Polymath
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The disparity between your verbal and math abilities is unusually large, even more so because you are also very good at logic. I hypothesize that, even though you might not have enough innate math talent to get a college degree in math, your difficulty passing calculus is the result of an accumulation of misunderstandings related to mediocre or poor teaching. As an experienced math teacher and tutor, my judgment is that anyone with an IQ two SDs or so above average is capable of fully understanding math up through 1-variable calculus (as are the majority of people 1 SD above averag, but pretty much no one in the left half of
This is a facepalm "Duh" moment, I hear this criticism all the time but it does not mean that "logic" depends on "set theory". There is a confusion here between what can be STATED and what can be KNOWN. The criticism only has any force if you think that all "logical truths" ought to be recognizable so that they can be effectively enumerated. But the critics don't mind that for any effective enumeration of theorems of arithmetic, there are true statements about integers that won't be included -- we can't KNOW all the true facts about integers, so the criticism of second-order logic boils down to saying that you don't like using... (read more)
There is a lot of psuedo-arguing going on here. I'm a mathematician who specializes in logic and foundations, I think I can settle most of the controversy with the following summary:
1) Second-order logic is a perfectly acceptable way to formalize mathematics-in-general, stronger than Peano Arithmetic but somewhat weaker than ZFC (comparable in proof-theoretic strength to "Type Theory" of "Maclane Set Theory" or "Bounded Zermelo Set Theory", which means sufficient for almost all mainstream mathematical research, though inadequate for results which depend on Frankel's Replacement Axiom).
2) First-order logic has better syntactic properties than Second-order logic, in particular it satisfies Godel's Completeness Theorem which guarantees that the syntax is adequate for the semantics. Second-order... (read 361 more words →)
I smelled a rat immediately and decided to evaluate all five statements as if they had been randomly replaced with their opposites, or not. All five sounded wrong to me, I could think of rationalizations on each side but the rationalizations for the way they were actually presented sounded more forced.
I realize you have probably had people tell you this already, and their attempts to explain Calculus to you have left you frustrated and more firmly convinced that it was beyond your capacity. But I don't propose to demonstrate my hypothesis in that way. Rather, I can try to double-crux this by showing you that your understanding of regular school mathematics isn't really what it should be and is what might actually be holding you back. In the spirit of your 3-question cognitive abilities quiz, here is a 3-question "ready for Calculus" diagnostic test I just made up (but which is informed by many years of teaching and tutoring students at