65 ideas
13860 | We can only learn from philosophers of the past if we accept the risk of major misrepresentation [Wright,C] |
11147 | Naturalistic philosophers oppose analysis, preferring explanation to a priori intuition [Margolis/Laurence] |
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] |
17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
9868 | An expression refers if it is a singular term in some true sentences [Wright,C, by Dummett] |
17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
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] |
17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
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] |
17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
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] |
11141 | Modern empiricism tends to emphasise psychological connections, not semantic relations [Margolis/Laurence] |
11142 | Body-type seems to affect a mind's cognition and conceptual scheme [Margolis/Laurence] |
11121 | Language of thought has subject/predicate form and includes logical devices [Margolis/Laurence] |
13865 | 'Sortal' concepts show kinds, use indefinite articles, and require grasping identities [Wright,C] |
13866 | A concept is only a sortal if it gives genuine identity [Wright,C] |
11120 | Concepts are either representations, or abilities, or Fregean senses [Margolis/Laurence] |
11122 | A computer may have propositional attitudes without representations [Margolis/Laurence] |
11124 | Do mental representations just lead to a vicious regress of explanations [Margolis/Laurence] |
11123 | Maybe the concept CAT is just the ability to discriminate and infer about cats [Margolis/Laurence] |
11125 | The abilities view cannot explain the productivity of thought, or mental processes [Margolis/Laurence] |
11140 | Concept-structure explains typicality, categories, development, reference and composition [Margolis/Laurence] |
13890 | Entities fall under a sortal concept if they can be used to explain identity statements concerning them [Wright,C] |
11128 | Classically, concepts give necessary and sufficient conditions for falling under them [Margolis/Laurence] |
11130 | Typicality challenges the classical view; we see better fruit-prototypes in apples than in plums [Margolis/Laurence] |
11129 | The classical theory explains acquisition, categorization and reference [Margolis/Laurence] |
11131 | It may be that our concepts (such as 'knowledge') have no definitional structure [Margolis/Laurence] |
11132 | The prototype theory is probabilistic, picking something out if it has sufficient of the properties [Margolis/Laurence] |
11133 | Prototype theory categorises by computing the number of shared constituents [Margolis/Laurence] |
11134 | People don't just categorise by apparent similarities [Margolis/Laurence] |
11135 | Complex concepts have emergent properties not in the ingredient prototypes [Margolis/Laurence] |
11136 | Many complex concepts obviously have no prototype [Margolis/Laurence] |
11138 | The theory theory is holistic, so how can people have identical concepts? [Margolis/Laurence] |
11137 | The theory theory of concepts says they are parts of theories, defined by their roles [Margolis/Laurence] |
11139 | Maybe concepts have no structure, and determined by relations to the world, not to other concepts [Margolis/Laurence] |
11146 | People can formulate new concepts which are only named later [Margolis/Laurence] |
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] |