28 ideas
| 13886 | Later Frege held that definitions must fix a function's value for every possible argument [Frege, by Wright,C] |
| 9845 | We can't define a word by defining an expression containing it, as the remaining parts are a problem [Frege] |
| 10019 | Only what is logically complex can be defined; what is simple must be pointed to [Frege] |
| 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] |
| 9886 | Cardinals say how many, and reals give measurements compared to a unit quantity [Frege] |
| 9889 | Real numbers are ratios of quantities [Frege, by Dummett] |
| 23626 | Transfinite ordinals are needed in proof theory, and for recursive functions and computability [Hossack] |
| 10020 | Frege's biggest error is in not accounting for the senses of number terms [Hodes on Frege] |
| 10553 | A number is a class of classes of the same cardinality [Frege, by Dummett] |
| 23621 | Numbers are properties, not sets (because numbers are magnitudes) [Hossack] |
| 23622 | We can only mentally construct potential infinities, but maths needs actual infinities [Hossack] |
| 9887 | Formalism misunderstands applications, metatheory, and infinity [Frege, by Dummett] |
| 8751 | Only applicability raises arithmetic from a game to a science [Frege] |
| 9891 | The first demand of logic is of a sharp boundary [Frege] |
| 9890 | The modern account of real numbers detaches a ratio from its geometrical origins [Frege] |
| 11846 | If we abstract the difference between two houses, they don't become the same house [Frege] |
| 7590 | Consequentialism emphasises value rather than obligation in morality [Scruton] |
| 7589 | Altruism is either emotional (where your interests are mine) or moral (where they are reasons for me) [Scruton] |
| 7595 | The idea of a right seems fairly basic; justice may be the disposition to accord rights to people [Scruton] |
| 7588 | Allegiance is fundamental to the conservative view of society [Scruton] |
| 7594 | Democrats are committed to a belief and to its opposite, if the majority prefer the latter [Scruton] |
| 7593 | Liberals focus on universal human freedom, natural rights, and tolerance [Scruton, by PG] |
| 7592 | For positivists law is a matter of form, for naturalists it is a matter of content [Scruton] |
| 7587 | The issue of abortion seems insoluble, because there is nothing with which to compare it [Scruton] |