that bark at trees > ...

> Of > course, this does require in some cases, taking > individuals as infima species (a hallowed > practice).

Not sure what that means.

The natural numbers greater than one follow the same rules as bunches, with "+" being the product and "in" being "is a divisor of". Then the primes are the individuals and "every bunch breaks down completely into individuals". Kinds are more like the real numbers.

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Posted by pycyn on Mon 28 of Nov., 2005 04:49 GMT posts: 2388

> On 11/27/05, John E Clifford > wrote: > > I'm not sure that it will work out that there > are > > kinds that do not break down into subkinds. > The > > tendency to dichotomize is pretty strong > after > > all. I can't think of a real case, anyhow. > > I was thinking of special abstract things like > the number seven. > Any kind of seven is seven, at least from some > point > of view.

I don't think I follow this. The number seven is a kind in that there is a natural seven and a rational one and a real one and so on, but that seems to be breaking down in ultimate kinds, pretty much any way you extend the list. And of course anything is some subkind is also a thing of the kind itself. So I have missed the point here.

> More normal kinds can be refined indefinitely: > dogs > fat dogs > fat ugly dogs > fat ugly dogs > that bark > fat > ugly dogs that bark at trees > ...

No, at a certain point you get down to individuals and, although they can be specified in a variety of ways, it is not clear that they are new kinds ("kind" is ambiguous between intensional and extensional versions; I suppose you mean this as inrtensional). In any case, the fact that it can be divide indefinitely only complicates the claim that we always get to the bottom; it does not deny it.

> > Of > > course, this does require in some cases, > taking > > individuals as infima species (a hallowed > > practice). > > Not sure what that means.

At the bottom level, the next lowest kind has only individuals as subkinds, each "one of a kind." But some might object to taking individuals as kinds. In that case the lowest kinds would have no subkinds and so are the sought lowest level into which the kind divides. I gather I am still missing your point.


> The natural numbers greater than one follow the > same rules > as bunches, with "+" being the product and "in" > being "is a divisor of". > Then the primes are the individuals and "every > bunch breaks down > completely into individuals". Kinds are more > like the real numbers.

I do hope this is true, relative consistency proofs using set theory are always a bit chancey. But I still don't get the kinds claim: it would seem that every number is then "in" every other and so there are no individuals. But the bit about every number being in every number tells me that the characterization of kinds is incomplete, for it is not in any sense fitting that every kind should be a subkind of every kind. At least, I don't know of a notion of kinds in which this would happen. Still missing the point?

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Posted by Anonymous on Mon 28 of Nov., 2005 12:31 GMT

On 11/27/05, John E Clifford wrote: > --- Jorge Llambías wrote: > > I was thinking of special abstract things like > > the number seven. > > Any kind of seven is seven, at least from some > > point > > of view. > > I don't think I follow this. The number seven is > a kind in that there is a natural seven and a > rational one and a real one and so on,

That's why I hedged "at least from some point of view". If natural sevens, rational sevens and real sevens are different kinds of sevens, then obviously sevens are not an ultimate kind.

> but that > seems to be breaking down in ultimate kinds, > pretty much any way you extend the list.

I'm not sure that if sevens can differ like that then natural sevens won't in turn be able to differ in some other way, but it doesn't really matter.

> And of > course anything is some subkind is also a thing > of the kind itself. So I have missed the point > here.

The point was that the restriction "every bunch breaks down completely into individuals" for the system of bunches is an independent restriction of all the other thesis listed, it doesn't follow from them but must be imposed. There are systems where it need not hold.

(I said that whereas it may be the case that *some* kinds might break down completely into ultimate kinds, not all kinds do. "Sevens" or "naturals sevens" *might* be an example of ultimate kinds, or perhaps there are no ultimate kinds, depending on your point of view. But whether or not sevens or natural sevens are ultimate kinds, not all kinds break down completely into ultimate kinds.)

> ("kind" is ambiguous between > intensional and extensional versions; I suppose > you mean this as inrtensional).

Yes.

> In any case, the > fact that it can be divide indefinitely only > complicates the claim that we always get to the > bottom; it does not deny it.

You can impose it as an additional condition, but it does not follow from the rest of the thesis.

> At the bottom level, the next lowest kind has > only individuals as subkinds, each "one of a > kind."

That is, if you assume there is a bottom level.

> But some might object to taking > individuals as kinds. In that case the lowest > kinds would have no subkinds and so are the > sought lowest level into which the kind divides. > I gather I am still missing your point.

My point is that you need not assume a bottom level.

> > The natural numbers greater than one follow the > > same rules > > as bunches, with "+" being the product and "in" > > being "is a divisor of". > > Then the primes are the individuals and "every > > bunch breaks down > > completely into individuals". Kinds are more > > like the real numbers. > > I do hope this is true, relative consistency > proofs using set theory are always a bit chancey. > But I still don't get the kinds claim: it would > seem that every number is then "in" every other > and so there are no individuals.

Well, I was keeping the "greater than one" restriction, so every number is "in" every number greater than or equal to itself. And indeed this is an example where there are no individuals, there is no bottom level.

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Posted by pycyn on Mon 28 of Nov., 2005 19:38 GMT posts: 2388

> On 11/27/05, John E Clifford > wrote: > > --- Jorge Llambías > wrote: > > > I was thinking of special abstract things > like > > > the number seven. > > > Any kind of seven is seven, at least from > some > > > point > > > of view. > > > > I don't think I follow this. The number seven > is > > a kind in that there is a natural seven and a > > rational one and a real one and so on, > > That's why I hedged "at least from some point > of view". > If natural sevens, rational sevens and real > sevens are > different kinds of sevens, then obviously > sevens are not > an ultimate kind.

But natural sevens, real sevens, and rational sevens might be.

> > but that > > seems to be breaking down in ultimate kinds, > > pretty much any way you extend the list. > > I'm not sure that if sevens can differ like > that then > natural sevens won't in turn be able to differ > in some other > way, but it doesn't really matter. > > > And of > > course anything is some subkind is also a > thing > > of the kind itself. So I have missed the > point > > here. > > The point was that the restriction "every bunch > breaks down > completely into individuals" for the system of > bunches is an > independent restriction of all the other thesis > listed, it doesn't > follow from them but must be imposed. There are > systems > where it need not hold.

Ahah! Yes, I think that that is true, though I don't think your remarks prove it. And ordinary system of intensional kinds might work for this however, either a poset or some sort of nexus (where a memger could fall under two or more members which are not directly related) and then the possibility of infinitely subdividing would keep generating new sets. But that might also mean that the set of individuals was infinite, not empty. It doesn't quite work yet.

> > > In any case, the > > fact that it can be divide indefinitely only > > complicates the claim that we always get to > the > > bottom; it does not deny it. > > You can impose it as an additional condition, > but it does > not follow from the rest of the thesis.

Well, of course, that is something one wants of one's axioms (which I suppose this must be then): that they are independent of other axioms. I hope that turns out to be true for all of them (if I ever get around to sorting out the theses into various types.

> > At the bottom level, the next lowest kind has > > only individuals as subkinds, each "one of a > > kind." > > That is, if you assume there is a bottom level.

