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

On 7/23/2024 3:44 PM, Mild Shock wrote:

Of course you can restrict yourself to
only so called "decidable" sentences A,
 i.e. sentences A where:
 True(L,A) v True(L,~A)
 But this doesn't mean that all sentences
are decidable, if the language allows for
example at least one propositional variables p,
 then you have aleady an example of an
undecidable sentences, you even don't
need anything Gödel, Russell, or who knows
 what, all you need is bivalence, which was
already postualated by Aristoteles.
 Principle of bivalence
https://en.wikipedia.org/wiki/Principle_of_bivalence
 if you assume that a propostional variable
is "variably", meaning it can take different truth
values depending on different possible worlds,
 or state of affairs, or valuations, or how ever
you want to call it. Then a propositional variable
is the prime example of an undecided sentence.
 

The key difference is that we no long use the misnomer
"undecidable" sentence and instead call it for what it
really is an expression that is not a truth bearer, or
proposition in L.

Mild Shock schrieb:

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.

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