18 Unconventional Essays on the Nature of Mathematics, edited by Reuben Hersh. New York: Springer, 2006.
Appraising Lakatos: Mathematics, Methodology, and the Man, edited by George Kampis, Ladisla V Kvasz, Michael Stöltzner. Dordrecht: Springer Science+Business Media, 2002.
Bacon, Andrew. A Philosophical Introduction to Higher-order Logics. New York Routledge, 2024.
Bigelow, John. The Reality of Numbers: A Physicalist’s Philosophy of Mathematics. Oxford: Clarendon Press, 1988.
Byers, William. How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics. Princeton: Princeton University Press, 2007.
Cellucci, Carlo. Rethinking Logic: Logic in Relation to Mathematics, Evolution, and Method. Dordrecht: Springer, 2013.
Conceptual and Procedural Knowledge: The Case of Mathematics, edited by James Hiebert. Hillsdale, NJ: L. Erlbaum Associates, 1986.
Feferman, Solomon. In the Light of Logic. New York: Oxford University Press, 1998.
Franzén, Torkel. Gödel’s Theorem: An Incomplete Guide to Its Use and Abuse. Wellesley, MA: A K Peters, 2005.
Haverkamp, Nick. Intuitionism vs. Classicism: A Mathematical Attack on Classical Logic. Frankfurt am Main: Vittorio Klostermann, 2015.
Hwang, SungWon; Roth, Wolff-Michael. Scientific & Mathematical Bodies: The Interface of Culture and Mind. Rotterdam: Sense Publishers, 2011.
Lakatos, Imre. Proofs and Refutations: the Logic of Mathematical Discovery, edited by John Worrall and Elie Zahar. Cambridge, UK; New York: Cambridge University Press, 1976.
Mancosu, Paolo. Abstraction and Infinity. Oxford: Oxford University Press, 2016.
The Metaphysics of Logic, edited by Penelope Rush. Cambridge: Cambridge University Press, 2014.
Novaes, Catarina Dutilh. Formal Languages in Logic: A Philosophical and Cognitive Analysis. Cambridge: Cambridge University Press, 2012.
The Palgrave Companion to the Philosophy of Set Theory, edited by Carolin Antos, Neil Barton, Giorgio Venturi. Cham: Palgrave Macmillan, 2025.
Placek, Tomasz. Mathematical Intuitionism and Intersubjectivity: A Critical Exposition of Arguments for Intuitionism. Dordrecht: Springer Science+Business Media, 1999.
Potter, Michael. Set Theory and Its Philosophy: A Critical Introduction. Oxford: Oxford University Press, 2004.
Roth, Wolff-Michael. The Mathematics of Mathematics: Thinking with the Late, Spinozist Vygotsky. Rotterdam: Sense Publishers, 2017.
Schmidt, João Vitor; Venturi, Giorgio. “Axioms and Postulates as Speech Acts,” Erkenntnis, 25 February 2023.
Steiner, Mark. The Applicability of Mathematics as a Philosophical Problem. Cambridge, MA; London: Harvard University Press, 1998.
van Inwagen, Peter; Craig, William Lane. Do Numbers Exist? A Debate about Abstract Objects, with a Foreword by Mark Balaguer. New York: Routledge, 2024.
Reviewed by Crispin Wright, Notre Dame Philosophical Reviews, 2025.06.4.
Weber, Zach. Paradoxes and Inconsistent Mathematics. Cambridge: Cambridge University Press, 2021.
Felgner, Ulrich. Philosophy of Mathematics in Antiquity and in Modern Times. Cham: Birkhäuser, 2023.
Graham, Loren; Kantor, Jean-Michel. Naming Infinity: A True Story of Religious Mysticism and Mathematical Creativity. Cambridge, MA: Belknap Press of Harvard University Press, 2009.
Hahn, Robert. The Metaphysics of the Pythagorean Theorem: Thales, Pythagoras, Engineering, Diagrams, and the Construction of the Cosmos out of Right Triangles. Albany: State University of New York Press, 2017.
Hansson, Sven Ove. “Technology and Mathematics,” Philosophy & Technology, vol. 33 (2020), pp. 117-139.
Hesseling, Dennis E. Gnomes in the Fog: The Reception of Brouwer's Intuitionism in the1920s. Basel: Springer Basel AG, 2003.
Heyting, Arend. “Disputation,” in Philosophy of Mathematics: Selected Readings, 2nd ed., edited by Paul Benacerraf & Hilary Putnam (Cambridge: Cambridge University Press, 1983), pp. 66-76.
