Standard Semantics is a Myth (Was: Re: FOM: Ambiguating)

[Martin Schlottmann]

John Mayberry wrote:
> 
<snip>
>
>         I say that the very formal axioms and rules that are complete
> for Henkin semantics are sound for standard semantics. "Not so." says
> Simpson "It depend on the meta-theory." Now what possible meaning could
> we attach to Simpson's words other than that the notion of standard
> semantics for second order logic is, well, ambiguous?
<snip>

Exactly. For example, what is the truth value of the
(appropriate analogon of) the continuum hypothesis?
Do we just have to take someone's word that it is
somehow decided in a mystical realm of Platonic ideas?
How do we decide that different people all refer to
the same "intended" meaning?

"Second order logic is a myth" is synonymous with
"standard semantics is a myth". The only way to
specify the semantics is to give an appropriate
formalization, which necessarily leaves open the
possibility of different interpretations.


-- 
Martin Schlottmann <martin_schlottmann at math.ualberta.ca>
Sessional Lecturer
Department of Mathematical Sciences, CAB 583
University of Alberta, Edmonton AB T6G 2G1, Canada