Proposed new syntax

[Antoon Pardon]

Op 24-08-17 om 04:02 schreef Steve D'Aprano:
>
> Unfortunately the interwebs are full of people, even mathematicians, that have a
> lot of misapprehensions and misunderstandings of Gödel's Incompleteness
> Theorems. For example, there's a comment here:
>
> "It's easy to prove that ZFC is consistent in the right theory, e.g.
> ZFC+Con(ZFC)"
>
> https://philosophy.stackexchange.com/questions/28303/if-the-zfc-axioms-cannot-be-proven-consistent-how-can-we-say-for-certain-that-a
>
> apparently without the slightest awareness that this would be begging the
> question. If you assume that ZFC is consistent, of course you can prove that
> ZFC is consistent.

Which seems to suggest his point went right over your head. His point being
that Gödel's 2nd Theorem mentions the specific theory in which you can't prove
particular axioms consistent.

What you can prove and what not is not an absolute but depending on the system
you are working with and he was just illustrating that, by providing a system
in which such a proof would be trivial, because the theorem to be proven was
just one of the axioms.

Begging the question is not applicable in this kind of studies. A proposition
is provable in a particular system or not, but it is important to specify
what system you are talking about.

-- 
Antoon Pardon