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Single Idea 21382

[filed under theme 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals ]

Full Idea

Of the small there is no smallest, but always a smaller.

Gist of Idea

Things get smaller without end

Source

Anaxagoras (fragments/reports [c.460 BCE], B03), quoted by Gregory Vlastos - The Physical Theory of Anaxagoras II

Book Ref

Vlastos,Gregory: 'Studies in Greek Phil I: The Presocratics', ed/tr. Graham,D.W [Princeton 1993], p.312

A Reaction

Anaxagoras seems to be speaking of the physical world (and probably writing prior to the emergence of atomism, which could have been a rebellion against he current idea).

The 9 ideas with the same theme [items too small to be measured]:

21382 Things get smaller without end [Anaxagoras]
18081 Nature uses the infinite everywhere [Leibniz]
18080 A tangent is a line connecting two points on a curve that are infinitely close together [Leibniz]
18091 Infinitesimals are ghosts of departed quantities [Berkeley]
18085 Values that approach zero, becoming less than any quantity, are 'infinitesimals' [Cauchy]
18086 Weierstrass eliminated talk of infinitesimals [Weierstrass, by Kitcher]
18110 Infinitesimals are not actually contradictory, because they can be non-standard real numbers [Bostock]
18083 With infinitesimals, you divide by the time, then set the time to zero [Kitcher]
18834 Infinitesimals do not stand in a determinate order relation to zero [Rumfitt]