Mathematical Problem-Solving and Ontology: An Exercise [Book Review]
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
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|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
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.
Similar books and articles
Yaroslav Sergeyev (2010). Counting Systems and the First Hilbert Problem. Nonlinear Analysis Series A 72 (3-4):1701-1708.
Valeria Giardino (2010). Intuition and Visualization in Mathematical Problem Solving. Topoi 29 (1):29-39.
Alvin I. Goldman (1983). Epistemology and the Theory of Problem Solving. Synthese 55 (1):21 - 48.
Julian C. Cole (2009). Creativity, Freedom, and Authority: A New Perspective On the Metaphysics of Mathematics. Australasian Journal of Philosophy 87 (4):589-608.
Roger Fontaine, Isabelle Nanty, Olivier Sorel & Valérie Pennequin (2011). Metacognition and Low Achievement in Mathematics: The Effect of Training in the Use of Metacognitive Skills to Solve Mathematical Word Problems. Thinking and Reasoning 16 (3):198-220.
Lisa M. Osbeck & Nancy J. Nersessian (2011). Affective Problem Solving: Emotion in Research Practice. Mind and Society 10 (1):57-78.
M. A. van Rees (2003). Pragma-Dialectical Analysis and Evaluation of Problem-Solving Discussion. Argumentation 17 (4):465-479.
Mary Leng (2005). Platonism and Anti-Platonism: Why Worry? International Studies in the Philosophy of Science 19 (1):65 – 84.
Jessica Carter (2004). Ontology and Mathematical Practice. Philosophia Mathematica 12 (3):244-267.
Added to index2010-06-09
Total downloads50 ( #82,273 of 1,792,244 )
Recent downloads (6 months)6 ( #139,362 of 1,792,244 )
How can I increase my downloads?