Combining Texts

All the ideas for 'On Second-Order Logic', 'On the Happy Life' and 'Logical Foundations of Probability'

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17 ideas

1. Philosophy / A. Wisdom / 2. Wise People
13560 A wise man is not subservient to anything [Seneca]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
14249 Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley]
10830 Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
10829 A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
10832 '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos]
5. Theory of Logic / K. Features of Logics / 4. Completeness
10834 Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos]
5. Theory of Logic / K. Features of Logics / 6. Compactness
13841 Why should compactness be definitive of logic? [Boolos, by Hacking]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10833 Many concepts can only be expressed by second-order logic [Boolos]
14. Science / D. Explanation / 1. Explanation / b. Aims of explanation
13048 Good explications are exact, fruitful, simple and similar to the explicandum [Carnap, by Salmon]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / a. Idealistic ethics
13558 The supreme good is harmony of spirit [Seneca]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
13559 I seek virtue, because it is its own reward [Seneca]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / j. Unity of virtue
13561 Virtue is always moderate, so excess need not be feared [Seneca]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
13562 It is shameful to not even recognise your own slaves [Seneca]
23. Ethics / C. Virtue Theory / 4. External Goods / c. Wealth
13564 There is far more scope for virtue if you are wealthy; poverty only allows endurance [Seneca]
13563 Why does your wife wear in her ears the income of a wealthy house? [Seneca]
13565 If wealth was a good, it would make men good [Seneca]
24. Political Theory / D. Ideologies / 5. Democracy / f. Against democracy
13557 Unfortunately the majority do not tend to favour what is best [Seneca]