Well, it turns out I was taking extensional kinds as my model and that does make a difference. The bottom level is more obviously the case here -- though I think it always is for anything that really might be called a kinds. I await a contrary case, but won't be either surprised or dismayed if one turns up, since my interest is not in kinds (about whivh I haven't given much thought) but about bunches, which I think I am close to defining.

> > But some might object to taking > > individuals as kinds. In that case the lowest > > kinds would have no subkinds and so are the > > sought lowest level into which the kind > divides. > > I gather I am still missing your point. > > My point is that you need not assume a bottom > level. > > > > The natural numbers greater than one follow > the > > > same rules > > > as bunches, with "+" being the product and > "in" > > > being "is a divisor of". > > > Then the primes are the individuals and > "every > > > bunch breaks down > > > completely into individuals".

Well, it turns out they aren't. The model disconfirms a+a=a at least.

>>> Kinds are > more > > > like the real numbers. > > > > I do hope this is true, relative consistency > > proofs using set theory are always a bit > chancey.

But alas this does not help in that matter.

> > But I still don't get the kinds claim: it > would > > seem that every number is then "in" every > other > > and so there are no individuals. > > Well, I was keeping the "greater than one" > restriction,

What restriction is that? We are looking only at real numbers (strictly?) greater than 1. But that does in no way take away from the fact that every one divides every one. I suppose you mean that the quotient in such a division has to be greater than one (or, apparently, one or greater) This will get an ordering and, of course, since there are no least real greater than 1 (I think this needs "strictly greater") there are no individuals, but the result is not very plausibly called a system of kinds, I don't think. >so > every number is "in" every number greater than > or equal to > itself. And indeed this is an example where > there are no > individuals, there is no bottom level.

But also no idempotence (is that the word I want? a+a=a) and probably not asymmetry: a in b & b in a => a=b, as this will dramatically reduce the number of kinds (and, indeed, give individuals). So it is still not the proof of independence that is wanted.

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Posted by Anonymous on Mon 28 of Nov., 2005 23:26 GMT

On 11/28/05, John E Clifford wrote: > --- Jorge Llambías wrote: > > The point was that the restriction "every bunch > > breaks down > > completely into individuals" for the system of > > bunches is an > > independent restriction of all the other thesis > > listed, it doesn't > > follow from them but must be imposed. There are > > systems > > where it need not hold. > > Ahah! Yes, I think that that is true, though I > don't think your remarks prove it.

Well, I guess you would first need to present it as a fomal thesis before a formal proof that it is not a theorem could be given.

> > > > The natural numbers greater than one follow > > the > > > > same rules > > > > as bunches, with "+" being the product and > > "in" > > > > being "is a divisor of". > > > > Then the primes are the individuals and > > "every > > > > bunch breaks down > > > > completely into individuals". > > Well, it turns out they aren't. The model > disconfirms a+a=a at least.

Hmm, right. To have that property, take all the powers of a prime

as equivalent, and 2
n*3
m = 2*3, etc.


For the case with no individuals you can take for example the open sets on the real line, with union as "+".

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Posted by pycyn on Tue 29 of Nov., 2005 00:09 GMT posts: 2388

> On 11/28/05, John E Clifford > wrote: > > --- Jorge Llambías > wrote: > > > The point was that the restriction "every > bunch > > > breaks down > > > completely into individuals" for the system > of > > > bunches is an > > > independent restriction of all the other > thesis > > > listed, it doesn't > > > follow from them but must be imposed. There > are > > > systems > > > where it need not hold. > > > > Ahah! Yes, I think that that is true, though > I > > don't think your remarks prove it. > > Well, I guess you would first need to present > it as a fomal > thesis before a formal proof that it is not a > theorem could > be given.

My point is that the system presented differs from mine in more than the one axiom and so can't prove independence of that axiom.

> > > > > The natural numbers greater than one > follow > > > the > > > > > same rules > > > > > as bunches, with "+" being the product > and > > > "in" > > > > > being "is a divisor of". > > > > > Then the primes are the individuals and > > > "every > > > > > bunch breaks down > > > > > completely into individuals". > > > > Well, it turns out they aren't. The model > > disconfirms a+a=a at least. > > Hmm, right. To have that property, take all the > powers of a prime

> as equivalent, and 2
n*3
m = 2*3, etc.


But your countercase is about the reals; what would be the corresponding move there?

> For the case with no individuals you can take > for example > the open sets on the real line, with union as > "+".

Nice; that does look to give a case that fits all the theses so far developed except the foundation one and what follows from it. But it still has nothing to do with bunches which are conceptually exactly founded in the way stated: a bunch is a bunch of things and when you get down to the things that is the end of the process (actually a step before, since in some versions unit bunches are the singleton of the thing, not the thing itself — but the thing is a member, not in in the relevant sense, which tends to be like inclusion in these versions). Can you think if a Lojbanically relevant use for kinds, those unfounded critters?

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Posted by Anonymous on Tue 29 of Nov., 2005 00:17 GMT

On 11/28/05, John E Clifford wrote: > --- Jorge Llambías wrote: > > For the case with no individuals you can take > > for example > > the open sets on the real line, with union as > > "+". > > Nice; that does look to give a case that fits all > the theses so far developed except the foundation > one and what follows from it. But it still has > nothing to do with bunches which are conceptually > exactly founded in the way stated: a bunch is a > bunch of things and when you get down to the > things that is the end of the process (actually a > step before, since in some versions unit bunches > are the singleton of the thing, not the thing > itself — but the thing is a member, not in in > the relevant sense, which tends to be like > inclusion in these versions).

That's clear, yes.

Can you think if a > Lojbanically relevant use for kinds, those > unfounded critters?

Certainly. (Intensional) kinds for example. Stages of individuals would be another.

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Posted by pycyn on Wed 30 of Nov., 2005 00:34 GMT posts: 2388

> On 11/28/05, John E Clifford > wrote:

> > Can you think if a > > Lojbanically relevant use for kinds, those > > unfounded critters? > > Certainly. (Intensional) kinds for example. > Stages of individuals > would be another.

1. I don't see anything bpeculiarly or immediately Lojbanic in these but it would be intersting to see something along that line.

2. Neither kinds nor stages of individuals seems to me to be like the real line in the relevant ways. Kinds have infima species, complete analytic heceities — individual concepts — in one direction, and complete state descriptions in the other, both of which become contradictory if further modified (of course, you may want to allow contradictory kinds, but even those have lower bounds). These are, of course, infinitely complex and so unlikely to be of much use, but the theory does allow them (indeed, I suspect that their existence can be proven in a usual formal system). As for stages, that will only work if time is really continuous, but it seems that it is discrete (or is that discreet?) though -- calculus being what it is — taking it as continuous is usally a nice shortcut.

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Posted by Anonymous on Wed 30 of Nov., 2005 13:53 GMT

On 11/29/05, John E Clifford wrote: > 2. Neither kinds nor stages of individuals seems > to me to be like the real line in the relevant > ways.

It depends on what you take to be *the* relevant ways, I suppose. In the only way I claimed them to be alike is in their satisfying all of the listed thesis except for the one about breaking down completely into individuals.

... > As for stages, that will only > work if time is really continuous, but it seems > that it is discrete (or is that discreet?) though > — calculus being what it is — taking it as > continuous is usally a nice shortcut.

