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