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

On 7/23/24 8:18 PM, olcott wrote:

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.

Which isn't a tually a mismomer, it just shows you dont understand the mtechnical meaning of the term. But then, since you decided not to learn about the fields, you don't know any of the technical meaning of the words, and just misuse them all.

 

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.