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Advanced Philosophy
Mathematics: An Intimidating Game
How philosophical doubts expose the effrontery of math textbooks.
I was a poor math student in high school. I was probably too lazy to excel at learning math’s mounting levels of complexity. But I think there was another, more interesting reason.
I still have a memory of sitting in math class, looking through the textbook, and seeing how each chapter added to the previous one with more and more definitions, proofs, and problems to be solved. In short, math class would lay out a tremendous volume of assumptions and inferences as well as a host of examples and exercises, which were all expressed with exquisite, daunting precision.
But I had trouble getting past the childlike, philosophical questions that kept coming to mind. I’d think, “Why should I assume that?” or “Why accept that definition?” This wasn’t a philosophy of math class, though, so no answers to such showstopping questions were forthcoming. You were just supposed to go along with the system. After all, the system was enormous and it worked so there was a lot to learn, and the clock was ticking. I did my best, I suppose, hobbled as I was by my naïve philosophical preoccupations.