60 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] |
10633 | 'Some critics admire only one another' cannot be paraphrased in singular first-order [Linnebo] |
10638 | A pure logic is wholly general, purely formal, and directly known [Linnebo] |
9868 | An expression refers if it is a singular term in some true sentences [Wright,C, by Dummett] |
10640 | Instead of complex objects like tables, plurally quantify over mereological atoms tablewise [Linnebo] |
10636 | Plural plurals are unnatural and need a first-level ontology [Linnebo] |
10639 | Plural quantification may allow a monadic second-order theory with first-order ontology [Linnebo] |
10635 | Second-order quantification and plural quantification are different [Linnebo] |
10641 | Traditionally we eliminate plurals by quantifying over sets [Linnebo] |
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] |
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] |
10643 | We speak of a theory's 'ideological commitments' as well as its 'ontological commitments' [Linnebo] |
13877 | Singular terms in true sentences must refer to objects; there is no further question about their existence [Wright,C] |
10637 | Ordinary speakers posit objects without concern for ontology [Linnebo] |
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] |
14064 | If a statue is identical with the clay of which it is made, that identity is contingent [Gibbard] |
14066 | A 'piece' of clay begins when its parts stick together, separately from other clay [Gibbard] |
14067 | Clay and statue are two objects, which can be named and reasoned about [Gibbard] |
14069 | We can only investigate the identity once we have designated it as 'statue' or as 'clay' [Gibbard] |
14076 | Essentialism is the existence of a definite answer as to whether an entity fulfils a condition [Gibbard] |
14077 | Essentialism for concreta is false, since they can come apart under two concepts [Gibbard] |
14070 | A particular statue has sortal persistence conditions, so its origin defines it [Gibbard] |
14073 | Claims on contingent identity seem to violate Leibniz's Law [Gibbard] |
14065 | Two identical things must share properties - including creation and destruction times [Gibbard] |
14074 | Leibniz's Law isn't just about substitutivity, because it must involve properties and relations [Gibbard] |
14072 | Possible worlds identity needs a sortal [Gibbard] |
14078 | Only concepts, not individuals, can be the same across possible worlds [Gibbard] |
14079 | Kripke's semantics needs lots of intuitions about which properties are essential [Gibbard] |
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] |
14071 | Naming a thing in the actual world also invokes some persistence criteria [Gibbard] |
17857 | We can accept Frege's idea of object without assuming that predicates have a reference [Wright,C] |
10634 | Predicates are 'distributive' or 'non-distributive'; do individuals do what the group does? [Linnebo] |