# Talks and Working Sessions

This is an overview (newest on top) of CLWF-seminars that fit within the scope of the project. For a more comprehensive list of our past activities, check our archive.

#### Reading group "Key issues in the philosophy of science" 2018-2019 moderated by Pieter Present (CLPS)

- Tuesday 8 November 2018 11.00-12.30, Room: 5B425 (“Consuming and Appropriating Practical Mathematics and the Mixed Mathematical Fields, or Being “Influenced” by Them: The Case of the Young Descartes” by John Shuster)

**Abstract.** We continue discussing various issues related to the philosophy of science, including the philosophy of mathematics. We are particularly concerned with methodology and practice, thereby focusing on reading articles rather than books.

#### "Virtue, Vice, and Deep Disagreement" Andrew Aberdein (Florida, USA)

- Tuesday 10 July 2018 11:00-13:00
- Room: 5C.406

**Abstract.** Deep disagreements are characteristically resistant to rational resolution. This paper explores the contribution a virtue-theoretic approach to argumentation can make towards settling the practical matter of what to do when confronted by apparent deep disagreement. Particular attention is paid to the vice of arrogance and the virtue of courage.

#### Reading group "Key issues in the philosophy of science" 2017-2018 moderated by Jip van Besouw (CLWF)

- Tuesday 26 June 2018 11.00-12.30, Room: 5B425 (“The Dilemma of Case Studies Resolved” by Richard M. Burian)
- Thursday 3 May 2018 11.00-12.30, Room: 5B425 (“Knowledge in Transit” by James Secord)
- Thursday 29 March 2018
**10.00-11.30**, Room: 5B425 (“Mathematical Concepts? The View from Ancient History” by Reviel Netz) - Thursday 15 February 2018 11.00-12.30, Room: 5B425 (“The World of Empiricism” by Bas van Fraassen)
- Wednesday 13 December 2017 11.00-12.30, Room: 5B425 (“Can There Be an Alternative Mathematics?” by David Bloor)
- Thursday 16 November 2017 11.00-12.30,
**Room: D215**(“Ten Problems in History and Philosophy of Science” by Peter Galison) - Wednesday 28 September 2017 11.00-12.30, Room: 5B425 (“From the History of Science to the History of Knowledge - and Back” by Jürgen Renn)

**Abstract.** We continue discussing various issues related to the philosophy of science, including the philosophy of mathematics. We are particularly concerned with methodology and practice, thereby focusing on reading articles rather than books.

#### "What distinguishes data from models?" Sabina Leonelli (Exeter)

- Thursday 21 June 2018 14:30-16:30
- Room: 5C.406

**Abstract.** I propose a framework that explicates and distinguishes the epistemic roles of data and models through consideration of their use in scientific practice. After arguing that Suppes’ characterization of data models falls short in this respect, I discuss a case of data processing within exploratory research in plant phenotyping, and use it to highlight the difference between practices aimed to make data usable as evidence and practices aimed to use data to represent a specific phenomenon. I then argue that whether a set of objects functions as data or models does not depend on intrinsic differences in their physical properties, level of abstraction or the degree of human intervention involved in generating them, but rather on their distinctive roles towards identifying and characterizing the targets of investigation.

**Important note.** This session is part of a series of lectures organised by the Ghent-Brussels Research Alliance. Participants are expected to study the underlying paper central to it, as the speaker will only present a 15 min summary of its essential claims before engaging in discussion. For more information, please contact Steffen Ducheyne.

#### "From explanation to understanding: normativity lost?" Henk de Regt (Amsterdam)

- Thursday 29 March 2018 14:30-16:30
- Room: 5C.406

**Abstract.** In recent years, scientific understanding has become a focus of attention in philosophy of science. Since understanding is typically associated with the pragmatic and psychological dimensions of explanation, shifting the focus from explanation to understanding may induce a shift from accounts that embody normative ideals to accounts that provide accurate descriptions of scientific practice. Not surprisingly, many ‘friends of understanding’ sympathize with a naturalistic approach to the philosophy of science. However, this raises the question of whether the proposed theories of understanding can still have normative power. In this paper I address this question by examining two theories of scientific understanding: Jan Faye’s pragmatic-rhetorical theory and my own contextual theory of scientific understanding. I argue that both theories leave room for normativity, despite their naturalistic tendencies. While my theory has first and foremost a descriptive and explanatory aim, namely to describe the criteria for understanding employed in scientific practice and to explain their function and historical variation, it can also serve as a basis for normative assessment of the understanding that scientific research delivers.

