Coming soon on Φ-Math

About

Mon, 01 Jan 0001 00:00:00 +0000

Φ-Math is a reading group in philosophy of mathematics from the Institute for Logic, Language and Computation (ILLC) at the University of Amsterdam.

Φ-Math was co-founded in 2020 by the first-year Master of Logic (MoL) students at the time Evan Iatrou and Noel Arteche.

It is currently managed by second year students Matteo Celli, Josje van der Laan and Marco de Mayda.

See the Board page for all the past memebers.

And a special thanks to Stefano Volpe for his great help with this new and improved website.

Board

Mon, 01 Jan 0001 00:00:00 +0000

Current Members

Matteo Celli (2025-current)
Josje van der Laan (2025-current)
Marco de Mayda (2024-current)

Past Members

Orestis Dimou Belegratis (2023-2025)
Alexander Lind (2023-2025)
Jan Gronwald (circa 2022-2023)

Founders

Evan Iatrou (circa 2020-2021)
Noel Arteche. (circa 2020-2021)

Logical Constants and Laws

Tue, 17 Mar 2026 16:00:00 +0100

For this session, our dear classmate Edoardo will tell us all about Martin-Löf’s impact on the philosophy of math and logic. The aim is to cover the topic in general, but for a text of focus we have the first two chapters of Per Martin-Löf’s On the Meanings of the Logical Constants and the Justifications of the Logical Laws.

Second-Order Logic: If not Set Theory in Sheep’s Clothing, What is it Then?

Wed, 04 Feb 2026 15:00:00 +0100

For this session of PhiMath, we read Bob Hale’s paper “Properties and the Interpretation of Second-Order Logic”. He defends a deflationary conception of properties, which are the things we quantify over in second order logic. According to Hale, something is a property iff there could be a predicate that stands for it.

He looks into Quine’s claim that second-order logic is “set theory in sheep’s clothing”, which he understands as a broader charge motivated by the idea that second-order quantification carries heavy existential commitments. According to him, his deflationary interpretation of second-order logic can resist Quine’s critique. During the meeting, we consider Hale’s proposal and its implications for second-order logic.

Mathematics, Like a Game?

Thu, 20 Nov 2025 15:00:00 +0100

This time, MoL alumnus Kirti Singh will present a paper co-authored with Klaas Landsman, titled “Is Mathematics Like a Game?”

As the name of the paper suggests, this session revisits the question of whether mathematics can be compared to a game. Drawing on ideas from Hilbert and Wittgenstein, Landsman and Singh argue that mathematics is best understood as a “rhododendron of language games”, where truth arises from the correctness of rule-following within the games rather than correspondence with reality. They propose a pluralist framework that connects the formal and applied sides of mathematics through inferential practices and axiomatization.

Truth and Proof: the Platonism in Mathematics

Thu, 02 Oct 2025 15:00:00 +0100

The PhiMath reading group is back for the academic year 2025/2026! We kick off with William Tait’s compelling exposition of the tension between Truth and Proof in Mathematics. Are mathematical proofs constructed or discovered by means of a proof? In the decade-long debate between constructivist and platonists, Tait defends Platonism by attacking some of Dummett’s main claims in favour of intuitionism. By adopting a similar approach towards the relaionship between language and reality as Dummet’s, he aims to downsize the accusations intuitionists wage against mathematical realists, arguing that proofs are merely representations of mathematical truth. The issues Tait brings up in this paper are extremely engaging for Intuitionists and Platonists alike, so come plenty and take part in the discussion!

Truth in Intuitionism

Mon, 23 Jun 2025 15:00:00 +0100

This time our classmates, Matteo and Josje, will presenet Panu Raatikainen’s Conceptions of truth in intuitionism.

We often summarize the intuitionist notion of truth as “truth as provability”, which marks a fundamental difference with the classical logicians. But in doing so, we overlook the fact that there are multiple competing conceptions of truth within intuitionism itself. Raatikainen presents a systematic overview of these different accounts, ranging from actualist to possibilist, and ultimately offers a critique of each, putting into question about the coherence of the intuitionist framework as a whole.

Modal Structuralism

Thu, 17 Apr 2025 15:00:00 +0100

Note the reschedule!

