12 ideas
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| 18812 | Split out the logical vocabulary, make an assignment to the rest. It's logical if premises and conclusion match [Tarski, by Rumfitt] |
| 13344 | X follows from sentences K iff every model of K also models X [Tarski] |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| 13343 | A 'model' is a sequence of objects which satisfies a complete set of sentential functions [Tarski] |
| 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] |
| 13190 | I don't admit infinite numbers, and consider infinitesimals to be useful fictions [Leibniz] |
| 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] |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| 13345 | Sentences are 'analytical' if every sequence of objects models them [Tarski] |