Logic Café colloquium of the Department of Philosophy

Do 10.11.2022 11:30-13:00 Uhr

11:30-13:00 Uhr,
 Yacin Hamami (Centre for Logic and Philosophy of Science of the Vrije Universiteit Brussel):
"What role(s) for intuition in rigorous mathematical reasoning?"



As everyone knows, it has been common in mathematics since the turn of the twentieth century to hold that intuition should play no role in rigorous mathematical reasoning (see, e.g., Hahn 1933/1980). However, recent works in the philosophy of mathematical practice (De Toffoli and Giardino, 2015, 2016) have challenged this orthodoxy by exhibiting cases of mathematical proofs whose validity is evaluated in practice by appealing in an essential way to intuition. This, in turn, has motivated the search for alternative conceptions of mathematical rigor (see, e.g., Larvor, 2019). In this talk, I will explore a middle ground between these two conceptions of the relation between rigor and intuition. More specifically, I will argue that it is possible to attribute substantial epistemic roles to intuition in our epistemology of proofs in practice while retaining the standard view of mathematical rigor (Hamami, 2022). This will be achieved by disentangling different forms of proof presentations as well as different epistemic processes operating on these proof presentations. In link with the previous talk, I will suggest that intuition can play significant roles in proof understanding and proof conviction insofar as intuition can be effectively relied upon to represent and evaluate (partial) proof plans (Hamami and Morris, forthcoming). I will then make precise proposals as to what sort of cognitive capacities may be involved when we are talking of "intuition" in these contexts. I will conclude with some considerations as to why the examples of mathematical proofs exhibited by De Toffoli and Giardino (2015, 2016) do not motivate a revision of our conception of rigor, but instead are better conceived as proof presentations optimized to convey understanding and conviction.  

  • Silvia De Toffoli and Valeria Giardino. An inquiry into the practice of proving in low-dimensional topology. Boston Studies in the Philosophy and History of Science, pages 315–336, Springer, Dordrecht, 2015.
  • Silvia De Toffoli and Valeria Giardino. Envisioning transformations—The practice of topology. Mathematical cultures: The London Meetings 2012–2014; pages 25–50, Birkhäuser, Basel, 2016.
  • Hans Hahn. The crisis in intuition. In B. McGuinness, editor, Hans Hahn. Empiricism, Logic and Mathematics : Philosophical Papers, pages 73– 102. D. Reidel, Dordrecht, 1933/1980.
  • Yacin Hamami. Mathematical rigor and proof. The Review of Symbolic Logic, 15(2), pages 409–449, 2022.
  • Yacin Hamami and Rebecca Morris. Plans and planning in mathematical proofs. The Review of Symbolic Logic, forthcoming.
  • Brendan Larvor. From Euclidean geometry to knots and nets. Synthese, 196, pages 2715–2736, 2019.


Upcoming events of the Logic Café:

Meetings in this semester will be held in presence, usually on Mondays, between 16:45 and 18:15. The meetings will be held in seminar room 3D (D0316, NIG; 3rd floor) at the Department of Philosophy, Universitätsstrasse 7.
Please see our website for further information on the Logic Café colloquium, for past events, and regular updates: https://logik-cafe.univie.ac.at