For this session we will look at Modality and Structuralism, section 15 of: Charles Parsons, Mathematical Thought and Its Objects, 1st ed. (Cambridge University Press, 2007). As the title suggests, Parson explores an acocunt of structuralism trough modal notions; the role of necessity and possibility in mathematical discourse, and the ontology of mathematical objects.

Does mathematics require an ontological commitment to abstract objects or can modal formulations capture mathematical truth without such commitments? Can modal logic provide a foundation for mathematical necessity? How does this modal structuralism compare to eliminative forms of structuralism?

Why is Burgess Not a Nominalist?

Tue, 11 Mar 2025 15:00:00 +0100

For this session, we will answer the title’s question with the short and sweet: John P. Burgess’s Why I Am Not a Nominalist, a broad overview against various forms of nominalism.

Burgess responds to nominalist attempts to dispense with abstract objects in mathematical and scientific discourse, challenging both instrumentalist and reconstructionist forms of nominalism, among others. Burgess purports to shift the burden of proof onto the nominalist rather than the realist, by arguing that nominalistic reconstructions need (and in his view fail) to account for the role of mathematics in science. His critique addresses Goodman, Quine, and Field, among others.

Intuiting the Infinite

Tue, 25 Feb 2025 15:00:00 +0100

For our first session of 2025, we will engage with Robin Jeshion’s Intuiting the Infinite. She defends Charles Parsons’ Kantian appeal to mathematical intuition to address the access problem of Platonism: If mathematical objects are abstract objects, how can we gain knowledge of them?

Jeshion argues that intuition plays a fundamental role in justifying our knowledge of the infinitude of natural numbers, responding to key criticisms about the cogency of arbitrary objects, vague representation, and the role of spatial and temporal structures in mathematical thought.

Your least and most favourite aspects of Phil. of Math

Fri, 29 Nov 2024 18:00:00 +0100

Another informal social gathering of our group for tea time! A good opportunity to get to know better the new members.

The topic: things that impressed and irritated us the most in the PoM during the 3 months the group runs. Of course, people can bring their own most and least favorite things regarding PoM outside of the group’s activity.

Infinity up on Trial: Reply to Feferman

Fri, 29 Nov 2024 17:00:00 +0100

In this session we will deal with a critique to some main ideas of Predicativists. They believe that, in some respects, arithmetic has some advantages that analysis and set-theory do not. Koellner puts this idea to the test.

Main Readings:

Koellner, Peter (2016). Infinity up on Trial: Reply to Feferman. Journal of Philosophy 113 (5/6):247-260.

Why be a Height Potentialist?

Fri, 01 Nov 2024 17:15:00 +0100

After talking about the infinite and Frege Arithmetic, it is time to turn to potentialism about set-theory. In this session we will turn to potentiality about the height of the cumulative hierarchy.

Main Readings:

Soysal, Z. (2024). Why be a Height Potentialist?. Journal for the Philosophy of Mathematics, 1, 155–175. https://doi.org/10.36253/jpm-2938

Aristotle meets Frege: from Potentialism to Frege Arithmetic

Fri, 18 Oct 2024 16:00:00 +0200

Our second meeting of the year continues along the lines of potentialism. Now we turn to Frege Arithmetic and a genuinely potentialist account of it.

Actual and Potential Infinity

Fri, 04 Oct 2024 16:00:00 +0200

Welcome to PhiMath 2024! In our first meeting for this academic year, we will discuss a paper by Linnebo and Shapiro on the notion of Potential Infinity.

Structuralism in Mathematics: Modal Set-Theoretic Structuralism

Fri, 16 Feb 2024 17:15:00 +0100

For our final meeting on structuralism, we cover the modal set-theoretic structuralism from Parsons and Linnebø. This rounds out the book we have been following and also our time with structuralism (for now).

Structuralism in Mathematics: Sui Generis and Modalities

Fri, 26 Jan 2024 17:15:00 +0100

For our next meeting on structuralism, we will be covering the two views championed by the authors of the textboock: Shapiro’s ante rem, or Sui Generis, structuralism and Hellman’s Modal Structuralism.

