22 ideas
9808 | Philosophy aims to reveal the grandeur of mathematics [Badiou] |
23623 | Predicativism says only predicated sets exist [Hossack] |
23624 | The iterative conception has to appropriate Replacement, to justify the ordinals [Hossack] |
23625 | Limitation of Size justifies Replacement, but then has to appropriate Power Set [Hossack] |
23628 | The connective 'and' can have an order-sensitive meaning, as 'and then' [Hossack] |
23627 | 'Before' and 'after' are not two relations, but one relation with two orders [Hossack] |
10631 | If 'x is heterological' iff it does not apply to itself, then 'heterological' is heterological if it isn't heterological [Hale/Wright] |
9812 | In mathematics, if a problem can be formulated, it will eventually be solved [Badiou] |
9813 | Mathematics shows that thinking is not confined to the finite [Badiou] |
23626 | Transfinite ordinals are needed in proof theory, and for recursive functions and computability [Hossack] |
10624 | The incompletability of formal arithmetic reveals that logic also cannot be completely characterized [Hale/Wright] |
23621 | Numbers are properties, not sets (because numbers are magnitudes) [Hossack] |
10629 | If structures are relative, this undermines truth-value and objectivity [Hale/Wright] |
10628 | The structural view of numbers doesn't fit their usage outside arithmetical contexts [Hale/Wright] |
23622 | We can only mentally construct potential infinities, but maths needs actual infinities [Hossack] |
10622 | The neo-Fregean is more optimistic than Frege about contextual definitions of numbers [Hale/Wright] |
9809 | Mathematics inscribes being as such [Badiou] |
9811 | It is of the essence of being to appear [Badiou] |
10626 | Objects just are what singular terms refer to [Hale/Wright] |
10630 | Abstracted objects are not mental creations, but depend on equivalence between given entities [Hale/Wright] |
10627 | Many conceptual truths ('yellow is extended') are not analytic, as derived from logic and definitions [Hale/Wright] |
9814 | All great poetry is engaged in rivalry with mathematics [Badiou] |