Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct

On 11/9/2024 1:32 PM, Alan Mackenzie wrote:

olcott <polcott333@gmail.com> wrote:
 

The assumption that ~Provable(PA, g) does not mean ~True(PA, g)
cannot correctly be the basis for any proof because it is only
an assumption.

 It is an assumption which swifly leads to a contradiction, therefore must
be false. 

You just said that the current foundation of logic leads to a contradiction. Too many negations you got confused.
When we assume that only provable from the axioms
of PA derives True(PA, g) then (PA ⊢ g) merely means
~True(PA, g) THIS DOES NOT LEAD TO ANY CONTRADICTION.

But you don't understand the concept of proof by
contradiction, and you lack the basic humility to accept what experts
say, so I don't expect this to sink in.
 

We know, by Gödel's Theorem that incompleteness does exist.  So the
initial proposition cannot hold, or it is in an inconsistent system.

 

Only on the basis of the assumption that
~Provable(PA, g) does not mean ~True(PA, g)

 No, there is no such assumption.  There are definitions of provable and
of true, and Gödel proved that these cannot be identical.
 

*He never proved that they cannot be identical*
The way that sound deductive inference is defined
to work is that they must be identical.
A conclusion IS ONLY true when applying truth
preserving operations to true premises.
It is very stupid of you to say that Gödel refuted that.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer