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The British Journal for the Philosophy of Science 2002 53(2):205-223; doi:10.1093/bjps/53.2.205
© 2002 by British Society for the Philosophy of Science
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What Perception Is Doing, and What it Is Not Doing, in Mathematical Reasoning

Dennis Lomas1

1 Charlottetown, Prince Edward Island, Canada. DenLom8{at}aol.com

What is perception doing in mathematical reasoning? To address this question, I discuss the role of perception in geometric reasoning. Perception of the shape properties of concrete diagrams provides, I argue, a surrogate consciousness of the shape properties of the abstract geometric objects depicted in the diagrams. Some of what perception is not doing in mathematical reasoning is also discussed. I take issue with both Parsons and Maddy. Parsons claims that we perceive a certain type of abstract object. Maddy claims (at least at one time claimed) that perception provides the basis for intuition of mathematical sets.

1 Mathematical reasoning with diagrams

2 Do we perceive abstract objects?

3 Do we perceive mathematical sets?


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