Ideas of Crispin Wright, by Theme

[British, fl. 1990, 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
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
The best way to understand a philosophical idea is to defend it
2. Reason / D. Definition / 7. Contextual Definition
The attempt to define numbers by contextual definition has been revived
5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
An expression refers if it is a singular term in some true sentences
6. Mathematics / A. Nature of Mathematics / 3. Numbers / a. Numbers
Number theory aims at the essence of natural numbers, giving their nature, and the epistemology
6. Mathematics / A. Nature of Mathematics / 3. Numbers / c. Priority of numbers
One could grasp numbers, and name sizes with them, without grasping ordering
6. Mathematics / A. Nature of Mathematics / 3. Numbers / p. Counting
Instances of a non-sortal concept can only be counted relative to a sortal concept
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Number / d. Peano arithmetic
Wright thinks Hume's Principle is more fundamental to cardinals than the Peano Axioms are
There are five Peano axioms, which can be expressed informally
Number truths are said to be the consequence of PA - but it needs semantic consequence
What facts underpin the truths of the Peano axioms?
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Number / f. Mathematical induction
It may be possible to define induction in terms of the ancestral relation
6. Mathematics / B. Foundations for Mathematics / 4. Definitions of Number / c. Fregean numbers
Sameness of number is fundamental, not counting, despite children learning that first
6. Mathematics / B. Foundations for Mathematics / 4. Definitions of Number / d. Hume's Principle
We derive Hume's Law from Law V, then discard the latter in deriving arithmetic
Frege has a good system if his 'number principle' replaces his basic law V
Wright says Hume's Principle is analytic of cardinal numbers, like a definition
It is 1-1 correlation of concepts, and not progression, which distinguishes natural number
6. Mathematics / B. Foundations for Mathematics / 4. Definitions of Number / e. Caesar problem
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
Number platonism says that natural number is a sortal concept
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
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
Treating numbers adjectivally is treating them as quantifiers
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
Wright has revived Frege's discredited logicism
The Peano Axioms, and infinity of cardinal numbers, are logical consequences of how we explain cardinals
The aim is to follow Frege's strategy to derive the Peano Axioms, but without invoking classes
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Logicism seemed to fail by Russell's paradox, Gödel's theorems, and non-logical axioms
Frege's platonism and logicism are in conflict, if logic must dictates an infinity of objects
The standard objections are Russell's Paradox, non-logical axioms, and Gödel's theorems
7. Existence / A. Nature of Existence / 2. Types of Existence
The idea that 'exist' has multiple senses is not coherent
7. Existence / D. Theories of Reality / 10. Ontological Commitment / b. Commitment of quantifiers
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
Contextually defined abstract terms genuinely refer to objects
9. Objects / A. Existence of Objects / 4. Individuation / e. Individuation by kind
Sortal concepts cannot require that things don't survive their loss, because of phase sortals
10. Modality / A. Necessity / 6. Logical Necessity
Logical necessity involves a decision about usage, and is non-realist and non-cognitive
18. Thought / D. Concepts / 1. Concepts / a. Concepts
A concept is only a sortal if it gives genuine identity
'Sortal' concepts show kinds, use indefinite articles, and require grasping identities
18. Thought / D. Concepts / 3. Structure of Concepts / b. Analysis of concepts
Entities fall under a sortal concept if they can be used to explain identity statements concerning them
18. Thought / D. Concepts / 6. Abstract Concepts / g. Abstracta by equivalence
If we can establish directions from lines and parallelism, we were already committed to directions
19. Language / A. Language / 6. Predicates
We can accept Frege's idea of object without assuming that predicates have a reference
19. Language / B. Meaning / 3. Meaning as Verification
A milder claim is that understanding requires some evidence of that understanding
19. Language / B. Meaning / 9. Meaning Holism
Holism cannot give a coherent account of scientific methodology
19. Language / D. Theories of Reference / 1. Reference theories
If apparent reference can mislead, then so can apparent lack of reference