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Single Idea 18081

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

Full Idea

Nature uses the infinite in everything it does.

Gist of Idea

Nature uses the infinite everywhere

Source

Gottfried Leibniz (works [1690]), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.1

Book Ref

Kitcher,Philip: 'The Nature of Mathematical Knowledge' [OUP 1984], p.236

A Reaction

[The quote can be tracked through Kitcher's footnote] He seems to have had in mind the infinitely small.

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]