FOM: deflationism and truth

[Volker Halbach]

I will comment on the postings by Neil Tennant (Mon, 11 Jan "more on
reflection, prosentences etc.") concerning deflationist theories of truth
and their relation to reflection principles.

In general there are very differing view on what deflationism is. But I
think it makes good sense to say that a deflationist theory of truth must
be at least conservative. Deflationists also often claim that the only
purpose of the truth predicate is the expression of infinite conjunctions
and disjunctions. There are conservative theories of truth that can serve
this purpose in a certain sense *and* be conservative, namely the theory of
T-sentences (as I have argued in my paper "Disquotationalism and Infinite
Conjunctions, to appear in Mind), but nevertheless I do not believe in the
disquotationalist theory, because truth can do more: we cannot only use it
for proving consistency of the original theory in the language without
truth, but we might even be able to replace talk about sets by talk about
truth, as I have indicated in my posting from Thu, 14 Jan "truth
predicates, predicativity and reflection". E.g. the "Tarskian" axioms of
truth are already much stronger than the T-sentences and not conservative
over PA (if we assume that also the induction scheme has be extendend to
the new language). Thus: no hope for deflationism, if it is parsed as
conservativity (or something implying conservativity).

Neil Tennant wrote:

>But it can be shown (or so I would argue) that a truth-avoiding
>prosentential extension of PA allows one to formalize quite faithfully
>the so-called "semantical argument" for the truth of the independent
>G"odel sentence, and also the meta-argument for the consistency of
>PA. In so far as prosententialism is very close in spirit to
>deflationism, this might show deflationism to be less vulnerable to
>refutation via the G"odel phenomena than Shapiro seems to suggest.

The only conclusion I draw from is that the prosentential extension of PA
is also not deflationist, even if this theory looks innocent to some people.