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Jack comments on "What Is Wrong With Our Thoughts" - Less Wrong
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Is saying "we could have a different axiomatic system" different from saying "2, 4, +, and = could all mean different things? Of course we've only defined the operations and terms that are useful to us. I don't care about the naturalness of '+' only that once I know the meaning of the operations and terms the answer is obvious and indisputable.
Math isn't my field, so my all means show me how I'm wrong.