Combining Texts

All the ideas for 'From Stimulus to Science', 'Principles of Nature and Grace based on Reason' and 'On boundary numbers and domains of sets'

expand these ideas     |    start again     |     specify just one area for these texts

---

9 ideas

2. Reason / B. Laws of Thought / 3. Non-Contradiction

6564	To affirm 'p and not-p' is to have mislearned 'and' or 'not' [Quine]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets

17832

Zermelo showed that the ZF axioms in 1930 were non-categorical [Zermelo, by Hallett,M]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII

13028

Replacement was added when some advanced theorems seemed to need it [Zermelo, by Maddy]

5. Theory of Logic / L. Paradox / 3. Antinomies

17626

The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers [Zermelo]

7. Existence / A. Nature of Existence / 5. Reason for Existence

5062	First: there must be reasons; Second: why anything at all?; Third: why this? [Leibniz]

7. Existence / C. Structure of Existence / 6. Fundamentals / c. Monads

19377

A monad and its body are living, so life is everywhere, and comes in infinite degrees [Leibniz]

12. Knowledge Sources / B. Perception / 1. Perception

19353

'Perception' is basic internal representation, and 'apperception' is reflective knowledge of perception [Leibniz]

15. Nature of Minds / A. Nature of Mind / 7. Animal Minds

5061	Animals are semi-rational because they connect facts, but they don't see causes [Leibniz]

21. Aesthetics / B. Nature of Art / 8. The Arts / a. Music

5063	Music charms, although its beauty is the harmony of numbers [Leibniz]