•  948
    What Is Left of the Active Externalism Debate?
    European Journal of Philosophy 25 (4): 1614-1639. 2017.
    Since the publication of Clark and Chalmers' Extended Mind paper, the central claims of that paper, viz. the thesis that cognitive processes and cognitive or mental states extend beyond the brain and body, have been vigorously debated within philosophy of mind and philosophy of cognitive science. Both defenders and detractors of these claims have since marshalled an impressive battery of arguments for and against “active externalism.” However, despite the amount of philosophical energy expended,…Read more
  •  117
    Non-representationalist cognitive science and realism
    Phenomenology and the Cognitive Sciences 13 (3): 461-475. 2014.
    Embodied and extended cognition is a relatively new paradigm within cognitive science that challenges the basic tenet of classical cognitive science, viz. cognition consists in building and manipulating internal representations. Some of the pioneers of embodied cognitive science have claimed that this new way of conceptualizing cognition puts pressure on epistemological and ontological realism. In this paper I will argue that such anti-realist conclusions do not follow from the basic assumptions…Read more
  •  28
    What are we doing when we perceive numbers?
    Behavioral and Brain Sciences 44. 2021.
    Clarke and Beck rightly contend that the number sense allows us to directly perceive number. However, they unnecessarily assume a representationalist approach and incur a heavy theoretical cost by invoking “modes of presentation.” We suggest that the relevant evidence is better explained by adopting a radical enactivist approach that avoids characterizing the approximate number system as a system for representing number.
  •  26
    Radical Enactivism and Ecological Psychology: Friends or Foes?
    Constructivist Foundations 11 (2): 320-322. 2016.
    Open peer commentary on the article “Perception-Action Mutuality Obviates Mental Construction” by Martin Flament Fultot, Lin Nie & Claudia Carello. Upshot: We examine whether there are any irreducible contradictions between ecological psychology and radical enactivism. We concentrate on two points of contention between the two approaches: the relevance of neural structures in understanding perception and the use of semantically loaded concepts in theorizing about perception.
  •  26
    Radicalizing numerical cognition
    Synthese 198 (Suppl 1): 529-545. 2020.
    In recent decades, non-representational approaches to mental phenomena and cognition have been gaining traction in cognitive science and philosophy of mind. In these alternative approach, mental representations either lose their central status or, in its most radical form, are banned completely. While there is growing agreement that non-representational accounts may succeed in explaining some cognitive capacities, there is widespread skepticism about the possibility of giving non-representationa…Read more
  •  21
    Hilbert's Tenth Problem for Rings of Rational Functions
    Notre Dame Journal of Formal Logic 43 (3): 181-192. 2002.
    We show that if R is a nonconstant regular (semi-)local subring of a rational function field over an algebraically closed field of characteristic zero, Hilbert's Tenth Problem for this ring R has a negative answer; that is, there is no algorithm to decide whether an arbitrary Diophantine equation over R has solutions over R or not. This result can be seen as evidence for the fact that the corresponding problem for the full rational field is also unsolvable
  •  20
    Elimination theory for addition and the Frobenius map in polynomial rings
    with Thanases Pheidas
    Journal of Symbolic Logic 69 (4): 1006-1026. 2004.
    We develop an elimination theory for addition and the Frobenius map over rings of polynomials. As a consequence we show that if F is a countable, recursive and perfect field of positive characteristic p, with decidable theory, then the structure of addition, the Frobenius map x→ xp and the property ‘x∈ F', over the ring of polynomials F[T], has a decidable theory.
  •  19
    Het bereik van het mentale
    Tijdschrift Voor Filosofie 74 (1): 103. 2012.
  •  13
    I examine to what extend Varela’s remarks on problem-solving can be applied to mathematical problem-solving. I argue that despite similarities between Varela’s epistemological model and recent advances in mathematics education research on problem-solving, trying to fit ideas and concepts from the latter domain in the Varelian mold runs the risk of misconstruing fundamental aspects of mathematical problem-solving.
  •  9
    How to Leave Descartes Behind
    Epistemology and Philosophy of Science 55 (3): 91-105. 2018.
    Both mainstream cognitive science and analytic philosophy of mind remain wedded to the Cartesian picture of the mind as an isolated, self-sufficient, and constitutively individual phenomenon. However, recently approaches to the mind (e.g. extended mind thesis, enactivism) that depart from the standard view have emerged. Aunifying thread that runs through these approaches can be summed up in the slogan: “to understand mental phenomena one cannot do away with the environment”. Differences between …Read more
  •  8
    Rigor and formalization
    Synthese 203 (3): 1-18. 2024.
    This paper critically examines and evaluates Yacin Hamami’s reconstruction of the standard view of mathematical rigor. We will argue that the reconstruction offered by Hamami is premised on a strong and controversial epistemological thesis and a strong and controversial thesis in the philosophy of mind. Secondly, we will argue that Hamami’s reconstruction of the standard view robs it of its original philosophical rationale, i.e. making sense of the notion of rigor in mathematical practice.
  • Uitgebreid, complementair, of omvattend? Het waar en het hoe van het mentale
    with Erik Myin
    Algemeen Nederlands Tijdschrift voor Wijsbegeerte 104 (3). 2012.
  • Strikt finitisme en de wiskundige praktijk
    Algemeen Nederlands Tijdschrift voor Wijsbegeerte 102 (3): 202-205. 2010.