Combining Texts

All the ideas for 'Defending the Axioms', 'On Note L to Bayle's 'Rorarius'' and 'The Philosophy of Philosophy'

expand these ideas     |    start again     |     specify just one area for these texts

23 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason
9593 Progress in philosophy is incremental, not an immature seeking after drama [Williamson]
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
9594 Correspondence to the facts is a bad account of analytic truth [Williamson]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
17610 The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
17620 Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17605 Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy]
17625 If two mathematical themes coincide, that suggest a single deep truth [Maddy]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
17615 Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
17618 Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
17614 The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]
7. Existence / D. Theories of Reality / 4. Anti-realism
9601 The realist/anti-realist debate is notoriously obscure and fruitless [Williamson]
7. Existence / D. Theories of Reality / 10. Vagueness / b. Vagueness of reality
9599 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
9602 Common sense and classical logic are often simultaneously abandoned in debates on vagueness [Williamson]
10. Modality / D. Knowledge of Modality / 1. A Priori Necessary
9598 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
16536 Williamson can't base metaphysical necessity on the psychology of causal counterfactuals [Lowe on Williamson]
9596 We scorn imagination as a test of possibility, forgetting its role in counterfactuals [Williamson]
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
9597 There are 'armchair' truths which are not a priori, because experience was involved [Williamson]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
9592 Intuition is neither powerful nor vacuous, but reveals linguistic or conceptual competence [Williamson]
20181 When analytic philosophers run out of arguments, they present intuitions as their evidence [Williamson]
15. Nature of Minds / B. Features of Minds / 2. Unconscious Mind
19355 The soul doesn't understand many of its own actions, if perceptions are confused and desires buried [Leibniz]
17. Mind and Body / A. Mind-Body Dualism / 5. Parallelism
19350 We should say that body is mechanism and soul is immaterial, asserting their independence [Leibniz]
19. Language / A. Nature of Meaning / 6. Meaning as Use
9595 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
9600 If languages are intertranslatable, and cognition is innate, then cultures are all similar [Williamson]
26. Natural Theory / A. Speculations on Nature / 4. Mathematical Nature
19356 Minds unconsciously count vibration beats in music, and enjoy it when they coincide [Leibniz]