20 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] |
17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [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] |
17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
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] |
17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
19065 | Soundness and completeness proofs test the theory of meaning, rather than the logic theory [Dummett] |
17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
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] |
20890 | Why do sexual relationships need permanence, if other relationships don't? [Punzo] |
20891 | Does engaging in sexual intercourse really need no more thought than playing tennis? [Punzo] |