Combining Texts

All the ideas for 'Abstraction Reconsidered', 'Truth by Convention' and 'Our Knowledge of Mathematical Objects'

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18 ideas

1. Philosophy / F. Analytic Philosophy / 6. Logical Analysis
If if time is money then if time is not money then time is money then if if if time is not money... [Quine]
2. Reason / D. Definition / 7. Contextual Definition
Definition by words is determinate but relative; fixing contexts could make it absolute [Quine]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
Quine quickly dismisses If-thenism [Quine, by Musgrave]
5. Theory of Logic / C. Ontology of Logic / 4. Logic by Convention
Logic needs general conventions, but that needs logic to apply them to individual cases [Quine, by Rey]
Claims that logic and mathematics are conventional are either empty, uninteresting, or false [Quine]
Logic isn't conventional, because logic is needed to infer logic from conventions [Quine]
If a convention cannot be communicated until after its adoption, what is its role? [Quine]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
If analytic geometry identifies figures with arithmetical relations, logicism can include geometry [Quine]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
There are four different possible conventional accounts of geometry [Quine]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
Abstraction from objects won't reveal an operation's being performed 'so many times' [Geach]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
If mathematics follows from definitions, then it is conventional, and part of logic [Quine]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
Proceduralism offers a version of logicism with no axioms, or objects, or ontological commitment [Fine,K]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
The objects and truths of mathematics are imperative procedures for their construction [Fine,K]
My Proceduralism has one simple rule, and four complex rules [Fine,K]
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
If concepts are just recognitional, then general judgements would be impossible [Geach]
18. Thought / D. Concepts / 3. Ontology of Concepts / b. Concepts as abilities
For abstractionists, concepts are capacities to recognise recurrent features of the world [Geach]
18. Thought / E. Abstraction / 8. Abstractionism Critique
The abstractionist cannot explain 'some' and 'not' [Geach]
Only a judgement can distinguish 'striking' from 'being struck' [Geach]