I have papers like this in my own notes from my university days. My doubt in mathematics was created when, one day, I was introduced to i, the square root of -1. Imaginary numbers. And I have done enough work in the philosophical foundations of mathematics to agree with the author when he questions some of the basic principles of this 'most certain' of all the sciences. Things like the use of axioms and the concept of infinite sets, for example. And I remember, from my own days, long discussions about the principle of substitutivity. My own view of mathematics is from the Mill and Kitcher school of thought - that it is a description of physical events, or physical operations. Why does this matter? Because "elementary mathematics needs to be understood in the right way, and the entire subject needs to be rebuilt so that it makes complete sense right from the beginning, without any use of dubious philosophical assumptions about infinite sets or procedures."
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