20 ideas
11103 | We aren't stuck with our native conceptual scheme; we can gradually change it [Quine] |
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] |
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] |
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] |
11092 | A river is a process, with stages; if we consider it as one thing, we are considering a process [Quine] |
11093 | We don't say 'red' is abstract, unlike a river, just because it has discontinuous shape [Quine] |
11101 | General terms don't commit us ontologically, but singular terms with substitution do [Quine] |
11096 | Discourse generally departmentalizes itself to some degree [Quine] |
11099 | Understanding 'is square' is knowing when to apply it, not knowing some object [Quine] |
11094 | 'Red' is a single concrete object in space-time; 'red' and 'drop' are parts of a red drop [Quine] |
11097 | Red is the largest red thing in the universe [Quine] |
17595 | To unite a sequence of ostensions to make one object, a prior concept of identity is needed [Quine] |
11095 | We should just identify any items which are indiscernible within a given discourse [Quine] |
490 | Everything happens by reason and necessity [Leucippus] |
11104 | Concepts are language [Quine] |
11102 | Apply '-ness' or 'class of' to abstract general terms, to get second-level abstract singular terms [Quine] |