Combining Texts

All the ideas for 'fragments/reports', 'Mathematics and the Metaphysicians' and 'Grounding, Transitivity and Contrastivity'

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10 ideas

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 / B. Foundations for Mathematics / 3. Axioms for Geometry
Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz]
7. Existence / C. Structure of Existence / 1. Grounding / a. Nature of grounding
As causation links across time, grounding links the world across levels [Schaffer,J]
If ground is transitive and irreflexive, it has a strict partial ordering, giving structure [Schaffer,J]
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
Self-evidence is often a mere will-o'-the-wisp [Russell]
14. Science / D. Explanation / 2. Types of Explanation / b. Contrastive explanations
Explaining 'Adam ate the apple' depends on emphasis, and thus implies a contrast [Schaffer,J]
26. Natural Theory / A. Speculations on Nature / 1. Nature
I take what is fundamental to be the whole spatiotemporal manifold and its fields [Schaffer,J]
26. Natural Theory / C. Causation / 1. Causation
Nowadays causation is usually understood in terms of equations and variable ranges [Schaffer,J]