[FOM] Deflationism and the Godel phenomena

Joseph Vidal-Rosset joseph.vidal-rosset at u-bourgogne.fr
Wed Feb 16 05:58:29 EST 2005

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Let me take participate to this interesting debate, even if I feel
weaker, from a strict logical point of view, than Neil, Torkel and you.
I know that you'll be indulgent. Please do not hesitate to correct my
mistakes on the list.

Jeffrey Ketland a écrit :

| Let me describe again what I *actually* did in my 1999 article, rather
| than what you appear to think I did. The 1999 article compared the
| disquotational theory and the Tarskian truth theory, in connection with
| two central conditions on a theory of truth:
| (i) The Conservation Condition (a deflationary truth theory should be
| conservative);

A deflationary truth theory is always conservative OVER a base theory,
right? I don't think that it makes sense to define conservativeness as
an absolute property. Am I right?

| (ii) The Adequacy Condition (adding truth axioms should give a proof of
| reflection principles, and in particular "All theorems of S are true").

Do we need at this point to grow up to the second order? I believe it.

| (Shapiro gave an almost identical line of argument.)
| I stated there that the Tarskian theory Tr(PA) satisfies the Adequacy
| Condition, but violated the Conservation Condition. I concluded that
| Tr(PA) was not deflationary. I said that any adequate theory would be
| non-deflationary (see quote below).

Was ABSOLUTELY not deflationary?

If Convention T is essentialy a deflationary scheme, then does it mean
that Convention T is not an adequate scheme for defining truth? But if I
remember, Convention T is proved by TA + Satisfaction  theory, right?
So you are not cautious enough when you say in your 199p paper that
"Deflationism is false".

| In your 2002 Mind article you quoted exactly one sentence from my
| article. There are, I'd guess, around 300 sentences in my article (25
| pages; 40 lines per page; 3 lines per sentence). You quoted just one
| sentence. So, you ignored the other 99.7% of the article. Great.

Jeff, I feel free to tell you that's not fair.
|Quotations are not proof of interest, neither proof of respect of a
point of view. Neil does not need support on this point. It's obvious
that his paper pays attention to your arguments and take them seriously.

| (C) Tr(PA) *does* prove G; and (PA + T-sentences) doesn't.

Is it because we are not at the same order with the former (Tr(PA)), or
is there precisely another reason that I have not understood?
So, does this proof exist thanks to the virtue, the substantiality of
truth, or more exactly because we are not at the same order and because
we're using other axioms? The reason of my question is in what follows.

| After all, it is obvious there that I am comparing two truth theories.
| And I say that one is more powerful than the other. And I am right. This
| is *exactly* what Shapiro and I were saying. And you've even conceded
| it. So, you admit that truth is (or can be) a powerful notion. (I.e., a
| Tarskian inductive definition and you let the truth predicate enter the
| induction scheme.) Great. That's exactly what we said. And if Shapiro
| and I are right, that probably means that deflationism about truth is
| refuted.

A couple of  questions:

1) Where, in the litterature, have you read that the Definition of
Deflationism is equivalent to the property of the conservativeness about
truth? (If conservativity is always relative to a theory, I do not see
how Deflationism could be defined absolutely by conservativeness.)

2) Deflationism is above all a philosophical, anti-metaphysical thesis
about truth. If you really believe that you have refuted it, do you
think that your logical refutation has positive philosophical
consequences? (For example an argument for mathematical realism?)
(I believe only that this logical development can only be a logical
clarification to get correct assertions about deflationism. It's not
surprising that Quine has never raised this argument against
Deflationism, but it is already, informally, in Gödel's philosophical

All the best,
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