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Bunches
''Isn't it funny how some selbri imply that an event really occurred, while others don't. Like:''


“Bunch” is a cover term for formally treated pluralities.  There are several realizations of this formalism: plural reference and quantification, L(esniewski)-sets, applied C(antor)-sets (with atoms but without the null set), mereological sums.  All of these can be ways for dealing with plurals within the language of logic.  They all share the following theses, which are just listed here, without any attempt to divide them into axioms, theorems and definitions (though some are probably obvious). No claim is made that this list is complete, even as a basis, but it does seem to be consistent (relative to standard set theory – not that that is altogether reassuring).  The notions treated here are “in” – the relation between pluralities and what make them up, “+” – the device for creating new pluralities by combining existing ones, “I” – “is an individual” (a bunch with no further components),  “-F” (and “F-“) – distributive predication (“collective predication,” including personal predication for individuals, is the norm), “F*” – “participates in Fing.”
mi catlu le nu do morsi


a in a (reflexive)
I watch you die (and you really do die, else how could I watch it?)


a in b and b in a => a=b (asymmetric)
mi tolpacna le nu do morsi


a in b and b in c => a in c (transitive)
I don't hope you die (and you probably didn't yet!)


[[jbocre: Aa|Aa]][[jbocre: Eb|Eb]] b in a
''So, watch me ignite a flame war:''


a in b or b in a or [[jbocre: Ec|Ec]](a in c and b in c)
mi tolpacna le nu da'inai do morsi


The one that surely exists is a+b
I don't hope you die (but yet, you do!)


a+a = a
I think that ''da'i'' marks whether the speakers thinks that the events so marked is a likely enough to be considered, but the event may still occur even if it was marked with ''da'i'' (or not occur even though it's marked with ''da'inai'').


a+b = b+a
''Somehow my instincts tell me a jbojbe would not be confused by this. The flame war will start when somebody tries to argue that, since da'inai is in inside nu, it somehow gets nullified. This, however, is valid too:''


a+(b+c) = (a+b)+c
mi catlu le nu da'i do morsi


a in a+b
I watch you allegedly die


b in a+b
''So what's with the phantom da'is in there that I must actively override, sometimes? --[[User:xod|la xod]]''


c in a+b => c = a+b or [[jbocre: Ed|Ed]] a+b = c+d
Some selbri, like djuno and catlu, are inherently factive: the abstractions they talk about have real-world counterparts.  Others, like kucli, are inherently non-factive. This is a fact about the Real World.


c in a+b => c = a+b or c in a or c in b or [[jbocre: Ed|Ed]] a+b = c+d
''Keep in mind that we had a very long flame war over djuno being factive. "know" is factive, but "djuno" is only relative to djuno4.''


a+b = a => b in a
''And are they facts about the real world? Or Englishistic factoids? Why can't I catlu something that never occurred? I could have been mistaken or dreaming. We already showed in a very long flame war that I can djuno a falsehood. --[[User:xod|la xod]]''


a in b => a+c in b+c
* Long, confused, and IMO pointless flamewar between xod and xorxes on the [[factivity of djuno|factivity of djuno]]. Thanks a bunch, guys, for not clarifying anything -- [[User:Nick Nicholas|nitcion]], fuming.


xI <=> [[jbocre: Aa: a in x]] x in a
----


xI <=>[[jbocre: Aa: a in x]] x = a
Perhaps, instead of calling selbri absolutely factive or absolutely not, we should say that we [[glork|glork]] their claims to be factual. If you say ''mi catlu le nu do morsi'', I will normally expect ''do ca morsi''--but not always. If you are standing on stage next to a hypnotist, I may expect that you are deluded (you're making a statement about your beliefs of the moment, but not about the world). Or I may recognize that you are talking about a hypothetical situation, or about the events of a puppet show, relying on the non-veridicality of ''le'' (you're making a statement about some ''munje'', but not about the real world). Or, if you're talking about me and I consider myself alive, I may have no idea why you're saying such a thing, but I'll still consider it false--maybe I would understand you to be saying "how can you be alive, I saw you die!" ''mi'e [[jezrax|jezrax]]''


[[jbocre: Aa|Aa]][[jbocre: Ex: x in a]](a = x or [[jbocre: Eb|Eb]] a = x+b)
* ''I like this. Adherence to reality may compel us to use these words in an predictable manner, but we probably shouldn't import that philosophy into the language, keeping it able to express confusing or nonsensical ideas. --[[User:xod|la xod]]''


(Here we use the convention of taking quantifiers involving x, y , z as being short for quantifiers restricted to individuals, so here [[jbocre: Ex: xI and x in a]].)
----


(Every bunch breaks down completely into individuals and there are is no empty bunch.)
Right. Let's start again, shall we?


