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Single Idea 13212

[filed under theme 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / c. Potential infinite ]

Full Idea

Nothing is actually infinite. A thing is infinite only potentially.

Gist of Idea

Infinity is only potential, never actual

Source

Aristotle (Coming-to-be and Passing-away (Gen/Corr) [c.335 BCE], 318a21)

Book Ref

Aristotle: 'The Basic Works of Aristotle', ed/tr. McKeon,Richard [Modern Library Classics 2001], p.480

A Reaction

Aristotle is the famous spokesman for this view, though it reappeared somewhat in early twentieth century discussions (e.g. Hilbert). I sympathise with this unfashionable view. Multiple infinites are good fun, but no one knows what they really are.

The 5 ideas with the same theme [infinity as just not coming to an end]:

13212 Infinity is only potential, never actual [Aristotle]
22929 Aristotle's infinity is a property of the counting process, that it has no natural limit [Aristotle, by Le Poidevin]
9632 Kant only accepts potential infinity, not actual infinity [Kant, by Brown,JR]
15938 Platonists ruin infinity, which is precisely a growing structure which is never completed [Dummett]
15940 The intuitionist endorses only the potential infinite [Lavine]