Combining Texts

All the ideas for 'fragments/reports', 'Believing the Axioms I' and 'Externalist Theories of Empirical Knowledge'

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19 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]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / e. The Lottery paradox
4261 The Lottery Paradox says each ticket is likely to lose, so there probably won't be a winner [Bonjour, by PG]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism
4255 Externalist theories of knowledge are one species of foundationalism [Bonjour]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / b. Basic beliefs
4257 The big problem for foundationalism is to explain how basic beliefs are possible [Bonjour]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / e. Pro-foundations
4256 The main argument for foundationalism is that all other theories involve a regress leading to scepticism [Bonjour]
13. Knowledge Criteria / C. External Justification / 1. External Justification
4258 Extreme externalism says no more justification is required than the truth of the belief [Bonjour]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / b. Anti-reliabilism
4259 External reliability is not enough, if the internal state of the believer is known to be irrational [Bonjour]
13. Knowledge Criteria / C. External Justification / 10. Anti External Justification
4260 Even if there is no obvious irrationality, it may be irrational to base knowledge entirely on external criteria [Bonjour]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]