1983 | Frege's Concept of Numbers as Objects |
p.41 | 10140 | We derive Hume's Law from Law V, then discard the latter in deriving arithmetic |
p.55 | 10142 | The attempt to define numbers by contextual definition has been revived |
p.71 | 8692 | Frege has a good system if his 'number principle' replaces his basic law V |
p.189 | 17441 | Wright thinks Hume's Principle is more fundamental to cardinals than the Peano Axioms are |
p.189 | 9868 | An expression refers if it is a singular term in some true sentences |
p.189 | 17440 | Wright says Hume's Principle is analytic of cardinal numbers, like a definition |
p.226 | 9878 | Contextually defined abstract terms genuinely refer to objects |
p.354 | 7804 | Wright has revived Frege's discredited logicism |
Intro | p.-10 | 13861 | Number theory aims at the essence of natural numbers, giving their nature, and the epistemology |
Intro | p.-9 | 13862 | There are five Peano axioms, which can be expressed informally |
Intro | p.-9 | 17853 | Number truths are said to be the consequence of PA - but it needs semantic consequence |
Intro | p.-8 | 17854 | What facts underpin the truths of the Peano axioms? |
Intro | p.-1 | 13863 | Logicism seemed to fail by Russell's paradox, Gödel's theorems, and non-logical axioms |
Intro | p.-1 | 13864 | Frege's platonism and logicism are in conflict, if logic must dictates an infinity of objects |
Pref | p.-12 | 13860 | We can only learn from philosophers of the past if we accept the risk of major misrepresentation |
1.i | p.2 | 13865 | 'Sortal' concepts show kinds, use indefinite articles, and require grasping identities |
1.i | p.3 | 13866 | A concept is only a sortal if it gives genuine identity |
1.i | p.3 | 13867 | Instances of a non-sortal concept can only be counted relative to a sortal concept |
1.i | p.4 | 13868 | Sortal concepts cannot require that things don't survive their loss, because of phase sortals |
1.i | p.4 | 13869 | Number platonism says that natural number is a sortal concept |
1.i | p.4 | 13870 | We can't use empiricism to dismiss numbers, if numbers are our main evidence against empiricism |
1.iii | p.10 | 13873 | Treating numbers adjectivally is treating them as quantifiers |
1.iii | p.14 | 13877 | Singular terms in true sentences must refer to objects; there is no further question about their existence |
1.iv | p.17 | 17857 | We can accept Frege's idea of object without assuming that predicates have a reference |
1.vii | p.44 | 13882 | A milder claim is that understanding requires some evidence of that understanding |
1.vii | p.49 | 13883 | The best way to understand a philosophical idea is to defend it |
2.x | p.83 | 13884 | The idea that 'exist' has multiple senses is not coherent |
2.xi | p.88 | 13885 | If apparent reference can mislead, then so can apparent lack of reference |
3.xiv | p.112 | 13888 | If numbers are extensions, Frege must first solve the Caesar problem for extensions |
3.xiv | p.114 | 13890 | Entities fall under a sortal concept if they can be used to explain identity statements concerning them |
3.xv | p.118 | 13892 | One could grasp numbers, and name sizes with them, without grasping ordering |
3.xv | p.120 | 13893 | It is 1-1 correlation of concepts, and not progression, which distinguishes natural number |
3.xv | p.120 | 13894 | Sameness of number is fundamental, not counting, despite children learning that first |
4.xix | p.161 | 17855 | It may be possible to define induction in terms of the ancestral relation |
4.xix | p.168 | 13899 | The Peano Axioms, and infinity of cardinal numbers, are logical consequences of how we explain cardinals |
4.xvi | p.131 | 13896 | The aim is to follow Frege's strategy to derive the Peano Axioms, but without invoking classes |
4.xvi | p.131 | 13895 | The standard objections are Russell's Paradox, non-logical axioms, and Gödel's theorems |
4.xviii | p.148 | 13898 | If we can establish directions from lines and parallelism, we were already committed to directions |
1986 | Inventing Logical Necessity |
p.126 | 7320 | Holism cannot give a coherent account of scientific methodology |
p.149 | 12189 | Logical necessity involves a decision about usage, and is non-realist and non-cognitive |