Combining Texts

All the ideas for 'Identity and Spatio-Temporal Continuity', 'Explaining Explanation' and 'The Philosophy of Mathematics'

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16 ideas

1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
Paradox: why do you analyse if you know it, and how do you analyse if you don't? [Ruben]
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]
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
'Ultimate sortals' cannot explain ontological categories [Westerhoff on Wiggins]
14. Science / A. Basis of Science / 4. Prediction
The 'symmetry thesis' says explanation and prediction only differ pragmatically [Ruben]
14. Science / D. Explanation / 1. Explanation / a. Explanation
Usually explanations just involve giving information, with no reference to the act of explanation [Ruben]
14. Science / D. Explanation / 1. Explanation / c. Direction of explanation
An explanation needs the world to have an appropriate structure [Ruben]
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
Most explanations are just sentences, not arguments [Ruben]
14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
The causal theory of explanation neglects determinations which are not causal [Ruben]
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
Reducing one science to another is often said to be the perfect explanation [Ruben]
14. Science / D. Explanation / 4. Explanation Doubts / a. Explanation as pragmatic
Facts explain facts, but only if they are conceptualised or named appropriately [Ruben]