Combining Texts

All the ideas for 'Defending the Axioms', 'What is an Emotion?' and 'Process and Reality'

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13 ideas

1. Philosophy / C. History of Philosophy / 2. Ancient Philosophy / c. Classical philosophy
European philosophy consists of a series of footnotes to Plato [Whitehead]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
With 'extensive connection', boundary elements are not included in domains [Whitehead, by Varzi]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy]
If two mathematical themes coincide, that suggest a single deep truth [Maddy]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]
7. Existence / B. Change in Existence / 2. Processes
In Whitehead 'processes' consist of events beginning and ending [Whitehead, by Simons]
18. Thought / A. Modes of Thought / 3. Emotions / a. Nature of emotions
Rage is inconceivable without bodily responses; so there are no disembodied emotions [James]
26. Natural Theory / C. Causation / 1. Causation
Whitehead held that perception was a necessary feature of all causation [Whitehead, by Harré/Madden]
27. Natural Reality / C. Space / 3. Points in Space
Whitehead replaced points with extended regions [Whitehead, by Quine]