[[jbocre: Ex|Ex]] x in a
* Presupposition is a fact. ''lo'' presupposes the existence of its referent, just the same as "The present King of France" does.
* Lojban indubitably has factive predicates. That is part of their definition. e.g. ''snada''


(This follows from the above but says more explicitly that no bunch is empty)
* Factivity means that, where A is the matrix proposition and B the complement, if A is true (in this world) then so is B. So, take the claim ''mi snada lenu mi cikna'' . If ''mi snada'' is true in this world, then ''mi cikna'' must be true in this world. By definition. Else, ''snada'' does not apply.
* This is not compromised by counterfactuals. ''.i da'i mi snada lenu mi cikna'' makes both A and B counterfactual. ''.i da'i mi snada lenu da'inai mi cikna'', however, is a paradox.


The above foundation thesis does not quite say that every bunch breaks down into individuals without remainder, or at best says it for finite bunches only. The following does a bit better:
** It need not be a paradox. If my awakeness is not a result of my trying to stay awake, then it is not a {da'inai se snada}. But it is an odd thing to say anyway. --[[User:xorxes|xorxes]]
* The same holds for ''catlu''. What you see happens: if you ''do'' see, then both A and B are true in this world. If you hallucinated that you saw it, then it wasn't real --- but neither was the seeing. Factivity says that either both ''nu catlu'' and ''se catlu'' are true in this world, or both ''nu catlu'' and ''se catlu'' are counterfactual.


[[jbocre: Ax: x in a]] x in b  => a in b
* xod claims that ''mi catlu le nu da'i do morsi'' is valid. If he means ''mi da'inai catlu le nu da'i do morsi'' is valid (or, better still, ''mi romu'ei catlu le nu do su'omu'ei morsi''), I say he is wrong. That's as much a paradox as saying ''da ge jetnu de gi jitfa de''.
* When verbs aren't factive, they aren't necessarily antifactive either: a verb that does not presuppose its complement may ''still'' have its complement be true. Thus both the following are perfectly acceptable: ''mi tolpacna le nu da'i do morsi''; ''mi tolpacna le nu da'inai do morsi''


Hence
* We are forgetting, however, in our eagerness to have a fight :-| , that all complement clauses in Lojban '''already''' have a presuppositional marker. ''lonu''.
* So if you say ''lo xelso cu djuno lo du'u do pilno lo tutci'', the source for the truth of ''du'u do pilno lo tutci'' is identical to the source for the existence of ''lo xelso''. They are both claimed to exist (to be true) in the prenex. And there ain't no epistemology place in the prenex.


[[jbocre: Ax: x in a]] x in b &amp; [[jbocre: Ay: y in b]] y in a => a = b
* That said, once you've admitted x4 into ''djuno'', I am quite prepared to admit it isn't factive any more. Because factivity ''does'' presume Absolute Truth. Or at least as much Absolute Truth as do prenexes, and ''lo noltaitru be le fasygu'e''. And that's incompatible with relative epistemologies.
* The distinction between ''djuno'' and ''krici'' then does indeed become nebulous. But not unformalisable.


this is essentially the foundation principle for sets and is taken as meaning that a set breaks down completely into its elements, even though we could work up a model in which there were a lot more things in there than the elements. The point is that if there are such other things, they never affect  any claim to be made -- even about the size of the bunch .
* In summary, on the broad picture I probably agree with xod. In all the details of the discussion, I found myself agreeing with xorxes instead. (The business about "if you extensionally would call each of your opinions true, how can you say you know some of your opinions to be false" was quite galling: I didn't expect xod to be so logical positivist. But then, I've had that misunderstanding with xod before.)
* Finally, jezrax's point is true: since the late '70s, linguists' understandin of presupposition has moved from semantic to pragmatic (i.e. glorkable.) But of course, if we're pretending to be a logical language, we're also pretending to hang on to at least some logical machinery.


