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

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.
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.