# Projects

## Human and Artificial Understanding in Mathematics - A comparative study of informal, but functionally valuable moves performed by mathematical agents. Vrije Universiteit Brussel

## Explanation in mathematics. A philosophical analysis of the explanatory force of mathematical proofs and visualizations and their role in scientific explanations. Vrije Universiteit Brussel

## The use of adaptive logics for the practice and the philosophy of mathematics and the use of mathematical tools for the abstract analysis of adaptive logics Ghent University

This project concerns an investigation into three aspects of the relation between mathematics and adaptive logics (AL's): it is investigated how (a) AL's can be used for the formal modeling of the mathematical practice, (b) AL's can solve problems of the foundations of mathematics, and © mathematical techniques can be used for the abstract study of AL's.

## Reverse Mathematics and Nonstandard Analysis: the actual infinite in the foundations of Mathematics Ghent University

Reverse Mathematics (RM) unveils the striking phenomenon that theorems of ordinary Mathematics fall in only five equivalence classes, although there are infinitely many nonequivalent classes in Logic. My project analyzes RM where equality = is replaced with $\approx$, equality up to infinitesimals from Nonstandard Analysis. There are applications in Physics and the Philosophy of Science.

## Reflection Spectra: Predicative Mathematics and Beyond Ghent University

By work of Austrian logician Kurt Gödel in the 1930s, no sound and

sufficiently strong computably enumerable arithmetic theory can

prove its own consistency. Soon after Gödel's work, G. Gentzen

provided an almost finitary proof of the consistency of Peano

Arithmetic, with only one extraneous component: a use of transfinite

induction up to a suitable ordinal number.

Ordinal analysis is the branch of proof ...

## Understanding mathematical development in children: the causal mechanisms of mathematical language and mathematical abilities KU Leuven

Mathematical competence positively affects school performance. Studies highlighted the effect of spatial skills on children's mathematical development. These spatial skills included nonlinguistic spatial representations (e.g. mental rotation). However, language has a spatial component as well (i.e. spatial language such as prepositions), and mathematical language (i.e. spatial and numerical terms) is a strong predictor of mathematical ...

## Reflections on Necessity and Normativity in Wittgenstein: A Philosophical Investigation into ‘the Must’ in Ethics and Mathematics. Vrije Universiteit Brussel

However, these are scarce and dense, which has led scholars to conclude that if they are to allow for an account of his (meta)ethical thought this should be done in concordance with the rest of his work. Yet, despite Wittgenstein’s own suggestions, few have tried to do so using his remarks on ...

## The Epistemology of Data Science: Mathematics and the Critical Research Agenda on Data Practices Vrije Universiteit Brussel

## Logic, stability and perturbation theory: novel bridges between the foundations of mathematics and operator algebras KU Leuven

As all other sciences rely on mathematics, I think of science as a building, with the ground floor being made up by mathematics. As we want to keep the building in good shape so it can grow in a creative, new and strong way, we need to take care of the foundations. Logic represents these foundations. It provides the framework for mathematics (consisting of the assumptions we work with) and general abstract tools for considering mathematical ...