Some reccos

[raghudotcc]

The links to the paper are to my dropbox. So, if you do find some of these interesting please upload them to GitHub and then link. I am saying this because I have lost a big chunk of my notes due to stale links in the past😅. I will add to this issue if I do find something, but it would be helpful to know what kind of resources you are looking for. The below list is a result of my interest in structuralism🙂.

Papers

• Paul Benacerraf. What numbers could not be
• Justin Clarke-Doane. What is the benacerraf problem
• Dirk Greimann. What is Frege's Julius Caesar Problem
• Solomon Feferman. Does mathematics need new axioms
• Alan Baker. Are there genuine mathematical explanations of physical phenomena
• Philip Ehrlich. The absolute arithmetic continuum and the unification of all numbers great and small
• Costas Drosos. Sets, Categories, and Structuralism
• Julian Cole. Creativity, Freedom and Authority - A New Perspective on the Metaphysics of Mathematics
• Bob Coeke. An alternative gospel of structures order, composition and process
• Mark Colyvan. Can the Eleatic principle be justified
• Charles Parsons. Realism and the debates on impredicativity
• Viktor Blåsjo. Hyperbolic space for tourist
• Tim Button. Structure and Categoricity: Determinacy of Reference and Truth-Value in the Philosophy of Mathematics
• A C Paseau. What's the Point of Complete Rigour
• R Brown. Category Theory: an abstract setting for analogy and comparison
• David Ellerman. A Theory of Adjoint Functors —with some Thoughts about their Philosophical Significance
• Alfred Tarski. The Semantic Conception of Truth and the Foundations of Semantics
• Joel Hamkins. Utilitarianism in Infinite Worlds

Mathoverflow discussions

• Thinking and Explaining. https://mathoverflow.net/questions/38639/thinking-and-explaining
• What does it mean for a number to be transcendental. https://math.stackexchange.com/questions/1686156/in-simple-english-what-does-it-mean-to-be-transcendental
• What is the next number on the constructibility sequence and what is the asymptotic growth? https://math.stackexchange.com/questions/3377988/what-is-the-next-number-on-the-constructibility-sequence-and-what-is-the-asympt

Books

• Burgess. Rigor and Structure
• Russell. An Essay on the Foundations on Geometry
• Knuth. Surreal Numbers
• Lakatos. Proofs and Refutations
• When Einstein Met Magritte (All Colors)

[prathyvsh]

This is definitely in the ballpark of what I am after. Some of this look pretty new and intriguing. Structuralism is an attractive position for investigation at the moment as I am having order theory / category theory explorations on the side. But I haven't been focusing on reading philosophy of structuralism materials exclusively yet. Waiting to find some time to finish reading these to gain some ground for my exploration at the moment:

• Nature of Mathematical Knowledge (Edna Kramer)
• Conceptual Roots of Mathematics (J. R. Lucas)
• Understanding Understanding Mathematics (Edwina Michiner)
• The Structure of Mathematics (Edwina Michiner)

Feel free to recommend any that is close to this and I’ll incorporate them one by one as I find time to parse and assimilate.