Numerical cognition and philosophy of mathematics. Dehaene’s (neuro)intuitionism and the relevance of language
Abstract
Can investigations carried out in the field of cognitive science about numerical cognition shed light on the issues traditionally raised by philosophers of mathematics? What kind of relation exists between the current neuroscientific research and the philosophical reflection on mathematics? This paper critically explores the answers to these questions provided by the French neuroscientist Stanislas Dehaene, identifying the framework of a possible future collaboration between these disciplinesReferences
BROUWER, Luitzen Egbertus Jan (1907), Over de grondslagen der wiskunde. Amsterdam, Maas & van Suchtelen; trad. ingl. On the foundations of mathematics in A. Heyting (1975), ed., L.E.J Brouwer Collected Works, vol. I, pp.11-101, NorthHolland, Amsterdam.
BROUWER, Luitzen Egbertus Jan (1912), Intuitionisme en formalisme, Amsterdam, Clausen; trad. Ingl. Intuitionism and Formalism, Bulletin of the American Mathematical Society 20, pp.81-96 e in Brouwer 1975, pp. 123-138.
BROUWER, Luitzen Egbertus Jan (1948), Consciousness, Philosophy and Mathematics, Proceedings of the 10 International Congress of Philosophy, Amsterdam 1948 III, pp. 1235-1249.
BROUWER, Luitzen Egbertus Jan (1975), On the foundations of mathematics in A.Heyting (1975), ed., L.E.J Brouwer Collected Works, vol. I, pp.11-101, NorthHolland, Amsterdam.
BROUWER, Luitzen Egbertus Jan (1981), Brouwer's Cambridge Lectures in Intuitionism. Cambridge, Cambridge University Press.
CELLUCCI, Carlo (2013), «Philosophy of mathematics: Making a fresh start», in Studies in History and Philosophy of Science Part A, Vol. 44, n. 1, pp. 32-42.
DEHAENE, Stanislas (1997), The Number Sense. How the mind creates mathematics, Oxford University Press, New York.
DEHAENE, Stanislas (2011), The Number Sense. How the mind creates mathematics, Revised and Updated Edition, Oxford University Press, New York.
DEHAENE, S., BRANNON, E. (2011), Space, time and number in the brain. Searching for the foundations of mathematical thought, Elsevier, Amsterdam.
GRISS, George François Cornelis (1946), Idealistische Filosofie. van Loghum Slaterus, Arnhem.
GRISS, George François Cornelis (1948), «Sur la négation (dans les mathématiques et la logique)», in Synthese, n. 7, pp. 71-74.
HEYTING, Arend (1958), «Blick von der intuitionistischen Warte», in Dialectica, n.12, pp. 332-345.
LO PIPARO, Franco (2014), «Nome e numero: una parentela», in Versus, n. 118, pp.185-196.
LONGO, G., VIAROUGE, A. (2010), «Mathematical intuition and the cognitive roots of mathematical concepts», in Topoi, Vol. 29, N. 1, pp. 15-27.
NUNEZ, Rafael, MARGHETIS, Tyler (2014), Cognitive Linguistics and the Concept(s) of Number, in COHEN-KADOSH, Roi, DOWKER, Ann (eds.), Oxford Handbook of Numerical Cognition, Oxford University Press, Oxford.
PIAGET, Jean (1952), The child’s conception of number, Norton, New York.
POPPER, Karl Raimund (1990), A world of propensities, Thoemmes, Bristol.
Sitografia
DEHAENE, Stanislas (2006), «Psychologie cognitive expérimentale. Cours: les fondements cognitifs de l’arithmétique élémentaire», in https://www.college-defrance.fr/media/stanislas-dehaene/UPL22033_dehaene_res0708.pdf
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