Combining Texts

All the ideas for 'Laches', 'The Raft and the Pyramid' 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]
2. Reason / A. Nature of Reason / 6. Coherence
The negation of all my beliefs about my current headache would be fully coherent [Sosa]
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 / 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]
12. Knowledge Sources / E. Direct Knowledge / 1. Common Sense
There are very few really obvious truths, and not much can be proved from them [Sosa]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / e. Pro-foundations
A single belief can trail two regresses, one terminating and one not [Sosa]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / f. Foundationalism critique
If mental states are not propositional, they are logically dumb, and cannot be foundations [Sosa]
Mental states cannot be foundational if they are not immune to error [Sosa]
13. Knowledge Criteria / C. External Justification / 2. Causal Justification
Vision causes and justifies beliefs; but to some extent the cause is the justification [Sosa]
23. Ethics / C. Virtue Theory / 3. Virtues / d. Courage
Being unafraid (perhaps through ignorance) and being brave are two different things [Plato]