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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: =?UTF-8?Q?Re=3A_G=C3=B6del=27s_Basic_Logic_Course_at_Notre_Dame_=28?=
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Date: Tue, 23 Jul 2024 15:43:50 -0500
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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