Combining Texts

All the ideas for 'Saundaranandakavya', 'Defending the Axioms' and 'Letters to Russell'

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13 ideas

1. Philosophy / D. Nature of Philosophy / 2. Invocation to Philosophy
Pursue truth with the urgency of someone whose clothes are on fire [Ashvaghosha]
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 / 3. Nature of Numbers / g. Real numbers
I wish to go straight from cardinals to reals (as ratios), leaving out the rationals [Frege]
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]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
The loss of my Rule V seems to make foundations for arithmetic impossible [Frege]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
Logical objects are extensions of concepts, or ranges of values of functions [Frege]
29. Religion / C. Spiritual Disciplines / 3. Buddhism
The Eightfold Path concerns morality, wisdom, and tranquillity [Ashvaghosha]
29. Religion / D. Religious Issues / 2. Immortality / d. Heaven
At the end of a saint, he is not located in space, but just ceases to be disturbed [Ashvaghosha]