Re: Torkel Franzen on truth

Newberry <newberryxy@xxxxxxxxx> writes:

On Dec 8, 2:04 pm, Alan Smaill <sma...@xxxxxxxxxxxxxxxx> wrote:
Newberry <newberr...@xxxxxxxxx> writes:
The cornerstone of TF's argument is that the consistency of ZFC is
provable in ZFC + an axiom of infinity, which is no longer manifestly
true. We hesitate as we go higher up in the chain of theories, hence -
according to TF - we are not better than any machine because we cannot
say about an arbitrary system that its Goedel formula is true. Yet he
is absolutely sure that PA and ZFC are consistent.

Where did TF claim that he was "absolutely sure that ... ZFC [is]
consistent"?

I see no evidence that that was his view in the cite you posted
earlier in the thread.

He has an entire chapter in his book "Skepticism and Confidence",
where he refutes the skeptics.

Having dug out the book in question, I now have the context
of the following.

"And given that the axioms of ZFC are so utterly compelling, so
obviously true in the world of sets, we can do no better than to adopt
these axioms as our starting point. Since the axioms are true, they
are also consistent." [p.105]

The very next sentence says:

"Again, the point at issue is not whether such a view of the axioms of
ZFC is justified, but whether it makes good sense to appeal to the
incompleteness theorem in criticism of it."

The context is exactly a critique of the argument that suggests
that *if* someone has certain knowledge of the truth of the axioms
of a system *then* they will run into trouble from the incompleteness
theorem. So the view expressed are *hypotheical*, not TF's at all.
And having set up the context clearly, TF reminds the reader
of the context afterwards.

"if the axioms of ZFC are manifestly true, they are obviously
consistent" [p.105]

As I said before, this is a conditional statement.
Why on earth do you think it expresses a commitment
to the antecedent being true?

At this rate someone will have to give us "The uses and abuses
of TF's writings".

(And, while I'm here, he does not refute scepticism in this chapter.)

--
Alan Smaill
.

Relevant Pages

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  • Re: Torkel Franzen on truth
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  • Re: Torkel Franzen on truth
    ... is absolutely sure that PA and ZFC are consistent. ... these axioms as our starting point. ... We do not know if PA's Goedel sentence is true. ...
    (sci.logic)