Combining Texts

All the ideas for 'Precis of 'Limits of Abstraction'', 'Sophistical Refutations' and 'The Ways of Paradox'

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18 ideas

2. Reason / A. Nature of Reason / 1. On Reason
2676 Didactic argument starts from the principles of the subject, not from the opinions of the learner [Aristotle]
2. Reason / A. Nature of Reason / 4. Aims of Reason
2675 Reasoning is a way of making statements which makes them lead on to other statements [Aristotle]
2. Reason / C. Styles of Reason / 1. Dialectic
2677 Dialectic aims to start from generally accepted opinions, and lead to a contradiction [Aristotle]
2. Reason / C. Styles of Reason / 3. Eristic
2674 Competitive argument aims at refutation, fallacy, paradox, solecism or repetition [Aristotle]
2. Reason / D. Definition / 2. Aims of Definition
10528 Definitions concern how we should speak, not how things are [Fine,K]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
21695 The set scheme discredited by paradoxes is actually the most natural one [Quine]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
21693 Russell's antinomy challenged the idea that any condition can produce a set [Quine]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / d. and
16967 'Are Coriscus and Callias at home?' sounds like a single question, but it isn't [Aristotle]
5. Theory of Logic / L. Paradox / 3. Antinomies
21691 Antinomies contradict accepted ways of reasoning, and demand revisions [Quine]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / a. Achilles paradox
21690 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
21689 A barber shaves only those who do not shave themselves. So does he shave himself? [Quine]
21694 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
21692 If we write it as '"this sentence is false" is false', there is no paradox [Quine]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
10529 If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K]
10530 Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K]
9. Objects / D. Essence of Objects / 10. Essence as Species
16149 Generic terms like 'man' are not substances, but qualities, relations, modes or some such thing [Aristotle]
9. Objects / F. Identity among Objects / 8. Leibniz's Law
11840 Only if two things are identical do they have the same attributes [Aristotle]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
10527 An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K]