praatika at mappi.helsinki.fi
Thu Mar 23 11:49:20 EST 2006
Quoting A.S.Virdi at lse.ac.uk:
> >In this case, there are (at least) two alternative interpretations:
> >(i) T-sentences say all there is to say about truth;
> (ii) the truth theory should not entail anything substantial;
> >i.e., it must be a conservative extension of the base theory.
> Many thanks for your reply! Firstly, your (i) and (ii) seem not to be
> mutually exclusive.
Indeed, the simple addition of T-sentences results to a conservative
extension. But it is a consistent position just to require (ii) but not to
commit oneself to (i) - that was my point.
> If deflationism entails that all there is to be said about the nature of
> truth can be gotten from
> the T-sentences AND that its utility derives from its being able to
> express things like soundness
> statements for PA (say) then the deflationist is in trouble; to get to
> the soundness principle she will need
> to appeal to Tarski's compositional theory of truth. BUT, in so doing,
> she would have to renege her deflationism!
Agreed (at least, in the conditional form: If...)
> However, on On Tues, 21 Mar 2006 Leon Horsten observes:
> >Tarski's compositional theory of truth, axiomatically expressed, does
> >not seem to be committed to facts or to a correspondence with facts.
> >Indeed, T(PA) and Tr(PA) do not mention facts at all. So in as much as
> >facts and correspondence to facts are metaphysical notions, it seems
> >that T(PA), Tr(PA) still deserve the label 'deflationary'.
> Many thanks for this! It is true that facts and correspondence do not
> feature in T(PA) nor Tr(PA) but this does not
> disqualify Tarski's theory from being a correspondence theory. Tarski has
> shown how, uncontroversially,
> one gets a *homomorphism* between sentences of the language concerned and
> elements/objects of the associated domain of discourse. Letting L be a
> first-order language and D a set-theoretical
> structure, one can then establish an interpretation function, I, mapping
> the non-logical constants of L into the
> domain X of D. For example, the truth definition of an atomic sentence
> with a two-place predicate P is:
> D |= P(a1,a2) iff <I(a1), I(a2)> is a member of I(P).
This is how you proceed in mature model theory. But this is not what Tarski
did in his path-breaking 1935 paper on the concept of truth, where he aimed
to define truth without assuming any semantical concepts. The
interpretation function is a semantical notion, in this sense. Therefore
Tarski explicitly defined primitive denotation (list-like def). But
consequently, his definition has a deflationist ring.
I've just written a paper on these matters. If you're interested, I can
send you a copy.
All the Best,
Ph.D., Academy Research Fellow,
Docent in Theoretical Philosophy
Department of Philosophy
University of Helsinki
Institute of Philosophy
School of Advanced Studies
University of London
E-mail: panu.raatikainen at helsinki.fi
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