Logic and Philosophy of Mathematics at Oxford


Philosophy of Mathematics seminar

Philosophy and Mathematics undergraduate course


Logic Seminar in the Mathematical Institute

Faculty of Philosophy


Philosophy of Mathematics Seminar

The seminar takes place on Mondays 4:30‐6:30 pm.

In-person meetings take place in the Ryle Room of the Radcliffe Humanities Building

Conveners: Daniel Isaacson, Chris Scambler, and James Studd

The topics of the seminar go beyond philosophy of mathematics in the strict sense. They include themes from formal logic, but also applications of formal methods in philosophy in general. Our speakers come from different subjects, including philosophy, computer science, and mathematics. The content of the talks varies from highly technical to purely informal.

Everyone is invited to attend the seminar. We welcome especially graduate and undergraduate students from all subject areas. It is perfectly acceptable to attend only selected talks.

We urge that participants abide by the Guidelines for respectful, constructive, and inclusive philosophical discussion

The seminar's YouTube channel with recordings of selected talks can be found here.

Trinity 2024

Unless indicated otherwise, talks will have a hybrid format (in-person in the Ryle Room of the Philosophy Faculty and online via Zoom).

All meetings of the seminar will be 4.30-6.30 p.m. Oxford time. A link for the Zoom meetings will be included in the email announcements circulated to the seminar’s mailing list. If you would like to be added to this list, please contact daniel.isaacson@philosophy.ox.ac.uk

Some online talks, including the discussion, may be recorded and posted on our YouTube channel.

29th April (week 2) Laura Crosilla (Oslo), Predicativity as invariance

13th May (week 4) William D’Alessandro (Oxford) Explanation in mathematics: a noetic account

27th May (week 6) Carl Posy (Hebrew University), Model theory, intuitionism, and paradox

10th June (week 8) Douglas Blue (Pittsburgh), Hierarchies of infinity

Hilary 2024

22nd January (week 2) Ali Enayat (University of Gothenberg), Categoricity-like properties in the first order realm. In person and via Zoom.

5th February (week 4) James Studd (LMH, Oxford), Contingentist sets as potentialist properties. In person and via Zoom.

19th February (week 6) Sharon Berry (Indiana University Bloomington), Mathematical access worries and accounting for knowledge of logical coherence. Via Zoom only.

4th March (week 8) Stella Moon (Czech Academy of Sciences Institute of Philosophy), Husserlian philosophy of mathematical practice and homotopy type theory. Via Zoom only.

Michaelmas 2023

16th October (week 2) Fenner Tanswell (Technische Universität Berlin) and Ásgeir Berg Matthíasson (University of Iceland), The philosophical implications of using large language models in mathematics Zoom only

30th October (week 4) Benjamin Marschall (Trinity College, Cambridge), Carnap, the conventionalist

13th November (week 6) Chris Scambler (All Souls College, Oxford), The possibility of potentialism

27th November (week 8) Hans Robin Solberg (Oxford), Are large cardinal axioms in bad company?

Trinity 2023

1st May (week 2) Daniel Isaacson (Oxford), Kripke on Gödel incompleteness

15th May (week 4) Xinhe Wu (Bristol), Boolean-valued models of set theory with urelements

22nd May (week 5) Joel David Hamkins (Notre Dame), Natural instances of illfoundedness and nonlinearity in the hierarchy of consistency strength

29th May (week 6) Anna Bellomo (Vienna) Bolzano’s measurable numbers

12th June (week 8) Andrew Bacon (USC), Mathematical modality: an investigation of set-theoretic contingency.Via Zoom only.

Hilary 2023

23rd January (week 2) Wesley Wrigley (London School of Economics), Absolutely undecidable arithmetical propositions

6th February (week 4) Mary Leng (York University), To be (thin) or not to be? Are thin objects fictional or are fictional objects thin?

20th February (week 6) Juhani Yli-Vakkuri (Australian Catholic University) and Zachary Goodsell (University of Southern California), New logical foundations for mathematics. Via Zoom only.

