From: holmes@garnet.idbsu.edu (Randall Holmes)
Subject: Re: Extensionalism (was re: Russell's Paradox)
Organization: Boise State University
Date: Sun, 15 Nov 1992 21:57:24 GMT

In article <1992Nov14.012610.8929@tamsun.tamu.edu> cmenzel@tamsun.tamu.edu (Chris Menzel) writes:
>In article <1992Nov3.092753.19804@dorsai.com> mutation@dorsai.com (Florian Lengyel) writes:
>>>>In article <1992Oct29.212223.20343@tamsun.tamu.edu>
>>>>cmenzel@tamsun.tamu.edu (Chris Menzel) writes:
>>>
>>>>>In article <1992Oct26.170430.14372@guinness.idbsu.edu>
>>>>>holmes@garnet.idbsu.edu (Randall Holmes) writes:
>>>
>>>RH:
>>>>>>_Contra_ Harter (miscellaneous quibbles):
>>>>>>
>>>>>>The Good Russell may have admitted the possibility of "intensions",
>>>>>>but the Exalted Quine has liberated us from the influence of those
>>>>>>"creatures of darkness".  Extensions are adequate for all admissable
>>>>>>purposes.
>>>
>>>CM:
>>>>>Really, Randall?!  Could you then please give me an extensional
>>>>>analysis of the sentences in the following arguments that explains why
>>>>>the first is valid but the second is not:
>>>>>
>>>>>1)  John believes there are spies.
>>>>>    Mary believes whatever John does.
>>>>>    Therefore, Mary believes there are spies.
>>>>>
>>>>>2)  John believes that 2+3=5.
>>>>>    Necessarily, 2+3=5 iff first-order logic is undecidable.
>>>>>    Therefore, John believes that first-order logic is undecidable.
>>>>>
>>>>>Or is a purpose admissible just in case it is amenable to
>>>>>extensionalist analysis?
>>
>>As for Chris Menzel's second argument, it is not clear to me
>>how to construe belief, that is, how one ought to parse "John believes
>>that 2+3=5" in order to compute valid inferences from it. There is more
>>going on here than the substitution of equal strings, but I would
>>consider the invalidity of the string substitution to be a failure
>>to parse "John believes that 2+3=5" , rather than an indication that 
>>the invalidity of the argument cannot be explained via extensional analysis.
>
>Sorry not to have been able to respond sooner.  My point was not to
>assert that the argument's invalidity *cannot* be explained
>extensionally; it was a challenge to Randall and other extensionalists
>simply to provide such a framework that would enable us to represent
>the logical form of the arguments in such a way as to provide cogent
>analyses of their validity or invalidity, as the case may be.  Their
>inability to provide such a framework suggests the inadequacy of
>extensionalism as a general philosophical ontology.
>
>For friends of intensionality such a framework is ready to hand
>(though not to say without puzzles of its own).  That-clauses are
>grammatical singular terms that denote propositions, which possess an
>internal structure akin to the grammatical structure of the
>that-clauses that denote them.  Sentences of the form "s believes
>that-A" are simple two place predications involving an object and a
>proposition.  Thus, the first argument above is of the form
>
>  Bel(j,p)
>  (x)(Bel(j,x) --> Bel(m,x))
>  ---
>  Bel(m,p)
>
>which is a simple, logically valid argument in first-order logic.  The
>second argument needs a little more apparatus to represent properly.
>For any formula A, let [A] be a singular term that denotes the
>proposition expressed by A.  (There are several intensional logics
>around that formalize these ideas.)  Given this, the second argument
>is of the form
>
>  Bel(j,[A])
>  [](A <--> B)
>  ---
>  Bel(j,[B]
>  
>Here the intuitive invalidity of the argument indicates that the logic
>of intensional abstracts like [A] does not permit general substitution
>of equivalent formulas, since in general these will express different
>propositions.  Granted, this doesn't really *explain* the invalidity
>of the argument in the way the above analysis explains the validity of
>the first argument, but it does provide us with a clear framework for
>representing the form of the argument and encoding the logic of the
>terms involved in a rigorous fashion.

But the extensionalist does have a simple recourse; let proposition =
sentence throughout.

>
>>MUTATION@DORSAI.COM
>>FLORIAN@NEOTERIC.COM
>
>Chris Menzel
>Philosophy Department
>Texas A&M University
>


-- 
The opinions expressed		|     --Sincerely,
above are not the "official"	|     M. Randall Holmes
opinions of any person		|     Math. Dept., Boise State Univ.
or institution.			|     holmes@opal.idbsu.edu