Combining Texts

All the ideas for 'Laches', 'Interview with Baggini and Stangroom' and 'Knowledge and the Philosophy of Number'

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16 ideas

1. Philosophy / A. Wisdom / 3. Wisdom Deflated
Don't assume that wisdom is the automatic consequence of old age [Plato]
1. Philosophy / H. Continental Philosophy / 1. Continental Philosophy
Analytic philosophy has much higher standards of thinking than continental philosophy [Williamson]
4. Formal Logic / E. Nonclassical Logics / 4. Fuzzy Logic
Fuzzy logic uses a continuum of truth, but it implies contradictions [Williamson]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
Predicativism says only predicated sets exist [Hossack]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
The iterative conception has to appropriate Replacement, to justify the ordinals [Hossack]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
Limitation of Size justifies Replacement, but then has to appropriate Power Set [Hossack]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
Formal logic struck me as exactly the language I wanted to think in [Williamson]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / d. and
The connective 'and' can have an order-sensitive meaning, as 'and then' [Hossack]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
'Before' and 'after' are not two relations, but one relation with two orders [Hossack]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / h. Ordinal infinity
Transfinite ordinals are needed in proof theory, and for recursive functions and computability [Hossack]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
Numbers are properties, not sets (because numbers are magnitudes) [Hossack]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
We can only mentally construct potential infinities, but maths needs actual infinities [Hossack]
7. Existence / D. Theories of Reality / 10. Vagueness / c. Vagueness as ignorance
Close to conceptual boundaries judgement is too unreliable to give knowledge [Williamson]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
What sort of logic is needed for vague concepts, and what sort of concept of truth? [Williamson]
12. Knowledge Sources / B. Perception / 1. Perception
How can one discriminate yellow from red, but not the colours in between? [Williamson]
23. Ethics / C. Virtue Theory / 3. Virtues / d. Courage
Being unafraid (perhaps through ignorance) and being brave are two different things [Plato]