Re: THIS STATEMENT HAS NO PROOF IN ANY SYSTEM = true or false?

poopdeville_at_gmail.com
Date: 01/28/05

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    Date: 27 Jan 2005 17:22:11 -0800

    Jeffrey Ketland wrote:
    > poopdeville@gmail.com wrote in message
    > >tchow@lsa.umich.edu wrote:
    > >> First of all, the way mathematicians *in fact* use the word "true"
    > >> violates your norms. They may be guilty of a philosophical
    > >transgression,
    > >> but if you want to understand what they're saying, you have to get
    > >used
    > >> to this usage whether you like it or not. I think this is how the
    > >whole
    > >> (sub)thread went flailing off in the first place: You just weren't
    > >used
    > >> to normal mathematical talk.
    > >>
    > >
    > >Of course. I addressed this in the paragraph you snipped. However,
    > >normal mathematical talk is still quite confused. Here I refer to
    your
    > >(and Jeffrey Ketland's, but mostly his) talk of disquotational
    schemes,
    > >with emphasis of Jeffrey's use of models and the real world and your
    > >group theory example at the end of your message.
    >
    > Sorry. I've snipped the rest, but this really is the heart of the
    matter.
    > Mathematical talk is *not confused*. Rather, you seem to be
    advocating some
    > unmotivated, and possibly incoherent, form of scepticism.

    What is incoherent is claimng that the truth conditions for the
    sentence "'AC' is true" are the same as the truth conditions for "'John
    Lennon was born in 1940' is true" with the explanation that the second
    is true because "John Lennon" refers to a real object. What is the
    real object to which "AC" refers? You explicitly chosen "the real
    world" to be the set of objects with respect to which the second
    sentence is to be evaluated. But you implicitly chose V (or some other
    structure) with respect to which evaluate the first and failed to
    supply this information, leaving the reader to suppose that you mean
    "the real world."

    My motivations are my own.

    >
    > Consider Goldbach's Conjecture, GC. Its truth condition is stated as
    > follows:
    > GC is *true* if and only if for every even number n, there are primes
    p1 and
    > p2 such that n = p1 + p2.
    >
    > At present, we do not know if GC is true or false. But this is a
    precise
    > analysis of what saying "GC is true" means.
    >
    > The above is an instance of the partial defintion giving what the
    word
    > "true" means. It illustrates how the word "true" is actually used,
    both in
    > ordinary life, in science and in mathematics. Truth for interpreted
    > statements is intrinsically disquotational, just as 7 is
    intrinsically
    > prime. This has nothing to do with the "redundancy theory", which
    Tarski
    > refuted. It is a central property of the notion of truth.

    You're doing it again. Where do these numbers live? Certainly not the
    same place John Lennon does. By the way, the disquotational theory of
    truth and the redundacy theory of truth are synonymous. This is basic
    in philosophy, but this case that I'm guilty of obfuscation too.

    > (Proof: Let (L, I) be an interpreted language and let T be the set of
    truths
    > in (L, I). Suppose that dom(I) contains all the expressions of L.
    Suppose
    > that L also contains a predicate True(x) which defines this set T.
    For each
    > expression E, let E* be a term in L such that E* denotes (in I) E.
    Then, for
    > any A in L, each sentence True(A*) <-> A is true in (L, I).
    Disquotation is
    > an intrinsic property of truth.

    A ha! You're actually using the standard formulation of a model
    theory to describe truth (via the disquotational-theory-esque
    construction that a sentence S is true iff I(S) = T, where I is the
    interpretation function). This is how I would proceed. But if you
    don't fix I, you have no basis with which to interpret. This is
    EXACTLY my point.

    'cid 'ooh

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