Combining Texts

All the ideas for 'fragments/reports', 'The Ways of Paradox' and 'Mathematical Explanation'

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14 ideas

4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
The set scheme discredited by paradoxes is actually the most natural one [Quine]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
Russell's antinomy challenged the idea that any condition can produce a set [Quine]
5. Theory of Logic / L. Paradox / 3. Antinomies
Antinomies contradict accepted ways of reasoning, and demand revisions [Quine]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / a. Achilles paradox
Whenever the pursuer reaches the spot where the pursuer has been, the pursued has moved on [Quine]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox
A barber shaves only those who do not shave themselves. So does he shave himself? [Quine]
Membership conditions which involve membership and non-membership are paradoxical [Quine]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
If we write it as '"this sentence is false" is false', there is no paradox [Quine]
9. Objects / D. Essence of Objects / 3. Individual Essences
Particular essence is often captured by generality [Steiner,M]
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
Maybe an instance of a generalisation is more explanatory than the particular case [Steiner,M]
14. Science / D. Explanation / 2. Types of Explanation / m. Explanation by proof
Explanatory proofs rest on 'characterizing properties' of entities or structure [Steiner,M]
19. Language / F. Communication / 3. Denial
Contradiction is impossible, since only one side of the argument refers to the true facts [Prodicus, by Didymus the Blind]
28. God / B. Proving God / 3. Proofs of Evidence / c. Teleological Proof critique
People used to think anything helpful to life was a god, as the Egyptians think the Nile a god [Prodicus]
28. God / C. Attitudes to God / 5. Atheism
The gods are just personified human benefits [Prodicus]
He denied the existence of the gods, saying they are just exaltations of things useful for life [Prodicus]