Combining Texts

All the ideas for 'The Philosophy of Philosophy', 'Set Theory and the Continuum Hypothesis' and 'A Completeness Theorem in Modal Logic'

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18 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason
Progress in philosophy is incremental, not an immature seeking after drama [Williamson]
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
Correspondence to the facts is a bad account of analytic truth [Williamson]
4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
Propositional modal logic has been proved to be complete [Kripke, by Feferman/Feferman]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / a. Systems of modal logic
With possible worlds, S4 and S5 are sound and complete, but S1-S3 are not even sound [Kripke, by Rossberg]
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
The variable domain approach to quantified modal logic invalidates the Barcan Formula [Kripke, by Simchen]
The Barcan formulas fail in models with varying domains [Kripke, by Williamson]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
We could accept the integers as primitive, then use sets to construct the rest [Cohen]
7. Existence / D. Theories of Reality / 4. Anti-realism
The realist/anti-realist debate is notoriously obscure and fruitless [Williamson]
7. Existence / D. Theories of Reality / 10. Vagueness / b. Vagueness of reality
There cannot be vague objects, so there may be no such thing as a mountain [Williamson]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
Common sense and classical logic are often simultaneously abandoned in debates on vagueness [Williamson]
10. Modality / D. Knowledge of Modality / 1. A Priori Necessary
Modal thinking isn't a special intuition; it is part of ordinary counterfactual thinking [Williamson]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / a. Conceivable as possible
Williamson can't base metaphysical necessity on the psychology of causal counterfactuals [Lowe on Williamson]
We scorn imagination as a test of possibility, forgetting its role in counterfactuals [Williamson]
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
There are 'armchair' truths which are not a priori, because experience was involved [Williamson]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
Intuition is neither powerful nor vacuous, but reveals linguistic or conceptual competence [Williamson]
When analytic philosophers run out of arguments, they present intuitions as their evidence [Williamson]
19. Language / A. Nature of Meaning / 6. Meaning as Use
You might know that the word 'gob' meant 'mouth', but not be competent to use it [Williamson]
24. Political Theory / B. Nature of a State / 5. Culture
If languages are intertranslatable, and cognition is innate, then cultures are all similar [Williamson]