x in a+b => x in a or x in b
--- mi'e [[User:Nick Nicholas|nitcion]]


a-F <=> [[jbocre: Ax: x in a]] xF 
----


(the “-“ is always on the predicate side, so for a following term, it would be “F-a.” Note: different terms may have F as predicate in different ways: aF-b, a-Fb, a-F-b, and aFb are all possible, even if b = a.)
* Presupposition is a fact. ''lo'' presupposes the existence of its referent, just the same as "The present King of France" does.
** Sorry to butt in, Nick, but did you mean ''le''? Surely you do. --[[User:And Rosta|And Rosta]]


a-F and b in a => b-F
**No, I actually do mean ''lo''. 'Cause it's  veridical.
* Lojban indubitably has factive, i.e. presupposing predicates. That is part of their definition. e.g. ''snada''


[[jbocre: Ea|Ea]] a=x+y
** Indubitably factive. But it is controversial to claim that they are presupposing. --[[User:And Rosta|And Rosta]]
* Logical presupposition means that, where A is the matrix proposition and B the complement, if A is true (in this world) then so is B. So, take the claim ''mi snada lenu mi cikna'' . If ''mi snada'' is true in this world, then ''mi cikna'' must be true in this world. By definition. Else, ''snada'' does not apply.


aF => a-*F
** You are describing factivity, not presupposition. If you negate A, is the sentence still saying (albeit not necessarily 'claiming') that B is true? If Yes, then there is presupposition. If No, then there isn't. The consensus regarding ''djuno'' when last it was debated on Lojban list was that ''djuno'' is factive but not presuppositional. --[[User:And Rosta|And Rosta]]
 
** (You mean, there's ever consensus in those discussions? Then the onus is on you guys to keep writing any such consensuses up.) The early definitions of factivity were in terms of presupposition. Things got more and more muddled through the '70s, but actually, I don't think that's germane to what I'm arguing, which is that ''da'inai'' is built in to some Lojban predicates, and ''da'i'' to others.
(ever member of a collective particpates in what the collective does)
 
(like -, * goes between argument and predicate -- pending a better notation)
 
a<1> <=> [[jbocre: Ex|Ex]] a = x (is a monad)
 
a<n+1> <=> [[jbocre: Eb: b in a]][[jbocre: Ex: x in a]] (b<n>  &amp; ~ x in b &amp; a = b + x)
 
aInf <=>[[jbocre: An|An]] [[jbocre: Eb: b in a]] b<n>

Latest revision as of 10:50, 8 June 2014

Isn't it funny how some selbri imply that an event really occurred, while others don't. Like:

mi catlu le nu do morsi

I watch you die (and you really do die, else how could I watch it?)

mi tolpacna le nu do morsi

I don't hope you die (and you probably didn't yet!)

So, watch me ignite a flame war:

mi tolpacna le nu da'inai do morsi

I don't hope you die (but yet, you do!)

I think that da'i marks whether the speakers thinks that the events so marked is a likely enough to be considered, but the event may still occur even if it was marked with da'i (or not occur even though it's marked with da'inai).

Somehow my instincts tell me a jbojbe would not be confused by this. The flame war will start when somebody tries to argue that, since da'inai is in inside nu, it somehow gets nullified. This, however, is valid too:

mi catlu le nu da'i do morsi

I watch you allegedly die

So what's with the phantom da'is in there that I must actively override, sometimes? --la xod

Some selbri, like djuno and catlu, are inherently factive: the abstractions they talk about have real-world counterparts. Others, like kucli, are inherently non-factive. This is a fact about the Real World.

Keep in mind that we had a very long flame war over djuno being factive. "know" is factive, but "djuno" is only relative to djuno4.

And are they facts about the real world? Or Englishistic factoids? Why can't I catlu something that never occurred? I could have been mistaken or dreaming. We already showed in a very long flame war that I can djuno a falsehood. --la xod

  • Long, confused, and IMO pointless flamewar between xod and xorxes on the factivity of djuno. Thanks a bunch, guys, for not clarifying anything -- nitcion, fuming.

Perhaps, instead of calling selbri absolutely factive or absolutely not, we should say that we glork their claims to be factual. If you say mi catlu le nu do morsi, I will normally expect do ca morsi--but not always. If you are standing on stage next to a hypnotist, I may expect that you are deluded (you're making a statement about your beliefs of the moment, but not about the world). Or I may recognize that you are talking about a hypothetical situation, or about the events of a puppet show, relying on the non-veridicality of le (you're making a statement about some munje, but not about the real world). Or, if you're talking about me and I consider myself alive, I may have no idea why you're saying such a thing, but I'll still consider it false--maybe I would understand you to be saying "how can you be alive, I saw you die!" mi'e jezrax

  • I like this. Adherence to reality may compel us to use these words in an predictable manner, but we probably shouldn't import that philosophy into the language, keeping it able to express confusing or nonsensical ideas. --la xod

Right. Let's start again, shall we?

