[FOM] Deflationism

[praatika@mappi.helsinki.fi]

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, 

Panu 


Panu Raatikainen
Ph.D., Academy Research Fellow,
Docent in Theoretical Philosophy
Department of Philosophy 
University of Helsinki
Finland

Visiting Fellow 
Institute of Philosophy
School of Advanced Studies 
University of London

E-mail: panu.raatikainen at helsinki.fi
 
http://www.helsinki.fi/collegium/eng/Raatikainen/raatikainen.htm