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.