•  41
    The Game of Fictional Mathematics: Review of M. Leng, Mathematics and Reality (review)
    Constructivist Foundations 8 (1): 126-128. 2012.
    Upshot: Leng attacks the indispensability argument for the existence of mathematical objects. She offers an account that treats the role of mathematics in science as an indispensable and useful part of theories, but retains nonetheless a fictionalist position towards mathematics. The result is an account of mathematics that is interesting for constructivists. Her view towards the nominalistic part of science is, however, more in conflict with radical constructivism
  •  38
    Mechanistic Explanation and Explanatory Proofs in Mathematics
    with Erik Weber
    Philosophia Mathematica 22 (2): 231-248. 2014.
    Although there is a consensus among philosophers of mathematics and mathematicians that mathematical explanations exist, only a few authors have proposed accounts of explanation in mathematics. These accounts fit into the unificationist or top-down approach to explanation. We argue that these models can be complemented by a bottom-up approach to explanation in mathematics. We introduce the mechanistic model of explanation in science and discuss the possibility of using this model in mathematics,…Read more
  •  27
    Computational Explanation in Cognitive Sciences: The Mechanist Turn
    Constructivist Foundations 10 (3): 426-429. 2015.
    Upshot: The computational theory of mind has been elaborated in many different ways throughout the last decades. In Explaining the Computational Mind, Milkowski defends his view that the mind can be explained as computational through his defense of mechanistic explanation. At no point in this book is there explicit mention of constructivist approaches to this topic. We will, nevertheless, argue that it is interesting for constructivist readers
  •  25
    Is Mathematics a Domain for Philosophers of Explanation?
    with Erik Weber
    Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 48 (1): 125-142. 2017.
    In this paper we discuss three interrelated questions. First: is explanation in mathematics a topic that philosophers of mathematics can legitimately investigate? Second: are the specific aims that philosophers of mathematical explanation set themselves legitimate? Finally: are the models of explanation developed by philosophers of science useful tools for philosophers of mathematical explanation? We argue that the answer to all these questions is positive. Our views are completely opposite to t…Read more
  •  17
    Mathematical Proofs in Practice: Revisiting the reliability of published mathematical proofs
    with Laszlo Kosolosky
    Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 29 (3): 345-360. 2014.
    Mathematics seems to have a special status when compared to other areas of human knowledge. This special status is linked with the role of proof. Mathematicians often believe that this type of argumentation leaves no room for errors and unclarity. Philosophers of mathematics have differentiated between absolutist and fallibilist views on mathematical knowledge, and argued that these views are related to whether one looks at mathematics-in-the-making or finished mathematics. In this paper we take…Read more