| 13860 | We can only learn from philosophers of the past if we accept the risk of major misrepresentation |
| 13883 | The best way to understand a philosophical idea is to defend it |
| 10142 | The attempt to define numbers by contextual definition has been revived |
| 9868 | An expression refers if it is a singular term in some true sentences |
| 13861 | Number theory aims at the essence of natural numbers, giving their nature, and the epistemology |
| 13892 | One could grasp numbers, and name sizes with them, without grasping ordering |
| 13867 | Instances of a non-sortal concept can only be counted relative to a sortal concept |
| 17441 | Wright thinks Hume's Principle is more fundamental to cardinals than the Peano Axioms are |
| 13862 | There are five Peano axioms, which can be expressed informally |
| 17853 | Number truths are said to be the consequence of PA - but it needs semantic consequence |
| 17854 | What facts underpin the truths of the Peano axioms? |
| 17855 | It may be possible to define induction in terms of the ancestral relation |
| 13894 | Sameness of number is fundamental, not counting, despite children learning that first |
| 10140 | We derive Hume's Law from Law V, then discard the latter in deriving arithmetic |
| 8692 | Frege has a good system if his 'number principle' replaces his basic law V |
| 17440 | Wright says Hume's Principle is analytic of cardinal numbers, like a definition |
| 13893 | It is 1-1 correlation of concepts, and not progression, which distinguishes natural number |
| 13888 | If numbers are extensions, Frege must first solve the Caesar problem for extensions |
| 13869 | Number platonism says that natural number is a sortal concept |
| 13870 | We can't use empiricism to dismiss numbers, if numbers are our main evidence against empiricism |
| 13873 | Treating numbers adjectivally is treating them as quantifiers |
| 7804 | Wright has revived Frege's discredited logicism |
| 13899 | The Peano Axioms, and infinity of cardinal numbers, are logical consequences of how we explain cardinals |
| 13896 | The aim is to follow Frege's strategy to derive the Peano Axioms, but without invoking classes |
| 13863 | Logicism seemed to fail by Russell's paradox, Gödel's theorems, and non-logical axioms |
| 13864 | Frege's platonism and logicism are in conflict, if logic must dictates an infinity of objects |
| 13895 | The standard objections are Russell's Paradox, non-logical axioms, and Gödel's theorems |
| 13884 | The idea that 'exist' has multiple senses is not coherent |
| 13877 | Singular terms in true sentences must refer to objects; there is no further question about their existence |
| 9878 | Contextually defined abstract terms genuinely refer to objects |
| 13868 | Sortal concepts cannot require that things don't survive their loss, because of phase sortals |
| 12189 | Logical necessity involves a decision about usage, and is non-realist and non-cognitive |
| 13865 | 'Sortal' concepts show kinds, use indefinite articles, and require grasping identities |
| 13866 | A concept is only a sortal if it gives genuine identity |
| 13890 | Entities fall under a sortal concept if they can be used to explain identity statements concerning them |
| 13898 | If we can establish directions from lines and parallelism, we were already committed to directions |
| 13882 | A milder claim is that understanding requires some evidence of that understanding |
| 7320 | Holism cannot give a coherent account of scientific methodology |
| 13885 | If apparent reference can mislead, then so can apparent lack of reference |
| 17857 | We can accept Frege's idea of object without assuming that predicates have a reference |