Logic Café colloquium of the Department of Philosophy

Do 10.11.2022 10:30-11:15 Uhr

10:30-11:15 Uhr
Simon Weisgerber (Universität Wien):
"Rigor, Visual Proofs and Types of Mathematical Justification".


Visual proofs, or "proofs without words" as they are commonly referred to by mathematicians, are often considered (as by Hamami (2022)) not to be valid or proper, let alone rigorous mathematical proofs. In my talk, I will argue that a specific visual proof (which is supposed to show that 1/2+1/4+1/8+1/16+...=1), although it might not be rigorous, is proper, in the sense that it functions properly as a justification for a piece of mathematical knowledge. To this end, I elaborate on Jody Azzouni's characterization of this visual proof (2013, 2020). I will argue that his assessment of the epistemic process associated with the proof can turn out to be essentially correct if we establish the correctness of an implicit assumption in an appropriate way first. The "appropriate way" I will offer is a justification of the assumption with the help of historical evidence from the history of mathematics. That is, besides two types of mathematical justification that are present in contemporary mathematical practice (justification via rigorous proof, and justification of mathematical theses, such as Church's thesis, mainly via quasi-empirical evidence) there is another type, namely mathematical justification via historical evidence.

  • Jody Azzouni. That We See That Some Diagrammatic Proofs Are Perfectly Rigorous. Philosophia Mathematica (III), 21(3): 323–338, 2013.
  • Jody Azzouni. The Algorithmic-Device View of Informal Rigorous Mathematical Proof. In Sriraman (ed.), Handbook of the History and Philosophy of Mathematical Practice, Springer, Cham, 2020.
  • Yacin Hamami. Mathematical rigor and proof. The Review of Symbolic Logic, 15(2), pages 409–449, 2022.
  • Simon Weisgerber. Visual Proofs as Counterexamples to the Standard View of Informal Mathematical Proofs? In Giardino, Linker, Burns, Bellucci, Boucheix, and Viana (eds.), Diagrammatic Representation and Inference. Diagrams 2022. Lecture Notes in Computer Science(), vol 13462, 37–53. Cham: Springer, 2022.


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