[FOM] Deflationism and the Godel phenomena
Jeffrey Ketland
ketland at ketland.fsnet.co.uk
Tue Feb 15 21:40:10 EST 2005
Neil Tennant wrote:
Jeffrey Ketland:
>> The intended meaning of this sentence was:
>>
>> (C) Tr(PA) *does* prove G; and (PA + T-sentences) doesn't.
Neil Tennant:
> In that case, why didn't you write exactly that, rather than the
> misleadidng, unambiguous, false claim that you wrote instead?
Why didn't I write that? Unfortunately, it didn't occur to me at the time
that what I wrote was ambiguous at all. I can assure you that I was claiming
something like (C). Namely, that there is at least one way to do this using
the truth-theoretic extension of PA. I.e., we can prove G in Tr(PA), and
that the theory with the disquotational T-sentences can't. And this is
right. The other interpretation (that there is no other way to do it) simply
didn't occur to me.
In any case, now you're claiming (above) that the sentence is
"unambiguous"!!
But this now seems to contradict what you said in 2002. Your analysis was
that my sentence has two readings. You wrote:
The quote given from Ketland at the end of the
previous section is acceptable when the word
'involves' is replaced by 'could be displayed by
invoking':
(i) our ability to recognize the truth of Gödel
sentences could be displayed by invoking
a theory of truth (Tarski's) which significantly
transcends the deflationary theories;
But it is unacceptable when 'involves' is replaced
by 'can be displayed only by invoking':
(ii) our ability to recognize the truth of Gödel
sentences can be displayed only by invoking
a theory of truth (Tarski's) which significantly
transcends the deflationary theories.
OK. I meant something like (i). According to your 2002 article, this is
"acceptable".
But now you seem to say that the sentence which you yourself treated as
ambiguous in 2002 has now become unambiguous.
It's ambiguous, I agree. As I pointed out in my Jan 2005 reply, (ii) is not
the intended reading. I simply did not assume (ii). It plays no role
anywhere in my article.
There seems to be nothing more to say on the matter, except to agree that I
said something ambiguous and that you chose the interpretation that I didn't
mean.
--- Jeff
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