Publications

You can find (most of) my papers for download also on my PhilPapers page, my academia.edu page, or my ResearchGate page.

Peer-reviewed scientific articles

  1. 2025 – “The need for ethical guidelines in mathematical research in the time of generative AI”. AI and Ethics. doi: 10.1007/s43681-025-00660-5. Download.
  2. 2025 – “Intelligence is not deception: from the Turing test to community-based ascriptions”. AI & Society. doi: 10.1007/s00146-024-02172-y. Download.
  3. 2025 – “How to Recognize Artificial Mathematical Intelligence in Theorem Proving”. Topoi. doi: 10.1007/s11245-025-10164-w. Download.
  4. 2025 – “How numeral words and symbols shape arithmetical cognition”. Cybernetics & Human Knowing, 31 (3-4), 111-128. With Frederik Stjernfelt.
  5. 2024 – “Where Does Cardinality Come From?”. Review of Philosophy and Psychology. doi: 10.1007/s13164-024-00746-9. With Bahram Assadian. Download.
  6. 2024 – “The Cognitive Foundations and Epistemology of Arithmatic and Geometry”. Internet Encyclopedia of Philosophy. Link.
  7. 2024 – “Theorem Proving in Artificial Neural Networks: New Frontiers in Mathematical AI”. European Journal for Philosophy of Science, 14, 4. doi: 10.1007/s13194-024-00569-6. Download.
  8. 2024 – “Why Do Numbers Exist? A Psychologist Constructivist Account”. Inquiry. doi: 10.1080/0020174X.2024.2305386. Download.
  9. 2023 – “Peirce’s Philosophy of Notations and the Trade-offs in Comparing Numeral Symbol Systems”. Cognitive Semiotics. doi: 10.1515/cogsem-2023-2007. With Frederik Stjernfelt. Pre-print.
  10. 2023 – “On Radical Enactivist Accounts of Arithmetical Cognition”. Ergo, 9, 57. doi.org/10.3998/ergo.3120 Download.
  11. 2023 – “Developing Artificial Human-Like Arithmetical Intelligence (and Why).” Minds and Machines. 1-18. doi: 10.1007/s11023-023-09636-y Download.
  12. 2023 – “From Maximal Intersubjectivity to Objectivity: An Argument from the Development of Arithmetical Cognition”. Topoi, 42, 271-281. doi: 1007/s11245-022-09842-w. Download.
  13. 2023 – “On What Ground Do Thin Objects Exist? In Search of the Cognitive Foundations of Number Concepts”. Theoria, 89(3), 298-313. doi:10.1111/theo.12366. Download.
  14. 2022 – “On the Development of Geometric Cognition: Beyond Nature vs. Nurture”. Philosophical Psychology, 35(4), 595-616. doi: 10.1080/09515089.2021.2014441 Pre-print.
  15. 2021 – “Objectivity in Mathematics, without Mathematical Objects”, Philosophia Mathematica, 29(3), 318-352. doi: 10.1093/philmat/nkab010. Pre-print.
  16. 2021 – “Bootstrapping of Integer Concepts: the Stronger Deviant‑interpretation Challenge (and How to Solve It)”. Synthese, 199 (3-4), 5791-5814 doi.org/10.1007/s11229-021-03046-2. Download.
  17. 2021 – “Descriptive Complexity, Computational Tractability, and the Logical and Cognitive Foundations of Mathematics”. Minds and Machines, 31,  75-98. doi: 10.1007/s11023-020-09545-4. Download.
  18. 2021 – “Cognitive and Computational Complexity: Considerations from Mathematical Problem Solving”. Erkenntnis, 86, 961-997. https://doi.org/10.1007/s10670-019-00140-3. Download.
  19. 2021 – “A fresh look at research strategies in computational cognitive science: The case of enculturated mathematical problem solving”. Synthese, 198, 3221-3263. https://doi.org/10.1007/s11229-019-02276-9. With Regina E. Fabry. Download.
  20. 2020 – “Complexity of Mental Integer Addition”. Journal of Numerical Cognition, 6(1), 148-163. With Stefan Buijsman. Pre-print.
  21. 2019 – “The Enculturated Move From Proto-Arithmetic to Arithmetic”. Frontiers in Psychology 10: 1454. doi: 10.3389/fpsyg.2019.01454. Download.
  22. 2018 – “Mathematical explanations and mathematical applications”, in Sriraman, B. (ed.) Handbook of Mathematics of the Arts and Sciences, Springer. doi: 10.1007/978-3-319-70658-0_30-1. Download.
  23. 2018 – “Early Numerical Cognition and Mathematical Processes”, THEORIA, 33 (2), 285-304, 494-503. Download.
  24. 2016 – “The Modal Status of Contextually A Priori Arithmetical Truths”, in Boccuni & Sereni (eds.): Philosophy of mathematics: objectivity, cognition, and proof, Springer. Download.
  25.  2016 – “The Great Gibberish: Mathematics in Western Popular Culture.” Larvor (ed.): In Mathematical Cultures: The London Meetings 2012-2014, Springer. Download.
  26. 2016 – “Frege, Dedekind, and the Epistemology of Arithmetic”, Acta Analytica, 31 (3), 297-318. Download.
  27. 2015 – “Assessing the ‘New Epistemology of Mathematics’”, Discipline filosofiche XXV, 1. Download.
  28. 2015 – “In search of aleph-null: how infinity can be created?”, Synthese, 192 (8), 2489-2511. Download.
  29. 2014 – “An Empirically feasible approach to the epistemology of arithmetic”, Synthese, 191 (17), 4201-4229. Download.
  30. 2012 – “Perspectives to Empirical Philosophy of Mathematics”, in Petrov, V. (ed.) Applied and Experimental Philosophy in the Knowledge Based Society East and West, pp. 170-80. Download.
  31. 2012 – “At What Stage Does Mathematical Understanding Arise? Toward Empirically Feasible Philosophy of Mathematics” (in Finnish, “Missä vaiheessa matemaattinen ymmärrys syntyy?”), in Viljanen, Siipi and Sintonen (eds.): Ymmärrys, Reports from the Department of Philosophy Vol. 25, University of Turku. Download.
  32. 2011 – “What Can We Deduce from Gödel’s Incompleteness Theorems in Philosophy?” (in Finnish, “Mitä Gödelin epätäydellisyysteoreemoista voidaan päätellä filosofiassa), Ajatus, Vol. 68, pp. 175-200. Download.

