Combining Texts

All the ideas for 'Philosophy of Mathematics', 'Principles of Nature and Grace based on Reason' and 'Introduction to Philosophical Papers I'

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10 ideas

1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
I tried to be unsystematic and piecemeal, but failed; my papers presuppose my other views [Lewis]
2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions only refer to entities outside the defined collection [Horsten]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
A theory is 'categorical' if it has just one model up to isomorphism [Horsten]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
Computer proofs don't provide explanations [Horsten]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
7. Existence / A. Nature of Existence / 5. Reason for Existence
First: there must be reasons; Second: why anything at all?; Third: why this? [Leibniz]
7. Existence / C. Structure of Existence / 6. Fundamentals / c. Monads
A monad and its body are living, so life is everywhere, and comes in infinite degrees [Leibniz]
12. Knowledge Sources / B. Perception / 1. Perception
'Perception' is basic internal representation, and 'apperception' is reflective knowledge of perception [Leibniz]
15. Nature of Minds / A. Nature of Mind / 7. Animal Minds
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
Music charms, although its beauty is the harmony of numbers [Leibniz]