**Important note.** This session is part of a series of lectures organised by the Ghent-Brussels Research Alliance. Participants are expected to study the underlying paper central to it, as the speaker will only present a 15 min summary of its essential claims before engaging in discussion. For more information, please contact Steffen Ducheyne.

#### "Epistemic Injustice in Mathematics" Jean Paul Van Bendegem and Colin Rittberg (CLWF)

- Wednesday 21 March 2018 15:00-17:00
- Room: 5C.406

**Abstract.** We investigate how epistemic injustice can manifest in mathematical practices. We do this as both a social epistemological and virtue-theoretic investigation of mathematical practices. We delineate the concept both positively – we show that folk theorems can be a source of epistemic injustice in mathematics – and negatively by exploring cases where the obstacles to participation in a mathematical practice do not amount to epistemic injustice. Having explored what epistemic injustice in mathematics can amount to, we use the concept to highlight a potential danger of intellectual enculturation.

#### "On Generalization of Definitional Equivalence to Languages with Non-Disjoint Signatures" Koen Lefever (CLWF)

- Monday 5 March 2018 15:30-17:00
- Room: 5C.406

#### "The classificatory function of diagrams: two examples from mathematics" Valeria Giardino (Paris) **NEW DATE**

- Thursday 22 February 2018 14:30-16:30
- Room: 5C.406

**Abstract.** In a recent paper, De Toffoli and Giardino (2014) analyzed the practice of knot theory, by focusing in particular on the use of diagrams to represent and study knots. To this aim, they distinguished between illustrations and diagrams. An illustration is static; by contrast, a diagram is dynamic, that is, it is closely related to some specific inferential procedures. In the case of knot diagrams, a diagram is also a well-defined mathematical object in itself, which can be used to classify knots. The objective of the present paper is to reply to the following questions: Can the classificatory function characterizing knot diagrams be generalized to other fields of mathematics? Our hypothesis is that dynamic diagrams that are mathematical objects in themselves are used to solve classification problems. To argue in favor of our hypothesis, we will present and compare two examples of classifications involving them: (i) the classification of compact connected surfaces (orientable or not, with or without boundary) in combinatorial topology; (ii) the classification of complex semisimple Lie algebras.

**Important note.** This session is part of a series of lectures organised by the Ghent-Brussels Research Alliance. Participants are expected to study the underlying paper central to it, as the speaker will only present a 15 min summary of its essential claims before engaging in discussion. For more information, please contact Steffen Ducheyne.

#### "Playing by the rules" Amirouche Moktefi (Tallinn)

- Wednesday 7 February 2018 15:00-17:00
- Room: 5C.406

**Abstract.** The usage of diagrams in mathematics has long faced skepticism. Since mathematical proofs were held to be formal and diagrams to be informal, there was no room that could be made for the latter within the former. Diagrams were rather viewed as mere pedagogical and heuristic devices that one might use with benefit in the context of discovery but that are redundant and unreliable in the context of justification. This skepticism faces two major objections in recent philosophy of mathematics. On the one hand, it has been shown that rigorous formal diagrammatic systems can be designed. Hence, it is possible to incorporate diagrammatic proofs without abandoning the ideal of formal proofs. On the other hand, it has been argued that mathematicians do not construct ideal proofs in their real practices and publications, but rather offer practical proofs that suffice to convince other mathematicians. Hence, diagrams do not need to be ‘formalized’ in order to be integrated or to stand as ‘acceptable’ proofs.
These diagram-friendly views capture two old understandings of diagrammatic proofs whose philosophical significance can be shown through a historical example: the diagrams of Venn and Carroll to solve the problem of elimination which preoccupied nineteenth-century logicians. The problem consists in finding what information regarding any combination of terms follows from a set of premises. For the purpose, John Venn published in 1880 a scheme offered as an improvement over Euler’s well-known circles. The method consisted in representing the complete information contained in the premises on a single diagram, then to see ‘at a glance’ the conclusion regarding specific terms. An inconvenience of this scheme, as pointed out by Louis Couturat (1914), is that it does not really tell how the conclusion is to be ‘extracted’ from the diagram. A rival scheme, published in 1886 by Lewis Carroll, demands that information is transferred from the premises-diagram to another diagram that would depict the conclusion. This transfer is achieved by following rules which are explicitly defined and strictly applied.
Although both Venn and Carroll introduced diagrammatic methods for the problem of elimination, they differ in their practices and demands on how a diagram ought to be manipulated. Venn appealed to imagination to work out the conclusion with a single diagram while Carroll applied rules on a diagram to derive other diagrams. The former method was said to lack rigor, but the latter can be accused of lacking naturalness and economy. This difference of practices, and the philosophical views that they embody, will be shown to resurface in the recent philosophical debates on the role of diagrams in mathematical practice.

