The Centre for Logic and Philosophy of Science (CLPS) of the Vrije Universiteit Brussel (VUB) will host its Third Masterclass in the Philosophy of Mathematical Practice on June, 1–3 with Valeria Giardino (CNRS, Institut Jean Nicod, Paris).

We intend the Masterclass to be a fully interactive event, with the twofold objective to understand in depth the materials presented in the lectures, and to provide early career researchers (PhD students and Postdocs) with an opportunity to discuss their ongoing work in a helpful and constructive environment. The lectures by Valeria Giardino will take place in the mornings, and will be followed by afternoon sessions with presentations by early career researchers in the Philosophy of Mathematical Practice. The exact titles of the lectures will be communicated at a later stage.

We invite early career researchers who would be interested to present their work to send us an abstract of at most 250 words by May, 1st. Please submit your abstract, including your affiliation information, via the following Google form: https://forms.gle/ZsyQBpGftXoDxvcy5 or by sending it to the following email address: joachim.frans@vub.be . The talks will be of a duration of around 20 minutes (not including discussion). Notification of acceptance will be sent out by the mid April. Notice that submitting an abstract is not mandatory for attending the Masterclass.

We ask people to register to the Masterclass by May, 15. There will be no attendance fees for the event, and attendance of the Masterclass is open to everyone interested. If you are planning to attend the Masterclass, please register via the following form: https://forms.gle/ZsyQBpGftXoDxvcy5 or by sending an email to: joachim.frans@vub.be if you do not want to use an Google form.

The Masterclass will take place at the Vrije Universiteit Brussel (VUB) on the Etterbeek campus, which is situated in Brussels, Belgium, in addition it is possible to participate online.

Mathematical cognition: core knowledge systems and (more importantly) beyond

The literature in cognitive science shows that humans and other animals are born with cognitive systems that are ready to work, for example to compare numerosities or shapes, and whose powers improve by learning new cognitive strategies. In this first talk, I will focus precisely on the practices that have been developed to this aim, which involve in many cases cognitive tools having a spatial nature. I will discuss to which point these objects are important to establish mathematics as we know it.

Cognitive tools for mathematics: anchors or props (or both)?

Edwin Hutchins defined “material anchors” as associating a conceptual structure with a material structure in order to stabilize conceptual representations. However, in some cases these material objects can be used as props to imagine “things” about what they represent. In this second talk, I will discuss the functioning of cognitive tools in the context of mathematics and the possible tension between these two roles.

The practice of mathematics: “trafficking in heterogeneity”

As Emily Grosholz summed up some years ago in the context of logical reasoning, “it is hard for a logician to admit that he is trafficking in heterogeneity”. However, this seems to be easily the case for a mathematician. In this third talk, I will introduce and discuss the more recent literature showing this “traffic” in multi-dimensional reasoning in mathematics, and present some new work of mine on the same topic.

The Masterclass is organized by Joachim Frans (CLPS, VUB), Yacin Hamami (Philosophy Department, ULiège), Colin Rittberg (Department of Philosophy, VU Amsterdam & CLPS, VUB), Deniz Sarikaya (CLPS, VUB), and Fenner Tanswell (CLPS, VUB).

For any questions write an email to joachim.frans@vub.be.

The Masterclass is supported by the Doctoral School of Human Sciences (DSh) of the Vrije Universiteit Brussel (VUB) and Centre for Logic & Philosophy of Science (CLPS) of the VUB.