Combining Texts

All the ideas for 'Mathematics and the Metaphysicians', 'The Ways of Paradox' and 'Nietzsche's Immoralism'

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13 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
To solve Zeno's paradox, reject the axiom that the whole has more terms than the parts [Russell]
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]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
In mathematic we are ignorant of both subject-matter and truth [Russell]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / b. Mark of the infinite
A collection is infinite if you can remove some terms without diminishing its number [Russell]
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
Self-evidence is often a mere will-o'-the-wisp [Russell]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / g. Moral responsibility
Unlike aesthetic evaluation, moral evaluation needs a concept of responsibility [Foot]
23. Ethics / C. Virtue Theory / 3. Virtues / c. Justice
The practice of justice may well need a recognition of human equality [Foot]