Combining Texts

All the ideas for 'Wiener Logik', 'Mathematics and the Metaphysicians' and 'The Theory of Transfinite Numbers'

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9 ideas

2. Reason / D. Definition / 2. Aims of Definition
A simplification which is complete constitutes a definition [Kant]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
A set is a collection into a whole of distinct objects of our intuition or thought [Cantor]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
Logic gives us the necessary rules which show us how we ought to think [Kant]
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]
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]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities
Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine]
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
Self-evidence is often a mere will-o'-the-wisp [Russell]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / b. Pro-externalism
If we knew what we know, we would be astonished [Kant]