Article ID: CBB693325107

What Numbers Could Not Be (for Aristotle) (2021)

unapi

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.

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Authors & Contributors
Tipton, Jason A.
Iwata, Naoya
Zhang, Butian
Zellini, Paolo
Robertson, David G.
Reynolds, Joshua
Concepts
Philosophy
Ontology
Philosophy of mathematics
Mathematics
Metaphysics
Number theory; number concept
Time Periods
Ancient
Medieval
Early modern
20th century
17th century
Places
Greece
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