Main Readings

Chapter 5 and 6 in Hellman, G., & Shapiro, S. (2018). Mathematical Structuralism (Elements in the Philosophy of Mathematics). Cambridge: Cambridge University Press. doi:10.1017/9781108582933

Structuralism in Mathematics: Categories

Fri, 15 Dec 2023 17:15:00 +0100

For our second meeting on Structuralism in mathematics, we will be focusing on the category-theoretical side of the discussion. Stemming from work in algebraic topology, category theory has since the 1950’s become an indisposable tool for mainstream mathematics and is seen by some to encode the structuralist philosophy into mathematics itself. We will be reading and discussing some thoughts around the plausibility of using category-theoretic foundations for mathematics and whether this really follows the structuralist philosophy.

Structuralism in Mathematics

Fri, 01 Dec 2023 17:15:00 +0100

We are now covering the theory of structuralism in mathematics. This first meeting will be an overview of the general position and its various parts together with specific focus on set-theoretic structuralism. Over the course of the coming meetings, we will spend some time on various conceptions of structuralism and their proponents.

Responses to Higher-Order Logic

Fri, 10 Nov 2023 17:15:00 +0100

We are continuing our discussion about Higher-Order Logic (HOL), this time focusing specifically on arguments against adopting Higher-Order logics for various purposes. These arguments range from (HOL) being set theory in disguise, the (lack of) applicability of (HOL) for its intended purposes, and the serious metalogical issues the logic faces.

Philosophy of Higher Order Logic

Thu, 12 Oct 2023 17:15:00 +0100

The reading group in the philosophy of mathematics is back and we hold the first meeting on the 12th of October. The topic will be Higher-Order Logic. We will base the discussion around Stewart Shapiro’s chapter “Higher-order logic” in The Oxford Handbook of Philosophy of Mathematics and Logic.

Basics of Mereology

Thu, 12 May 2022 17:15:00 +0100

This time we take a recourse to mereology! In his talk, Elias Bronner will introduce the philosophical motivations for the field, Leśniewski’s nominalistic position. Further, we will discuss basic mereology and its relation to Boolean Algebras. Elias will conclude with touching upon a recent interpretation of mereology within set theory by J.D. Hamkins which suggests that mereology is too weak of a system to serve as a foundation for mathematics.

Mathematical Intuition

Thu, 21 Apr 2022 17:15:00 +0100

This time we continued Derek So’s discussion of phenomenology, its recent developments and relations to linear logic and embodied cognition.

Main Readings:

Tieszen, R. Mathematical Intuition: Phenomenology and Mathematical Knowledge. Dodrecht-Boston-London: Kluwer Academic Publishers.

Additional Readings:

Zahavi, D. Husserl’s Phenomenology, Stanford Univ. Press, pp. 14-26.
A fragment on categorial intuition by Jan Gronwald.

Mathematical Intuition

Thu, 07 Apr 2022 17:15:00 +0100

In relation to the first chapter of “Mathematical Intuition” by Richard Tiszen, we discussed some notions of Husserl’s phenomenology that pertain to the categorial intuition.

Derek So introduced us to some basic concepts of Husserl’s phenomenology. We focused on intentionality, synthetic and eidetic intuition. Then briefly discussed the different conceptions of intuition in more contemporary phenomenology.

Main Readings:

Tieszen, R. Mathematical Intuition: Phenomenology and Mathematical Knowledge. Dodrecht-Boston-London: Kluwer Academic Publishers. SUBCHAPTER 2. OF CH. 2, “INTENTIONALITY AND INTUITION”, pp. 21-25.

Mathematical Intuition

Fri, 11 Mar 2022 17:15:00 +0100

We partially discussed the 1st chapter from “Mathematical Intuition” by Richard Tiszen.

Main Readings

Tieszen, R. Mathematical Intuition: Phenomenology and Mathematical Knowledge. Dodrecht-Boston-London: Kluwer Academic Publishers.

The Philosophical Misconceptions of the Incompleteness Theorem

Fri, 25 Feb 2022 17:15:00 +0100

We discussed some popular misinterpretations of Gödel’s Theorem.

These were (1) Lucas/Penrose style of arguments against mechanism, (2) GIT as a confirmation of Platonism, (3) The “postmodern” interpretation.

The talk was given by Jan Gronwald.

