Re:Doing Mathematics Differently
by dllthomas on Friday February 26, 2016 @09:50PM
(#11185838)
This seems to be a technical objection that dodges the meat of the parent's comment. In what sense is it true that a given theorem follows from a given set of axioms and a given choice of inference rules?
[ Parent
| on HN ]
A “theorem” is by definition a statement in a mathematical theory that has a proof. In what sense is this true? Well, that depends on what “true” means in your model... :-p
I agree with parent comment. At the heart of your disagreement is that you seem to use definition from logic of what axioms are, while your opponents use "definitions" from metamathematics.
Umm. I've been of the understanding that we never change the inference rules, Can you point to some branch of mathematics that involves a change of inference rules?
At my level of understanding, it seems a reasonable characterization of intuitionistic logic to say that it operates with a more restricted set of inference rules. It was the parent who made the stronger claim about differences here, and they speak a bit more to the topic in nearby comments.