Combining Texts

All the ideas for 'Leibniz: Guide for the Perplexed', 'III.10 On Restraining your Will' and 'Believing the Axioms I'

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16 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
13011 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
13014 Extensional sets are clearer, simpler, unique and expressive [Maddy]
13013 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
13021 The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy]
13022 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
13023 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
13024 Efforts to prove the Axiom of Choice have failed [Maddy]
13025 Modern views say the Choice set exists, even if it can't be constructed [Maddy]
13026 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
13019 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
13018 Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy]
9. Objects / B. Unity of Objects / 2. Substance / d. Substance defined
19347 Substance needs independence, unity, and stability (for individuation); also it is a subject, for predicates [Perkins]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
20482 Virtue inspires Stoics, but I want a good temperament [Montaigne]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
20480 There is not much point in only becoming good near the end of your life [Montaigne]
25. Social Practice / A. Freedoms / 3. Free speech
20481 Nothing we say can be worse than unsaying it in the face of authority [Montaigne]
25. Social Practice / E. Policies / 1. War / c. Combatants
20479 People at home care far more than soldiers risking death about the outcome of wars [Montaigne]