Combining Texts

All the ideas for 'Symposium', 'Conditionals' and 'Believing the Axioms I'

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21 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 / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
14352 '¬', '&', and 'v' are truth functions: the truth of the compound is fixed by the truth of the components [Jackson]
10. Modality / B. Possibility / 8. Conditionals / b. Types of conditional
14360 Possible worlds for subjunctives (and dispositions), and no-truth for indicatives? [Jackson]
10. Modality / B. Possibility / 8. Conditionals / c. Truth-function conditionals
14353 Modus ponens requires that A→B is F when A is T and B is F [Jackson]
14354 When A and B have the same truth value, A→B is true, because A→A is a logical truth [Jackson]
14355 (A&B)→A is a logical truth, even if antecedent false and consequent true, so it is T if A is F and B is T [Jackson]
10. Modality / B. Possibility / 8. Conditionals / d. Non-truthfunction conditionals
14358 In the possible worlds account of conditionals, modus ponens and modus tollens are validated [Jackson]
14359 Only assertions have truth-values, and conditionals are not proper assertions [Jackson]
14357 Possible worlds account, unlike A⊃B, says nothing about when A is false [Jackson]
10. Modality / B. Possibility / 8. Conditionals / f. Pragmatics of conditionals
14356 We can't insist that A is relevant to B, as conditionals can express lack of relevance [Jackson]
22. Metaethics / B. Value / 2. Values / h. Fine deeds
5845 Niceratus learnt the whole of Homer by heart, as a guide to goodness [Xenophon]