#### "Rationality of mathematical proofs" Yacin Hamami (CLWF)

- Tuesday 23 January 2018 14:00-16:00
- Room: 5C.406

#### "Conceptual distances between scientific theories" Koen Lefever (CLWF)

- Monday 27 November 2017 12:00-14:00
- Room: 5C.406

#### "A new kind of objectivity" Andrew Arana (Paris)

- Thursday 16 November 2017 14:00-16:00
- Room: 5C.402

**Abstract.** This talk is about a new kind of objectivity that is not merely construed as intersubjectivity, but rather as the result of bringing together as many plural perspectives as possible. To really know is to know completely, and this is only possible if we can take on as many perspectives as we can. As a philosopher of mathematics, Andrew Arana will use mathematics as a case-study, but he aims to present his take on objectivity more generally.

**Important note.** This session is part of a series of lectures organised by the Ghent-Brussels Research Alliance. Participants are expected to study the underlying paper central to it, as the speaker will only present a 15 min summary of its essential claims before engaging in discussion. For more information, please contact Steffen Ducheyne.

#### "Changing the subject - Considerations on when groups should be regarded as epistemic agents" Sven Delarivière (CLWF)

- Monday 16 October 2017 12:00-14:00
- Room: 5C.406

#### "A mathematical revolution in pictures: Re-gestalt in diagrams" Irina Starikova (San Paulo)

- Monday 9 October 2017 16:00-18:00
- Room: D.313

#### "On the marginalization and the mathematization of paper folding" Michael Friedman (Berlin)

- Tuesday 4 May 2017, 15:00-17:00
- Room: 5C402

**Abstract.** In 1893 the Indian mathematician Tandalam Sundara Row has published his book Geometrical Exercises in Paper Folding in Madras. The book was recommended in 1895 by Felix Klein, which in turn led to the 1934 discovery of the Italian mathematician Margherita P. Beloch, that one can - with paper folding! - solve equations of degree 3 and 4. Beloch's discoveries were indeed groundbreaking (though ignored for several decades), but the question remains - how did the practice of paper folding come to be considered as a mathematical one in India? And why until 1989 no one has heard on Beloch’s discoveries? The answer to this question is to be found in the United Kingdom. I claim that Row was influenced from two practices, both exported from the UK to the Indian colony: the Fröbelian paper folding and the methodologies of Olaus Henrici (1840-1918) for teaching mathematics. While the playful activities of Fröbel in British kindergartens were at that time hardly considered as mathematical (opposed to Fröbel's explicit intent), when transferred to India they began being conceptualized as such. In addition, Henrici, who advocated the use and production of physical mathematical models and rejected the learning by heart of Euclid, used folding as a legitimate operation to teach geometry. But also in this case, while being partially rejected in the UK, Henrici's ideas were more accepted in India. I therefore intend in my talk to examine these two practices. Both practices came together in India and culminated in Row's book and eventually led to Beloch’s work – though the her work was only discovered during the end of the 80s in Italy; Row's and Beloch's works will be also examined concerning the ignorance and marginalization of the mathematical knowledge proposed by them.

#### "Mathematical depth: a case study of the philosophy of mathematical practice" Andrew Arana (Paris)

- Tuesday 18 April 2017, 15:00-17:00
- Room: D.1.08

**Abstract.** Mathematicians judge some theorems, definitions, and proofs to be deep, ordinarily using this as an evaluation of merit. We articulate several different criteria for measuring depth, indicating pros and cons of each. We use Szemerédi's theorem as an example throughout, making the various proposals more concrete. At the same time, we will discuss how these criteria arise from an analysis of mathematical practice, thus discussing aspects of the methodology of the the philosophy of mathematical practice.

