40 ideas
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] |
13472 | Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD] |
8958 | In Field's version of science, space-time points replace real numbers [Field,H, by Szabó] |
9546 | Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara] |
18742 | Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew] |
18217 | Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H] |
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] |
9476 | If dispositions are more fundamental than causes, then they won't conceptually reduce to them [Bird on Lewis] |
18213 | Abstract objects are only applicable to the world if they are impure, and connect to the physical [Field,H] |
8425 | For true counterfactuals, both antecedent and consequent true is closest to actuality [Lewis] |
18222 | Beneath every extrinsic explanation there is an intrinsic explanation [Field,H] |
8424 | Determinism says there can't be two identical worlds up to a time, with identical laws, which then differ [Lewis] |
9917 | 'Abstract' is unclear, but numbers, functions and sets are clearly abstract [Field,H] |
8420 | A proposition is a set of possible worlds where it is true [Lewis] |
8405 | A theory of causation should explain why cause precedes effect, not take it for granted [Lewis, by Field,H] |
8427 | I reject making the direction of causation axiomatic, since that takes too much for granted [Lewis] |
10392 | It is just individious discrimination to pick out one cause and label it as 'the' cause [Lewis] |
8419 | The modern regularity view says a cause is a member of a minimal set of sufficient conditions [Lewis] |
8421 | Regularity analyses could make c an effect of e, or an epiphenomenon, or inefficacious, or pre-empted [Lewis] |
17525 | The counterfactual view says causes are necessary (rather than sufficient) for their effects [Lewis, by Bird] |
17524 | Lewis has basic causation, counterfactuals, and a general ancestral (thus handling pre-emption) [Lewis, by Bird] |
8397 | Counterfactual causation implies all laws are causal, which they aren't [Tooley on Lewis] |
8423 | My counterfactual analysis applies to particular cases, not generalisations [Lewis] |
8426 | One event causes another iff there is a causal chain from first to second [Lewis] |
4795 | Lewis's account of counterfactuals is fine if we know what a law of nature is, but it won't explain the latter [Cohen,LJ on Lewis] |
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] |