26 ideas
9921 | 'True' is only occasionally useful, as in 'everything Fermat believed was true' [Burgess/Rosen] |
9924 | Modal logic gives an account of metalogical possibility, not metaphysical possibility [Burgess/Rosen] |
17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
9933 | The paradoxes are only a problem for Frege; Cantor didn't assume every condition determines a set [Burgess/Rosen] |
9928 | Mereology implies that acceptance of entities entails acceptance of conglomerates [Burgess/Rosen] |
5637 | Nowadays logic is seen as the science of extensions, not intensions [Scruton] |
17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
9926 | A relation is either a set of sets of sets, or a set of sets [Burgess/Rosen] |
17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
9932 | The paradoxes no longer seem crucial in critiques of set theory [Burgess/Rosen] |
9923 | We should talk about possible existence, rather than actual existence, of numbers [Burgess/Rosen] |
17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
9925 | Structuralism and nominalism are normally rivals, but might work together [Burgess/Rosen] |
9934 | Number words became nouns around the time of Plato [Burgess/Rosen] |
17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
9918 | Abstract/concrete is a distinction of kind, not degree [Burgess/Rosen] |
9929 | Much of what science says about concrete entities is 'abstraction-laden' [Burgess/Rosen] |
9927 | Mathematics has ascended to higher and higher levels of abstraction [Burgess/Rosen] |
9930 | Abstraction is on a scale, of sets, to attributes, to type-formulas, to token-formulas [Burgess/Rosen] |
5636 | Cartesian 'ideas' confuse concepts and propositions [Scruton] |
9919 | The old debate classified representations as abstract, not entities [Burgess/Rosen] |
5660 | Allegiance is prior to the recognition of individual rights [Scruton] |
5653 | A right is a power which is enforced in the name of justice [Scruton] |
9922 | If space is really just a force-field, then it is a physical entity [Burgess/Rosen] |