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

On 7/23/24 4:43 PM, olcott wrote:

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:
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True(L,p)
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Nor is ihe case that:
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True(L,~p)
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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,
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making True(L,~p) impossible.
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 We are not using propositional logic we are using an extension
of Montague Semantics such that every natural language meaning
can be formalized.

Then you aren't in the same system as Tarski, and prove yourself to be a liar.

 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.

Are you SURE about that?

 There is no possible world where this sentence or its
negation are true: "This sentence is not true".

How do you know that?

 

olcott schrieb:

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

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

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

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https://www.liarparadox.org/Haskell_Curry_45.pdf
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*It sustains this idea*
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L is the language of a formal mathematical system.
x is an expression of that language.
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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.
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~True(L,x) ∧ ~True(L,~x)
means that x is not a truth-bearer in L.
It does not mean that L is incomplete
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