18 ideas
11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
17963 | The facts of geometry, arithmetic or statics order themselves into theories [Hilbert] |
17966 | Axioms must reveal their dependence (or not), and must be consistent [Hilbert] |
10631 | If 'x is heterological' iff it does not apply to itself, then 'heterological' is heterological if it isn't heterological [Hale/Wright] |
17967 | To decide some questions, we must study the essence of mathematical proof itself [Hilbert] |
17965 | The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert] |
17964 | Number theory just needs calculation laws and rules for integers [Hilbert] |
10624 | The incompletability of formal arithmetic reveals that logic also cannot be completely characterized [Hale/Wright] |
10628 | The structural view of numbers doesn't fit their usage outside arithmetical contexts [Hale/Wright] |
10629 | If structures are relative, this undermines truth-value and objectivity [Hale/Wright] |
10622 | The neo-Fregean is more optimistic than Frege about contextual definitions of numbers [Hale/Wright] |
10626 | Objects just are what singular terms refer to [Hale/Wright] |
10630 | Abstracted objects are not mental creations, but depend on equivalence between given entities [Hale/Wright] |
10627 | Many conceptual truths ('yellow is extended') are not analytic, as derived from logic and definitions [Hale/Wright] |
11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |
17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |