18 ideas
21959 | Metaphysics is the most general attempt to make sense of things [Moore,AW] |
9193 | ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett] |
9194 | The main alternative to ZF is one which includes looser classes as well as sets [Dummett] |
9195 | Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett] |
9186 | First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett] |
9187 | Logical truths and inference are characterized either syntactically or semantically [Dummett] |
9191 | Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett] |
12215 | The existence of numbers is not a matter of identities, but of constituents of the world [Fine,K] |
9192 | The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett] |
12211 | It is plausible that x^2 = -1 had no solutions before complex numbers were 'introduced' [Fine,K] |
12209 | The indispensability argument shows that nature is non-numerical, not the denial of numbers [Fine,K] |
12214 | 'Exists' is a predicate, not a quantifier; 'electrons exist' is like 'electrons spin' [Fine,K] |
12212 | Just as we introduced complex numbers, so we introduced sums and temporal parts [Fine,K] |
12216 | Real objects are those which figure in the facts that constitute reality [Fine,K] |
12218 | Being real and being fundamental are separate; Thales's water might be real and divisible [Fine,K] |
12217 | For ontology we need, not internal or external views, but a view from outside reality [Fine,K] |
12213 | Ontological claims are often universal, and not a matter of existential quantification [Fine,K] |
21958 | Appearances are nothing beyond representations, which is transcendental ideality [Moore,AW] |