Yes. Whether or not time is really continuous is not important from the language point of view. All that matters is that it can be taken as continuous. Lojban certainly supports this view, implicit for example in the word {ru'i}.

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Posted by pycyn on Wed 30 of Nov., 2005 14:48 GMT posts: 2388

> On 11/29/05, John E Clifford > wrote: > > 2. Neither kinds nor stages of individuals > seems > > to me to be like the real line in the > relevant > > ways. > > It depends on what you take to be *the* > relevant ways, I suppose. > In the only way I claimed them to be alike is > in their satisfying > all of the listed thesis except for the one > about breaking down > completely into individuals.

Cases?

> ... > > As for stages, that will only > > work if time is really continuous, but it > seems > > that it is discrete (or is that discreet?) > though > > — calculus being what it is — taking it as > > continuous is usally a nice shortcut. > > Yes. Whether or not time is really continuous > is not > important from the language point of view. All > that > matters is that it can be taken as continuous. > Lojban > certainly supports this view, implicit for > example in the > word {ru'i}.

Well, {ru'i} doesn't seem to have anything to do with the cntinuum; it merely means "without significant interruption" "whenever there is an occasion" even.

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Posted by Anonymous on Wed 30 of Nov., 2005 15:04 GMT

On 11/30/05, John E Clifford wrote: > --- Jorge Llambías wrote: > > > On 11/29/05, John E Clifford > > wrote: > > > 2. Neither kinds nor stages of individuals > > seems > > > to me to be like the real line in the > > relevant > > > ways. > > > > It depends on what you take to be *the* > > relevant ways, I suppose. > > In the only way I claimed them to be alike is > > in their satisfying > > all of the listed thesis except for the one > > about breaking down > > completely into individuals. > > Cases?

Cases of what?

> Well, {ru'i} doesn't seem to have anything to do > with the cntinuum; it merely means "without > significant interruption" "whenever there is an > occasion" even.

So you take time to be *linguistically* discrete? Interesting.

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Posted by pycyn on Wed 30 of Nov., 2005 17:03 GMT posts: 2388

> On 11/30/05, John E Clifford > wrote: > > --- Jorge Llambías > wrote: > > > > > On 11/29/05, John E Clifford > > > wrote: > > > > 2. Neither kinds nor stages of > individuals > > > seems > > > > to me to be like the real line in the > > > relevant > > > > ways. > > > > > > It depends on what you take to be *the* > > > relevant ways, I suppose. > > > In the only way I claimed them to be alike > is > > > in their satisfying > > > all of the listed thesis except for the one > > > about breaking down > > > completely into individuals. > > > > Cases? > > Cases of what?

Things we might really use that satisfy all the theses not tied with foundation. > > > Well, {ru'i} doesn't seem to have anything to > do > > with the continuum; it merely means "without > > significant interruption" "whenever there is > an > > occasion" even. > > So you take time to be *linguistically* > discrete? Interesting.

Well, I didn't say so; I just made a comment about {ru'i}, which seems to me to say nothing about the nature of time. But, so far as I can tell, Lojban at least (but I think English too) treats time as discrete in most situations -- other than certain kinds of scientific talk, perhaps.

temci tem tei time x1 is the time-duration/interval/period/elapsed time from time/event x2 to time/event x3

It comes in chunks.

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Posted by Anonymous on Thu 01 of Dec., 2005 01:26 GMT

On 11/30/05, John E Clifford wrote: > --- Jorge Llambías wrote: > > On 11/30/05, John E Clifford > > wrote: > > > --- Jorge Llambías > > wrote: > > > > > > > On 11/29/05, John E Clifford > > > > wrote: > > > > > 2. Neither kinds nor stages of > > individuals > > > > seems > > > > > to me to be like the real line in the > > > > relevant > > > > > ways. > > > > > > > > It depends on what you take to be *the* > > > > relevant ways, I suppose. > > > > In the only way I claimed them to be alike > > is > > > > in their satisfying > > > > all of the listed thesis except for the one > > > > about breaking down > > > > completely into individuals. > > > > > > Cases? > > > > Cases of what? > > Things we might really use that satisfy all the > theses not tied with foundation.

Dogs, unicorns, events of running, theories, lies, all kinds of things.


> > > Well, {ru'i} doesn't seem to have anything to > > do > > > with the continuum; it merely means "without > > > significant interruption" "whenever there is > > an > > > occasion" even. > > > > So you take time to be *linguistically* > > discrete? Interesting. > > Well, I didn't say so; I just made a comment > about {ru'i}, which seems to me to say nothing > about the nature of time.

Oh, I agree. It only says something about how time is dealt with linguistically, not about its nature.

> But, so far as I can > tell, Lojban at least (but I think English too) > treats time as discrete in most situations -- > other than certain kinds of scientific talk, > perhaps.

So when you ask how long something took, you expect some number of indivisible chunks as an answer?

> temci tem tei time x1 is the > time-duration/interval/period/elapsed time from > time/event x2 to time/event x3 > > It comes in chunks.

I always thought x1 of temci was a continuous interval rather than a (very large?) number of (very small?) chunks.

If you mean that the x1 is one chunk, then the system of time chunks seems to satisfy all the theses not tied with foundation.

mu'o mi'e xorxes

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Posted by pycyn on Thu 01 of Dec., 2005 16:55 GMT posts: 2388

> On 11/30/05, John E Clifford > wrote: > > --- Jorge Llambías > wrote: > > > On 11/30/05, John E Clifford > > > wrote: > > > > --- Jorge Llambías > > > wrote: > > > > > > > > > On 11/29/05, John E Clifford > > > > > wrote: > > > > > > 2. Neither kinds nor stages of > > > individuals > > > > > seems > > > > > > to me to be like the real line in the > > > > > relevant > > > > > > ways. > > > > > > > > > > It depends on what you take to be *the* > > > > > relevant ways, I suppose. > > > > > In the only way I claimed them to be > alike > > > is > > > > > in their satisfying > > > > > all of the listed thesis except for the > one > > > > > about breaking down > > > > > completely into individuals. > > > > > > > > Cases? > > > > > > Cases of what? > > > > Things we might really use that satisfy all > the > > theses not tied with foundation. > > Dogs, unicorns, events of running, theories, > lies, all kinds of things. > I'm not sure whether you, the at least occasional champion of contextual relevance, have here brought in some totally irrelevant set of theses or whether you have some (unnamed) relation and operator for each of these sets that satisfies all the theses for "in" and "+" on the Bunches page, except those that rest on the foundation thesis. I can't think what those relations and operators might be: the obvious ones for dogs and and lies - packs — and for unicorns — herds -- all seem to be founded, that is, get down eventually to individual dogs or lies or unicorns (lies may not be order-irrelevant, that is may fail symmetry).

> > > > Well, {ru'i} doesn't seem to have > anything to > > > do > > > > with the continuum; it merely means > "without > > > > significant interruption" "whenever there > is > > > an > > > > occasion" even. > > > > > > So you take time to be *linguistically* > > > discrete? Interesting. > > > > Well, I didn't say so; I just made a comment > > about {ru'i}, which seems to me to say > nothing > > about the nature of time. > > Oh, I agree. It only says something about how > time > is dealt with linguistically, not about its > nature.

