Università Roma Tre

Synthetic reasoning between sense and concept

The course aims to investigate the theory of gesture understood as a dynamic and continuous process of synthesis between sense and concept. In particular, starting from an analysis of the notion of synthetic judgment, the theory of transcendental schematism and mathematical and geometrical synthesis in Kant, we will then move on to analyze the metaphysical and mathematical question of the infinite and continuum in Georg Cantor and Charles S. Peirce. Finally, a proposal of mathematical gesture as a cognitive process will be explored.

The program syllabus will unfold as follows:
- Analysis of the Kantian distinction between synthetic and analytic judgments
- Analysis of Transcendental Schematism and the Kantian idea of the construction of mathematical and geometrical synthesis
- Proposal of an interpretative hypothesis of transcendental schematism as an active and dynamic synthesis of sense and concept through gesture
- Examination of Peirce's proposal of a logic of continuity
- Examination of Poincaré's conception of mathematics
- Proposal of a hypothesis on the mathematical gesture as a cognitive process starting with Giuseppe Longo

- I. Kant, “Introduction” and “On the schematism of pure concepts of understanding”, in Critique of the Pure Reason, Cambridge University Press 1998.
- C. S. Peirce, “Detached Ideas continued and the Dispute between Nominalists and Realists", in The New Elements of Mathematics (NEM), edited by C. Eisele, Mouton Publishers 1976, 4: 331-346.
- Henri Poincaré, Science and Hypothesis, Introduction, first and second part
- G. Maddalena, The Philosophy of Gesture, McGill Queens Univ 2015.
- G. Longo, "Gestualità umana nelle prove e l'incompletezza del formalismo", in Matematica e senso, Mimesis 2021, pp. 127-163.
- G. Baggio, Transcendental schematism and Quasi-transcendental semiotics. A working hypothesi. In S.P.̈. Krzysztof Piotr Skowronski (a cura di), Kant and Pragmatism, Nordic Pragmatism Network, 2019, pp. 77-97.

Recommended Texts

- G. Cantor, “Comunicazioni per la dottrina del transfinito (§§ 1-7)”, in La filosofia dell’infinito. Scritti scelti (1884-1888), Mimesis 2021, pp. 45-82.
- F. Zalamea, Peirce’s Continuum. A Methodological and Mathematical Approach.
- G. Maddalena, Metafisica per assurdo. Peirce e i problemi dell’epistemologia contemporanea, Rubbettino 2009, pp.127-223.
- F. La Mantia, C. Alunni, F. Zalamea (eds.), Diagrams and Gestures. Mathematics, Philosophy, and Linguistics, Springer 2023
- D.F. Wallace, Everything and More. A Compact History of Infinity, W. W. Norton & Company 2003