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Re: [lojban] {zo'e} as close-scope existentially quantified plural variable
I'm not too clear on what you thought I was proposing, though it must not be too far from what I have in mind. I am not sure that Hans' paper will help you much, for, while I taken over some things from him in terms of dynamic domains and alternate domains, I have developed somewhat differently, as Lojban seems to require.
Particular quantification is the old term for existential quantification, with the advantage that it does not appear to claim more than something is in the domain, in particular, does not appear to claim it is the extension of "exist" {zasti}.
Sorry about the mumble there; I am just never sure which procedure works best: a supply of things that turn up in different guises in each world or a different set of things for each world, somehow sometimes linked between worlds. Neither is perfect, but each has it's uses. (Hindu v. Buddhist, as so many things are).
Sent from my iPad
On Oct 21, 2011, at 15:00, Martin Bays <mbays@sdf.org> wrote:
> * Friday, 2011-10-21 at 08:46 -0700 - John E Clifford <kali9putra@yahoo.com>:
>
>> If you want to say that flying dodos look silly, then your domain of discourse
>> (at least in Lojban) contains flying dodos. {lo} expressions always imply the
>> particular quantification on their defining predication. Not that such things
>> need exist, of course (part of the reason I use "particular" rather than
>> "existential" for that quantifier)
> What's particular quantification? I'm not familiar with the term.
>
>> It is not clear that this is a different approach to tense and
>> intensions, though it may be a different approach to domains of
>> discourse (looking at Kamp again).
>
> Discourse representation theory? Should I just read about that if I want
> to understand you? I think I do have Kamp's paper on my harddrive.
>
>> The properties these nonexistent things may have probably derive from
>> the ones they have in worlds where they exist (not necessarily the
>> same things, mind you, but the things at the other end of some sort of
>> projection)
>
> Not really with you here.
>
> Well, it seems that I didn't understand correctly your solution. I don't
> see much wrong with the solution I understood you as proposing... but
> I'm happy to have multiple working solutions before having to pick one!
>
> Martin
>
>> ----- Original Message ----
>> From: Martin Bays <mbays@sdf.org>
>> To: lojban@googlegroups.com
>> Sent: Fri, October 21, 2011 9:16:20 AM
>> Subject: Re: [lojban] {zo'e} as close-scope existentially quantified plural
>> variable
>>
>> * Friday, 2011-10-21 at 05:51 -0400 - John E. Clifford <kali9putra@yahoo.com>:
>>
>>> I think there may be other possibilities. For example, {lo broda} may
>>> return a bunch, all of the subbunches in a partition of which broda in
>>> sense i.
>>
>> OK, we can call that sense (is).
>>
>> ('s' being the roman numeral for 1/2, apparently)
>>
>>> So, the glorked (whence this word btw) have to be unicorns in
>>> some world. Why not in this one?
>>
>> Because there aren't any unicorns in it.
>>
>> How about if it had been "flying dodos look silly"? Would you want the
>> flying dodos to be in this present world (by which I mean: to ca ca'a
>> vofli je cipnrdodo)?
>>
>>> That is my intention; otherwise I have a mess of problems about cross-
>>> worlds identity and the meaning of predication (which, partly,
>>> I suppose, is why you want to add {ka'e}).
>>
>> I don't see how you can coherently get around this mess.
>>
>>> Now, depending on the context, {lo pavelseljirna cu lazni} may or may
>>> not take us to a world where unicorns exist, but the point is that it
>>> does not have to; we can and do fold nonexistent unicorns -- items in
>>> the extension of {pavelsejirna} -- into our current domain of
>>> discourse, which depends on what we say, not on the facts.
>>
>> It seems you have some very different setup for handling tenses and
>> intension than the one I've been assuming - in which there might well be
>> entities in the domain of discourse which satisfy pavyseljirna_w for
>> some worlds w, but they won't satisfy pavyseljirna_{w_0} for this world
>> w_0, because no unicorns currently exist.
>>
>> Could you explain your setup? I don't see what it could be.
>>
>> Martin
>>
>>> On Oct 20, 2011, at 20:10, Martin Bays <mbays@sdf.org> wrote:
>>>
>>>> * Thursday, 2011-10-20 at 12:26 -0400 - John E. Clifford
>>> <kali9putra@yahoo.com>:
>>>>
>>>>> Now I am mor con used than before. Why is there only one bunch off
>>>>> people living in glass houses and why must they all exist at one time
>>>>> / in one world, and why can't they? I am unclear what restrictions
>>>>> you are placing on worlds an domains. I am also unclear as to what
>>>>> you think the logical form of "People who live in glass houses should
>>>>> install proper insulation" is.
