69 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] |
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] |
12154 | Are 'word token' and 'word type' different sorts of countable objects, or two ways of counting? [Geach, by Perry] |
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] |
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] |
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] |
10735 | Abstraction from objects won't reveal an operation's being performed 'so many times' [Geach] |
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] |
13884 | The idea that 'exist' has multiple senses is not coherent [Wright,C] |
13877 | Singular terms in true sentences must refer to objects; there is no further question about their existence [Wright,C] |
8780 | Attributes are functions, not objects; this distinguishes 'square of 2' from 'double of 2' [Geach] |
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] |
8969 | We should abandon absolute identity, confining it to within some category [Geach, by Hawthorne] |
16075 | Denial of absolute identity has drastic implications for logic, semantics and set theory [Wasserman on Geach] |
12152 | Identity is relative. One must not say things are 'the same', but 'the same A as' [Geach] |
16073 | Leibniz's Law is incomplete, since it includes a non-relativized identity predicate [Geach, by Wasserman] |
11910 | Being 'the same' is meaningless, unless we specify 'the same X' [Geach] |
12189 | Logical necessity involves a decision about usage, and is non-realist and non-cognitive [Wright,C, by McFetridge] |
8775 | A big flea is a small animal, so 'big' and 'small' cannot be acquired by abstraction [Geach] |
8776 | We cannot learn relations by abstraction, because their converse must be learned too [Geach] |
10732 | If concepts are just recognitional, then general judgements would be impossible [Geach] |
2567 | You can't define real mental states in terms of behaviour that never happens [Geach] |
2568 | Beliefs aren't tied to particular behaviours [Geach] |
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] |
8781 | The mind does not lift concepts from experience; it creates them, and then applies them [Geach] |
10731 | For abstractionists, concepts are capacities to recognise recurrent features of the world [Geach] |
13890 | Entities fall under a sortal concept if they can be used to explain identity statements concerning them [Wright,C] |
8769 | If someone has aphasia but can still play chess, they clearly have concepts [Geach] |
8770 | 'Abstractionism' is acquiring a concept by picking out one experience amongst a group [Geach] |
13898 | If we can establish directions from lines and parallelism, we were already committed to directions [Wright,C] |
8771 | 'Or' and 'not' are not to be found in the sensible world, or even in the world of inner experience [Geach] |
8772 | We can't acquire number-concepts by extracting the number from the things being counted [Geach] |
8773 | Abstractionists can't explain counting, because it must precede experience of objects [Geach] |
8774 | The numbers don't exist in nature, so they cannot have been abstracted from there into our languages [Geach] |
8778 | Blind people can use colour words like 'red' perfectly intelligently [Geach] |
8777 | If 'black' and 'cat' can be used in the absence of such objects, how can such usage be abstracted? [Geach] |
8779 | We can form two different abstract concepts that apply to a single unified experience [Geach] |
10733 | The abstractionist cannot explain 'some' and 'not' [Geach] |
10734 | Only a judgement can distinguish 'striking' from 'being struck' [Geach] |
13882 | A milder claim is that understanding requires some evidence of that understanding [Wright,C] |
7320 | Holism cannot give a coherent account of scientific methodology [Wright,C, by Miller,A] |
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] |
22489 | 'Good' is an attributive adjective like 'large', not predicative like 'red' [Geach, by Foot] |
19896 | It is not a law if not endorsed by the public [Hooker,R] |
19891 | Rule of law is superior to autonomy, because citizens can see what is expected [Hooker,R] |
19897 | Human laws must accord with the general laws of Nature [Hooker,R] |
17005 | Natural things observe certain laws, and things cannot do otherwise if they retain their forms [Hooker,R] |