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

On 11/8/2024 9:05 AM, Alan Mackenzie wrote:

olcott <polcott333@gmail.com> wrote:

On 11/8/2024 5:58 AM, Alan Mackenzie wrote:

In comp.theory olcott <polcott333@gmail.com> wrote:

On 11/6/2024 2:34 PM, Alan Mackenzie wrote:

In comp.theory olcott <polcott333@gmail.com> wrote:

On 11/6/2024 10:45 AM, Alan Mackenzie wrote:

As I have continually made clear in my posts "like 2 + 2 = 4" includes
the halting theorem, Gödel's theorem, and Tarski's theorem.

Your misconceptions are not my errors.
You cannot possibly prove that they are infallible that best that you
can show is that you believe they are infallible.

When the operations are limited to applying truth preserving
operations to expressions of language that are stipulated to be true
then True(L,x) ≡ (L ⊢ x) and False(L, x) ≡ (L ⊢ ~x)
Then (Incomplete(L) ≡  ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x))) becomes
(¬TruthBearer(L,x) ≡  ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)))
Incompleteness utterly ceases to exist

Incompleteness is an essential property of logic systems

What I said about is a semantic tautology just like 2 + 3 = 5. Formal
systems are only incomplete when the term "incomplete" is a dysphemism
for the inability of formal systems to correctly determine the truth
value of non-truth-bearers.

which can do anything at all.  If what you assert is true (which I
doubt), then your system would be incapable of doing anything useful.