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Ad Hoc classes (PhD Project: Epistemology and Philosophy of Mathematics and Logic).

The Foundations of The Foundations of Arithmetic – Abstraction, Grounding, and Aristotelianism (a.a. 2019/20)

Programma

The main actors in this course will be abstraction principles and grounding. The former are familiar from abstractionism in the philosophy of mathematics, namely the project – which originates from Frege’s The Foundations of Arithmetic – of recovering significant portions of mathematics on the basis of such principles. The notion of metaphysical dependence or grounding has also attracted much attention in the current literature, where many now argue that non-causal explanations, which are central to many branches of philosophy, should be regimented by a primitive notion of grounding rather than in other (e.g. modal) terms. In this course we will go over the dominant conception(s) of metaphysical dependence by exploring a ground-theoretic reconstruction of abstractionist programs in the philosophy of mathematics (esp. Hale’s and Wright’s neo-logicism, Rayo’s trivialism, Linnebo’s minimalism, and some recent proposals for forms of Aristotelianism about mathematical objects), highlighting some problems and showing their consequences for the theory of grounding in general. We will end up by considering some puzzles of ground and discussing how those puzzles are related to the familiar set-theoretic paradoxes.

Svolgimento

April 15th 2020, 11.00-13.00; 14.00-16.00   
April 22nd 2020, 11.00-13.00; 14.00-16.00
April 29th 2020, 11.00-13.00

Bibliografia

  • Wright, C. (1983). Frege’s Conception of Numbers as Objects. Aberdeen: Aberdeen University Press. [selections]
  • Linnebo, Ø. (2012). “Metaontological Minimalism”, Phil. Compass, 7 (2): 139-51.
  • Rayo, A. (2015). “Nominalism, Trivialism, Logicism”. Philosophia Mathematica, 23 (1): 65-86
  • Donaldson, T. (2017).  “The (Metaphysical) Foundations of Arithmetic?”, Noûs, 51 (4): pp. 75-801.

Esame

The evaluation will be based on (active) participation to classes.

Credits: 2.

Luca Zanetti

Assegnista

Ciclo : XXXV

Tipologia corso : Tipo a

Periodo: Semestre II

Anno accademico: 2019-2020

Luogo : Aula 1-17

Durata : 8 ore