Main Readings:

(Benacerraf, 1967) God, the Devil and Gödel. in: The Monist 51(1): pp. 9-32.
(Copeland and Shagrir, 2013), Turing versus Gödel on Computability and the Mind, in: B. Copeland, C. Posy, O. Shagrir (ed.), „Computability: Turing, Gödel, Church, and Beyond”. Cambridge, Mass.: MIT Press.

Wangs Paradox: Dummets Case against Strict Finitism

Fri, 16 Apr 2021 17:15:00 +0100

Tomasz will introduce us to Michael Dummet’s famous argument against strict finitism in the philosophy of mathematics. Dummet observed that every strict finitist is committed to the paradox arising with the use of vague expressions – the Sorites paradox – and concluded that “strict finitism is, therefore, an untenable position”. Or is it?

Slides used in the presentation are available here.

Main reading:

Dummett, M. (1975). Wang’s paradox. Synthese, 30(3), 301-324.

Additional Bibliography

Conceptions of the Continuum

Fri, 19 Feb 2021 17:15:00 +0100

Next reading will be Solomon Feferman’s Conceptions of the Continuum, available here.

Marta will present the paper, followed by a discussion.

Slides used in the presentation are available here.

Gödel Incompleteness Theorems, Free Will and Mathematical Thought

Fri, 05 Feb 2021 17:15:00 +0100

Our next reading meeting will revolve around Solomon Feferman’s article Gödel’s Incompleteness Theorems, Free Will and Mathematical Thought.

The paper can be freely accessed from the Mathematics Department site at the University of Stanford.

During the meeting, Ezra will present the paper, followed by a discussion.

Slides used in the presentation are available here.

Why Philosophers Should Care about Computational Complexity

Fri, 22 Jan 2021 17:15:00 +0100

Next reading meeting will touch on theoretical computer science. We will be seeing how computational complexity can potentially offer new insights into philosophy of mathematics. We will be reading Scott Aaronson’s survey paper Why Philosophers Should Care about Computational Complexity.

For the meeting, we expect attendants to read in advance sections 1-5, 8-9 and 12 of the paper, available here.

The meeting will have a presentation by Andrea and Noel, followed, as usual, by a discussion.

Towards a Philosophy of Music

Fri, 08 Jan 2021 17:15:00 +0100

We will be reading Iannis Xenakis’ Formalized Music: Thought and Mathematics in Composition, where mathematics and music come together.

During the session, Paul Maurice will present the paper, followed by a discussion.

Gödel Ontological Argument

Mon, 21 Dec 2020 19:00:00 +0100

For this special Christmas meeting, Rodrigo will be introducing Kurt Gödel’s argument about the existence of God, a classic medieval argument formalized in modal logic.

No reading preparation is required.

During the session, Rodrigo will present the argument, followed by a discussion.

Slides used during the presentation are available here. See also a handout with the proof.

Mathematics and Transcendental Phenomenology

Fri, 11 Dec 2020 17:15:00 +0100

Our third reading will be Richard Tieszen’s Richard’s Mathematics and Transcendental Phenomenology.

For this session we expect attendants to have read in advance the full second chapter from the book containing the essay; that is:

Tieszen, R. (2005). Mathematics and Transcendental Phenomenology. In Phenomenology, Logic, and the Philosophy of Mathematics (pp. 46–68), Chapter 2. Cambridge: Cambridge University Press.

The text can be accessed freely by University of Amsterdam students through this link to the library catalogue. (Recently there have been problems when accessing online collections, so it might be necessary to open the link on an incognito tab).

The Linguistics of Numerals

Fri, 04 Dec 2020 19:00:00 +0100

What are numeral words, and how do they work in different languages? Can we extract meaningful insights on the nature of numbers by inspecting the linguistics of the words that denote them?

During the session, Bobby will present an overview of the topic and the different research approaches to date, followed by a discussion.

Slides used in the presentation are available here

What Numbers Could Not Be

Fri, 27 Nov 2020 17:15:00 +0100

Our second reading will be Paul Benacerraf’s What Numbers Could Not Be.

For this session we expect attendants to have read in advance:

Benacerraf, Paul. “What Numbers Could Not Be.” The Philosophical Review 74, no. 1 (1965): 47-73.

The article can be accessed freely by University of Amsterdam students through JSTOR, by logging in with the institution.

