Combining Texts

All the ideas for 'What is so bad about Contradictions?', 'Believing the Axioms I' and 'Euthydemus'

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18 ideas

2. Reason / B. Laws of Thought / 3. Non-Contradiction
9123 Someone standing in a doorway seems to be both in and not-in the room [Priest,G, by Sorensen]
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]
8. Modes of Existence / D. Universals / 6. Platonic Forms / b. Partaking
304 Beautiful things must be different from beauty itself, but beauty itself must be present in each of them [Plato]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
16120 Knowing how to achieve immortality is pointless without the knowledge how to use immortality [Plato]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
303 Say how many teeth the other has, then count them. If you are right, we will trust your other claims [Plato]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / d. Ethical theory
302 What knowledge is required to live well? [Plato]
22. Metaethics / C. The Good / 1. Goodness / e. Good as knowledge
301 Only knowledge of some sort is good [Plato]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / f. The Mean
305 Something which lies midway between two evils is better than either of them [Plato]