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

On 7/23/2024 3:36 PM, Mild Shock wrote:

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.
 

We are not using propositional logic we are using an extension
of Montague Semantics such that every natural language meaning
can be formalized.
L is an actual language and p is a specific static constant
finite string expression of that language.
There is no possible world where the living animal
of a puppy is a 15 story office building.
There is no possible world where this sentence or its
negation are true: "This sentence is not true".

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
>

 

--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer