Is there any readings on philosophy of mathematics that does not fall into studies of logical foundations of mathematics such as "definition of 1", "incompleteness theorems", "number systems" or set theory etc. But rather about understanding mathematical phenomenon in a (presumably encompassing) philosophical framework. For example, how to understand Fourier transformation and its utility in terms of metaphysics, philosophical connotation of central limit theorem etc.


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I would recommend Imre Lakatos' Proofs and Refutations, which is a philosophical study of how to do mathematics, not so much of what mathematicians are actually playing with.

Zeno's paradoxes and the history of the calculus, the "mechanics of infinitesimals", are also examples which carry a strong thread of the how and the why and of what makes a proof valid; how do you jump from an infinite series to its end point, without breaking something?

So really, you can chase up the ontology, epistemology, phenomenology, etc. of mathematics - pure and/or applied - as you feel inclined.


Here is a good introduction from the Stanford Encyclopedia of Philosophy.

Here are a couple of very informative and easy to read foundational works that focus on philosophy (but still have some technical details):

Gottlob Frege, The Foundations of Arithmetic discusses what exactly a number is and answers (among other things) the question, "Why does the proposition 2=1+1 provide us with any information? After all, isn't this just saying that 2 is equal to itself, using different names for 2?"

Alfred N. Whitehead, The Concept of Nature discusses what geometric objects like lines and points are.

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