53 ideas
| 13860 | We can only learn from philosophers of the past if we accept the risk of major misrepresentation [Wright,C] |
| 13883 | The best way to understand a philosophical idea is to defend it [Wright,C] |
| 10142 | The attempt to define numbers by contextual definition has been revived [Wright,C, by Fine,K] |
| 23445 | Naďve set theory says any formula defines a set, and coextensive sets are identical [Linnebo] |
| 4975 | A thought can be split in many ways, so that different parts appear as subject or predicate [Frege] |
| 9868 | An expression refers if it is a singular term in some true sentences [Wright,C, by Dummett] |
| 23447 | In classical semantics singular terms refer, and quantifiers range over domains [Linnebo] |
| 23443 | The axioms of group theory are not assertions, but a definition of a structure [Linnebo] |
| 23444 | To investigate axiomatic theories, mathematics needs its own foundational axioms [Linnebo] |
| 13861 | Number theory aims at the essence of natural numbers, giving their nature, and the epistemology [Wright,C] |
| 13892 | One could grasp numbers, and name sizes with them, without grasping ordering [Wright,C] |
| 13867 | Instances of a non-sortal concept can only be counted relative to a sortal concept [Wright,C] |
| 17441 | Wright thinks Hume's Principle is more fundamental to cardinals than the Peano Axioms are [Wright,C, by Heck] |
| 13862 | There are five Peano axioms, which can be expressed informally [Wright,C] |
| 17853 | Number truths are said to be the consequence of PA - but it needs semantic consequence [Wright,C] |
| 17854 | What facts underpin the truths of the Peano axioms? [Wright,C] |
| 23446 | You can't prove consistency using a weaker theory, but you can use a consistent theory [Linnebo] |
| 9949 | There is the concept, the object falling under it, and the extension (a set, which is also an object) [Frege, by George/Velleman] |
| 13894 | Sameness of number is fundamental, not counting, despite children learning that first [Wright,C] |
| 10140 | We derive Hume's Law from Law V, then discard the latter in deriving arithmetic [Wright,C, by Fine,K] |
| 8692 | Frege has a good system if his 'number principle' replaces his basic law V [Wright,C, by Friend] |
| 17440 | Wright says Hume's Principle is analytic of cardinal numbers, like a definition [Wright,C, by Heck] |
| 13893 | It is 1-1 correlation of concepts, and not progression, which distinguishes natural number [Wright,C] |
| 13888 | If numbers are extensions, Frege must first solve the Caesar problem for extensions [Wright,C] |
| 23448 | Mathematics is the study of all possible patterns, and is thus bound to describe the world [Linnebo] |
| 13869 | Number platonism says that natural number is a sortal concept [Wright,C] |
| 13870 | We can't use empiricism to dismiss numbers, if numbers are our main evidence against empiricism [Wright,C] |
| 13873 | Treating numbers adjectivally is treating them as quantifiers [Wright,C] |
| 13899 | The Peano Axioms, and infinity of cardinal numbers, are logical consequences of how we explain cardinals [Wright,C] |
| 13896 | The aim is to follow Frege's strategy to derive the Peano Axioms, but without invoking classes [Wright,C] |
| 7804 | Wright has revived Frege's discredited logicism [Wright,C, by Benardete,JA] |
| 13863 | Logicism seemed to fail by Russell's paradox, Gödel's theorems, and non-logical axioms [Wright,C] |
| 13895 | The standard objections are Russell's Paradox, non-logical axioms, and Gödel's theorems [Wright,C] |
| 23441 | Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo] |
| 23442 | Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo] |
| 13884 | The idea that 'exist' has multiple senses is not coherent [Wright,C] |
| 18995 | Frege mistakenly takes existence to be a property of concepts, instead of being about things [Frege, by Yablo] |
| 13877 | Singular terms in true sentences must refer to objects; there is no further question about their existence [Wright,C] |
| 10317 | It is unclear whether Frege included qualities among his abstract objects [Frege, by Hale] |
| 9878 | Contextually defined abstract terms genuinely refer to objects [Wright,C, by Dummett] |
| 10535 | Frege's 'objects' are both the referents of proper names, and what predicates are true or false of [Frege, by Dummett] |
| 13868 | Sortal concepts cannot require that things don't survive their loss, because of phase sortals [Wright,C] |
| 13866 | A concept is only a sortal if it gives genuine identity [Wright,C] |
| 13865 | 'Sortal' concepts show kinds, use indefinite articles, and require grasping identities [Wright,C] |
| 9839 | Frege equated the concepts under which an object falls with its properties [Frege, by Dummett] |
| 13890 | Entities fall under a sortal concept if they can be used to explain identity statements concerning them [Wright,C] |
| 4973 | As I understand it, a concept is the meaning of a grammatical predicate [Frege] |
| 13898 | If we can establish directions from lines and parallelism, we were already committed to directions [Wright,C] |
| 9167 | Frege felt that meanings must be public, so they are abstractions rather than mental entities [Frege, by Putnam] |
| 13882 | A milder claim is that understanding requires some evidence of that understanding [Wright,C] |
| 13885 | If apparent reference can mislead, then so can apparent lack of reference [Wright,C] |
| 17857 | We can accept Frege's idea of object without assuming that predicates have a reference [Wright,C] |
| 4974 | For all the multiplicity of languages, mankind has a common stock of thoughts [Frege] |