Nothing even linguistically. And if it did, it would say that time is not even dense, let alone analogous to the real line, since ti says that there is nothing between two occurrences of the event called continuous. As for other linguistic evidence, we note that we have concepts like "next," {lamji} which clearly apply to time and suggest a well-ordering, not even a dense one again.

> > But, so far as I can > > tell, Lojban at least (but I think English > too) > > treats time as discrete in most situations -- > > other than certain kinds of scientific talk, > > perhaps. > > So when you ask how long something took, you > expect > some number of indivisible chunks as an answer?

Yup — and that is what I get: a day, a second, 3.5 nanoseconds, and so on. Always with a unit (by definition in Lojban's case) and always with a discrete total. I suppose it is conceivable that someone say "root 2 seconds" but I would take that to be some sort of scientific talk, since I don't see how he would have measured it.

> > temci tem tei time > x1 is the > > time-duration/interval/period/elapsed time > from > > time/event x2 to time/event x3 > > > > It comes in chunks. > > I always thought x1 of temci was a continuous > interval > rather than a (very large?) number of (very > small?) chunks.

That is about what it is scientifically, perhaps, but not linguistically, where the answer is always in terms of (variously sized) chunks.

> If you mean that the x1 is one chunk, then the > system of > time chunks seems to satisfy all the theses not > tied with > foundation.

Well, the system of sizes of time chunks is probably dense (not a continuum. since the lower bound is outside the system, not being an interval). But on any given occasion the answer is linguistically in terms of some unit. Scientifically, this may be an approximation, but we were after the linguistic facts here, not the scientific.

I am not quite sure how we got off on this intersting but so far rather useless discussion (nor do I care). So, back to the point: any additional theses that seemed to be required for bunches? Any surprising consequences of these theses — particularly ones that show the set inconsistent? Independence proofs for anything other than the foundation thesis?

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Posted by Anonymous on Thu 01 of Dec., 2005 20:35 GMT

On 12/1/05, John E Clifford wrote: > --- Jorge Llambías wrote: > > On 11/30/05, John E Clifford wrote: > > > Things we might really use that satisfy all the > > > theses not tied with foundation. > > > > Dogs, unicorns, events of running, theories, > > lies, all kinds of things. > > > I'm not sure whether you, the at least occasional > champion of contextual relevance, have here > brought in some totally irrelevant set of theses

No, just the ones you have listed.

> or whether you have some (unnamed) relation and > operator for each of these sets that satisfies > all the theses for "in" and "+" on the Bunches > page, except those that rest on the foundation > thesis.

No, not any unnamed relation, just the "subkind" relation I named the first time I mentioned kinds.

> > > > > Well, {ru'i} doesn't seem to have anything to do > > > > > with the continuum; it merely means "without > > > > > significant interruption" "whenever there is an > > > > > occasion" even. > > Nothing even linguistically. And if it did, it > would say that time is not even dense, let alone > analogous to the real line, since ti says that > there is nothing between two occurrences of the > event called continuous.

Why two occurrences? It says something about the one event being continuous.

> As for other linguistic > evidence, we note that we have concepts like > "next," {lamji} which clearly apply to time and > suggest a well-ordering, not even a dense one > again.

I don't and never disputed that we often treat time discretely. { roi} is the clearest example in Lojban for that, I think. The question at hand is whether or not we sometimes treat it as if it were continuous (independently of its true physical nature.)


> > So when you ask how long something took, you > > expect > > some number of indivisible chunks as an answer? > > Yup — and that is what I get: a day, a second, > 3.5 nanoseconds, and so on.

You take 3.5 nanoseconds as counting half-nanoseconds? Otherwise, if nanoseconds are treated as indefinitely divisible, it sounds as a continuous measure.

And in Lojban it is even more clear, because a duration is {lo navysnidu be li 3.5} and not {3.5 navysnidu}

> Always with a unit > (by definition in Lojban's case) and always with > a discrete total. I suppose it is conceivable > that someone say "root 2 seconds" but I would > take that to be some sort of scientific talk, > since I don't see how he would have measured it.

You take the fact that we don't normally use irrational numbers as measures as evidence that we consider things to be discretely (and finitely) divisible? Very interesting point of view, even if hard to understand.

> > I always thought x1 of temci was a continuous > > interval > > rather than a (very large?) number of (very > > small?) chunks. > > That is about what it is scientifically, perhaps, > but not linguistically, where the answer is > always in terms of (variously sized) chunks.

No, I'm not talking about it scientifically, I mean in ordinary contexts. I cannot normally conceive of durations as strings of little time-chunks. It never occurred to me that others would think of that as the natural point of view.

> > If you mean that the x1 is one chunk, then the > > system of > > time chunks seems to satisfy all the theses not > > tied with > > foundation. > > Well, the system of sizes of time chunks is > probably dense (not a continuum. since the lower > bound is outside the system, not being an > interval). But on any given occasion the answer > is linguistically in terms of some unit. > Scientifically, this may be an approximation, but > we were after the linguistic facts here, not the > scientific.

There are many units that measure continuous quantities, so I don't see how the answer being in terms of a unit makes it a bunch measure. Especially if you allow fractional measures!

> I am not quite sure how we got off on this > intersting but so far rather useless discussion > (nor do I care). So, back to the point: any > additional theses that seemed to be required for > bunches?

It would be nice to have the foundation theses expressed formally. I'm not quite sure how that would go.

> Any surprising consequences of these > theses — particularly ones that show the set > inconsistent?

I can't see anything strange in them.

> Independence proofs for anything > other than the foundation thesis?

None of the others seem especially noteworthy to me. The "no empty bunches" is slightly ambiguous. What does "empty" mean? I take it it does not mean that every bunch has at least one bunch in it because that follows directly from every bunch being in itself, so I suppose it means that for every bunch there is at least one *individual* bunch in it. I would say this thesis goes closely together with the foundation one (and it is in fact stated in the same parenthetical comment).

mu'o mi'e xorxes

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Posted by pycyn on Fri 02 of Dec., 2005 05:25 GMT posts: 2388

> On 12/1/05, John E Clifford > wrote: > > --- Jorge Llambías > wrote: > > > On 11/30/05, John E Clifford > wrote: > > > > Things we might really use that satisfy > all the > > > > theses not tied with foundation. > > > > > > Dogs, unicorns, events of running, > theories, > > > lies, all kinds of things. > > > > > I'm not sure whether you, the at least > occasional > > champion of contextual relevance, have here > > brought in some totally irrelevant set of > theses > > No, just the ones you have listed. > > > or whether you have some (unnamed) relation > and > > operator for each of these sets that > satisfies > > all the theses for "in" and "+" on the > Bunches > > page, except those that rest on the > foundation > > thesis. > > No, not any unnamed relation, just the > "subkind" relation > I named the first time I mentioned kinds.

But that is 1) not obviously unfounded and 2) not not obviously connect with the various things you mentioned. They are all kinds, I suppose, and have various subkinds. But they are also just the sorts of things where the subkind relation is founded on individuals (I am not sure there are subkinds that are not so founded, outside of mathematics perhaps).

