22 ideas
5988 | Anaximander produced the first philosophy book (and maybe the first book) [Anaximander, by Bodnár] |
1496 | The earth is stationary, because it is in the centre, and has no more reason to move one way than another [Anaximander, by Aristotle] |
9944 | We understand some statements about all sets [Putnam] |
10065 | Perhaps If-thenism survives in mathematics if we stick to first-order logic [Musgrave] |
10061 | The If-thenist view only seems to work for the axiomatised portions of mathematics [Musgrave] |
10050 | A statement is logically true if it comes out true in all interpretations in all (non-empty) domains [Musgrave] |
10049 | Logical truths may contain non-logical notions, as in 'all men are men' [Musgrave] |
9937 | I do not believe mathematics either has or needs 'foundations' [Putnam] |
9939 | It is conceivable that the axioms of arithmetic or propositional logic might be changed [Putnam] |
10058 | No two numbers having the same successor relies on the Axiom of Infinity [Musgrave] |
9940 | Maybe mathematics is empirical in that we could try to change it [Putnam] |
9941 | Science requires more than consistency of mathematics [Putnam] |
10063 | Formalism is a bulwark of logical positivism [Musgrave] |
10062 | Formalism seems to exclude all creative, growing mathematics [Musgrave] |
14874 | Anaximander saw the contradiction in the world - that its own qualities destroy it [Anaximander, by Nietzsche] |
9943 | You can't deny a hypothesis a truth-value simply because we may never know it! [Putnam] |
10060 | Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave] |
405 | The essential nature, whatever it is, of the non-limited is everlasting and ageless [Anaximander] |
13222 | The Boundless cannot exist on its own, and must have something contrary to it [Aristotle on Anaximander] |
1495 | Anaximander introduced the idea that the first principle and element of things was the Boundless [Anaximander, by Simplicius] |
404 | Things begin and end in the Unlimited, and are balanced over time according to justice [Anaximander] |
1746 | The parts of all things are susceptible to change, but the whole is unchangeable [Anaximander, by Diog. Laertius] |