Combining Texts

All the ideas for 'Through the Looking Glass', 'Mathematics without Foundations' and 'Principles of Nature and Grace based on Reason'

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12 ideas

4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
9944 We understand some statements about all sets [Putnam]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
9937 I do not believe mathematics either has or needs 'foundations' [Putnam]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
9939 It is conceivable that the axioms of arithmetic or propositional logic might be changed [Putnam]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
9940 Maybe mathematics is empirical in that we could try to change it [Putnam]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
9941 Science requires more than consistency of mathematics [Putnam]
7. Existence / A. Nature of Existence / 3. Being / e. Being and nothing
21982 I only wish I had such eyes as to see Nobody! It's as much as I can do to see real people. [Carroll,L]
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]
7. Existence / D. Theories of Reality / 4. Anti-realism
9943 You can't deny a hypothesis a truth-value simply because we may never know it! [Putnam]
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]