Combining Texts

All the ideas for 'fragments/reports', 'What is Good?' and 'Believing the Axioms I'

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18 ideas

1. Philosophy / C. History of Philosophy / 3. Earlier European Philosophy / c. Later medieval philosophy
Lucretius was rediscovered in 1417 [Grayling]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
New axioms are being sought, to determine the size of the continuum [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
Extensional sets are clearer, simpler, unique and expressive [Maddy]
The Axiom of Extensionality seems to be analytic [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy]
Infinite sets are essential for giving an account of the real numbers [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
Efforts to prove the Axiom of Choice have failed [Maddy]
Modern views say the Choice set exists, even if it can't be constructed [Maddy]
A large array of theorems depend on the Axiom of Choice [Maddy]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
Musical performance can reveal a range of virtues [Damon of Ath.]
23. Ethics / C. Virtue Theory / 3. Virtues / e. Honour
In an honour code shame is the supreme punishment, and revenge is a duty [Grayling]
25. Social Practice / F. Life Issues / 4. Suicide
If suicide is lawful, but assisting suicide is unlawful, powerless people are denied their rights [Grayling]
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
Religion gives answers, comforts, creates social order, and panders to superstition [Grayling]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
To make an afterlife appealing, this life has to be denigrated [Grayling]
In Greek mythology only heroes can go to heaven [Grayling]