#### "A Pluralist Mathematical Practice" Michele Friend (Washington, DC)

- Thursday 16 March 2017 14:00-16:00
- Room: D.2.18

**Abstract.** “The Andréka-Németi group” is the honorary name given to some Hungarian logicians and scientists who have started a programme to give the logical foundations of theories of physics. They started with special relativity, and extended this to general relativity and beyond. In this paper I explain their methodology in four stages, focusing on the relativity theories, sometimes mention how it is different from other methodologies in physics and at the end, point out some senses in which it is a pluralist practice. In the following sections it should be understood that one goes back-and-forth between the stages. None is ever completed. Note also that while I explain the methodology I shall make some philosophical remarks, contrasting the work of the Andréka-Németi group to the more traditional methodology of physics. In particular, I shall call on the distinction between a ‘law’ of physics and an ‘axiom’ of logic as they use the term.

**Important note.** This session is part of a series of lectures organised by the Ghent-Brussels Research Alliance. Participants are expected to study the underlying paper central to it, as the speaker will only present a 15 min summary of its essential claims before engaging in discussion. For more information, please contact Steffen Ducheyne.

#### "Experimenting with visual imagery in mathematical practice" Irina Starikova (San Paulo)

- Friday 10 March 2017 12:00-14:00
- Room: 5C402

**Abstract.** In this talk I will try to show how a specific kind of human cognitive ability can contribute to mathematical thinking, even at research level. I refer to our ability to transform visual images mentally, that is, in visual imagination. The reality of visual mental images as genuine cognitive representations and our ability to mentally transform them was made credible by research of Shepard and colleagues in the 1970s1 and later more extensively investigated by many researchers.2 My claim is that the ability to transform visual mental images in various ways from an initial image (usually originating from a seen external diagram) can be used in a somewhat experimental way to solve mathematical problems and to form new ideas. I will illustrate this with examples of region-bounded image transformations (e.g. rotations) and field-general transformations (e.g. scanning and zooming out) from graph theory and geometric group theory.

#### "Formalism freeness and entanglement: Is invariance across logical frameworks possible?" Juliette Kennedy (Helsinki)

- Friday 3 March 2017 15:00-17:00
- Room: 5C404

**Abstract.** The notion of computability is robust in the sense that the class of computable functions can be defined in many conceptually distinct ways. We consider robustness in general, i.e. invariance with respect to formal frameworks, in the hope of developing the natural language, or naive set-theoretical perspective.

#### "On the Contents of non-Linguistic Representations in Mathematics" David Waszek (IHPST, Paris)

- Thursday 26 January 2017 14:00-16:00
- Room: 5C402

#### "Brain representation of complex mathematical concepts and rules" Marie Amalric (UNICOG, Paris)

- Thursday 12 January 2017 14:00-16:00
- Room: 5C402

#### "From Euclidean Geometry to Geometric Group Theory: does Manders' account of Euclidean plane geometry offer a model for the analysis of contemporary mathematical proofs?" Brendan Larvor (University of Hertfordshire, UK)

- Thursday 19 January 2017 14:00-16:00
- Room: 5C406

**Abstract.** This paper assumes the success of arguments against the view that mathematical proofs are sketches of, indicators of or recipes for formal derivations. This requires an alternative account of the logic of mathematical proofs. This paper first examines Manders’ analysis of Euclidean diagram use as a possible model—this supplies five questions to take forward to further cases; second, it asks these five questions about some case-studies that might prima facie be thought to analyse modern mathematics in something like Manders’ style; and third, it ask what more those studies must do in order to achieve for their cases what Manders achives for Euclidean diagram-use, given the abstract and infinitary nature of much of contemporary mathematics. This third phase yields a hypothesis about the conditions under which appeals to mental models in proofs might be considered rigorous. The case-studies concern low-dimensional topology, knot theory and geometric group theory.

**Important note.** This session is part of a series of lectures organised by the Ghent-Brussels Research Alliance. Participants are expected to study the underlying paper central to it, as the speaker will only present a 15 min summary of its essential claims before engaging in discussion. For more information, please contact Steffen Ducheyne.

