In the free excerpt from Lectures on the Philosophy of Mathematics, published by MIT Press in 2021, the author introduces the philosophy of mathematics grounded in mathematical inquiry and practice. Discussing Dedekind’s categoricity result for arithmetic and structuralism, the text delves into the philosophy that emphasizes the importance of isomorphism-invariance in math. The structuralism idea highlights the role of structures in math, regardless of individual objects. Unique structural roles of numbers like zero, 1/2, and √2 are explored, with a focus on Leibnizian and pointwise definable structures. Categoricity and isomorphism orbits play a crucial role in defining mathematical structures and identifying them uniquely.
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