## 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 and Chris Scambler.
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.
### Michaelmas 2024
** This term, all 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.
21st October 2024 (week 2) Balthasar Grabmayr (Tübingen), Computation and the structure of arithmetic ** Rescheduled to 16 June 2025 (week 8)**
4th November 2024 (week 4) Silvia De Toffoli (Pavia), How to prove things with diagrams
18th November 2024 (week 6) Fabian Pregel (Oxford), Is logical consequence a relation between Fregean thoughts?
2nd December (week 8) James Studd (Oxford), Contingentist sets as potentialist properties
### Trinity 2024
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. ** Postponed until Michaelmas 2024 **
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:
31 May, 2024 |