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I have my Bachelors' degree in Math, so I can tell you what the pros think about it: https://aimath.org/textbooks/approved-textbooks/judson/ is an example of a college-level text covering the subfield most relevant to what you're thinking about here. Mathematics is based on a series of axioms (semi-)arbitrarily declared true. All other traits of mathematics ...


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Here is my way of looking at "the unreasonable effectiveness of mathematics". In the real world, counting macroscopic objects like pebbles or people is useful because in the real world, neither of these two things can spontaneously pop into or out of existence. Counting them has meaning. Then we discover that we can represent those counts ...


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Long comment When in mathematics we write 1+2+3+4=10 we are not making some sort of "metaphysical claim": we are asserting that when we evaluate the left-hand side expression (we "compute" 1+2+3+4) the process will terminate after a finite number of steps and the resulting value of the process will be the same as the right-hand side. Thus,...


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It's a great question. How do finite, imprecise, error-prone real-world objects, such as an abacus or a computer, touch the infinite perfect realm of mathematics? Try this analogy. Suppose you have an infinite group, with a⊙b defined for every pair of elements. Now suppose you take a finite subset S of the group elements, and define a new operation ⊗, ...


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I can see how the saying, "correlation is not causation," might make you think that causation is not mathematical. Nothing could be further from the truth. Correlation is not causation, but statistics encompasses more than mere correlation. Judea Pearl's approach to causation is a successful one, and I'd recommend checking out his book. In ...


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You are asking about a very rich field called measurement theory. The standard textbooks are the three volumes of Foundations of Measurement by Krantz, Luce, Suppes, and Tversky (Volume 1 here).


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Partial answer: A computer does not implement mathematical, economic or any other type of concepts. It is our reason which gives the input and output symbols of mathematical or economic sense. For example, your money in the bank is just represented by a nanometer-scale-size magnetized surface. Do computers implement an economic concept in such physical fact? ...


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