During the session, Evan will present the paper, followed by a discussion.

Constructive vs. Non-Constructive Proofs

Fri, 20 Nov 2020 18:00:00 +0100

We will join for a Zoom tea where we will discuss constructive and non-constructive proofs.

We ask participants, although not necessary, to have a constructive and a non-constructive proof of a theorem they find interesting or illustrative, along with a relevant philosophical input.).

Towards a Semiotics of Mathematics

Fri, 13 Nov 2020 17:15:00 +0100

Our opening reading will be Brian Rotman’s Towards a Semiotics of Mathematics, where mathematics is presented as an activity essentially done through writing. In order to understand what it means to read and write mathematics and what limitations this imposes on mathematics, Rotman introduces a semiotic model drawing from both Peircean and continental semiotics.

For this session we expect attendants to have read in advance the pages 97-111 from Rotman’s seminal paper:

Is Second-Order Logic Set Theory in Sheep Clothing?

Thu, 02 Apr 2020 17:15:00 +0100

Tibo will give a short presentation supporting the (in)famous Quine thesis that SOL is in reality ST, followed by a debate. The rules will be uploaded in due time.

Slides used during the presentation are available here (link now unfortunately broken).

Suggested Bibliography (They are freely accessible from your UvA student account)

Quine W.V.O., Philosophy of Logic (2nd Edition), Chapter 5: ‘The Scope of Logic’, Harvard University Press, 1986. [PDF accessible from the UvA Library]

Joel David Hamkins | Book Presentation: Lectures on the Philosophy of Mathematics

Thu, 19 Mar 2020 17:15:00 +0100

Professor Joel David Hamkins will present to Φ-Math his upcoming book Lectures on the Philosophy of Mathematics. The presentation will contain an overview of the book’s contents and motivation with a focus on selected philosophical problems tackled in it, followed by a discussion/questions from attendants.

Is the Physical World a Mathematical Structure?

Thu, 12 Mar 2020 17:15:00 +0100

On March 12th we will try a debate format. Rover will present the main arguments of M. Tegmark’s Mathematical Universe Hypothesis (MUH) followed by the debate. Rules of the debate will be announced soon. Meanwhile, Tegmark’s paper can be found here.

Slides used during the presentation are available here.

Anna Bellomo | Bolzano, Collections, Sets and Infinity

Wed, 26 Feb 2020 17:15:00 +0100

Anna Bellomo presented her ongoing PhD research on Bolzano’s conceptions of infinity, as well as her involvement on the e-Ideas framework.

‘In the philosophy of mathematics circles, Bernard Bolzano (1871-1848) is mostly known for two things: his contributions to the so-called rigorisation of analysis, and his proto-Cantorian theory of size for infinite sets. In this talk, I will focus on the latter and summarise some recent findings suggesting that, contrary to what has been so far the default interpretation of Bolzano’s treatment of the countable infinite, his focus was not a theory of size for infinite sets, but solving some problems relating to the treatment of (non-convergent) infinite sequences.’

Pieter Adriaans | An Information Theoretical Perspective on the Separation of the classes P and NP

Wed, 12 Feb 2020 17:15:00 +0100

The P vs. NP problem, one of the seven Millenium Problems, is one of the most relevant unsolved question in theoretical computer science. The progress in the last decade, however, has been little. Can information theory and philosophy of information provide new insights as to why these classes should be distinct (or the same)? Pieter Adriaans will be offering a talk on the subject, followed by a discussion.

‘In this talk, I will present a perspective on the P vs. NP problem in the context of philosophy of information. P is the class of decision problems that can be solved in time polynomial to the length of their input by a deterministic computer. NP is the class of problems that can be solved in polynomial time by a non-deterministic computer. This description gives a direct relation with the philosophical question of determinism versus non-determinism and the problem of the interaction between information and computation. This suggests that a careful analysis of the flow of information through computational processes might help us to understand the P vs. NP problem better. Unfortunately, the existing theories of information are not very adequate for this purpose. Shannon information is based on a statistical notion of entropy that is not directly applicable. Kolmogorov complexity defines a structural concept of entropy that is asymptotic and not computable. Apart from that the classes of problems known to be in NP do not have a structure that easily facilitates the application of information theory. There is, for example, no univocal theory of information measurement for finite sets of numbers. This complicates an information theoretical analysis of the subset sum problem and related problems in NP considerably. I therefore propose to look at a new class of problems that I call Multiple Mutual Key (MMK) decision problems. The case for MMK not being in P is at least prima facie stronger than for other problems in NP since the checking function is a repeated application of one time pad code ciphers, which is a provably safe encryption technique. Apart from that problems in MMK are constraint free: any binary string of an adequate length defines an MMK decision problem. This implies that the average case complexity is high and makes it easy to apply maximum entropy techniques.’