> > > > > > Well, {ru'i} doesn't seem to have > anything to do > > > > > > with the continuum; it merely means > "without > > > > > > significant interruption" "whenever > there is an > > > > > > occasion" even. > > > > Nothing even linguistically. And if it did, > it > > would say that time is not even dense, let > alone > > analogous to the real line, since ti says > that > > there is nothing between two occurrences of > the > > event called continuous. > > Why two occurrences? It says something about > the one event > being continuous.

Yes, but you want to make it say something about the continuum and that takes looking at pairs of things (between any two there is another, every pair of sets contains at least one bound, and so on).

> > As for other linguistic > > evidence, we note that we have concepts like > > "next," {lamji} which clearly apply to time > and > > suggest a well-ordering, not even a dense one > > again. > > I don't and never disputed that we often treat > time discretely. > { roi} is the clearest example in > Lojban for that, > I think. The question at hand is whether or not > we sometimes > treat it as if it were continuous > (independently of its true > physical nature.)

Well, that is not the apparent question you raised at the beginning, but of course we do treat it that way sometimes when we are doing scientific things. But I doubt that there is a use of {temci} or other temporal words outside of specialized contexts that is clearly taking time as continuous. We tend to measure time and that gets us into units and definite fractions of units. At best we take time as continuous when we think about a thing called "time" rather than what is happening.

> > > So when you ask how long something took, > you > > > expect > > > some number of indivisible chunks as an > answer? > > > > Yup — and that is what I get: a day, a > second, > > 3.5 nanoseconds, and so on. > > You take 3.5 nanoseconds as counting > half-nanoseconds? > Otherwise, if nanoseconds are treated as > indefinitely divisible, > it sounds as a continuous measure.

But they are not indefinitely divided. In any given case, we stop with fixed fractions of units. We could, of course, take a more precise fraction of that unit, but that process cannot go on indefinitely except in theory. That is, in theory time is continuous in the mathematical sense, but in ordinary language we treat it as discrete, varying the units involved as is convenient. And it was the latter issue that you began by raising.

> And in Lojban it is even more clear, because a > duration is > {lo navysnidu be li 3.5} and not {3.5 > navysnidu}

Now, that is an interesting point (there was bound to be one eventually). Lojban doesn't have units, only measure functions which give raw numbers. But would we ever say "its duration in seconds is root 2" as we can say that its length in inches is? If we can say it (outside of examples), what does it mean?

> > Always with a unit > > (by definition in Lojban's case) and always > with > > a discrete total. I suppose it is > conceivable > > that someone say "root 2 seconds" but I would > > take that to be some sort of scientific talk, > > since I don't see how he would have measured > it. > > You take the fact that we don't normally use > irrational > numbers as measures as evidence that we > consider > things to be discretely (and finitely) > divisible? Very > interesting point of view, even if hard to > understand.

We don't even take advantage of the putative infinite divisibility of time intervals in the way we do of space, for example. And, of course (in both cases) scientific work, when striving for accuracy, always gets down to units that are not further divisible.

> > > I always thought x1 of temci was a > continuous > > > interval > > > rather than a (very large?) number of (very > > > small?) chunks. > > > > That is about what it is scientifically, > perhaps, > > but not linguistically, where the answer is > > always in terms of (variously sized) chunks. > > No, I'm not talking about it scientifically, I > mean in ordinary > contexts. I cannot normally conceive of > durations as strings > of little time-chunks. It never occurred to me > that others > would think of that as the natural point of > view.

I am just going — as I took you to be wanting -- on the linguistic evidence. How you conceive it may well be influenced by all sorts of things, but your speech always comes out in chunks, like the dictionary says. > > > > If you mean that the x1 is one chunk, then > the > > > system of > > > time chunks seems to satisfy all the theses > not > > > tied with > > > foundation. > > > > Well, the system of sizes of time chunks is > > probably dense (not a continuum. since the > lower > > bound is outside the system, not being an > > interval). But on any given occasion the > answer > > is linguistically in terms of some unit. > > Scientifically, this may be an approximation, > but > > we were after the linguistic facts here, not > the > > scientific. > > There are many units that measure continuous > quantities, > so I don't see how the answer being in terms of > a unit > makes it a bunch measure. Especially if you > allow fractional > measures!

The point is that you don't use all that continuity stuff; you just use finitely divided units (thus giving rise to smaller units: deci, centi and so on). Now, there may be no theoretical end to how much smaller the units are, but we don't pursue that in language; we take a convenient unit and stick with it (for a sentence or so at least).

> > I am not quite sure how we got off on this > > interesting but so far rather useless > discussion > > (nor do I care). So, back to the point: any > > additional theses that seemed to be required > for > > bunches? > > It would be nice to have the foundation theses > expressed formally. > I'm not quite sure how that would go.

How much more formal do you want than that every bunch breaks down without remainder (or loss) into individuals? I even wrote it out in quasi-formal language and will — when I get a symbolism I am comfortable with — do it again in that formalism. What is obscure here?

> > Any surprising consequences of these > > theses — particularly ones that show the set > > inconsistent? > > I can't see anything strange in them. > > > Independence proofs for anything > > other than the foundation thesis? > > None of the others seem especially noteworthy > to me. > The "no empty bunches" is slightly ambiguous. > What does > "empty" mean? I take it it does not mean that > every bunch > has at least one bunch in it because that > follows directly > from every bunch being in itself, so I suppose > it means that > for every bunch there is at least one > *individual* bunch in it. > I would say this thesis goes closely together > with the > foundation one (and it is in fact stated in the > same parenthetical comment).

Yes, that sounds about right. Didn't I say that. It follows from foundation but could be listed separately if I didn't before.

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45px|xodPosted by xod on Fri 02 of Dec., 2005 05:35 GMT posts: 143

Jorge Llambías wrote:

>On 12/1/05, John E Clifford wrote: > > >>--- Jorge Llambías wrote: >> >> >> >>>I always thought x1 of temci was a continuous >>>interval >>>rather than a (very large?) number of (very >>>small?) chunks. >>> >>> >>That is about what it is scientifically, perhaps, >>but not linguistically, where the answer is >>always in terms of (variously sized) chunks. >> >> > >No, I'm not talking about it scientifically, I mean in ordinary >contexts. I cannot normally conceive of durations as strings >of little time-chunks. It never occurred to me that others >would think of that as the natural point of view. > >

It's not. That we generally refer to non-zero intervals of time does not mean that we treat it as discrete. Those interval endpoints can be situated anywhere in the timeline, and that means we treat it as continuous. Furthermore, people refer to instants and moments which have no duration, like a point in space has no size. A pixel, however, does have size. And there is no analogous time-pixel in English.


-- username=admin password=21232f297a57a5a743894a0e4a801fc3

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Posted by Anonymous on Fri 02 of Dec., 2005 14:38 GMT

On 12/1/05, John E Clifford wrote: > --- Jorge Llambías wrote: > > > No, not any unnamed relation, just the > > "subkind" relation > > I named the first time I mentioned kinds. > > But that is 1) not obviously unfounded and 2) not > not obviously connect with the various things you > mentioned. They are all kinds, I suppose, and > have various subkinds. But they are also just > the sorts of things where the subkind relation is > founded on individuals

It's becoming hard for me to tell what the argument is about here. My claim is that kinds satisfy all the theses listed except the foundation one, because for the most part kinds always have proper subkinds.

