62 ideas
13860 | We can only learn from philosophers of the past if we accept the risk of major misrepresentation [Wright,C] |
11159 | My account shows how the concept works, rather than giving an analysis [Fine,K] |
13883 | The best way to understand a philosophical idea is to defend it [Wright,C] |
11157 | Modern philosophy has largely abandoned real definitions, apart from sortals [Fine,K] |
11171 | Defining a term and giving the essence of an object don't just resemble - they are the same [Fine,K] |
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] |
13867 | Instances of a non-sortal concept can only be counted relative to a sortal concept [Wright,C] |
23026 | We know mathematical axioms, such as subtracting equals from equals leaves equals, by a natural light [Leibniz] |
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] |
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] |
11151 | An object is dependent if its essence prevents it from existing without some other object [Fine,K] |
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] |
11152 | Essences are either taken as real definitions, or as necessary properties [Fine,K] |
11161 | Essentially having a property is naturally expressed as 'the property it must have to be what it is' [Fine,K] |
11160 | Simple modal essentialism refers to necessary properties of an object [Fine,K] |
11158 | Essentialist claims can be formulated more clearly with quantified modal logic [Fine,K] |
13189 | A necessary feature (such as air for humans) is not therefore part of the essence [Leibniz] |
11167 | Metaphysical necessity is a special case of essence, not vice versa [Fine,K] |
16537 | Essence as necessary properties produces a profusion of essential properties [Fine,K, by Lowe] |
11163 | The nature of singleton Socrates has him as a member, but not vice versa [Fine,K] |
11164 | It is not part of the essence of Socrates that a huge array of necessary truths should hold [Fine,K] |
10935 | An essential property of something must be bound up with what it is to be that thing [Fine,K, by Rami] |
10936 | Essential properties are part of an object's 'definition' [Fine,K, by Rami] |
11165 | If Socrates lacks necessary existence, then his nature cannot require his parents' existence [Fine,K] |
11166 | The subject of a proposition need not be the source of its necessity [Fine,K] |
11169 | Conceptual necessities rest on the nature of all concepts [Fine,K] |
11162 | Socrates is necessarily distinct from the Eiffel Tower, but that is not part of his essence [Fine,K] |
11168 | Metaphysical necessities are true in virtue of the nature of all objects [Fine,K] |
19432 | Intelligible truth is independent of any external things or experiences [Leibniz] |
19430 | We know objects by perceptions, but their qualities don't reveal what it is we are perceiving [Leibniz] |
19431 | There is nothing in the understanding but experiences, plus the understanding itself, and the understander [Leibniz] |
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] |
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] |
11170 | Analytic truth may only be true in virtue of the meanings of certain terms [Fine,K] |
11172 | The meaning of 'bachelor' is irrelevant to the meaning of 'unmarried man' [Fine,K] |