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

Axiomathes 20 (2-3):295-312 (2010)
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.
Keywords Mathematical experience  Intentionality  Mathematical practice  Constituted platonism
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References found in this work BETA
Richard Tieszen (2005). Consciousness of Abstract Objects. In David Woodruff Smith & Amie Lynn Thomasson (eds.), Phenomenology and Philosophy of Mind. Oxford: Clarendon Press.
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