#### "Why proof presentation matters" Rebecca Morris (Carnegie Mellon University, Pittsburgh)

- Thursday 8 December 2016 14:00-16:00
- Room: E.0.03

**Abstract.** When we read a new proof, we hope to attain three goals: (i)
to check it's correct; (ii) to recall it later; (iii) to reuse the
ideas it contains. Ideally, we would also like to achieve these goals
efficiently, without expending unnecessary energy. In this talk I
present a framework to further analyze these goals and argue that
meeting them is crucial to the advancement of mathematical knowledge.
I argue that the way a proof is presented can have a big effect on
whether, and how efficiently, we achieve our goals, and illustrate
these issues with a case study from geometry.

#### Reading group "Key issues in the philosophy of science" 2016-2017 moderated by Jip van Besouw (CLWF)

- Wednesday 7 June 2017 11.00-12.30, Room: 5B425 (“The Application of Mathematics to Natural Science” by Mark Steiner)
- Wednesday 6 April 2017 11.00-12.30, Room: 5B425 (“The Persistence of Epistemic Objects Through Scientific Change” by Hasok Chang)
- Wednesday 1 March 2017 11.00-12.30, Room: 5B425 (“A material theory of induction” by John Norton)
- Thursday 19 January 2017 11.00-12.30, Room: 5B425 (“Why is there philosophy of mathematics at all?” by Ian Hacking)
- Wednesday 30 November 2016 11.00-12.30, Room: 5B425 (“The function of measurement in modern physical science” by Thomas Kuhn)

**Abstract.** We intend to discuss various issues related to the philosophy of science in general, particularly concerning methodology and practice, thereby focusing on reading articles rather than books.

#### "Categorical Model Theory and Knowledge-How" Andrei Rodin (Russian Academy of Sciences )

- Tuesday 8 November 2016 15:00
- Room: 5C402

**Picture proof on our Flickr page**

**Abstract.** Categorical Model theory (CMT) stems from the functorial semantics of algebraic theories proposed by Lawvere in his thesis back in 1963. Today this theory uses a family of concepts of model none of which is fairly standard. An evidence is provided by the present-day Homotopy Type theory where presently there is no full agreement among the researchers as to what counts as a model of this theory and what does not (even if there is a consensus that certain constructions do qualify as models). Further, the technical concept(s) of model considered in CMT lack so far any generally accepted epistemological underpinning. It remains unclear whether or not the classical Tarskian notion of model based on the T-schema applies in CMT in all cases. I argue that this classical notion is not adequate for accounting for models of HoTT. As a remedy I show how HoTT and its models can be understood as vehicles for knowledge-how (and also for the propositional knowledge-that, which also has a place in this scheme). This feature of HoTT and the related CMT ideas suggests applications in Knowledge Representation some of which will be described in the talk.

#### "Aspects of Diagrammatic Reasoning in Category Theory" Silvia De Toffoli (Stanford)

#### "The Regress of Carroll's Tortoise and Geometric Diagrams" John Mumma (California State)

- Friday 8 July 2016 14:00-16:00
- Room: 5C406

**Abstract De Toffoli.** In this talk we will analyze some specific issues concerning the use
of diagrams in category theory. The motivation comes from Cornfield’s
“Toward a philosophy of real mathematics”, where the author sets forth
a research program to investigate issues which emerges from higher
category theory. This case is particularly interesting because it
allows to bridge the gap between algebraic and geometric reasoning in
mathematics. In fact, category theory is at the same time an abstract
mathematical field, where the reasoning is algebraic in nature, and a
field in which it is possible to exploit an intuition which is
geometric in nature, through a well-defined notation. We will
introduce both the algebraic and the graphical language used in
category theory, and we will explain in which sense they are one the
dual of the other. We will argue that there is not a better notation,
but that each of them has specific advantages and drawbacks; it
depends on the context of use which one is more effective. By
introducing a more sophisticated example and looking at categories
that also have a monoidal structure, the real advantages of the
graphical language will become clear. Although both algebraic and
graphical language are two-dimensional and can be considered
diagrammatic notations, we will argue that it is only with the
graphical language that we exploit topological intuition to reason. As
a consequence, the analysis of these two languages will allow us to
define more sharply the distinction between graphic and diagrammatic
notations. Our background thesis is that these languages can be
interpreted as cognitive instruments, used by the practitioner not
only as essential heuristic aids, but as tools to reason and more
specifically to prove new results.

