13190
|
I don't admit infinite numbers, and consider infinitesimals to be useful fictions [Leibniz]
|
|
Full Idea:
Notwithstanding my infinitesimal calculus, I do not admit any real infinite numbers, even though I confess that the multitude of things surpasses any finite number, or rather any number. ..I consider infinitesimal quantities to be useful fictions.
|
|
From:
Gottfried Leibniz (Letters to Samuel Masson [1716], 1716)
|
|
A reaction:
With the phrase 'useful fictions' we seem to have jumped straight into Harty Field. I'm with Leibniz on this one. The history of mathematics is a series of ingenious inventions, whenever they seem to make further exciting proofs possible.
|
6019
|
If someone squashed a horse to make a dog, something new would now exist [Mnesarchus]
|
|
Full Idea:
If, for the sake of argument, someone were to mould a horse, squash it, then make a dog, it would be reasonable for us on seeing this to say that this previously did not exist but now does exist.
|
|
From:
Mnesarchus (fragments/reports [c.120 BCE]), quoted by John Stobaeus - Anthology 179.11
|
|
A reaction:
Locke would say it is new, because the substance is the same, but a new life now exists. A sword could cease to exist and become a new ploughshare, I would think. Apply this to the Ship of Theseus. Is form more important than substance?
|