Mathematical Problem-Solving and Ontology: An Exercise [Book Review]
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jonathan Jenkins Ichikawa
Jack Alan Reynolds
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Axiomathes 20 (2-3):295-312 (2010)
In this paper the reader is asked to engage in some simple problem-solving in classical pure number theory and to then describe, on the basis of a series of questions, what it is like to solve the problems. In the recent philosophy of mind this “what is it like” question is one way of signaling a turn to phenomenological description. The description of what it is like to solve the problems in this paper, it is argued, leads to several morals about the epistemology and ontology of classical pure mathematical practice. Instead of simply making philosophical judgments about the subject matter in advance, the exercise asks the reader to briefly engage in a mathematical practice and to then reflect on the practice.
|Keywords||Mathematical experience Intentionality Mathematical practice Constituted platonism|
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References found in this work BETA
John R. Searle (1983). Intentionality: An Essay in the Philosophy of Mind. Cambridge University Press.
Richard Tieszen (2010). Mathematical Realism and Transcendental Phenomenological Realism. In Mirja Hartimo (ed.), Phenomenology and Mathematics. Springer 1--22.
Richard Tieszen (2005). Consciousness of Abstract Objects. In David Woodruff Smith & Amie Lynn Thomasson (eds.), Phenomenology and Philosophy of Mind. Oxford: Clarendon Press
Citations of this work BETA
Jens Erik Fenstad (2015). On What There is—Infinitesimals and the Nature of Numbers. Inquiry 58 (1):57-79.
Richard Tieszen (2015). Arithmetic, Mathematical Intuition, and Evidence. Inquiry 58 (1):28-56.
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