**Abstract Mumma.** The infinite regress that the tortoise generates in Lewis Carroll's
‘What the Tortoise Said to Achilles’ can be understood as a puzzle
concerning how reasoners come to accept mathematical proofs as
logically valid. In my talk, I examine this puzzle in the context of
diagrammatic proofs in elementary geometry. In supporting an
inferences in such a proof, a geometric diagram exhibits the
inference's premise and conclusion in a single spatial configuration.
I explore how this feature of geometric diagrams speaks to the issues
raised by the tortoise's regress.

#### "Mathematical Virtues and the Practice of Proving" Fenner Tanswell (St-Andrews)

- Tuesday 16 June 2016 15:00-17:00
- Room: 5C406

**Abstract.** In this talk I will be investigating the application of virtue epistemology to questions concerning mathematical knowledge. In particular, I shall present the case for how and why this provides us with the tools to account for the nature of proof and rigour as they are found in mathematical practice, overcoming obstacles that hinder the opposing formalist-reductionist approach. I will finish with a case study of the ongoing difficulties with verifying the correctness of Mochizuki's proof of the abc conjecture, and the role that mathematical virtues and vices are playing there.

#### "Context-sensitivity and (scientific) realism reconciled in light of Putnam’s pragmatist theory of knowledge" Matthieu Guillermin (UCL)

- Thursday 9 June 2016 15.00-17.00
- Room: 5C406

**Abstract.** My research aims at elaborating an epistemological framework that is suited to usual monodisciplinary scientific investigations (such as natural sciences) as well as to interdisciplinary or transdisciplinary configurations (in which borders between disciplines or between science and society need to be crossed). One of the main hypotheses of my work is that such an epistemological framework should permit laying out a context-sensitive and realist picture of rational inquiry. Obviously, the pioneering work of Kuhn about the notions of paradigm and incommensurability is crucial when discussing context-sensitivity of scientific or rational investigations. Nevertheless, it raises serious issues concerning the possibility to defend a (scientific) realist picture of, then contextualized, scientific inquiries that would also do justice to their claim to rationality and objectivity, and, more broadly, to (scientific) realism.

In my presentation, I’ll expose the manner such issues can be circumvented on the ground of Putnam’s work. As I’ll show, Putnam’s commonsense realism – when correctly understood as the conclusion of a coherent philosophical journey through different unsatisfying form of realism (metaphysical realism, internal realism) – allows admitting the irreducibility of context-sensitivity in rational inquiries without undermining (scientific) realism. I’ll then propose an original interpretation of contextually-driven divergences between research processes, combining competing and complementary perspectives. Finally, I’ll discuss the way rationality and objectivity can be reconsidered to accommodate this acknowledgement of context-sensitivity. As a matter of conclusion, I’ll show that this general picture of rational inquiry permits accounting, in a single epistemological look, for monodisciplinary as well as inter and transdisciplinary investigations, and that it brings interesting insights about the specific type of inter-paradigm work that should be deployed during such boundary crossing research processes.

#### "Why Virtues? And do they lead to pluralism?" Colin Rittberg (CLWF)

- Thursday 26 May 2016 15.00-17.00
- Room: 5C406

**Abstract.** The teachability of a mathematical system of thought is not indicative of its truth. Nonetheless, there is something good about teachability; we might call it a virtue. But why would we want to talk about virtues? Are we not (or should we not be) interested in truth?
In this talk I will present some half-baked ideas about a virtue-based approach to a debate some set theorists are currently having and ask you to help me sort through the pieces: which deserve to be put back into the oven again? Which can already be discarded? And which pieces deserve chocolate sprinkles?

