•  16
    The importance of expert knowledge in big data and machine learning
    with Jens Ulrik Hansen
    Synthese 201 (2): 1-21. 2023.
    According to popular belief, big data and machine learning provide a wholly novel approach to science that has the potential to revolutionise scientific progress and will ultimately lead to the ‘end of theory’. Proponents of this view argue that advanced algorithms are able to mine vast amounts of data relating to a given problem without any prior knowledge and that we do not need to concern ourselves with causality, as correlation is sufficient for handling complex issues. Consequently, the hum…Read more
  • The Intended Model of Arithmetic
    Dissertation, University of Paris 1 Sorbonne-Pantheon. 2010.
  •  3
    Situated Counting
    Review of Philosophy and Psychology 12 (4): 721-744. 2020.
    We present a model of how counting is learned based on the ability to perform a series of specific steps. The steps require conceptual knowledge of three components: numerosity as a property of collections; numerals; and one-to-one mappings between numerals and collections. We argue that establishing one-to-one mappings is the central feature of counting. In the literature, the so-called cardinality principle has been in focus when studying the development of counting. We submit that identifying…Read more
  •  37
    Cognitive Structuralism: Explaining the Regularity of the Natural Numbers Progression
    Review of Philosophy and Psychology 13 (1): 127-149. 2022.
    According to one of the most powerful paradigms explaining the meaning of the concept of natural number, natural numbers get a large part of their conceptual content from core cognitive abilities. Carey’s bootstrapping provides a model of the role of core cognition in the creation of mature mathematical concepts. In this paper, I conduct conceptual analyses of various theories within this paradigm, concluding that the theories based on the ability to subitize (i.e., to assess anexactquantity of …Read more
  •  8
    Intensionality in mathematics: problems and prospects: Introduction to the special issue
    with Marianna Antonutti Marfori
    Synthese 198 (Suppl 5): 995-999. 2021.
  •  27
    This paper reassesses the criticism of the Lucas-Penrose anti-mechanist argument, based on Gödel’s incompleteness theorems, as formulated by Krajewski : this argument only works with the additional extra-formal assumption that “the human mind is consistent”. Krajewski argues that this assumption cannot be formalized, and therefore that the anti-mechanist argument – which requires the formalization of the whole reasoning process – fails to establish that the human mind is not mechanistic. A simil…Read more
  •  15
    Implicit and Explicit Examples of the Phenomenon of Deviant Encodings
    Studies in Logic, Grammar and Rhetoric 63 (1): 53-67. 2020.
    The core of the problem discussed in this paper is the following: the Church-Turing Thesis states that Turing Machines formally explicate the intuitive concept of computability. The description of Turing Machines requires description of the notation used for theinputand for theoutput. Providing a general definition of notations acceptable in the process of computations causes problems. This is because a notation, or an encoding suitable for a computation, has to be computable. Yet, using the con…Read more
  •  18
    Situated Counting
    Review of Philosophy and Psychology 12 (4): 1-24. 2020.
    We present a model of how counting is learned based on the ability to perform a series of specific steps. The steps require conceptual knowledge of three components: numerosity as a property of collections; numerals; and one-to-one mappings between numerals and collections. We argue that establishing one-to-one mappings is the central feature of counting. In the literature, the so-called cardinality principle has been in focus when studying the development of counting. We submit that identifying…Read more
  •  10
    The main objective of this paper is to design a common background for various philosophical discussions about adequate conceptual analysis of “computation”.
  • Magnitude and Number Sensitivity of the Approximate Number System in Conceptual Spaces
    with Aleksander Gemel
    In Peter Gärdenfors, Antti Hautamäki, Frank Zenker & Mauri Kaipainen (eds.), Conceptual Spaces: Elaborations and Applications, Springer Verlag. 2019.
  •  42
    Can Church’s thesis be viewed as a Carnapian explication?
    Synthese 198 (Suppl 5): 1047-1074. 2019.
    Turing and Church formulated two different formal accounts of computability that turned out to be extensionally equivalent. Since the accounts refer to different properties they cannot both be adequate conceptual analyses of the concept of computability. This insight has led to a discussion concerning which account is adequate. Some authors have suggested that this philosophical debate—which shows few signs of converging on one view—can be circumvented by regarding Church’s and Turing’s theses a…Read more
  •  20
    La métalangue d'une syntaxe inscriptionnelle
    History and Philosophy of Logic 32 (2). 2011.
    History and Philosophy of Logic, Volume 32, Issue 2, Page 191-193, May 2011
  •  9
    La métalangue d'une syntaxe inscriptionnelle (review)
    History and Philosophy of Logic 32 (2): 191-193. 2011.
    Denis Miéville, La métalangue d'une syntaxe inscriptionnelle, Neuchâtel: Centre de Recherches Sémiologique – Travaux de logique, 2009. 174 p...