15 ideas
17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
12219 | Whether a modal claim is true depends on how the object is described [Quine, by Fine,K] |
17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
10922 | Objects are the values of variables, so a referentially opaque context cannot be quantified into [Quine] |
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] |
16901 | The equivalent algebra model of geometry loses some essential spatial meaning [Burge] |
17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
16902 | Peano arithmetic requires grasping 0 as a primitive number [Burge] |
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] |
10923 | Aristotelian essentialism says a thing has some necessary and some non-necessary properties [Quine] |
10921 | Necessity can attach to statement-names, to statements, and to open sentences [Quine] |
10924 | Necessity is in the way in which we say things, and not things themselves [Quine] |
16892 | Is apriority predicated mainly of truths and proofs, or of human cognition? [Burge] |