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What Numbers Could Not Be (for Aristotle)
- Journal of the History of Philosophy
- Johns Hopkins University Press
- Volume 59, Number 2, April 2021
- pp. 193-219
- 10.1353/hph.2021.0024
- Article
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abstract:
Consensus is building that, for Aristotle, number cannot be a heap and so must rather be a tight unity (a whole). Scholars commenting on the relevant passages typically conclude, further, that number is a hylomorphic unity. After showing that these passages do not support such readings, I examine Aristotle's statements about the ontological status of number. I find that his position is that number is a special kind of heap: a measured heap. Since a measured heap has identity criteria, it is distinct from a mere heap; and since the arrangement of its parts makes no difference to its identity, it is also distinct from a whole.