21 ideas
9978 | Analytic philosophy focuses too much on forms of expression, instead of what is actually said [Tait] |
9986 | The null set was doubted, because numbering seemed to require 'units' [Tait] |
17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
9984 | We can have a series with identical members [Tait] |
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] |
10502 | We can rise by degrees through abstraction, with higher levels representing more things [Arnauld,A/Nicole,P] |
18258 | We can only know the exterior world via our ideas [Arnauld,A/Nicole,P] |
16784 | Forms make things distinct and explain the properties, by pure form, or arrangement of parts [Arnauld,A/Nicole,P] |
10499 | We know by abstraction because we only understand composite things a part at a time [Arnauld,A/Nicole,P] |
10501 | A triangle diagram is about all triangles, if some features are ignored [Arnauld,A/Nicole,P] |
10500 | No one denies that a line has width, but we can just attend to its length [Arnauld,A/Nicole,P] |
9981 | Abstraction is 'logical' if the sense and truth of the abstraction depend on the concrete [Tait] |
9982 | Cantor and Dedekind use abstraction to fix grammar and objects, not to carry out proofs [Tait] |
9985 | Abstraction may concern the individuation of the set itself, not its elements [Tait] |
9972 | Why should abstraction from two equipollent sets lead to the same set of 'pure units'? [Tait] |
9980 | If abstraction produces power sets, their identity should imply identity of the originals [Tait] |