27 ideas
5988 | Anaximander produced the first philosophy book (and maybe the first book) [Anaximander, by Bodnár] |
19066 | Philosophy aims to understand the world, through ordinary experience and science [Dummett] |
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] |
19067 | A successful proof requires recognition of truth at every step [Dummett] |
19060 | Truth-tables are dubious in some cases, and may be a bad way to explain connective meaning [Dummett] |
9967 | 'Impure' sets have a concrete member, while 'pure' (abstract) sets do not [Jubien] |
11066 | Deduction is justified by the semantics of its metalanguage [Dummett, by Hanna] |
19058 | Syntactic consequence is positive, for validity; semantic version is negative, with counterexamples [Dummett] |
19063 | Beth trees show semantics for intuitionistic logic, in terms of how truth has been established [Dummett] |
19059 | In standard views you could replace 'true' and 'false' with mere 0 and 1 [Dummett] |
19062 | Classical two-valued semantics implies that meaning is grasped through truth-conditions [Dummett] |
9968 | A model is 'fundamental' if it contains only concrete entities [Jubien] |
19065 | Soundness and completeness proofs test the theory of meaning, rather than the logic theory [Dummett] |
9965 | There couldn't just be one number, such as 17 [Jubien] |
9966 | The subject-matter of (pure) mathematics is abstract structure [Jubien] |
9964 | Since mathematical objects are essentially relational, they can't be picked out on their own [Jubien] |
9963 | If we all intuited mathematical objects, platonism would be agreed [Jubien] |
9962 | How can pure abstract entities give models to serve as interpretations? [Jubien] |
14874 | Anaximander saw the contradiction in the world - that its own qualities destroy it [Anaximander, by Nietzsche] |
9969 | The empty set is the purest abstract object [Jubien] |
19061 | An explanation is often a deduction, but that may well beg the question [Dummett] |
19064 | Holism is not a theory of meaning; it is the denial that a theory of meaning is possible [Dummett] |
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] |
404 | Things begin and end in the Unlimited, and are balanced over time according to justice [Anaximander] |
1495 | Anaximander introduced the idea that the first principle and element of things was the Boundless [Anaximander, by Simplicius] |
1746 | The parts of all things are susceptible to change, but the whole is unchangeable [Anaximander, by Diog. Laertius] |