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Full-Text Articles in Ancient Philosophy
Aristotle On Mathematical Existence, Phil Corkum
Aristotle On Mathematical Existence, Phil Corkum
The Society for Ancient Greek Philosophy Newsletter
Do mathematical objects exist in some realm inaccessible to our senses? It may be tempting to deny this. For one thing, how we could come to know mathematical truths, if such knowledge must arise from causal interaction with non-empirical objects? However, denying that mathematical objects exist altogether has unsettling consequences. If you deny the existence of mathematical objects, then you must reject all claims that commit you to such objects, which means rejecting much of mathematics as it is standardly understood. For, as David Papineau (1990) vividly puts it, it is doublethink to deny that mathematical objects exist but to …