On Sat, Sep 21, 2002 at 11:50:20PM -0700, Brent Meeker wrote:
> I was not aware that 2nd-order logic precluded independent
> propositions. Is this true whatever the axioms and rules of
> inference?
It depends on the axioms, and the semantic rules (not rules of inference
which is a deductive concept). Here's a good page for clarification
between semantic concepts and deductive concepts:
http://www.joh.cam.ac.uk/societies/moral/mathlogic.htm. It can be
confusing because in first-order logic they happen to coincide, but that's
not the case in second-order logic. And again, second order theories *can*
be categorical, whereas first-order theories can not be.
Received on Sun Sep 22 2002 - 13:31:28 PDT