Ideas of Crispin Wright, by Theme

[British, b.1942, Professor at University of St Andrew's, then Stirling, and New York University.]

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1. Philosophy / C. History of Philosophy / 1. History of Philosophy
13860 We can only learn from philosophers of the past if we accept the risk of major misrepresentation
2. Reason / C. Styles of Reason / 1. Dialectic
13883 The best way to understand a philosophical idea is to defend it
2. Reason / D. Definition / 7. Contextual Definition
10142 The attempt to define numbers by contextual definition has been revived [Fine,K]
5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
9868 An expression refers if it is a singular term in some true sentences [Dummett]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
13861 Number theory aims at the essence of natural numbers, giving their nature, and the epistemology
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
13892 One could grasp numbers, and name sizes with them, without grasping ordering
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / d. Counting via concepts
13867 Instances of a non-sortal concept can only be counted relative to a sortal concept
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17441 Wright thinks Hume's Principle is more fundamental to cardinals than the Peano Axioms are [Heck]
17853 Number truths are said to be the consequence of PA - but it needs semantic consequence
13862 There are five Peano axioms, which can be expressed informally
17854 What facts underpin the truths of the Peano axioms?
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
13894 Sameness of number is fundamental, not counting, despite children learning that first
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
10140 We derive Hume's Law from Law V, then discard the latter in deriving arithmetic [Fine,K]
8692 Frege has a good system if his 'number principle' replaces his basic law V [Friend]
17440 Wright says Hume's Principle is analytic of cardinal numbers, like a definition [Heck]
13893 It is 1-1 correlation of concepts, and not progression, which distinguishes natural number
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem
13888 If numbers are extensions, Frege must first solve the Caesar problem for extensions
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
13869 Number platonism says that natural number is a sortal concept
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
13870 We can't use empiricism to dismiss numbers, if numbers are our main evidence against empiricism
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
13873 Treating numbers adjectivally is treating them as quantifiers
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
13899 The Peano Axioms, and infinity of cardinal numbers, are logical consequences of how we explain cardinals
13896 The aim is to follow Frege's strategy to derive the Peano Axioms, but without invoking classes
7804 Wright has revived Frege's discredited logicism [Benardete,JA]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
13863 Logicism seemed to fail by Russell's paradox, Gödel's theorems, and non-logical axioms
13895 The standard objections are Russell's Paradox, non-logical axioms, and Gödel's theorems
7. Existence / A. Nature of Existence / 2. Types of Existence
13884 The idea that 'exist' has multiple senses is not coherent
7. Existence / D. Theories of Reality / 11. Ontological Commitment / b. Commitment of quantifiers
13877 Singular terms in true sentences must refer to objects; there is no further question about their existence
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
9878 Contextually defined abstract terms genuinely refer to objects [Dummett]
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
13868 Sortal concepts cannot require that things don't survive their loss, because of phase sortals
10. Modality / A. Necessity / 6. Logical Necessity
12189 Logical necessity involves a decision about usage, and is non-realist and non-cognitive [McFetridge]
18. Thought / D. Concepts / 1. Concepts / a. Nature of concepts
13865 'Sortal' concepts show kinds, use indefinite articles, and require grasping identities
13866 A concept is only a sortal if it gives genuine identity
18. Thought / D. Concepts / 4. Structure of Concepts / b. Analysis of concepts
13890 Entities fall under a sortal concept if they can be used to explain identity statements concerning them
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
13898 If we can establish directions from lines and parallelism, we were already committed to directions
19. Language / A. Nature of Meaning / 5. Meaning as Verification
13882 A milder claim is that understanding requires some evidence of that understanding
19. Language / A. Nature of Meaning / 7. Meaning Holism / b. Language holism
7320 Holism cannot give a coherent account of scientific methodology [Miller,A]
19. Language / B. Reference / 1. Reference theories
13885 If apparent reference can mislead, then so can apparent lack of reference
19. Language / C. Assigning Meanings / 3. Predicates
17857 We can accept Frege's idea of object without assuming that predicates have a reference