Combining Texts

All the ideas for 'fragments/reports', 'Believing the Axioms I' and 'Are Freedom and Equality Compatible?'

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17 ideas

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.]
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
The right-wing conception of freedom is based on the idea of self-ownership [Cohen,GA]
Plenty of people have self-ownership, but still lack autonomy [Cohen,GA]
25. Social Practice / C. Rights / 4. Property rights
It is plausible that no one has an initial right to own land and natural resources [Cohen,GA]
It is doubtful whether any private property was originally acquired legitimately [Cohen,GA]
Every thing which is now private started out as unowned [Cohen,GA]