#### A series of talks by Ken Manders (Pittsburgh)

- Friday 13 May 2016 15.00-17.00:
*“Notations and Forms of Thought”*, Room: 5C404 - Tuesday 17 May 2016 14.00-16.00:
*“Control your Levels of Detail”*, Room: 5C406 - Thursday 19 May 2016 15.00-17.00:
*“Structure your Search Space”*, Room: 5C406

**Abstracts** **Picture proof on our Flickr page (lecture 1)**

#### "The Logic(s) of Informal Proofs" Brendan Larvor (CLWF)

- Thursday 28 April 2016 15.00-17.00, Room: 5C402
- Thursday 12 May 2016 15.00-17.00, Room: 5C406

**Abstract.** Most mathematical proofs do not present formal derivations. So how do they work?

#### "Relying on others in mathematics" Line Andersen (Aarhus)

- Thursday 14 April 2016 15.00-17.00
- Room: 5C406

**Abstract.** In this paper, we outline an account of when a mathematician can rely on a mathematical proposition in her own proofs without knowing a proof of it. We do so by showing how John Hardwig’s (1985, 1991) classical account of the role of testimony in science can be revised to accommodate mathematics. We shall argue that a mathematician A cannot rely on the truth of a proposition on the basis of the testimony of a single mathematician B who has checked the validity of its proof. Even in cases where A knows that B is morally and epistemically reliable, more testifiers are needed. How many depends on how long and technical the proof is, on the cost for A of building on the proof if it is invalid, and on what A knows about the expertise of the testifiers. But it does not seem to depend on what A knows about their moral character. Our argument suggests that there is a difference between the role of moral trust in science and mathematics. This may provide a sense in which the epistemic authority bestowed upon mathematics is justified.

#### "Mathematical Virtues and the Practice of Proving" Fenner Tanswell (St-Andrews) CANCELLED

- Tuesday 22 March 2016 13.00-15.00
- Room: 5C402

**Abstract.** In this talk I will be investigating the application of virtue epistemology to questions concerning mathematical knowledge. In particular, I shall present the case for how and why this provides us with the tools to account for the nature of proof and rigour as they are found in mathematical practice, overcoming obstacles that hinder the opposing formalist-reductionist approach. I will finish with a case study of the ongoing difficulties with verifying the correctness of Mochizuki's proof of the abc conjecture, and the role that mathematical virtues and vices are playing there.

#### "How to study mathematical explanation in philosophy?" Joachim Frans (CLWF)

- Thursday 10 March 2016 15.00-17.00
- Room: 5C406

#### "Logic and argumentation in Belgium: The role of Leo Apostel" Jean Paul Van Bendegem (CLWF)

- Thursday 11 February 2016 15.00-17.00
- Room: 5C402

**Abstract.** To understand present-day research in logic and argumentation theory in Belgium, it is necessary to highlight the unique contribution of Leo Apostel. The first part of the paper deals with his main intellectual influences, namely Chaïm Perelman, Rudolf Carnap, and Jean Piaget. In the second part the Signific Movement and the Erlangen School are discussed, leading up to the present situation and thus to the promised understanding.

#### Reading group "Mathematical knowledge and the interplay of practices" (José Ferreiros) moderated by Brendan Larvor (CLWF)

- Thursday 17 December 2015 13.00-14.30, Room: 5C402
- Thursday 11 February 2016 13.00-14.30, Room: 5C402
- Thursday 23 February 2016 13.00-14.30, Room: 5C402
- Thursday 10 March 2016 13.00-14.30, Room: 5C406
- Tuesday 22 March 2016 15.30-17.00, Room: 5C402
**CANCELLED** - Thursday 14 April 2016 13.00-14.30, Room: 5C406
- Thursday 21 April 2016 13.00-14.30, Room: 5C402
**CANCELLED** - Thursday 28 April 2016 13.00-14.30, Room: 5C402
- Thursday 12 May 2016 13.00-14.30, Room: 5C406
- Thursday 26 May 13.00-14.30, Room: 5C406
- Thursday 9 June 2016 13.00-14.30, Room: 5C406

**Abstract.** We're discussing a new book by the former (first) president of the Association for the Philosophy of Mathematical Practice (APMP), who will moreover participate to our Internal board meeting and Seminar Logic and Philosophy of Mathematical Practices of 18-19 February 2016.

#### Reading group "Albert Lautman" moderated by Brendan Larvor (CLWF)

- Thursday 12 November 2015 13.00-14.30, Room: 6G308
- Thursday 26 November 2015 13.00-14.30, Room: 5C402

**Abstract.** We're discussing some of the shorter essays of this French philosopher of mathematics, both in original and English versions.