The individual dog "Fido", for example, would not normally be taken as a kind of dog. If someone asks "What kind of dog do you have?", answering "Fido" would be odd.

Whether or not we use individuals in order to form our conception of kinds is, it seems to me, a separate issue. Even if it were true in all cases (which seems doubtful), it does not follow that a system of kinds must include the foundation thesis.

> But I doubt that there is a > use of {temci} or other temporal words outside of > specialized contexts that is clearly taking time > as continuous. We tend to measure time and that > gets us into units and definite fractions of > units. At best we take time as continuous when we > think about a thing called "time" rather than > what is happening.

I can only report that I think of the flow of events as something continuous. Even when watching a movie for example, even _knowing_ that what I'm seeing is really a discrete sequence of images, I can't help but seeing it as something continuous.

> But would we ever say "its duration in > seconds is root 2" as we can say that its length > in inches is? If we can say it (outside of > examples), what does it mean?

I don't think one would normally say that the length of something in inches is root 2. I don't see much difference in the way we measure lengths and durations.

> We don't even take advantage of the putative > infinite divisibility of time intervals in the > way we do of space, for example.

I see no significant difference in the way we treat space and time. In fact cross metaphores are very prevalent.


> > It would be nice to have the foundation theses > > expressed formally. > > I'm not quite sure how that would go. > > How much more formal do you want than that every > bunch breaks down without remainder (or loss) > into individuals? I even wrote it out in > quasi-formal language and will — when I get a > symbolism I am comfortable with — do it again in > that formalism. What is obscure here?

It's not exactly obscure, I can intuitively understand pretty well what it means. But I see nothing close to a formalization (of that particular thesis) yet.

xod wrote: > That we generally refer to non-zero intervals of time does not > mean that we treat it as discrete. Those interval endpoints can be > situated anywhere in the timeline, and that means we treat it as > continuous.

I agree.

> Furthermore, people refer to instants and moments which have > no duration, like a point in space has no size. A pixel, however, does > have size. And there is no analogous time-pixel in English.

I think "moments" are sometimes thought of as having duration ("wait a moment" for example) and sometimes as points. dictionary.com has:

1. A brief, indefinite interval of time. 2. A specific point in time, especially the present time: He is not here at the moment.

mu'o mi'e xorxes

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Posted by Anonymous on Fri 02 of Dec., 2005 15:56 GMT

Jorge Llambías scripsit:

> I don't think one would normally say that the length > of something in inches is root 2. I don't see much > difference in the way we measure lengths and > durations.

The trouble is that "length" is polymorphic; we speak of the measured length of a physical object (which is a rational interval, like "10 cm +/- 5%") as well as the calculated or stipulated length of a mathematical object (which is a single real number). Duration is not treated symmetrically: we do not talk of the duration of a mathematical object, so all durations are measured values.

-- I marvel at the creature: so secret and John Cowan so sly as he is, to come sporting in the pool [email protected] before our very window. Does he think that http://www.reutershealth.com Men sleep without watch all night? --Faramir http://www.ccil.org/~cowan

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Posted by Anonymous on Fri 02 of Dec., 2005 16:43 GMT

On 12/2/05, John.Cowan wrote: > The trouble is that "length" is polymorphic; we speak of the measured > length of a physical object (which is a rational interval, like > "10 cm +/- 5%") as well as the calculated or stipulated length of a > mathematical object (which is a single real number). Duration is not > treated symmetrically: we do not talk of the duration of a mathematical > object, so all durations are measured values.

I agree that when we measure an object, whether in space or time, we obtain as a result a rational number, with some explicit or implicit error. But I don't think this means that we conceive of the object as consisting of a discrete aggregate of unit objects in whatever scale we are using. I'm pretty sure I don't anyway.

As for abstractions, it's true that Euclidean space is more familiar than Minkowski spacetime, and time is not treated symmetrically with space in important ways, but as far as continuity goes, I don't really see a difference.

mu'o mi'e xorxes

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Posted by pycyn on Fri 02 of Dec., 2005 17:30 GMT posts: 2388

> On 12/1/05, John E Clifford > wrote: > > --- Jorge Llambías > wrote: > > > > > No, not any unnamed relation, just the > > > "subkind" relation > > > I named the first time I mentioned kinds. > > > > But that is 1) not obviously unfounded and 2) > not > > not obviously connect with the various things > you > > mentioned. They are all kinds, I suppose, > and > > have various subkinds. But they are also > just > > the sorts of things where the subkind > relation is > > founded on individuals > > It's becoming hard for me to tell what the > argument is > about here. My claim is that kinds satisfy all > the theses > listed except the foundation one, because for > the most > part kinds always have proper subkinds. > > The individual dog "Fido", for example, would > not normally > be taken as a kind of dog. If someone asks > "What kind of > dog do you have?", answering "Fido" would be > odd. > > Whether or not we use individuals in order to > form our > conception of kinds is, it seems to me, a > separate issue. > Even if it were true in all cases (which seems > doubtful), it > does not follow that a system of kinds must > include > the foundation thesis.

Well, the way I would do kinds — as collocations of properties, the foundation thesis is, I think, derivable, since there comes a point when all the properties are dealt with one way or the other and those kinds cannot have subkinds other than themselves. But you may do kinds differently and that may well give different results. Or you may exclude transcendental kinds, which takes an anti-foundation axiom, I think. I said that some people did not like individuals as infima species and took you as saying you were not one of those; I stand corrected.

In any case, this argument is otiose: the issue was whether ther was a useful system that did not have the foundation thesis but otherwise was like bunches and we have that, thank you, in union of real line segments (well, I am not sure about useful, but it is surely good enough for the purpose at hand: showing that tha thesis is indepndent of the others).

> > But I doubt that there is a > > use of {temci} or other temporal words > outside of > > specialized contexts that is clearly taking > time > > as continuous. We tend to measure time and > that > > gets us into units and definite fractions of > > units. At best we take time as continuous > when we > > think about a thing called "time" rather than > > what is happening. > > I can only report that I think of the flow of > events as > something continuous. Even when watching a > movie > for example, even _knowing_ that what I'm > seeing is really > a discrete sequence of images, I can't help but > seeing > it as something continuous.

But the issue is not how you think of the flow of events (loading the issue) or what you say in English or anything other than what is the linguistic nature of time in Lojban. And the answer seems to be that time is always in measurable intervals each immediately preceded and immediately followed by another interval. These intervals may be measured to any desired degree of precision, that is a measure function in terms of some unit may take a rational number with any desired sized denominator (not reals because you cannot measure irrationals nor even compute them in one dimension). So, the systems for measuring times are dense, but what they measure are discrete. All of which is again largely irrelevant. I did not claim that time was discrete or even that Lojban treats time as discrete — that was attributed to me by xorxes to cover his misreading of a Lojban word. However, as you see, the claim that Lojban treats time as discrete can be carried quite a ways. Whether it is far enough to give a definitive answe, I am not sure. And, as I have said before, I don't really care, since nothing seems to hang on the answer at the moment.

> > But would we ever say "its duration in > > seconds is root 2" as we can say that its > length > > in inches is? If we can say it (outside of > > examples), what does it mean? > > I don't think one would normally say that the > length > of something in inches is root 2. I don't see > much > difference in the way we measure lengths and > durations.

