more from this thinker     |     more from this text

Single Idea 18091

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

Full Idea

The infinitesimals are the ghosts of departed quantities.

Gist of Idea

Infinitesimals are ghosts of departed quantities

Source

George Berkeley (The Analyst [1734]), quoted by David Bostock - Philosophy of Mathematics 4.3

Book Ref

Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.96

A Reaction

[A famous phrase, but as yet no context for it]

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]