Combining Texts

All the ideas for 'Believing the Axioms I', 'Elements of Intuitionism (2nd ed)' and 'Truth is not the Primary Epistemic Goal'

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16 ideas

4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
18832 Mathematical statements and entities that result from an infinite process must lack a truth-value [Dummett]
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]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
19566 Epistemology does not just concern knowledge; all aspects of cognitive activity are involved [Kvanvig]
11. Knowledge Aims / A. Knowledge / 5. Aiming at Truth
19568 Making sense of things, or finding a good theory, are non-truth-related cognitive successes [Kvanvig]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / c. Defeasibility
19567 The 'defeasibility' approach says true justified belief is knowledge if no undermining facts could be known [Kvanvig]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / b. Anti-reliabilism
19570 Reliabilism cannot assess the justification for propositions we don't believe [Kvanvig]