Combining Texts

All the ideas for 'works', 'Letters to Hugo Boxel' and 'What is Cantor's Continuum Problem?'

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15 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
We perceive the objects of set theory, just as we perceive with our senses [Gödel]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes
Set-theory paradoxes are no worse than sense deception in physics [Gödel]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg]
If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
Basic mathematics is related to abstract elements of our empirical ideas [Gödel]
12. Knowledge Sources / B. Perception / 1. Perception
Our images of bodies are not produced by the bodies, but by our own minds [Augustine, by Aquinas]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Our minds grasp reality by direct illumination (rather than abstraction from experience) [Augustine, by Matthews]
20. Action / B. Preliminaries of Action / 2. Willed Action / a. Will to Act
Augustine created the modern concept of the will [Augustine, by Matthews]
21. Aesthetics / A. Aesthetic Experience / 5. Natural Beauty
The most beautiful hand seen through the microscope will appear horrible [Spinoza]
22. Metaethics / B. Value / 2. Values / g. Love
Love, and do what you will [Augustine]
22. Metaethics / C. The Good / 1. Goodness / b. Types of good
Pagans produced three hundred definitions of the highest good [Augustine, by Grayling]
23. Ethics / D. Deontological Ethics / 2. Duty
Augustine said (unusually) that 'ought' does not imply 'can' [Augustine, by Matthews]
29. Religion / B. Monotheistic Religion / 4. Christianity / d. Heresy
Augustine identified Donatism, Pelagianism and Manicheism as the main heresies [Augustine, by Matthews]
29. Religion / D. Religious Issues / 3. Problem of Evil / b. Human Evil
Augustine said evil does not really exist, and evil is a limitation in goodness [Augustine, by Perkins]