36 ideas
| 8092 | Logic was merely a branch of rhetoric until the scientific 17th century [Devlin] |
| 8081 | 'No councillors are bankers' and 'All bankers are athletes' implies 'Some athletes are not councillors' [Devlin] |
| 8085 | Modern propositional inference replaces Aristotle's 19 syllogisms with modus ponens [Devlin] |
| 8086 | Predicate logic retains the axioms of propositional logic [Devlin] |
| 9570 | In Field's Platonist view, set theory is false because it asserts existence for non-existent things [Field,H, by Chihara] |
| 8091 | Situation theory is logic that takes account of context [Devlin] |
| 8087 | Golden ages: 1900-1960 for pure logic, and 1950-1985 for applied logic [Devlin] |
| 8089 | Montague's intensional logic incorporated the notion of meaning [Devlin] |
| 10260 | Logical consequence is defined by the impossibility of P and ¬q [Field,H, by Shapiro] |
| 8082 | Where a conditional is purely formal, an implication implies a link between premise and conclusion [Devlin] |
| 8072 | Sentences of apparent identical form can have different contextual meanings [Devlin] |
| 8075 | Space and time are atomic in the arrow, and divisible in the tortoise [Devlin] |
| 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] |
| 18216 | Abstractions can form useful counterparts to concrete statements [Field,H] |
| 18214 | Mathematics is only empirical as regards which theory is useful [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] |
| 8088 | People still say the Hopi have no time concepts, despite Whorf's later denial [Devlin] |
| 18222 | Beneath every extrinsic explanation there is an intrinsic explanation [Field,H] |
| 9917 | 'Abstract' is unclear, but numbers, functions and sets are clearly abstract [Field,H] |
| 8073 | How do we parse 'time flies like an arrow' and 'fruit flies like an apple'? [Devlin] |
| 8076 | The distinction between sentences and abstract propositions is crucial in logic [Devlin] |
| 7861 | Libet says the processes initiated in the cortex can still be consciously changed [Libet, by Papineau] |
| 6660 | Libet found conscious choice 0.2 secs before movement, well after unconscious 'readiness potential' [Libet, by Lowe] |
| 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] |