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.
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 ...
The role of statistical learning in the development of mathematics KU Leuven
Mathematics is a fundamental tool in life, however there is a lack of a clear scientific understanding about how math learning is precisely achieved. The central premise underlying this project is that mathematics is fundamentally a language that uses meaningful symbols which must be organized according to a finite set of rules in order to exchange ideas, concepts and theories among people. One of the most impactful insights that emerged from ...
Turing and Wittgenstein: Opponent or Ally? A New Interpretation of Wittgenstein’s 1939 Cambridge Lectures on the Foundations of Mathematics Vrije Universiteit Brussel
and of AI. Ludwig Wittgenstein is generally recognized as one of the
most influential philosophers of the 20th Century. The most intriguing
interaction between Turing and Wittgenstein was Turing’s attendance
at Wittgenstein’s lectures on the Foundations of Mathematics in
1939. Detailed notes of Wittgenstein’s 1939 lectures survive, and
...
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 ...
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 ...