Scientific books (monographs)

  1. 2024 – Numerical Cognition and the Epistemology of Arithmetic. Cambridge University Press, 252p. ISBN: 9781009468886
  2. 2009 – Truth, Proof and Gödelian Arguments: A Defence of Tarskian Truth in Mathematics, Philosophical Studies from the University of Helsinki, Vol. 23, 308p. Download.

 Edited volumes

  1. 2020 – Synthese Special Issue: Mathematical Cognition and Enculturation, with Catarina Dutilh Novaes. Download  the Introduction, written by me.

Book reviews

  1. 2018 – Extended book review – Caleb Everett: Numbers and the Making of Us, Journal of Numerical Cognition (with Paula Quinon). Download.
  2. 2018 – Sorin Bangu (ed.): Naturalizing Logico-Mathematical Knowledge, The Philosophical Quarterly. https://doi.org/10.1093/pq/pqy051. Download.

Non-peer-reviewed scientific articles

  1. 2024 – “Wissenschaftstheoretisch Reflexionen zu Research Software Engineering”. RWTH Themen Forschungsmagazin, 1, 80-83. With Gramelsberger, G., Heyen, D., Kasprowicz, D., Kerksieck, F., Venator, T. & Wenz, D.
  2. 2023 – Blog entry: “On Radical Enactivist Accounts of Arithmetical Cognition”. Ergo Blog. https://ergoblog.org/markus-pantsar-on-radical-enactivist-accounts-of-arithmetical-cognition/
  3. 2022 – “Twitter and the Aphoristic (Re)turn in Thought, Knowledge and Education.” Educational Philosophy and Theory. doi: 10.1080/00131857.2022.2132937. With Fuller, S., Gorman, D., Dusek, V., Babich, B., Basbøll, T. & Rider, S.
  4. 2020 – “Mathematical Cognition and Enculturation: Introduction to the Synthese Special Issue”. Synthese, 197, 3647-3655. doi: 10.1007/s11229-019-02478-1

Theses

  1. 2004 – Arguments against strong artificial intelligence, Master’s thesis in theoretical philosophy, University of Helsinki.
  2. 2004 – Gödel’s Incompleteness Theorems, Laudatur thesis in mathematics, University of Helsinki.