Standard Semantics is a Myth (Was: Re: FOM: Ambiguating)
martin_schlottmann at math.ualberta.ca
Wed Mar 24 17:13:47 EST 1999
John Mayberry wrote:
> 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?
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>
Department of Mathematical Sciences, CAB 583
University of Alberta, Edmonton AB T6G 2G1, Canada
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