Re: all the incompleteness proofs are worthless untill...

On Mar 20, 10:33 pm, "elsiemelsi" <cyprin...@xxxxxxxxxxxxxxx> wrote:
you say
No. He is saying he talks about P

i say
note the word employed
employed means used


There are two senses in which the word "used" might be used.

(1) In proving a result about some mathematical object, I might make
use of the fact that the mathematical object has some property or
other. I am then "using" the property in question to help me with my
proof.
(2) In proving a theorem, I might make use of some axiom, such as the
axiom of choice. I am then "using" the axiom.

When Goedel says he is "using" certain properties of the system P, the
fact that P has the properties in question can be proved in Bounded
Arithmetic. So his proof goes through in Bounded Arithmetic. He is not
using the axioms of P in his argument. He is talking about them and
the properties that they have.
.

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