31 ideas
9108 | From an impossibility anything follows [William of Ockham] |
9107 | A proposition is true if its subject and predicate stand for the same thing [William of Ockham] |
16300 | Ockham had an early axiomatic account of truth [William of Ockham, by Halbach] |
9570 | In Field's Platonist view, set theory is false because it asserts existence for non-existent things [Field,H, by Chihara] |
10260 | Logical consequence is defined by the impossibility of P and ¬q [Field,H, by Shapiro] |
9106 | The word 'every' only signifies when added to a term such as 'man', referring to all men [William of Ockham] |
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] |
9113 | Just as unity is not a property of a single thing, so numbers are not properties of many things [William of Ockham] |
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] |
9110 | The words 'thing' and 'to be' assert the same idea, as a noun and as a verb [William of Ockham] |
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] |
15388 | Universals are single things, and only universal in what they signify [William of Ockham] |
18213 | Abstract objects are only applicable to the world if they are impure, and connect to the physical [Field,H] |
9109 | If essence and existence were two things, one could exist without the other, which is impossible [William of Ockham] |
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] |
9105 | Some concepts for propositions exist only in the mind, and in no language [William of Ockham] |
2685 | The Greek 'philia' covers all good and fruitful relationships [Cooper,JM] |
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] |