Combining Texts

All the ideas for 'Letter to G.H. Schaller', 'Believing the Axioms I' and 'Public Text and Common Reader'

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17 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
13013 The Axiom of Extensionality seems to be analytic [Maddy]
13014 Extensional sets are clearer, simpler, unique and expressive [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]
16. Persons / F. Free Will / 5. Against Free Will
4871 A thing is free if it acts only by the necessity of its own nature [Spinoza]
21. Aesthetics / A. Aesthetic Experience / 3. Taste
12163 Literary meaning emerges in comparisons, and tradition shows which comparisons are relevant [Scruton]
21. Aesthetics / B. Nature of Art / 5. Art as Language
12162 In literature, word replacement changes literary meaning [Scruton]
21. Aesthetics / C. Artistic Issues / 1. Artistic Intentions
12159 Without intentions we can't perceive sculpture, but that is not the whole story [Scruton]
21. Aesthetics / C. Artistic Issues / 3. Artistic Representation
12160 In aesthetic interest, even what is true is treated as though it were not [Scruton]
21. Aesthetics / C. Artistic Issues / 5. Objectivism in Art
12161 We can be objective about conventions, but love of art is needed to understand its traditions [Scruton]