81 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] |
| 10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
| 10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
| 3005 | 'Jocasta' needs to be distinguished from 'Oedipus's mother' because they are connected by different properties [Fodor] |
| 9868 | An expression refers if it is a singular term in some true sentences [Wright,C, by Dummett] |
| 10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
| 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] |
| 10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
| 13867 | Instances of a non-sortal concept can only be counted relative to a sortal concept [Wright,C] |
| 10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
| 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] |
| 10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
| 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] |
| 10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
| 10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
| 10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
| 10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
| 10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
| 10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
| 10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
| 10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
| 10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
| 10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
| 10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
| 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] |
| 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] |
| 7014 | A particle and a coin heads-or-tails pick out to perfectly well-defined predicates and properties [Fodor] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 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] |
| 3008 | Evolution suggests that innate knowledge of human psychology would be beneficial [Fodor] |
| 2990 | Contrary to commonsense, most of what is in the mind seems to be unlearned [Fodor] |
| 3009 | Sticklebacks have an innate idea that red things are rivals [Fodor] |
| 2994 | In CRTT thought may be represented, content must be [Fodor] |
| 15494 | We can't use propositions to explain intentional attitudes, because they would need explaining [Fodor] |
| 7326 | Intentionality doesn't go deep enough to appear on the physicists' ultimate list of things [Fodor] |
| 3001 | Behaviourism has no theory of mental causation [Fodor] |
| 2993 | Any piece of software can always be hard-wired [Fodor] |
| 3011 | Causal powers must be a crucial feature of mental states [Fodor] |
| 5498 | Mind is a set of hierarchical 'homunculi', which are made up in turn from subcomponents [Fodor, by Lycan] |
| 2995 | Supervenience gives good support for mental causation [Fodor] |
| 2991 | Hume's associationism offers no explanation at all of rational thought [Fodor] |
| 3002 | If mind is just physical, how can it follow the rules required for intelligent thought? [Fodor] |
| 2992 | We may be able to explain rationality mechanically [Fodor] |
| 2988 | Folk psychology is the only explanation of behaviour we have [Fodor] |
| 3010 | Belief and desire are structured states, which need mentalese [Fodor] |
| 2999 | Obsession with narrow content leads to various sorts of hopeless anti-realism [Fodor] |
| 3012 | Do identical thoughts have identical causal roles? [Fodor] |
| 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] |
| 13890 | Entities fall under a sortal concept if they can be used to explain identity statements concerning them [Wright,C] |
| 13898 | If we can establish directions from lines and parallelism, we were already committed to directions [Wright,C] |
| 2998 | Grice thinks meaning is inherited from the propositional attitudes which sentences express [Fodor] |
| 3006 | Whatever in the mind delivers falsehood is parasitic on what delivers truth [Fodor] |
| 3007 | Many different verification procedures can reach 'star', but it only has one semantic value [Fodor] |
| 13882 | A milder claim is that understanding requires some evidence of that understanding [Wright,C] |
| 3004 | The meaning of a sentence derives from its use in expressing an attitude [Fodor] |
| 3000 | Meaning holism is a crazy doctrine [Fodor] |
| 3003 | Very different mental states can share their contents, so content doesn't seem to be constructed from functional role [Fodor] |
| 2996 | Mental states may have the same content but different extensions [Fodor] |
| 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] |