  • Presupposition is a fact. lo presupposes the existence of its referent, just the same as "The present King of France" does.
  • Lojban indubitably has factive predicates. That is part of their definition. e.g. snada
  • Factivity means that, where A is the matrix proposition and B the complement, if A is true (in this world) then so is B. So, take the claim mi snada lenu mi cikna . If mi snada is true in this world, then mi cikna must be true in this world. By definition. Else, snada does not apply.
  • This is not compromised by counterfactuals. .i da'i mi snada lenu mi cikna makes both A and B counterfactual. .i da'i mi snada lenu da'inai mi cikna, however, is a paradox.
    • It need not be a paradox. If my awakeness is not a result of my trying to stay awake, then it is not a {da'inai se snada}. But it is an odd thing to say anyway. --xorxes
  • The same holds for catlu. What you see happens: if you do see, then both A and B are true in this world. If you hallucinated that you saw it, then it wasn't real --- but neither was the seeing. Factivity says that either both nu catlu and se catlu are true in this world, or both nu catlu and se catlu are counterfactual.
  • xod claims that mi catlu le nu da'i do morsi is valid. If he means mi da'inai catlu le nu da'i do morsi is valid (or, better still, mi romu'ei catlu le nu do su'omu'ei morsi), I say he is wrong. That's as much a paradox as saying da ge jetnu de gi jitfa de.
  • When verbs aren't factive, they aren't necessarily antifactive either: a verb that does not presuppose its complement may still have its complement be true. Thus both the following are perfectly acceptable: mi tolpacna le nu da'i do morsi; mi tolpacna le nu da'inai do morsi
  • We are forgetting, however, in our eagerness to have a fight :-| , that all complement clauses in Lojban already have a presuppositional marker. lonu.
  • So if you say lo xelso cu djuno lo du'u do pilno lo tutci, the source for the truth of du'u do pilno lo tutci is identical to the source for the existence of lo xelso. They are both claimed to exist (to be true) in the prenex. And there ain't no epistemology place in the prenex.
  • That said, once you've admitted x4 into djuno, I am quite prepared to admit it isn't factive any more. Because factivity does presume Absolute Truth. Or at least as much Absolute Truth as do prenexes, and lo noltaitru be le fasygu'e. And that's incompatible with relative epistemologies.
  • The distinction between djuno and krici then does indeed become nebulous. But not unformalisable.
  • In summary, on the broad picture I probably agree with xod. In all the details of the discussion, I found myself agreeing with xorxes instead. (The business about "if you extensionally would call each of your opinions true, how can you say you know some of your opinions to be false" was quite galling: I didn't expect xod to be so logical positivist. But then, I've had that misunderstanding with xod before.)
  • Finally, jezrax's point is true: since the late '70s, linguists' understandin of presupposition has moved from semantic to pragmatic (i.e. glorkable.) But of course, if we're pretending to be a logical language, we're also pretending to hang on to at least some logical machinery.

--- mi'e nitcion


  • Presupposition is a fact. lo presupposes the existence of its referent, just the same as "The present King of France" does.
    • Sorry to butt in, Nick, but did you mean le? Surely you do. --And Rosta
    • No, I actually do mean lo. 'Cause it's veridical.
  • Lojban indubitably has factive, i.e. presupposing predicates. That is part of their definition. e.g. snada
    • Indubitably factive. But it is controversial to claim that they are presupposing. --And Rosta
  • Logical presupposition means that, where A is the matrix proposition and B the complement, if A is true (in this world) then so is B. So, take the claim mi snada lenu mi cikna . If mi snada is true in this world, then mi cikna must be true in this world. By definition. Else, snada does not apply.
    • You are describing factivity, not presupposition. If you negate A, is the sentence still saying (albeit not necessarily 'claiming') that B is true? If Yes, then there is presupposition. If No, then there isn't. The consensus regarding djuno when last it was debated on Lojban list was that djuno is factive but not presuppositional. --And Rosta
    • (You mean, there's ever consensus in those discussions? Then the onus is on you guys to keep writing any such consensuses up.) The early definitions of factivity were in terms of presupposition. Things got more and more muddled through the '70s, but actually, I don't think that's germane to what I'm arguing, which is that da'inai is built in to some Lojban predicates, and da'i to others.