4 ideas
15380 | Barcan:nothing comes into existence; Converse:nothing goes out; Both:domain is unchanging [Vervloesem] |
Full Idea: Intuitively, the Barcan formula says that nothing comes into existence when moving from a possible world to an alternative world. The converse says that nothing goes out of existence. Together they say the domain of quantification is fixed for all worlds. | |
From: Koen Vervloesem (Barcan Formulae [2010]) | |
A reaction: Stated so clearly, they sound absurd. The sensible idea, I suppose, is that you can refer to all the things from any world, but that doesn't mean they are possible. Shades of Meinong. 'Square circles' are not possible. |
18086 | Weierstrass eliminated talk of infinitesimals [Weierstrass, by Kitcher] |
Full Idea: Weierstrass effectively eliminated the infinitesimalist language of his predecessors. | |
From: report of Karl Weierstrass (works [1855]) by Philip Kitcher - The Nature of Mathematical Knowledge 10.6 |
18092 | Weierstrass made limits central, but the existence of limits still needed to be proved [Weierstrass, by Bostock] |
Full Idea: After Weierstrass had stressed the importance of limits, one now needed to be able to prove the existence of such limits. | |
From: report of Karl Weierstrass (works [1855]) by David Bostock - Philosophy of Mathematics 4.4 | |
A reaction: The solution to this is found in work on series (going back to Cauchy), and on Dedekind's cuts. |
1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |
Full Idea: The Egyptians were the first to claim that the soul of a human being is immortal, and that each time the body dies the soul enters another creature just as it is being born. | |
From: Herodotus (The Histories [c.435 BCE], 2.123.2) |