6th March (week 8) Andreas Ditter (Queen’s College Oxford), Higher-order essences

Michaelmas 2022

17th Oct (week 2) Carlo Nicolai (King’s College London), Graph conceptions of properties

The seminar will not take place in week 4; instead, we will meet in week 5:

7th Nov (week 5) A.C. Paseau and Fabian Pregel (Oxford), Deductivism: a new appraisal

14th Nov (week 6) Wilfried Sieg (Carnegie-Mellon), Proofs as objects

28th Nov (week 8) Frederique Janssen-Lauret (Manchester), Founding mothers: Women’s contributions to logic in the early analytic period

Trinity 2022

2nd May (week 2) Carolin Antos (Konstanz) Defective concepts and pluralism in mathematics Hybrid meeting: in the Ryle Room and via Zoom

16th May (week 4) Alex Roberts (Oxford) Modality and modalities Hybrid meeting: in the Ryle Room and via Zoom

30th May (week 6) Crispin Wright (NYU) Making Exceptions via Zoom only

13th June (week 8) Luca Incurvati (Amsterdam) On logical and scientific strength via Zoom only

Hilary 2022

24th January (week 2) Chris Scambler (All Souls) Axiomatic Potentialism Hybrid meeting: in the Ryle Room and via Zoom

7th February (week 4) Kit Fine (NYU) Postulation and Possibility Hybrid meeting: in the Ryle Room and via Zoom

21st February (week 6) Paolo Mancosu (Berkeley and Paris) How many points are in a line segment? From Grosseteste to the theory of numerosities via Zoom only

7th March (week 8) Zeynep Soysal (Rochester) Fixing mathematical content via Zoom only

Michaelmas 2021

18th October (week 2) Eileen Nutting (Kansas) Approaches to Ordinal Abstraction via Zoom

1st November (week 4) Joel David Hamkins (Oxford) Fregean abstraction in Zermelo-Fraenkel set theory via Zoom

15th November (week 6) Keith Hossack (Birkbeck) The known universe Hybrid meeting: in the Ryle Room and via Zoom

29th November (week 8) Beau Mount (Konstanz) Goliath’s Sword: Repurposing Fictionalism to Tame Choice Sequences via Zoom

Trinity 2021

3 May (week 2) Sorin Bangu (Bergen and Oxford) Two dualisms in later Wittgenstein's writings on mathematics

17 May (week 4) Charles Parsons (Harvard), Evidence and the hierarchy of mathematical theories

31 May (week 6) Andrea Reichenberger (Paderborn), Rózsa Péter on the philosophy and foundations of mathematics

14 June (week 8) Andrea Cantini (Florence), Reflecting and unfolding

Hilary 2021

week 2 (25 January) David Corfield (Kent) Modal Homotopy Type Theory

week 4 (8 February) Máté Szabo (Oxford) Max Newman’s Influence on Turing’s Early Work

week 6 (22 February) Peter Koellner (Harvard) Two Futures: Pattern or Chaos

week 8 (8 March) Giovanna Corsi (Bologna) From Kripke to Lewis and beyond: A foundational study of quantified modal logic

Michaelmas 2020

Some recordings of the talks are available here on our YouTube channel.

All talks will take place at 4.30 p.m. UK time.

week 2 (19 October) Patricia Blanchette (Notre Dame) Frege on Caesar and Hume's Principle

week 4 (2 November) Rebecca Morris Intellectual virtues in mathematics

week 6 (16 November) Stephen Yablo (MIT) How and Why to be Logically Non-Omniscient

week 8 (30 November) Neil Barton (Konstanz) Algebraic Levels and Incomplete Structures

Trinity 2020

The Philosophy of Mathematics Seminar will not meet in Trinity term because of the public health restrictions. We will reschedule talks by the speakers who were scheduled to speak this term when possible. 

Hilary 2020

Previously some of the talks were announced for different dates. Now all talks have been scheduled for even weeks.

week 2 (27 January) Tim Button (UCL) Loving the universe

week 4 (10 February) Martin Fischer (Munich) Predicativity, Potentiality and Partiality

week 6 (24 February) Peter Fritz (Australian Catholic University Melbourne) Why Intensionalism?

week 8 (9 March) Hanoch Ben-Yami (Central European University) The Quantified Argument Calculus: Introduction, Overview, and Future Directions

week 8 (Thursday, 12 March, Lecture Room) Charles Parsons (Harvard), Evidence and the hierarchy of mathematical theories Because of travel restrictions, Professor Parsons' talk has had to be cancelled.

