Combining Texts

All the ideas for 'Subjectivist's Guide to Objective Chance', 'What is Analytic Philosophy?' and 'The Philosophy of Mathematics'

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12 ideas

1. Philosophy / F. Analytic Philosophy / 1. Nature of Analysis
Analysis must include definitions, search for simples, concept analysis, and Kant's analysis [Glock]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett]
The main alternative to ZF is one which includes looser classes as well as sets [Dummett]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Logical truths and inference are characterized either syntactically or semantically [Dummett]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
German and British idealism is not about individual ideas, but the intelligibility of reality [Glock]
18. Thought / D. Concepts / 4. Structure of Concepts / h. Family resemblance
The variety of uses of 'game' may be that it has several meanings, and isn't a single concept [Glock]
We might say that the family resemblance is just a consequence of meaning-as-use [Glock]
26. Natural Theory / D. Laws of Nature / 4. Regularities / b. Best system theory
Lewis later proposed the axioms at the intersection of the best theories (which may be few) [Mumford on Lewis]