Combining Texts

All the ideas for 'fragments/reports', 'Believing the Axioms I' and 'An Essay in Aesthetics'

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24 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 / C. Self-Awareness / 3. Limits of Introspection
20429 Most of us are too close to our own motives to understand them [Fry]
21. Aesthetics / A. Aesthetic Experience / 2. Aesthetic Attitude
20424 Imaginative life requires no action, so new kinds of perception and values emerge in art [Fry]
20427 Everyone reveals an aesthetic attitude, looking at something which only exists to be seen [Fry]
21. Aesthetics / A. Aesthetic Experience / 4. Beauty
20433 'Beauty' can either mean sensuous charm, or the aesthetic approval of art (which may be ugly) [Fry]
21. Aesthetics / A. Aesthetic Experience / 6. The Sublime
20430 In life we neglect 'cosmic emotion', but it matters, and art brings it to the fore [Fry]
21. Aesthetics / B. Nature of Art / 2. Art as Form
20431 Art needs a mixture of order and variety in its sensations [Fry]
21. Aesthetics / B. Nature of Art / 3. Art as Imitation
20423 If graphic arts only aim at imitation, their works are only trivial ingenious toys [Fry]
20428 Popular opinion favours realism, yet most people never look closely at anything! [Fry]
21. Aesthetics / C. Artistic Issues / 1. Artistic Intentions
20432 When viewing art, rather than flowers, we are aware of purpose, and sympathy with its creator [Fry]
21. Aesthetics / C. Artistic Issues / 4. Emotion in Art
20425 In the cinema the emotions are weaker, but much clearer than in ordinary life [Fry]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
20426 For pure moralists art must promote right action, and not just be harmless [Fry]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
1748 Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]