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SilasBarta comments on Preface to a Proposal for a New Mode of Inquiry - Less Wrong
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I will formalize it. I don't know what your second statement means; to me induction and deduction are completely different. 2+2=4 is a deductive statement, provably true within the context of a certain formal system. "Mars is red" is an inductive statement, it can't be derived from some larger theory; we believe it because of empirical evidence.
I trust you've read the discussions and articles regarding the status of purported "a priori" knowledge, then? If not, I have reason to suspect your ideas will not appear informed and will thus not yield inslight.