Re: Gödel's Basic Logic Course at Notre Dame (Was: Analytic Truth-makers)

Thats a little bit odd to abolish incompletness.
Take p, an arbitrary propositional variable.
Its neither the case that:
True(L,p)
Nor is ihe case that:
True(L,~p)
Because there are always at least two possible worlds.
One possible world where p is false, making True(L,p)
impossible, and one possible world where p is true,
making True(L,~p) impossible.
olcott schrieb:

On 7/23/2024 7:02 AM, Mild Shock wrote:

Little bit odd reference to mathematical logic for 2024.
>
olcott schrieb:

Curry, Harkell B. 1977. Foundations of Mathematical Logic. Page:45

 https://www.liarparadox.org/Haskell_Curry_45.pdf
 *It sustains this idea*
 L is the language of a formal mathematical system.
x is an expression of that language.
 When we understand that True(L,x) means that there is a finite
sequence of truth preserving operations in L from the semantic
meaning of x to x in L, then mathematical incompleteness is abolished.
 ~True(L,x) ∧ ~True(L,~x)
means that x is not a truth-bearer in L.
It does not mean that L is incomplete