>>>>
>>>> Hmm. Probably I'm making some assumption which you're not, leading to
>>>> confusion. But I'm not sure what that assumption might be. So let me
>>>> just express again the issue in different words:
>>>>
>>>> Ignoring all the more subtle issues we've been discussing, there are two
>>>> basic possible bunch-theoretic meanings for {lo}. When applied to
>>>> a unary predicate P, it either
>>>> (i) returns a bunch X such that P(X)
>>>> or (ii) returns a bunch X such that for every atom x below X, P(x).
>>>>
>>>> ("atom x below X" could also be written "individual x in the bunch X";
>>>> I'll continue to use the 'atom' terminology because I think it best
>>>> indicates that individuals aren't disjoint from bunches - individuals
>>>> are just "singleton" bunches. I'll use the notation "x <= X" to mean
>>>> that x is an atom below X (so lower case variables are "singular
>>>> variables", i.e. are variables on the atoms sort))
>>>>
>>>> If we write {lo pavyseljirna cu lazni} to mean "unicorns are lazy"
>>>> (which I believe is true - who ever heard of a pack-unicorn or
>>>> a unicorn-plough?), the unary predicate in question is probably
>>>> (slightly) more precisely expressed by {ka'e pavyseljirna}, and is:
>>>>
>>>> U(X) <=> "there exists a world w such that pavyseljirna(X) in w".
>>>>
>>>> Under (i) we get:
>>>>
>>>> {lo pavyseljirna cu lazni}
>>>> -> GL X:U(X). lazni(X)
>>>> == "for a glorked bunch X such that U(X) holds, lazni(X) holds"
>>>>
>>>> whereas under (ii) we get:
>>>>
>>>> {lo pavyseljirna cu lazni}
>>>> -> GL X:(FA x <= X. U(x)). lazni(X)
>>>> == "for a glorked bunch X such that U(x) holds for every atom
>>>> x below X, lazni(X) holds" .
>>>>
>>>> Substituting in the definition of U and using distributivity, under (i) we
>>> get:
>>>>
>>>> GL X:(EX w. pavyseljirna_w(X)). lazni(X)
>>>> == GL X:(EX w. FA x <= X. pavyseljirna_w(x)). lazni(X)
>>>> == "for a glorked bunch X such that for some world every atom below
>>>> X is a unicorn, X is lazy"
>>>>
>>>> while under (ii) we get:
>>>>
>>>> GL X:(FA x <= X. EX w. pavyseljirna_w(x)). lazni(X)
>>>> == "for a glorked X such that for every atom below X there is
>>>> a world in which it is a unicorn, X is lazy" .
>>>>
>>>> So the (ii) case is the one we want, if we want to get at the sense of
>>>> the english "unicorns are lazy".
>>>>
>>>> Did that make any more sense?
>>>>
>>>> Martin
>>>>
>>>>> On Oct 19, 2011, at 22:41, Martin Bays <mbays@sdf.org> wrote:
>>>>>
>>>>>> * Wednesday, 2011-10-19 at 19:11 -0700 - John E Clifford
>>> <kali9putra@yahoo.com>:
>>>>>>
>>>>>>> U\I'm not going to worry about {loi} etc. until I am sutre about {lo} and
>>> then
>>>
>>>>>>> see what is lefyt over that needs dealing with. {lo cipnrdodo) refers
>>>>>>> to all the dodos there ever were (suppose that is right for this
>>>>>>> context), all of which are thus in the domain of discourse and also in
>>>>>>> the extension of {cipnrdodo}. What problem are you having; I just
>>>>>>> don't see it?
>>>>>>
>>>>>> Hmm. So you'd want every dodo which ever lived to now cipnrdodo - even
>>>>>> if it doesn't zasti, nevermind jmive?
>>>>>>
>>>>>> That might work for some cases, but what if we want to say "people in
>>>>>> glass houses should install proper insulation"? Even if the people in
>>>>>> question (who mostly don't zasti in this possible world, nevermind now)
>>>>>> were to ca ca'a prenu, they surely couldn't ca ca'a nenri su'o blaci
>>>>>> zdani; nor is there any other world in which they all do.
