24 ideas
19066 | Philosophy aims to understand the world, through ordinary experience and science [Dummett] |
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] |
13011 | New axioms are being sought, to determine the size of the continuum [Maddy] |
13013 | The Axiom of Extensionality seems to be analytic [Maddy] |
13014 | Extensional sets are clearer, simpler, unique and expressive [Maddy] |
13021 | The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy] |
13022 | Infinite sets are essential for giving an account of the real numbers [Maddy] |
13023 | The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy] |
13024 | Efforts to prove the Axiom of Choice have failed [Maddy] |
13025 | Modern views say the Choice set exists, even if it can't be constructed [Maddy] |
13026 | A large array of theorems depend on the Axiom of Choice [Maddy] |
13019 | The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy] |
13018 | Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy] |
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] |
19065 | Soundness and completeness proofs test the theory of meaning, rather than the logic theory [Dummett] |
2614 | Modern phenomenalism holds that objects are logical constructions out of sense-data [Ayer] |
2615 | The concept of sense-data allows us to discuss appearances without worrying about reality [Ayer] |
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] |