Dean McHugh | Newcomb Paradox

Sun, 19 Jan 2020 17:15:00 +0100

On the last Friday of January, we will have the pleasure to host Dean McHugh presenting Newcomb’s Paradox, a game-theoretical problem in decision theory with many diverse philosophical implications.

Luca Incurvati | Book Presentation: Conceptions of Set and the Foundations of Mathematics

Wed, 15 Jan 2020 17:15:00 +0100

Luca Incurvati will be presenting his recently published book Conceptions of Set and the Foundations of Mathematics. The book is accessible through the UvA Library.

Book summary:

Sets are central to mathematics and its foundations, but what are they? In this book Luca Incurvati provides a detailed examination of all the major conceptions of set and discusses their virtues and shortcomings, as well as introducing the fundamentals of the alternative set theories with which these conceptions are associated. He shows that the conceptual landscape includes not only the naïve and iterative conceptions but also the limitation of size conception, the definite conception, the stratified conception and the graph conception. In addition, he presents a novel, minimalist account of the iterative conception which does not require the existence of a relation of metaphysical dependence between a set and its members. His book will be of interest to researchers and advanced students in logic and the philosophy of mathematics.

Calendar

Mon, 01 Jan 0001 00:00:00 +0000

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Suggest a topic or paper! We are happy for external feedback. You may:

If there’s a paper you have been wanting to read and would like to do so in a group, you can suggest it and it will be part of an upcoming Reading Meeting. If you already know the paper you are welcome to do a short presentation before the discussion, but we are happy to read papers that nobody has approached before!

Coming soon on Φ-Math

About

Board

Current Members

Past Members

Founders

Logical Constants and Laws

Second-Order Logic: If not Set Theory in Sheep’s Clothing, What is it Then?

Mathematics, Like a Game?

Truth and Proof: the Platonism in Mathematics

Truth in Intuitionism

Modal Structuralism

Why is Burgess Not a Nominalist?

Intuiting the Infinite

Your least and most favourite aspects of Phil. of Math

Infinity up on Trial: Reply to Feferman

Why be a Height Potentialist?

Aristotle meets Frege: from Potentialism to Frege Arithmetic

Actual and Potential Infinity

Structuralism in Mathematics: Modal Set-Theoretic Structuralism

Structuralism in Mathematics: Sui Generis and Modalities

Structuralism in Mathematics: Categories

Structuralism in Mathematics

Responses to Higher-Order Logic

Philosophy of Higher Order Logic

Basics of Mereology

Mathematical Intuition

Mathematical Intuition

Mathematical Intuition

The Philosophical Misconceptions of the Incompleteness Theorem

Wangs Paradox: Dummets Case against Strict Finitism

Conceptions of the Continuum

Gödel Incompleteness Theorems, Free Will and Mathematical Thought

Why Philosophers Should Care about Computational Complexity

Towards a Philosophy of Music

Gödel Ontological Argument

Mathematics and Transcendental Phenomenology

The Linguistics of Numerals

What Numbers Could Not Be

Constructive vs. Non-Constructive Proofs

Towards a Semiotics of Mathematics

Is Second-Order Logic Set Theory in Sheep Clothing?

Joel David Hamkins | Book Presentation: Lectures on the Philosophy of Mathematics

Is the Physical World a Mathematical Structure?

Anna Bellomo | Bolzano, Collections, Sets and Infinity

Pieter Adriaans | An Information Theoretical Perspective on the Separation of the classes P and NP

Dean McHugh | Newcomb Paradox

Luca Incurvati | Book Presentation: Conceptions of Set and the Foundations of Mathematics

Calendar

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Contact Us

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