>>>>>>
>>>>>> So the bunch of them doesn't satisfy {prenu gi'e nenri su'o blaci
>>>>>> zdani} - since there's only one bunch, we would need that the bunch
>>>>>> satisfies this in some given world. It doesn't.
>>>>>>
>>>>>> But each atom (person, in this case) in the bunch does satisfy {prenu
>>>>>> gi'e nenri su'o blaci zdani}. So for {lo prenu poi nenri su'o blaci
>>>>>> zdani} to get the bunch, we'd need the quantifier over worlds to go
>>>>>> inside a quantifier over the bunch. The gadri seems the right place
>>>>>> to specify this.
>>>>>>
>>>>>> Martin
>>>>>>
>>>>>>> ----- Original Message ----
>>>>>>> From: Martin Bays <mbays@sdf.org>
>>>>>>> To: lojban@googlegroups.com
>>>>>>> Sent: Wed, October 19, 2011 1:44:49 PM
>>>>>>> Subject: Re: [lojban] {zo'e} as close-scope existentially quantified
>>> plural
>>>
>>>>>>> variable
>>>>>>>
>>>>>>> * Tuesday, 2011-10-18 at 01:44 -0400 - Martin Bays <mbays@sdf.org>:
>>>>>>>
>>>>>>>> * Tuesday, 2011-10-18 at 00:47 -0400 - Martin Bays <mbays@sdf.org>:
>>>>>>>>
>>>>>>>>> * Monday, 2011-10-17 at 19:46 -0700 - John E Clifford
>>>>>>> <kali9putra@yahoo.com>:
>>>>>>>>>> ----- Original Message ----
>>>>>>>>>> From: Martin Bays <mbays@sdf.org>
>>>>>>>>>>> Maybe I finally understand what you mean with your "kinds = maximal
>>>>>>>>>>> bunches" idea. Let's see.
>>>>>>>>>>>
>>>>>>>>>>> I've been implicitly assuming that in {lo broda}, the tense inside
>> the
>>>>>>>>>>> description is by default copied from outside it. So {mi ca ca'a
>> nelci
>>>>>>>>>>> lo pavyseljirna} == {mi ca ca'a nelci lo ca ca'a pavyseljirna}, which
>>> is
>>>>>>>>>>> false if there are no unicorns.
>>>>>>>>>>
>>>>>>>>>> I suppose the tense (if there is one) is as contextual as everything
>>> else
>>>
>>>>>>>> about
>>>>>>>>
>>>>>>>>>> descriptions. The same as the bridi surely is a good guess in general,
>>> but
>>>
>>>>>>>> may
>>>>>>>>
>>>>>>>>>> be obviously wrong in other circumstances. For example, in
>>> generalities,
>>>
>>>>>>>> the
>>>>>>>>
>>>>>>>>>> tense (if that is the right notion) is probably past, present, future
>>> and
>>>
>>>>>>>>>> possible.
>>>>>>>>>
>>>>>>>>> Right, so I think I do understand you.
>>>>>>>>>
>>>>>>>>> Does this work?
>>>>>>>>
>>>>>>>> But there's something of a problem: if the plural referent of {lo broda}
>>>>>>>> is meant to satisfy broda, what tense can give us e.g. all dodos ever?
>>>>>>>> The plural referent of {lo pu cipnrdodo} must satisfy {pu cipnrdodo},
>>>>>>>> i.e. must have satisfied {cipnrdodo} at some point in the past. But that
>>>>>>>> means we're picking up some dodos all of which existed at the same time.
>>>>>>>>
>>>>>>>> So it seems we'd have to have the rule be that {ro lo broda cu broda},
>>>>>>>> rather than {lo broda cu broda}, for this to work.
>>>>>>>
>>>>>>> ...and then it might make sense to have {loi broda} be the same as {lo},
>>>>>>> except that the plural referent is required to broda (rather than the
>>>>>>> atoms below it brodaing). So while {lo pu cipnrdodo} could get the bunch
>>>>>>> (aka plurality) of all dodos ever, {loi pu cipnrdodo} would have to get
>>>>>>> a bunch all of which cipnrdodod at the same past time (which might imply
>>>>>>> that they were all alive at the same time, or if dead at least not too
>>>>>>> far decomposed...).
>>>>>>>
>>>>>>> So this contains some of the essence of the historical meaning of {loi},
>>>>>>> and is usefully distinct from (the understanding under discussion of)
>>>>>>> {lo}.
>>>>>>>
>>>>>>> Martin
>>>>>>>
>>>>>>> --
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>>>>>
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