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latanius comments on Open Thread, April 15-30, 2013 - Less Wrong
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I have a super dumb question.
So, if you allow me to divide by zero, I can derive a contradiction from the basic rules of arithmetic to the effect that any two numbers are equal. But there's a rule that I cannot divide by zero. In any other case, it seems like if I can derive a contradiction from basic operations of a system of, say, logic, then the logician is not allowed to say "Well...don't do that".
So there must be some other reason for the rule, 'don't divide by zero.' What is it?
Didn't they do the same with set theory? You can derive a contradiction from the existence of "the set of sets that don't contain themselves"... therefore, build a system where you just can't do that.
(of course, coming from the axioms, it's more like "it wasn't ever allowed", like in Kindly's comment, but the "new and updated" axioms were invented specifically so that wouldn't happen.)