From: cmenzel@tamsun.tamu.edu (Chris Menzel)
Subject: Re: Extensionalism (was re: Russell's Paradox)
Organization: Texas A&M University, College Station
Date: Sat, 14 Nov 1992 01:26:10 GMT

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.

>MUTATION@DORSAI.COM
>FLORIAN@NEOTERIC.COM

Chris Menzel
Philosophy Department
Texas A&M University

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