Michaelmas 2019

14 October (week 1) Albert Visser (Utrecht) What is a Provability Predicate?

28 October (week 3) Sam Roberts (Oslo) Ultimate V

11 November (week 5) Dan Isaacson (Oxford) Kreisel’s philosophy of mathematics

25 November (week 7) Tim Williamson (Oxford) Impossible worlds and semantic compositionality

Trinity 2019

13 May (week 3) Florian Steinberger (Birkbeck) Logical pluralism and logical normativity

27 May (week 5) Lavinia Picollo (UCL) A theory of untyped structured propositions

10 June (week 7) Kentaro Fujimoto (Bristol) Predicates and second-order logic

17 June (week 8) Volker Halbach (Oxford) The fourth grade of modal involvement

Hilary 2019

14 January (Monday of 1st week): Michal Godziszewski (Warsaw) Local Disquotation, Semantic Non-Conservativity of Truth, and Models of Set Theory

17 January (Thursday of 1st week) at 11.00 a.m. in the Mathematical Institute: John Baldwin (Illinois) (joint with the Logic Seminar) Philosophical implications of the paradigm shift in model theory

28 January (Monday of 3rd week) Menachem Magidor (Hebrew University) Independence in Mathematics: Is It Relevant?

11 February (Monday of 5th week) Mateusz Lelyk (Warsaw) The Implicit Commitments Thesis Meets the Tarski Boundary. (revised title)

18 February (Monday of 6th week) Marcus Giaquinto (UCL) A priori and a posteriori in mathematics  

Michaelmas 2018

Week 2 (15 Oct) No seminar Conference Necessary Beings: A Conference in Memory of Bob Hale in London. James Ladyman's talk has been moved to week 7.

Week 4 (29 October) Joel Hamkins (Oxford) On set-theoretic mereology as a foundation of mathematics

Week 6 (12 November) Laura Crosilla (Birmingham) Predicativity, indefinite extensibility and the natural numbers

week 7 (19 November) James Ladyman (Bristol) The Philosophical Logic of Homotopy Type Theory

Week 8 (26 November) Alex Paseau (Oxford) Which Cardinality Quantifiers are Logical?

Trinity 2018

Week 3 (7 May) Jack Woods (Leeds) Structuralist Neo-logicism

Week 4 (14 May), Benedict Eastaugh (Munich) Does nonclassical truth impair mathematical reasoning?

Week 5 (21 May) Gabriel Uzquiano (USC) Cantorian Counterexamples and the Limits of Thought

Week 8 (11 June) Marianna Antonutti Marfori (Munich) On the Significance of Mathematical Hierarchies

Week 11 (Friday, 6 July), 2pm, Francesca Poggiolesi (Paris) From logical to conceptual grounding: intelligibility and asymmetry of the notion

Hilary 2018

Week 2 (22 Jan) Michal Tomasz Godziszewski (Warsaw) On the Nonabsoluteness of Satisfaction

Week 5 (12 Feb) Beau Mount (Oxford) Bivalence, Fidelity, and Large-Cardinal Reflection: Variations on a Kreiselian Theme

Week 7 (26 Feb) Jean-Michel Salanskis (University of Paris Nanterre) A History of Non-Standard Approaches

Week 8 (5 March) Cheryl Misak (University of Toronto) Frank Ramsey's Contributions to Mathematics and Its Foundations, with Biographical Asides

Michaelmas 2017

Week 2 (16 Oct) Leon Horsten (Bristol) Arbitrary natural numbers

Week 3 (23 Oct) Kentaro Fujimoto (Bristol) Predicativism about classes

Week 5 (6 Nov) Dan Waxman (Oxford and Hong Kong) Did Gentzen Prove the Consistency of Arithmetic?