#### "The erosion of a distinction" Colin Rittberg (CLWF)

- Thursday 22 October 2015 15.00-17.00
- Room: 5C402

**Abstract.** How to philosophise about mathematics? It is a common view that the question what role mathematical practice should play in our philosophical investigations divides the philosophers of mathematics into two camps: the mainstream philosophers of mathematics pay little attention to mathematical practice, the philosophers of mathematical practice claim that mathematical practice should not or even cannot be ignored in our philosophical investigations. In this talk, I argue that the distinction between mainstream philosophy of mathematics and philosophy of mathematical practice is eroding.

#### "Tools for thought: cognitive issues and open problems" Valeria Giardino (ENS, Paris)

- Friday 29 May 2015 14.00-16.00
- Room: 5C404

**Abstract** The objective of the talk will be to sketch out the elements for a conceptual framework explaining the role of cognitive artifacts as inferential tools. First, I will introduce the view that most of human cognition is embodied, in a sense to define, and I will discuss how this feature of cognition relates to the use of space in representing information. Secondly, I will focus on two aspects characterizing cognitive tools: their relation to writing and the analysis of the actions that are performed on them. Finally, I will propose a possible ‘big picture’ to account for the use of most cognitive tools in science based on the ability of diagramming.

#### "The Finite and the Infinite: Reflections on Hilbert's Metamathematics" Matthias Schirn (MCMP)

- Tuesday 21 April 2015 14.00-16.00 (TBC)
- Room: 5C402
- Handout

#### "Whitehead and Mathematical Beauty" Ronny Desmet (CLWF)

Talk by Ronny Desmet (CLWF)

- Tuesday 10 March 2015 11.00-13.30
- Room: 5C404

#### "The different roles of ontological and epistemic notions in logic" Göran Sundholm (Leiden)

- Friday 27 Februari 2015 13.00-15.00
- Room: 5C402

**Abstract.** After the “ontological turn” in logic (Bolzano, Wittgenstein's Tractatus, Tarskian model theory) that was effected during 1837 to 1936 (and consolidated by Tarski-Vaught in 1957), the epistemic role of logic has been largely neglected: instead of inference from judgements known to a conclusion getting known, one has dealt with the
relation of consequence between propositions. The validity of an inference from premises to conclusion—an epistemic notion par excellence—has been replaced by the ontological—“alethic”—holding of (logical) consequence between
antecedent and consequent propositions.

Drawing like Frege upon an interpreted, contentful formal language, I consider the dichotomy between inference and consequence in some detail and work out a number of correspondences regarding judgement and proposition, validity and holding, premise and antecedent, etc. In particular, I deal with the difference between consequence and logical consequence, and the epistemic role of assumptions in Natural Deduction Derivations. Finally also the significance of the completeness theorem will be considered from a contentful perspective.

#### "Minimizing Transitive Trust Threats in Software Management Systems" Giuseppe Primiero (Middlesex)

- Friday 23 January 2015 13.00-15.00
- Room: 5C402

**Abstract.** Software installation processes represent a common source of threats to system security, functionality and performance. The minimum install problem considers preservation of the system's profile consistency, under the requirement that the minimum number of dependencies be satisfied when a package is installed. We extend the minimum install problem with the additional condition of minimizing the number of transitive authorisations of trusted installation repositories. Our solution is based on SecureNDC, a Coq library implementing the typed natural deduction calculus SecureND using an explicit trust function. In SecureNDC, this function bridges the access to repositories and the rights to install a software package. We devise an algorithm based on a cut-elimination theorem to compute the minimal number of repositories to be trusted, in order to perform a safe package installation process preserving profile consistency. This is joint work with Jaap Boender and Franco Raimondi.

#### "Mathematical Pull" Colin Rittberg (Hertfordshire)

- Friday 28 November 2014 10.00-12.00
- Room: 5C402

**Abstract.** I argue that mathematics can actively influence philosophy. I present a case-study, taken from contemporary set theory, in which mathematicians connect mathematics to a metaphysical debate in such a way that by doing more mathematics a new argument in the philosophical debate can be obtained; mathematics pulls the metaphysical debate. This shows an important aspect of the connectedness of mathematics and philosophy.

#### "When realism meets pragmatism: Putnam's epistemological shift" Mathieu Guillermin (UCLouvain)

- Friday 8 May 2014 13.00
- Room: 5C402

#### "The heterogeneity of mathematics" Jean Paul Van Bendegem (CLWF)

- Friday 8 May 2014 14.00
- Room: 5C402