56 ideas
13860 | We can only learn from philosophers of the past if we accept the risk of major misrepresentation [Wright,C] |
19456 | Philosophy is distinguished from other sciences by its complete lack of presuppositions [Feuerbach] |
13883 | The best way to understand a philosophical idea is to defend it [Wright,C] |
16539 | A definition of a circle will show what it is, and show its generating principle [Lowe] |
16540 | Defining an ellipse by conic sections reveals necessities, but not the essence of an ellipse [Lowe] |
16548 | An essence is what an entity is, revealed by a real definition; this is not an entity in its own right [Lowe] |
10142 | The attempt to define numbers by contextual definition has been revived [Wright,C, by Fine,K] |
16549 | Simple things like 'red' can be given real ostensive definitions [Lowe] |
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] |
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] |
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] |
16545 | The essence of lumps and statues shows that two objects coincide but are numerically distinct [Lowe] |
16546 | The essence of a bronze statue shows that it could be made of different bronze [Lowe] |
16551 | Grasping an essence is just grasping a real definition [Lowe] |
16542 | Explanation can't give an account of essence, because it is too multi-faceted [Lowe] |
16552 | If we must know some entity to know an essence, we lack a faculty to do that [Lowe] |
16533 | Logical necessities, based on laws of logic, are a proper sub-class of metaphysical necessities [Lowe] |
16531 | 'Metaphysical' necessity is absolute and objective - the strongest kind of necessity [Lowe] |
16532 | 'Epistemic' necessity is better called 'certainty' [Lowe] |
16543 | If an essence implies p, then p is an essential truth, and hence metaphysically necessary [Lowe] |
16544 | Metaphysical necessity is either an essential truth, or rests on essential truths [Lowe] |
16538 | We could give up possible worlds if we based necessity on essences [Lowe] |
16534 | 'Intuitions' are just unreliable 'hunches'; over centuries intuitions change enormously [Lowe] |
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] |
16535 | A concept is a way of thinking of things or kinds, whether or not they exist [Lowe] |
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] |
16550 | Direct reference doesn't seem to require that thinkers know what it is they are thinking about [Lowe] |
17857 | We can accept Frege's idea of object without assuming that predicates have a reference [Wright,C] |
16547 | H2O isn't necessary, because different laws of nature might affect how O and H combine [Lowe] |