Well the length of a diagonal of a unit square is root 2. That one comes up a lot.

> > We don't even take advantage of the putative > > infinite divisibility of time intervals in > the > > way we do of space, for example. > > I see no significant difference in the way we > treat space > and time. In fact cross metaphores are very > prevalent.

They are in English and that habit has been built into Lojban, so I suppose that we havce to say that Lojban treats them the same. But, of course, Lojban taks space as coming in discrete chunks, measured rationally (although in two or more dimension you can compute irrationals so they can come in as well). > > > > It would be nice to have the foundation > theses > > > expressed formally. > > > I'm not quite sure how that would go. > > > > How much more formal do you want than that > every > > bunch breaks down without remainder (or loss) > > into individuals? I even wrote it out in > > quasi-formal language and will — when I get > a > > symbolism I am comfortable with — do it > again in > > that formalism. What is obscure here? > > It's not exactly obscure, I can intuitively > understand > pretty well what it means. But I see nothing > close to > a formalization (of that particular thesis) > yet.

As you are fond of saying in similar situations, what exactly do you want? I hope that, as I do, you will give a fairly precise answer.

I gather that the point is that there is no thesis that says directly "Every bunch breaks down without remainder into individuals" although (for finite bunches only, admittedly)the foundation thesis (what I am calling ...) does amount to that by induction. But even that presupposes something to induce on and the symbolism does not yet have that — the depth (or cardinality) of a bunch. As noted, we could go over to the corresponding sets and work it out there but it would be nicer not to have to use that apparatus. I have a few variant systems which look promising for getting this point across (and, if worse comes to worst, I can always check out the various systems that batches represent to see how they do it.)

> xod wrote: > > That we generally refer to non-zero intervals > of time does not > > mean that we treat it as discrete. Those > interval endpoints can be > > situated anywhere in the timeline, and that > means we treat it as > > continuous. > > I agree. No, by defintion thend points are always immediately adjacent to another event — the previous and the next. There is no timeline on which they are laid out; the timeline is in Lojban (if it can be done at all) an abstraction from sequences of intervals — the rest is not in the language but in what is said in the language.

> > Furthermore, people refer to instants and > moments which have > > no duration, like a point in space has no > size. A pixel, however, does > > have size. And there is no analogous > time-pixel in English. > > I think "moments" are sometimes thought of as > having duration > ("wait a moment" for example) and sometimes as > points. > dictionary.com has: > > 1. A brief, indefinite interval of time. > 2. A specific point in time, especially the > present time: He is not > here at the moment.

In any case, that ia bout English, not Lojban. There are no time points in Lojban, only intervals of time.

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Posted by pycyn on Fri 02 of Dec., 2005 18:57 GMT posts: 2388

wrote:

> --- Jorge Llambías > wrote:

> > > > > > It would be nice to have the foundation > > theses > > > > expressed formally. > > > > I'm not quite sure how that would go. > > > > > > How much more formal do you want than that > > every > > > bunch breaks down without remainder (or > loss) > > > into individuals? I even wrote it out in > > > quasi-formal language and will — when I > get > > a > > > symbolism I am comfortable with — do it > > again in > > > that formalism. What is obscure here? > > > > It's not exactly obscure, I can intuitively > > understand > > pretty well what it means. But I see nothing >

> close to > a formalization (of that particular thesis) > yet.

<situations, what exactly do you want? I hope that, as I do, you will give a fairly precise answer.

I gather that the point is that there is no thesis that says directly "Every bunch breaks down without remainder into individuals" although (for finite bunches only, admittedly)the foundation thesis (what I am calling ...) does amount to that by induction. But even that presupposes something to induce on and the symbolism does not yet have that — the depth (or cardinality) of a bunch. As noted, we could go over to the corresponding sets and work it out there but it would be nicer not to have to use that apparatus. I have a few variant systems which look promising for getting this point across (and, if worse comes to worst, I can always check out the various systems that batches represent to see how they do it.)>>

And there is at a very simple level [ax:x in a Ax:x in a] x in b => a in b whence [ax: x in a Ax: x in a]x in b & [ay: y in b Ay: y in b] y in a => a = b

This still may not be totally explicit, but it does say that all that counts are individuals (if there are other things they are wholly determined by the indivuals and we have no other things offered so far. I suppose we could have an array of functions, one for each number such that, for a bunch with n individual members, fn of those members is also a member (and indeed, to really work, fi for each i membered subunch). The functions don't need ever make a difference but they would mean that technically bunches don't decompose into individuals without remainder - not even the bunches called individuals, apparently. It may be, of course, that what I called foundations prevents that, since if we take one individual out (even with its f1) what remains would not be a bunch in these terms since it would contain fns for subunches which are no longer in it. Is that enough?

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Posted by Anonymous on Fri 02 of Dec., 2005 18:59 GMT

On 12/2/05, John E Clifford wrote: > Well, the way I would do kinds — as collocations > of properties, the foundation thesis is, I think, > derivable, since there comes a point when all the > properties are dealt with one way or the other

Do you presuppose that only a finite number of properties are available? Otherwise, why would there come a point when all the properties are dealt with?


> But the issue is not how you think of the flow of > events (loading the issue) or what you say in > English or anything other than what is the > linguistic nature of time in Lojban.

Originally the issue was whether or not stages of individuals constituted an example of a system without the foundation thesis.

Even reducing the issue to the linguistic nature of time in Lojban, I am not at all convinced that Lojban treats time differently than other languages. In my view, Lojban does not impose a particular conception of discrete or continuous time on its speakers. Both views would seem to be available and represented.


> However, as you > see, the claim that Lojban treats time as > discrete can be carried quite a ways. Whether it > is far enough to give a definitive answe, I am > not sure. And, as I have said before, I don't > really care, since nothing seems to hang on the > answer at the moment.

Nothing seems to hang on the answer, true. (Except, perhaps, the issue of whether stages of individuals constitute an example of a system without the foundation thesis, but we already have other examples anyway.)


> > But I see nothing close to > > a formalization (of that particular thesis) yet. > > As you are fond of saying in similar situations, > what exactly do you want? I hope that, as I do, > you will give a fairly precise answer.

I don't require anything, really. All I said was that it would be nice to see that thesis expressed in formal terms, like all the others in the page, in terms of "in" and "+" and not in terms of undefined (though intuitively clear) things like "breaks down completely". But I certainly won't be accusing you of not making sense if such a formal statement turns out to be difficult or for whatever reason inconvenient.

> > xod wrote: > > > That we generally refer to non-zero intervals > > of time does not > > > mean that we treat it as discrete. Those > > interval endpoints can be > > > situated anywhere in the timeline, and that > > means we treat it as > > > continuous. > > > > I agree. > No, by defintion thend points are always > immediately adjacent to another event — the > previous and the next. There is no timeline on > which they are laid out; the timeline is in > Lojban (if it can be done at all) an abstraction > from sequences of intervals — the rest is not in > the language but in what is said in the language.

Couldn't {ze'e} be pretty much a representation of the timeline?

> > 1. A brief, indefinite interval of time. > > 2. A specific point in time, especially the > > present time: He is not here at the moment. > > In any case, that ia bout English, not Lojban. > There are no time points in Lojban, only > intervals of time.

