[hist-analytic] UG and UI in System G-HP et al.

jlsperanza at aol.com jlsperanza at aol.com
Wed Jun 16 22:39:50 EDT 2010


I may have to revise Grice´s "Vacuous Names", in Hintikka/Davidson, "Words and objections", Reidel (1969) and I´m pleased Jones mentioned Meinong -- as does Grice (about System  [G]  ["not creating a Meinongian jungle"]). Recall the thing is called "Vacuous Names", so it may well be what Bayne wants to refer to -- if he is not _referring_ to. 
 
Bayne responding to Jones:

" [M]y concern with existential quantification is ... 
skepticism as to the role of quantification  [ a]s a 
logical description of the concept of a limit
in calculus."

and later speaking of a scenario where
 
"the limit of the function does not exist"
 
---- The comments by Jones:
 
scenario where: 

"there may not be a limit either,
Lim f(x)
x -> a
does not always exist."

and later to Bayne´s 

"limit may be defined even when 'a' doesn't exist (as what x goes to)"
 
and Jones:

"I presume you mean here f is not defined at a, rather than 
that a does not exist."

Then Bayne had written:
 
"My concern here is that quantification, e.g. UG, may be possible where a does not exist."
 
---- which I THINK is the point of Grice presenting his System Q to Quine. His "Vacuous Names". Apparently, the whole volume, "Words & Objections: essays in the work of W. V. Quine" had appeared as a special volume of Synthese. When that special issue was turned into a book, Grice was commissioned to add his festschrift paper, "Vacuous Names", which merited a reply by Quine -- "Reply to Grice": "forbiddingly complex" -- a sort of "thanks, but no thanks". I was disappointed by Quine´s short reply which never even TOUCHED on the topic that had inspired Grice to write "Vacuous Names", viz. ´vacuity´. (Incidentally, I was also pretty disappointed when Ostertag edited only the SECOND part of "Vacuous Names" in his own edited "Definite descripitions". If Grice had wanted to emphasise the description he would have written, "Vacuous Descriptions" -- such as they don´t exist -- rather than vacuous names!
 
---- (The whole idea of "vacuous" is an amusement for Grice. Of course no name is VACUOUS. It may be referent-lacking, but qua name the point is more of an amusement than anything else). When it comes to numbers, the amusement is double. For, as Carnap would say, "Numbers exist", or "fail to exist" for that matter, hardly makes sense!).
 
Jones: 

"This doesn't happen in any logic I know of, i.e. you only 
quantify over things which do exist."
 
One of the examples by Grice -- from memory. There may be some divergence.
 
At the Merseyside Geographical Society:
 
A  "Yes?"
 
B  "I´m here with my friend. We´ve come to pay tribute to Marmaduke Bloggs"
 
A  "Marmaduke Bloggs?"
 
B  "The man who climbed Mount Everest on hands and knees".
 
A  "But he doesn´t exist!"
 
B  "What do you mean?¨
 
A "I mean what I say. He was totally invented by journalists."
 
----------- The Merseyside Geographical Society was having a coktail in recognition of Marmaduke Bloggs. B is disappointed.
 
B  "So -- someone is not going to come to the party, after all"
 
A  "I don´t suppose you heard me distinctly. I said he doesn´t exist."
 
A  "It´s YOU who hasn´t seemed to have heard me distinctly. I said that he (someone) isn´t attending the party. That´s all. Cheers!
 
------
 
Jones hits it in the head, as they say:

"(I dare say if you were keen you could formalise a 
Meinongian logic in which unusual things happen.)"
 
------- Or adopt something like System G, which creates no Meinongian jungle. And where you CAN quantify over existentials which don´t exist, provided you specify that the negation is taken maximally: "Something is not coming to the party". "It is not the case that there is something that is coming to the party". Or something. Grice´s system "creates no Meinongian jungle" because it´s only in connection with the NEGATION of non-existents that you start to make sense. Or something.
 
"[Y]ou can write something like, "for all x such that P x then Q x", which is a way of quantifying over P's whether or not there are any. In that case you might say, if P is always false, that you 
have quantified over something which does not exist, though I think that's a confusing way of putting it.  Really you did a restricted quantification the effect of which was to quantify over nothing."
 
So perhaps I am pleased to have mentioned in this forum that Jones has a lot of very useful tips when dealing with "nothing". I called him our "vacuity" expert.
 
"for all x such that P x then Q x"
 
I would of course drop the "then" (Grice was _scared_ by the "then" if all we mean is the horseshoe -- WoW:"Indicative Conditionals"):
 
(x)Fx )  Gx
 
"which is a way of quantifying over P's whether or not there are any. In that case you might say, if P is always false, that you have quantified over something which does not exist".
--- Very good point,
"of quantifying over Ps whether or not there are any"
---- Strictly, I would distinguish between minding my Ps and minding my Qs, and minding my Pxs and my Qxs. As such, in first-order predicate calculus, the question as to whether P or Q exists is sort of "external" or at least second-order -- i.e. it does not raise. It´s x, y, z, ... etc, which exist (or fail to exist). But of course I follow Jones´s point:
---- "which is a way of quantifying over X". It is the case where no instantiation of P occurs, such that Px is always false -- under an interpretation --.
 
---- We have to give Quine a lot of credit here. Think that for Strawson, "existence" is more like a Kantian thing of "spatio-temporal continuity". To give credit to Strawson, and the anti-Kantian "existence IS a predicate" we need an altogether dissimilar System -- System S-pf -- of course, complete with truth-value gaps!
 
Jones:
 
"I think that's a confusing way of putting it.  Really you did a restricted quantification the effect of which was to quantify over nothing."

----- Much ADO about nothing if you axe [sic] me!
 
J. L. Speranza
 
------ Great to have the "look inside" thing for Bayne´s book, too!  

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