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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
by dllthomas 11y ago
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?
- catnaroek 11y agoA “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
- js8 11y agoI 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.
- aangjie 11y agoUmm. 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?
- dllthomas 11y agoAt 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.
- aangjie 11y agoUmm. 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?