Re: Semantics of First-Order Languages

On Feb 29, 3:37 am, malc...@xxxxxxxxx wrote:
the language of set theory is just an
instance of a first order logic language, which is precisely the kind
of thing one is trying to give sense.

Not all circles are vicious.
You have to stop SOMEwhere.
This objection is about as sensible as saying
you don't understand what an axiom is because
provability is what axioms are trying to found.

More to the point, nobody is trying to "give sense"
to an first-order language. If you actually want to do that,
you do it via THE AXIOMS, NOT the semantics. And
the sense you give is not even specific to THAT language,
in any case, since the exact same sense would be had
by a different language with different names for all the
predicates and functions, as long as they had isomorphic
arities and the axioms were translated isomorphically
into the other language.
.

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