25 ideas
| 9376 | A sentence may simultaneously define a term, and also assert a fact [Boghossian] |
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| 9375 | Conventionalism agrees with realists that logic has truth values, but not over the source [Boghossian] |
| 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] |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| 23026 | We know mathematical axioms, such as subtracting equals from equals leaves equals, by a natural light [Leibniz] |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| 13189 | A necessary feature (such as air for humans) is not therefore part of the essence [Leibniz] |
| 19432 | Intelligible truth is independent of any external things or experiences [Leibniz] |
| 9369 | 'Snow is white or it isn't' is just true, not made true by stipulation [Boghossian] |
| 9367 | The a priori is explained as analytic to avoid a dubious faculty of intuition [Boghossian] |
| 9373 | That logic is a priori because it is analytic resulted from explaining the meaning of logical constants [Boghossian] |
| 9380 | We can't hold a sentence true without evidence if we can't agree which sentence is definitive of it [Boghossian] |
| 9384 | We may have strong a priori beliefs which we pragmatically drop from our best theory [Boghossian] |
| 19430 | We know objects by perceptions, but their qualities don't reveal what it is we are perceiving [Leibniz] |
| 19431 | There is nothing in the understanding but experiences, plus the understanding itself, and the understander [Leibniz] |
| 9374 | If we learn geometry by intuition, how could this faculty have misled us for so long? [Boghossian] |
| 9378 | If meaning depends on conceptual role, what properties are needed to do the job? [Boghossian] |
| 9377 | 'Conceptual role semantics' says terms have meaning from sentences and/or inferences [Boghossian] |
| 9372 | Could expressions have meaning, without two expressions possibly meaning the same? [Boghossian] |
| 17721 | There are no truths in virtue of meaning, but there is knowability in virtue of understanding [Boghossian, by Jenkins] |
| 9368 | Epistemological analyticity: grasp of meaning is justification; metaphysical: truth depends on meaning [Boghossian] |