Week 6 (13 Nov) Salvatore Florio and Nicholas Jones (Birmingham) Unrestricted Quantification and the Structure of Type Theory

Week 8 (27 Nov) Dora Achourioti (Amsterdam) Truth and Groundedness

Trinity 2017

Week 1 (24 April) Ursula Martin (Mathematical Institute, and Department of Computer Science, University of Oxford), Crafting the mathematical machine

Week 1 (Thursday, 27 April) Peter Hylton (Department of Philosophy, University of Illinois at Chicago), Analyticity, yet again, 4.30-6.30 p.m., Thursday, in the Lecture Room of the Radcliffe Humanities Building, Woodstock Road, Oxford OX2 6GG

Week 3 (8 May) Damian Rössler (Mathematical Institute, Oxford University), A few remarks on the development of mathematical theories

Week 4 (15 May) Ian Rumfitt (All Souls College, Oxford), Neo-Fregeanism and the Burali-Forti Paradox

Hilary 2017

Week 2 (23 January) Volker Halbach (Oxford), The substitutional theory of logical consequence  

Week 3 (30 January) Catrin Campbell-Moore (Bristol), Limits in the Revision Theory 

Week 5 (13 February) Doukas Kapantais (Athens), “Consistency, a catchword making the second incompleteness theorem more spectacular than the first.” Comments on a comment by Georg Kreisel 

Week 6 (20 February) Øystein Linnebo (Oslo), Generality explained: A truth-maker semantics

Week 8 (6 March) Donald Gillies (King’s College London), An Aristotelian approach for contemporary mathematics 

Michaelmas 2016

Week 1 (10 October) Fenner Tanswell (Oxford), Proof, Rigour and Mathematical Virtues

Week 2 (17 October) Thomas Schindler (Cambridge), Deflationism, Classes, and the Epistemology of Arithmetic

Week 4 (31 October) Johannes Stern (Bristol), The Sky is the Limit: Reconsidering the Equivalence Scheme

Week 5 (7 November) Crispin Wright (NYU), Intuitionism and the Sorites

Week 7 (21 November) Walter Dean (Warwick), Incompleteness via paradox (and completeness)

Trinity 2016

Week 2 (2 May): Graham E Leigh (Technische Universität Wien), The Simple Truth

Week 3 (9 May): Dana Scott (Carnegie Mellon and UC Berkeley), Why Mathematical Proof?

Week 7 (6 June): James Studd (Oxford), The Caesar problem – towards a piecemeal solution

Week 8 (13 June): Janine Gühler (Oxford), Aristotle on mathematical truth

Hilary 2016

W2 (25 January): Alex Paseau (Oxford), Capturing consequence

W5 (15 February): Peter Simons (Trinity College Dublin), Collections

W7 (29 February): Leon Horsten (Bristol), On the logic of truth

W8 (7 March): Marcus Giaquinto (University College London), Mathematical proof: assessment of an empirical contribution to a philosophical dispute

Michaelmas 2015

W2 (19 October): Jeremy Gray (Open University and Warwick), Weyl and meaning

W3 (26 October): Andrew Arana (University of Paris 1), Non- Euclidean geometry and geometrical content

W6 (16 November): Alf Coles (Graduate School of Education, University of Bristol), A relational view of the concept of number; pedagogical, neuroscientific, and philosophical considerations

W7 (23 November): Adrian Mathias (Cambridge and La Réunion), The silence. (This talk will be about the Cambridge reaction to Gödel's discoveries of 1930/31)  

W7 (26 November): Benedikt Löwe (Cambridge and Amsterdam), Modal logic and Multiverses. This talk is joint with the Logic Seminar and will take place in the Mathematical Institute C5 (next door to the Radcliffe Humanities Building).

W8 (30 Nov): Juliette Kennedy (Cambridge and Helsinki), Entanglement and Formalism Freeness Revisited: Templates From Logic and Set Theory

Trinity 2015

W2: Kai Wehmeier, Truth in Modal Language

W5: Michael Sheard, Weak Deflationism and a Transactional Approach to Truth

W7: Owen Griffiths (joint with Alex Paseau), In Defence of Isomorphism Invariance

W8: Jonathan Payne, Absolute Generality and Expressibility

Hilary 2015

W1: Volker Halbach, Three Levels of Intensionality

W3: Peter Koepke, Natural Formalism

W5: Albert Visser, Collection, Lemmas, Reflection

W7: John Crossley, Programs from Proofs

W8: Matti Eklund, Incoherentism about Vagueness

27 Mar: Paolo Mancosu, In good company?  On Hume’s Principle and assignment of numbers to infinite concept

Michaelmas 2014

W0, 6 Oct, 11am-1pm, Colin Matthew Room: Oswaldo Chateaubriand, Objects, Properties, and Structures

