Combining Texts

All the ideas for 'Mathematics without Numbers', 'Modal Logic within Counterfactual Logic' and 'Causation in a Physical World'

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13 ideas

4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
In S5 matters of possibility and necessity are non-contingent [Williamson]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend]
Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara]
Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman]
10. Modality / A. Necessity / 1. Types of Modality
Necessity is counterfactually implied by its negation; possibility does not counterfactually imply its negation [Williamson]
10. Modality / B. Possibility / 8. Conditionals / a. Conditionals
Strict conditionals imply counterfactual conditionals: □(A⊃B)⊃(A□→B) [Williamson]
10. Modality / B. Possibility / 9. Counterfactuals
Counterfactual conditionals transmit possibility: (A□→B)⊃(◊A⊃◊B) [Williamson]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
Rather than define counterfactuals using necessity, maybe necessity is a special case of counterfactuals [Williamson, by Hale/Hoffmann,A]
15. Nature of Minds / C. Capacities of Minds / 2. Imagination
Imagination is important, in evaluating possibility and necessity, via counterfactuals [Williamson]
26. Natural Theory / C. Causation / 1. Causation
Explain single events by general rules, or vice versa, or probability explains both, or they are unconnected [Field,H]
26. Natural Theory / C. Causation / 5. Direction of causation
Physical laws are largely time-symmetric, so they make a poor basis for directional causation [Field,H]
Identifying cause and effect is not just conventional; we explain later events by earlier ones [Field,H]
The only reason for adding the notion of 'cause' to fundamental physics is directionality [Field,H]