39 ideas
| 19066 | Philosophy aims to understand the world, through ordinary experience and science [Dummett] |
| 2661 | Dialectic is speech cast in the form of logical argument [Cicero] |
| 19067 | A successful proof requires recognition of truth at every step [Dummett] |
| 2673 | There cannot be more than one truth [Cicero] |
| 19060 | Truth-tables are dubious in some cases, and may be a bad way to explain connective meaning [Dummett] |
| 9570 | In Field's Platonist view, set theory is false because it asserts existence for non-existent things [Field,H, by Chihara] |
| 11066 | Deduction is justified by the semantics of its metalanguage [Dummett, by Hanna] |
| 10260 | Logical consequence is defined by the impossibility of P and ¬q [Field,H, by Shapiro] |
| 19058 | Syntactic consequence is positive, for validity; semantic version is negative, with counterexamples [Dummett] |
| 2669 | Dialectic assumes that all statements are either true or false, but self-referential paradoxes are a big problem [Cicero] |
| 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] |
| 8958 | In Field's version of science, space-time points replace real numbers [Field,H, by Szabó] |
| 18221 | 'Metric' axioms uses functions, points and numbers; 'synthetic' axioms give facts about space [Field,H] |
| 8757 | The Indispensability Argument is the only serious ground for the existence of mathematical entities [Field,H] |
| 18212 | Nominalists try to only refer to physical objects, or language, or mental constructions [Field,H] |
| 10261 | The application of mathematics only needs its possibility, not its truth [Field,H, by Shapiro] |
| 18218 | Hilbert explains geometry, by non-numerical facts about space [Field,H] |
| 9623 | Field needs a semantical notion of second-order consequence, and that needs sets [Brown,JR on Field,H] |
| 18215 | It seems impossible to explain the idea that the conclusion is contained in the premises [Field,H] |
| 18214 | Mathematics is only empirical as regards which theory is useful [Field,H] |
| 18216 | Abstractions can form useful counterparts to concrete statements [Field,H] |
| 18210 | Why regard standard mathematics as truths, rather than as interesting fictions? [Field,H] |
| 18211 | You can reduce ontological commitment by expanding the logic [Field,H] |
| 8959 | Field presumes properties can be eliminated from science [Field,H, by Szabó] |
| 18213 | Abstract objects are only applicable to the world if they are impure, and connect to the physical [Field,H] |
| 2664 | If we have complete healthy senses, what more could the gods give us? [Cicero] |
| 2665 | How can there be a memory of what is false? [Cicero] |
| 20800 | Every true presentation can have a false one of the same quality [Cicero] |
| 18222 | Beneath every extrinsic explanation there is an intrinsic explanation [Field,H] |
| 19061 | An explanation is often a deduction, but that may well beg the question [Dummett] |
| 9917 | 'Abstract' is unclear, but numbers, functions and sets are clearly abstract [Field,H] |
| 19064 | Holism is not a theory of meaning; it is the denial that a theory of meaning is possible [Dummett] |
| 2672 | Virtues must be very detached, to avoid being motivated by pleasure [Cicero] |
| 18223 | In theories of fields, space-time points or regions are causal agents [Field,H] |
| 18220 | Both philosophy and physics now make substantivalism more attractive [Field,H] |
| 18219 | Relational space is problematic if you take the idea of a field seriously [Field,H] |