I have to agree with anonymous. Having read your discussions of “true-by-definition” and arguments about labels for the past couple of weeks, I wonder what ax you are grinding against Aristotle. Who is making the claim that logical inference yields empirically significant inferences? Why do you see the lack of empirically significant inferences as some kind of point against Aristotelian syllogism?
Aristotle was one of the first, if not the first, to attempt to formalize reasoning. Sometimes when I read these posts, I feel like your are failing to distinguish between an inference and an induction. As Hume argues (forcefully, in my opinion), induction based on empirical observations can never be certain. I don’t take this as a point against induction, but rather as a caution against those who use it thoughtlessly.
Finally, the fact that logical inference can never yield an empirically significant result may not be equivalent to saying that logical inference is pointless. Unlike the classic proof of socrates’ mortality, there are many tautologies that are not obviously tautological. The most famous of these may be “If A is a formal system that allows the development of arithmetic , then there is no set of axioms, B, such that all true statements in A are provable from B.” This is a hasty statement of Goedel’s incompleteness theorem. This statement is tautological, but does that make it an unimpressive inference? This is a tautology that has been extremely empirically helpful, if only insofar as it freed up the time of those struggling to prove the completeness of arithmetic.
I have to agree with anonymous. Having read your discussions of “true-by-definition” and arguments about labels for the past couple of weeks, I wonder what ax you are grinding against Aristotle. Who is making the claim that logical inference yields empirically significant inferences? Why do you see the lack of empirically significant inferences as some kind of point against Aristotelian syllogism? Aristotle was one of the first, if not the first, to attempt to formalize reasoning. Sometimes when I read these posts, I feel like your are failing to distinguish between an inference and an induction. As Hume argues (forcefully, in my opinion), induction based on empirical observations can never be certain. I don’t take this as a point against induction, but rather as a caution against those who use it thoughtlessly. Finally, the fact that logical inference can never yield an empirically significant result may not be equivalent to saying that logical inference is pointless. Unlike the classic proof of socrates’ mortality, there are many tautologies that are not obviously tautological. The most famous of these may be “If A is a formal system that allows the development of arithmetic , then there is no set of axioms, B, such that all true statements in A are provable from B.” This is a hasty statement of Goedel’s incompleteness theorem. This statement is tautological, but does that make it an unimpressive inference? This is a tautology that has been extremely empirically helpful, if only insofar as it freed up the time of those struggling to prove the completeness of arithmetic.