10 ideas
13412 | Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf] |
13413 | We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf] |
13411 | If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf] |
23026 | We know mathematical axioms, such as subtracting equals from equals leaves equals, by a natural light [Leibniz] |
13415 | An adequate account of a number must relate it to its series [Benacerraf] |
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] |
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] |
1556 | By nature people are close to one another, but culture drives them apart [Hippias] |