W2, 20 Oct: Kobi Kremnitzer, Towards a Neo-Pragmatist Philosophy of (Pure) Mathematics

W4: Gabriel Uzquiano, Class Forms of Cantor’s Theorem

W6: John Wigglesworth, Naive Modal Set Theory

W7: Leon Horsten, Set Probabilities

Trinity Term 2014

W1, 28 Apr: Timothy Williamson (Oxford), Semantic Paradoxes and Abductive Methodology
W3, 12 May: Matthias Schirn (Munich), Logical Abstraction and Logical Objects
W5, 26 May: Carlo Nicolai (Oxford), Notes on Typed Truth and Consistency Assertions
W7, 9 Jun: Brendan Larvor (Hertfordshire), The Logic of Informal Proofs

Hilary Term 2014

W3, 3 Feb: Øystein Linnebo (Oslo), Parsons on Modality in Mathematics
W5, 17 Feb: Andrew Irvine (UBC), Categoricity and Alethic Modality
W6, 24 Feb: Peter Aczel (Manchester), The Structure Identity Principle in Set Theory and Type Theory
W8, 10 Mar: Julien Murzi (Kent/Munich), A Note on Instability and Revenge

Michaelmas Term 2013:

W2, 21 Oct: Jon Litland (Oslo), The Downwards Justification Procedure and the Completeness and Stability of Intuitionistic Logic
(This meeting will take place in the Seminar Room on the 3rd floor of the Radcliffe Humanities Building, rather than the Ryle Room)

W4, 4 Nov: Robbie Williams (Leeds), Rational Illogicality
W6, 18 Nov: Graham Leigh (Oxford), What’s in a T-sentence?
W8, 2 Dec: Nicholas Jones (Merton), Representors and Artefacts

Trinity Term 2013

W1, 22 Apr: Eckehart Koehler (Vienna), Goedel vs. Carnap on Logical Syntax
W2, 29 Apr: Tatiana Arrigoni (Trento), The Hyperuniverse Program: mathematical and philosophical aspects
W3, 6 May: James Studd (Oxford), Abstraction Reconceptualized
W4, 13 May: Jeffrey Ketland (Oxford), Leibniz Equivalence (GRADUATE TRAINING ROOM, GROUND FLOOR)
W5, 20 May: 2-4 pm Kobi Kremnitzer (Oxford), What is Geometry? (SEMINAR ROOM, 3rd FLOOR)
4:30-6:30 pm David Corfield (Kent), What might philosophy make of homotopy type theory? (RYLE ROOM)
W6, 27 May: Kentaro Fujimoto (Bristol), Some miscellaneous topics from the problem of implicit commitment in accepting set theory
W7, 3 Jun: Albert Visser (Utrecht) , Inconsistency Statements
W8, 10 Jun: Marianna Antonutti (Bristol), Human effective computability and Absolute Undecidability

Hilary Term 2013

W1, 14 Jan: Samson Abramsky (Oxford), Intensionality, definability and computation
W3, 28 Jan: Philip Welch (Bristol), Conceptual Structuralism
W5, 11 Feb: Richard Kaye (Birmingham), Adding Standardness to Nonstandard Models
W6, 18 Feb: Robert Thomas (Manitoba), Modality in Mathematics: Possibilities for whom?
W7, 25 Feb: Ole Thomassen Hjortland (Munich), Truth, Paracompleteness and Substructural Logics

Michaelmas Term 2012

W1, 8 Oct: Ralf Schindler (Münster), Dilemmas and Truths in Set Theory
W2, 15 October: Anton Setzer (Swansea), Proof theory of Martin-Loef Type Theory
W3, 22 October: no seminar (RI opening)
W4, 29 October: Karl-Georg Niebergall (Berlin), On the underdetermination of theories
W5, 5 November: Peter Hacker (Oxford), Wittgenstein on the nature of proof in mathematics.
W6, 12 Nov: Toby Meadows (Bristol), Sets, supersets and closure
W7, 19 Nov: Boris Zilber (Oxford), On continuity and its alternatives
W8, 26 Nov: Paul Egré (Paris), Borel on the Heap

