A mathematician reflects on the useful and reliable illusion of reality in mathematics

Erkenntnis 68 (3):359 - 379 (2008)
Recent years have seen a growing acknowledgement within the mathematical community that mathematics is cognitively/socially constructed. Yet to anyone doing mathematics, it seems totally objective. The sensation in pursuing mathematical research is of discovering prior (eternal) truths about an external (abstract) world. Although the community can and does decide which topics to pursue and which axioms to adopt, neither an individual mathematician nor the entire community can choose whether a particular mathematical statement is true or false, based on the given axioms. Moreover, all the evidence suggests that all practitioners work with the same ontology. (My number 7 is exactly the same as yours.) How can we reconcile the notion that people construct mathematics, with this apparent choice-free, predetermined objectivity? I believe the answer is to be found by examining what mathematical thinking is (as a mental activity) and the way the human brain acquired the capacity for mathematical thinking.
Keywords Philosophy   Logic   Ethics   Ontology   Epistemology   Philosophy
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References found in this work BETA
George Lakoff (1980). Metaphors We Live By. University of Chicago Press.
Derek Bickerton (1996). Language and Human Behavior. Seattle: University Washington Press.
Jacques Hadamard (1949). The Psychology of Invention in the Mathematical Field. Philosophy and Phenomenological Research 10 (2):288-289.

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