Knowledge and understanding: Students will be expected to acquire essential knowledge about some of the major philosophical problems concerning the foundations and epistemology of mathematics.
Use of knowledge and understanding: The course will provide students with tools for the application of rigorous methods of reasoning in diverse circumstances, with particular attention to mathematical proofs.
Ability to draw conclusions: The course will emphasize the relevance of accurate argumentation and the application of logical and formal tools to correct reasoning in mathematics and epistemology.
Communication skills: Strong emphasis will be placed on the capacity to discuss theoretical problems clearly and systematically, and to motivate through rigorous arguments one's point of view.
Ability to learn: Independent elaboration of the material presented in class will be encouraged. Knowledge acquisition will be facilitated through class discussions.
Familiarity with elementary sentential and predicate (both first- and higher-order) logic is recommended. Also, attendance to Philosophy of Mathematics: Epistemology and Practice (180008-EN) by Andrea Sereni (MOD1) and Silvia De Toffoli (MOD2) is recommended for an introduction to basic issues in the philosophy of mathematics.
Lectures accompanied by seminar-style discussions and general Q&A sessions. The active participation of students will be strongly encouraged. In the final seminar an opportunity will be provided for students to offer short presentations — perhaps 15 minutes in duration for class discussion— on issues arising.
Written exam in (take-home) paper form, possibly followed by (remote) oral exam depending on the paper's quality. Eligible topics, and criteria, for the paper will be made available during classes.
Recommended pre-reading before seminars start:
—Boghossian and Peacocke,eds. Introduction; Casullo, “Four problems”
All recommended pre-readings will be in the online folder for the module
Handouts will be available at the seminars.
The course will consist of 6 three hour long sessions, each divided into two 90 minute seminars on the same day
Session 1— Overview and the Problem of Characterising a priori knowledge; Quinean scepticism
(Pre-reading: Quine, “Two Dogmas”, Wright, “Inventing Logical Necessity” pp. 189-94)
Session 2— The Characterisation problem (cont.) and a second recent Sceptic (Hawthorne)
(Pre-reading: Hawthorne, “A Priority and Externalism”)
Session 3— The Characterisation problem (cont.) and a third recent Sceptic (Williamson)
(Pre-reading: Williamson, “How Deep….?”
Session 4 — Further reflections on the stock characterisation of a priori justification as "justification independent of experience"
(No pre-reading)
Session 5— The basic a priori and the imagination; Non-Cognitivism and Wittgenstein
(Pre reading: Wittgenstein Remarks on the Foundations of mathematics Part I §§25-32)
Session 6—On Our Knowledge of Basic Logical and Arithmetical Truths
(Pre-reading: Wright, “Logical Non-cognitivism”)
An extended reading list will be circulated.
