Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Defending the Axioms' and 'Last Fragments'

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13 ideas

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 / 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]
14. Science / B. Scientific Theories / 1. Scientific Theory
General statements about nature are not valid [Novalis]
17. Mind and Body / A. Mind-Body Dualism / 8. Dualism of Mind Critique
The whole body is involved in the formation of thoughts [Novalis]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
25. Social Practice / E. Policies / 5. Education / d. Study of history
Persons are shaped by a life history; splendid persons are shaped by world history [Novalis]
26. Natural Theory / A. Speculations on Nature / 1. Nature
Nature is a whole, and its individual parts cannot be wholly understood [Novalis]
26. Natural Theory / A. Speculations on Nature / 4. Mathematical Nature
The basic relations of nature are musical [Novalis]