What about {mokca}:

mokca moc point ; 'moment' x1 is a point/instant/moment 0-dimensional shape/form in/on/at time/place x2 x1 is dimensionless; (cf. jipno, jganu, linji, stuzi, tcika)

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Posted by Anonymous on Fri 02 of Dec., 2005 19:34 GMT

On 12/2/05, John E Clifford wrote: > And there is at a very simple level > [ax:x in a Ax:x in a] x in b => a in b > whence > [ax: x in a Ax: x in a]x in b & [ay: y in b Ay: y in b] y in a => a = b > > This still may not be totally explicit, but it > does say that all that counts are individuals (if > there are other things they are wholly determined > by the indivuals and we have no other things > offered so far.

That, together with Ex x in a, would seem to do it, as far as I can tell.

Now all that remains is sorting out the axioms from the theorems. :-)

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Posted by pycyn on Fri 02 of Dec., 2005 21:26 GMT posts: 2388

> On 12/2/05, John E Clifford > wrote: > > Well, the way I would do kinds — as > collocations > > of properties, the foundation thesis is, I > think, > > derivable, since there comes a point when all > the > > properties are dealt with one way or the > other > > Do you presuppose that only a finite number of > properties > are available? Otherwise, why would there come > a point > when all the properties are dealt with? Not finite, but I do assume that all kinds are in the system. So, "point" may be a bad choice of words, since the point comes with the system already.

> > But the issue is not how you think of the > flow of > > events (loading the issue) or what you say in > > English or anything other than what is the > > linguistic nature of time in Lojban. > > Originally the issue was whether or not stages > of > individuals constituted an example of a system > without the foundation thesis.

True but that somehow led to this muck about time in Lojban, whose formulation I think I have correctly.

> Even reducing the issue to the linguistic > nature of time > in Lojban, I am not at all convinced that > Lojban treats > time differently than other languages. In my > view, > Lojban does not impose a particular conception > of discrete or continuous time on its speakers. > Both > views would seem to be available and > represented. Then, the issue was ill-formed. That is, if there is no one way that Lojban treats time, there is no one way that Lojban views time. I am not sure I agree with the first part of this, but that doesn't really matter. We can, to be sure, do allsorts of things with languages that don't deal with things that way — process philosophy in English, a static metaphysical language, for example )Buddhism in Sanskrit is even worse)-- so the fact that we can talk about time as a continuum or as series doesn't tell us what it is in the language.

> > However, as you > > see, the claim that Lojban treats time as > > discrete can be carried quite a ways. > Whether it > > is far enough to give a definitive answer, I > am > > not sure. And, as I have said before, I > don't > > really care, since nothing seems to hang on > the > > answer at the moment. > > Nothing seems to hang on the answer, true. > (Except, > perhaps, the issue of whether stages of > individuals > constitute an example of a system without the > foundation > thesis, but we already have other examples > anyway.) > > > > > But I see nothing close to > > > a formalization (of that particular thesis) > yet. > > > > As you are fond of saying in similar > situations, > > what exactly do you want? I hope that, as I > do, > > you will give a fairly precise answer. > > I don't require anything, really. All I said > was that it would > be nice to see that thesis expressed in formal > terms, like > all the others in the page, in terms of "in" > and "+" and not > in terms of undefined (though intuitively > clear) things like > "breaks down completely". But I certainly won't > be accusing > you of not making sense if such a formal > statement turns > out to be difficult or for whatever reason > inconvenient.

But the foundation thesis is in terms of "+" and "in." In what way is it defective? Any thing other than that it applies only to finite cases?

> > > xod wrote: > > > > That we generally refer to non-zero > intervals > > > of time does not > > > > mean that we treat it as discrete. Those > > > interval endpoints can be > > > > situated anywhere in the timeline, and > that > > > means we treat it as > > > > continuous. > > > > > > I agree. > > No, by definition the end points are always > > immediately adjacent to another event — the > > previous and the next. There is no timeline > on > > which they are laid out; the timeline is in > > Lojban (if it can be done at all) an > abstraction > > from sequences of intervals — the rest is > not in > > the language but in what is said in the > language. > > Couldn't {ze'e} be pretty much a representation > of the > timeline? Well, unqualified it would seem to apply to events that take up all of time, but that doesn't give a time *line,* just an all-inclusive interval (a slight misnomer, obviously).

> > > 1. A brief, indefinite interval of time. > > > 2. A specific point in time, especially the > > > present time: He is not here at the moment. > > > > In any case, that is about English, not > Lojban. > > There are no time points in Lojban, only > > intervals of time. > > What about {mokca}: > > mokca moc point ; 'moment' > x1 is a point/instant/moment [http://www.lojban.org/tiki/0-dimensional%3Cbr%20/%3E%3E%20shape/form 0-dimensional > shape/form] > in/on/at time/place x2 > x1 is dimensionless; (cf. jipno, jganu, > linji, stuzi, tcika)

Well, that seems to be a spatial term extended by analogy to time, once we get the idea that there is an analogy to use. It does not jibe with {temci}, which is the authoritative word aon time, I suppose.

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Posted by Anonymous on Sat 03 of Dec., 2005 15:37 GMT

On 12/2/05, John E Clifford wrote: > We can, to be sure, > do allsorts of things with languages that don't > deal with things that way — process philosophy > in English, a static metaphysical language, for > example )Buddhism in Sanskrit is even worse)-- so > the fact that we can talk about time as a > continuum or as series doesn't tell us what it is > in the language.

That assumes that there is something that it is in the language. I see no evidence for this underlying picture of time that Lojban is supposed to support, but maybe I haven't looked in the right places.

mokca > Well, that seems to be a spatial term extended by > analogy to time, once we get the idea that there > is an analogy to use. It does not jibe with > {temci}, which is the authoritative word aon > time, I suppose.

I don't see any reason to suppose {temci} to be more authoritative than {mokca}. Is it because it uses "time" as its keyword?

In any case, I don't see that either {temci} or {mokca} would favour a continuous or discrete view of time, since both are compatible with both. In a continuous timeline, there is no problem in having continuous intevals between intervals, or in having points within the intervals. In a discrete view, there is no problem in the constituents being points and the intervals between two other intervals consisting of a finite number of points. I wouldn't even hesitate a mokca in using mokca for a quantum of time with some very brief finite duration despite the double insistence in the definition for 0-dimension.

If the language had some underlying preference for one of the views, I would look for it in the closed class of structure words, not in the open class of brivla. It is trivial to introduce brivla with meanings such as "x1 is a discrete quantum of time" or "x1 is a continuous stretch of time", or whatever one prefers, and the language is practically left untouched by having those words.

Now, if we examine the tense words (I suppose that's the most obvious place to look for a bias in the language with respect to this) I can't find a single one of them that would favour one view or the other.

ca, pu, ba only address the ordering of events, but both discrete and continuous intervals can be ordered.

zi, za, zu, ze'i, ze'a, ze'u give lengths of intervals. I have an easier time in thinking of lengths as continuous, but again they can be thought of as a relatively small/large number of discrete constituents too, so this is not decisive.

ru'i, di'i, ta'e say how an event covers an interval, but the interval again can be thought of as a continuous stretch or as a chain of little chunks. Similarly for roi.

So, if there is an underlying view favoured by the language, where or how is it expressed?

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