Trinity Term 2012

W1, 23 Apr: “Third New College Logic Meeting”
W2, 30 Apr: Walter Dean (Warwick), Dedekind's Categoricity Theorem, induction, and mathematical communication
W3, 7 May: Alan Weir (Glasgow), Can formalism be revived?
W5, 21 May: Andrew Bacon (Oxford), A general approach to revenge paradoxes
W6, 28 May: Alan Baker (Oxford), Making sense of mathematical counterfactuals
W7, 4 June: Felix Mühlhölzer (Göttingen), How arithmetic is about numbers. A Wittgensteinian perspective
W8, 11 June: Alex Paseau (Oxford), Some remarks on proof and non-deductive evidence in mathematics

Hilary Term 2012

W1, 16 Jan: Timothy Williamson (Oxford), Informal Validity and Intended Models in Modal Logic
W2, 23 Jan, Gabriel Uzquiano (USC), Indefinite Extensibility Revisited
W2, 24 Jan, 2-4 pm, EXAMINATION SCHOOLS, Juliette Kennedy (Helsinki):
Change the Logic, Change the Meaning? Quine’s Dictum and the Case of Set theory
W2, 24 Jan, 4:30-6:30 pm, Jouko Väänänen (Helsinki), Second order logic, set theory and foundations of mathematics
W3, 30 Jan, Peter Schuster (Leeds), Proof, Computation, Preservation: a Case Study from Algebra
W4, 6 Feb, Kobi Kremnitzer (Oxford), Homotopy Type Theory: a new language for mathematics
W5, 13 Feb, Kentaro Sato (Bern), N versus the other Infinite
W6, 20 Feb, Christopher von Bülow (Konstanz), Shapiro’s and Hellman’s Structuralism (Abstract)
W7, 27 Feb: Salvatore Florio (Birkbeck, Kansas State), Semantics and the Plural Conception of Reality
W8, 5 Mar: Benedikt Löwe (Hamburg), Formalization is Idealization

Michelmas Term 2011

W1, 10 Oct: Lev Beklemishev (Lomonossov University Moscow), Provability Algebras: a Survey
W2, 17 Oct: Alex Paseau (Oxford), Mathematical Knowledge without Proof
W3, 24 Oct: Richard Pettigrew (Bristol), Indispensability arguments and instrumental nominalism (Abstract)
W4, 31 Oct: Timothy Bays (Notre Dame), Some Remarks on the Foundations of Arithmetic
W5, 7 Nov: Luca Incurvati, The Graph Conception of Set
W6, 14 Nov: Peter Schroeder-Heister (Tübingen), Proof-Theoretic Semantics, Self-Contradiction and the Format of Deductive Reasoning
W7, TUESDAY 22 Nov: Michael Rathjen (Leeds), On the (Unreasonable?) Effectiveness of Ideal Elements
W8, 28 Nov: Sean Walsh (Birkbeck College), Knowledge and Schemata

Trinity Term 2011

W1: Daniel Isaacson, What is Achieved by Zermelo’s proof of quasi-categoricity of second-order ZF?
W2a: Philip Welch, A Reflection Principle implying PD
W2b: Dirk Van Dalen, Brower’s Notion of Choice Sequence
W3: Mathieu Marion, Wittgenstein and Goodstein on the Equation Calculus and Uniqueness Rule
W4: Richard Heck, The Strength of Truth Theories
W5: Hannes Leitgeb, A Theory of Truth for Propositions
W6: Lev Beklemishev, On Provability Algebras for Theories of Iterated Truth
W7: John Burgess, Structure and Rigor
W8: Stewart Shapiro, Open Texture, Computability and Church’s Thesis

Hilary Term 2011

W1: Ian Rumfitt, Determinacy and Bivalence in Set Theory
W2: Albert Visser, Sameness of Theories
W3: Jeffrey Ketland, Nominalistic Adequacy
W4: Volker Halbach, T-sentences
W5: Ed Zalta, A Defense of Logicism
W6: Øystein Linnebo, Absolute but Indefinite Generality
W7: Antony Anderson, Church-Frege intensional logic with an application to Bolzano’s proof that there are infinite multiplicities
W8: Leon Horsten, The Absolutely Infinite


last change: 24 August, 2023