Hill, Claire Ortiz; Rosado Haddock, Guillermo E. Husserl or Frege?: Meaning, Objectivity, and Mathematics. Chicago: Open Court, 2000.
An Historical Introduction to the Philosophy of Mathematics: A Reader, edited by Russell Marcus and Mark McEvoy. London; New York: Bloomsbury Academic, 2016.
Mancosu, Paolo. The Adventure of Reason: Interplay between Philosophy of Mathematics and Mathematical Logic, 1900-1940. Oxford: Oxford University Press, 2010.
Nirenberg, David and Ricardo L. Uncountable: a Philosophical History of Number and Humanity from Antiquity to the Present. Chicago: University of Chicago Press, 2021.
Pre-modern Mathematical Thought: The Latin Discussion (13th-16th Centuries), edited by Clelia V. Crialesi. Boston: Brill, July 2025.
Scriba, Christoph J.; Schreiber, Peter. 5000 Years of Geometry: Mathematics in History and Culture. Basel: Birkhäuser (Springer), 2015.
Space: a History, edited by Andrew Janiak. New York: Oxford University Press, 2020.
van Atten, Mark. Essays in Gödel’s Reception of Leibniz, Husserl and Brouwer. Cham: Springer. 2015. (Logic, Epistemology, and the Unity of Science; vol. 35)
van Atten, Mark. On Brouwer. Toronto: Wadsworth, 2004.
Cohen, Paul J. Set Theory and the Continuum Hypothesis, with a new introduction by Martin Davis. Mineola, NY: Dover Publications, 2008.
Krantz, Steven G. The Proof Is in the Pudding: the Changing Nature of Mathematical Proof. New York; London: Springer, 2011.
Netz, Reviel. The Shaping of Deduction in Greek Mathematics: a Study in Cognitive History. Cambridge, UK; New York: Cambridge University Press, 1999.
Stillwell, John. The Story of Proof: Logic and the History of Mathematics. Princeton, NJ: Princeton University Press, 2022.
Contributions to the History of Indian Mathematics. New Delhi: Hindustan Book Agency, 2005. See esp.:
Patte, François. “The Karani: How to Use Integers to Make Accurate Calculations on Square Roots.”
Joseph, George Gheverghese. A Passage to Infinity: Medieval Indian Mathematics from Kerala and Its Impact. New Delhi; Thousand Oaks: SAGE Publications, 2009.
Plofker, Kim. Mathematics in India. Princeton: Princeton University Press, 2009.
The Questions of King Milinda (Milindapanha): Book II. Chapter 2; translated by T. W. Rhys Davids. [On continuity & discontinuity.]
Compass and Straightedge: Why? by Dave Peterson, Math Doctors, October 21, 2019
Straightedge and compass construction – Wikipedia
“What is the Relationship Between Logic and Reality?” by R. Dumain
Argumentation & Controversies: Selected Bibliography
Category Theory — History & Philosophy: An Introductory Bibliography
Dialectics in A Dictionary of Marxist Thought / Roy Edgley, Roy Bhaskar, Robert M. Young
Essence of dialectical method vs ideology: key links
History of Chinese Logic, Argumentation, & Rhetoric to 1950: Essential Bibliography
History, Sociology, & Scope of Logic: Select Bibliography
Indian Logic & Argumentation: Selected Bibliography
Irony, Paradox, & Reductio ad Absurdum: Selected Online Sources
Jean van Heijenoort: Essential Books
John Dewey’s Logic: A Select Bibliography
Lenin on Aristotle (& other Aristotle references)
Lewis Carroll’s Logic Games, Mathematical Recreations, Puzzles & Paradoxes
Philosophy of Paraconsistency & Associated Logics (Web Guide)
Susan Haack — An Introductory Guide
Note: This is not to be considered a comprehensive bibliography, nor can I trace the paths by which these sources were discovered. They are all relevant to a large ongoing project on the philosophy of mathematics and logic. Other bibliographies created and to come focus on areas minimized (but not absent) here: the philosophy and history of logic (largely separated from mathematics) in general and in specific civilizational traditions, ‘informal logic’, reasoning and psychology in broader contexts, paraconsistent logic, category theory, pedagogy. and crucially, dialectical treatments of the formal sciences (Hegelian, Marxian, Marxist, Ilyenkovian, Vygotskian, etc.). Theorization of the historical and social development of abstraction and the formal sciences in relation to and beyond practical activity is at stake here.
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