Mathematical Problem-Solving and Ontology: An Exercise [Book Review]

Axiomathes 20 (2-3):295-312 (2010)
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Abstract

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.

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Citations of this work

Arithmetic, Mathematical Intuition, and Evidence.Richard Tieszen - 2015 - Inquiry: An Interdisciplinary Journal of Philosophy 58 (1):28-56.
On What There is—Infinitesimals and the Nature of Numbers.Jens Erik Fenstad - 2015 - Inquiry: An Interdisciplinary Journal of Philosophy 58 (1):57-79.

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References found in this work

Intentionality: An Essay in the Philosophy of Mind.John R. Searle - 1983 - New York: Cambridge University Press.
Intentionality: An Essay in the Philosophy of Mind.John R. Searle - 1983 - New York: Oxford University Press.
What is it like to be a bat?Thomas Nagel - 1974 - Philosophical Review 83 (October):435-50.
The Rediscovery of the Mind.John R. Searle - 1992 - MIT Press. Edited by Ned Block & Hilary Putnam.
Logical investigations.Edmund Husserl - 2000 - New York: Routledge. Edited by Dermot Moran.

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