53 ideas
| 13860 | We can only learn from philosophers of the past if we accept the risk of major misrepresentation [Wright,C] |
| 2945 | Most philosophers start with reality and then examine knowledge; Descartes put the study of knowledge first [Lehrer] |
| 2946 | You cannot demand an analysis of a concept without knowing the purpose of the analysis [Lehrer] |
| 13883 | The best way to understand a philosophical idea is to defend it [Wright,C] |
| 9821 | A definition need not capture the sense of an expression - just get the reference right [Frege, by Dummett] |
| 10142 | The attempt to define numbers by contextual definition has been revived [Wright,C, by Fine,K] |
| 9585 | Since every definition is an equation, one cannot define equality itself [Frege] |
| 9868 | An expression refers if it is a singular term in some true sentences [Wright,C, by Dummett] |
| 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] |
| 17446 | Counting rests on one-one correspondence, of numerals to objects [Frege] |
| 9582 | Husserl rests sameness of number on one-one correlation, forgetting the correlation with numbers themselves [Frege] |
| 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] |
| 9586 | In a number-statement, something is predicated of a concept [Frege] |
| 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] |
| 9580 | Our concepts recognise existing relations, they don't change them [Frege] |
| 9589 | Numbers are not real like the sea, but (crucially) they are still objective [Frege] |
| 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] |
| 9577 | The naďve view of number is that it is like a heap of things, or maybe a property of a heap [Frege] |
| 13873 | Treating numbers adjectivally is treating them as quantifiers [Wright,C] |
| 7804 | Wright has revived Frege's discredited logicism [Wright,C, by Benardete,JA] |
| 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] |
| 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] |
| 13884 | The idea that 'exist' has multiple senses is not coherent [Wright,C] |
| 9578 | If objects are just presentation, we get increasing abstraction by ignoring their properties [Frege] |
| 13877 | Singular terms in true sentences must refer to objects; there is no further question about their existence [Wright,C] |
| 9878 | Contextually defined abstract terms genuinely refer to objects [Wright,C, by Dummett] |
| 13868 | Sortal concepts cannot require that things don't survive their loss, because of phase sortals [Wright,C] |
| 9581 | Many people have the same thought, which is the component, not the private presentation [Frege] |
| 13865 | 'Sortal' concepts show kinds, use indefinite articles, and require grasping identities [Wright,C] |
| 13866 | A concept is only a sortal if it gives genuine identity [Wright,C] |
| 13890 | Entities fall under a sortal concept if they can be used to explain identity statements concerning them [Wright,C] |
| 9579 | Disregarding properties of two cats still leaves different objects, but what is now the difference? [Frege] |
| 9587 | How do you find the right level of inattention; you eliminate too many or too few characteristics [Frege] |
| 13898 | If we can establish directions from lines and parallelism, we were already committed to directions [Wright,C] |
| 9588 | Number-abstraction somehow makes things identical without changing them! [Frege] |
| 9583 | Psychological logicians are concerned with sense of words, but mathematicians study the reference [Frege] |
| 9584 | Identity baffles psychologists, since A and B must be presented differently to identify them [Frege] |
| 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] |