82 ideas
13860 | We can only learn from philosophers of the past if we accept the risk of major misrepresentation [Wright,C] |
18835 | Logic doesn't have a metaphysical basis, but nor can logic give rise to the metaphysics [Rumfitt] |
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] |
18819 | The idea that there are unrecognised truths is basic to our concept of truth [Rumfitt] |
18826 | 'True at a possibility' means necessarily true if what is said had obtained [Rumfitt] |
18803 | Semantics for propositions: 1) validity preserves truth 2) non-contradition 3) bivalence 4) truth tables [Rumfitt] |
18814 | 'Absolute necessity' would have to rest on S5 [Rumfitt] |
18798 | It is the second-order part of intuitionistic logic which actually negates some classical theorems [Rumfitt] |
18799 | Intuitionists can accept Double Negation Elimination for decidable propositions [Rumfitt] |
18830 | Most set theorists doubt bivalence for the Continuum Hypothesis, but still use classical logic [Rumfitt] |
18843 | The iterated conception of set requires continual increase in axiom strength [Rumfitt] |
18836 | A set may well not consist of its members; the empty set, for example, is a problem [Rumfitt] |
18837 | A set can be determinate, because of its concept, and still have vague membership [Rumfitt] |
18845 | If the totality of sets is not well-defined, there must be doubt about the Power Set Axiom [Rumfitt] |
18815 | Logic is higher-order laws which can expand the range of any sort of deduction [Rumfitt] |
18805 | Classical logic rules cannot be proved, but various lines of attack can be repelled [Rumfitt] |
18804 | The case for classical logic rests on its rules, much more than on the Principle of Bivalence [Rumfitt] |
18827 | If truth-tables specify the connectives, classical logic must rely on Bivalence [Rumfitt] |
18739 | Three stages of philosophical logic: syntactic (1905-55), possible worlds (1963-85), widening (1990-) [Horsten/Pettigrew] |
18813 | Logical consequence is a relation that can extended into further statements [Rumfitt] |
18808 | Normal deduction presupposes the Cut Law [Rumfitt] |
18840 | When faced with vague statements, Bivalence is not a compelling principle [Rumfitt] |
18741 | Logical formalization makes concepts precise, and also shows their interrelation [Horsten/Pettigrew] |
18802 | In specifying a logical constant, use of that constant is quite unavoidable [Rumfitt] |
9868 | An expression refers if it is a singular term in some true sentences [Wright,C, by Dummett] |
18800 | Introduction rules give deduction conditions, and Elimination says what can be deduced [Rumfitt] |
18809 | Logical truths are just the assumption-free by-products of logical rules [Rumfitt] |
18744 | Models are sets with functions and relations, and truth built up from the components [Horsten/Pettigrew] |
18807 | Monotonicity means there is a guarantee, rather than mere inductive support [Rumfitt] |
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] |
18842 | Maybe an ordinal is a property of isomorphic well-ordered sets, and not itself a set [Rumfitt] |
13867 | Instances of a non-sortal concept can only be counted relative to a sortal concept [Wright,C] |
18834 | Infinitesimals do not stand in a determinate order relation to zero [Rumfitt] |
18846 | Cantor and Dedekind aimed to give analysis a foundation in set theory (rather than geometry) [Rumfitt] |
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] |
7804 | Wright has revived Frege's discredited logicism [Wright,C, by Benardete,JA] |
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] |
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] |
18740 | If 'exist' doesn't express a property, we can hardly ask for its essence [Horsten/Pettigrew] |
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] |
18839 | An object that is not clearly red or orange can still be red-or-orange, which sweeps up problem cases [Rumfitt] |
18838 | The extension of a colour is decided by a concept's place in a network of contraries [Rumfitt] |
18816 | Metaphysical modalities respect the actual identities of things [Rumfitt] |
18825 | S5 is the logic of logical necessity [Rumfitt] |
18824 | Since possibilities are properties of the world, calling 'red' the determination of a determinable seems right [Rumfitt] |
18828 | If two possibilities can't share a determiner, they are incompatible [Rumfitt] |
18745 | A Tarskian model can be seen as a possible state of affairs [Horsten/Pettigrew] |
18747 | The 'spheres model' was added to possible worlds, to cope with counterfactuals [Horsten/Pettigrew] |
18748 | Epistemic logic introduced impossible worlds [Horsten/Pettigrew] |
18746 | Possible worlds models contain sets of possible worlds; this is a large metaphysical commitment [Horsten/Pettigrew] |
18750 | Using possible worlds for knowledge and morality may be a step too far [Horsten/Pettigrew] |
18821 | Possibilities are like possible worlds, but not fully determinate or complete [Rumfitt] |
18831 | Medieval logicians said understanding A also involved understanding not-A [Rumfitt] |
18820 | In English 'evidence' is a mass term, qualified by 'little' and 'more' [Rumfitt] |
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] |
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] |
18817 | We understand conditionals, but disagree over their truth-conditions [Rumfitt] |
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] |
18829 | The truth grounds for 'not A' are the possibilities incompatible with truth grounds for A [Rumfitt] |