Combining Texts

All the ideas for 'Axiomatic Thought', 'Introduction to 'Absolute Generality'' and 'Rule Utilitarianism and Euthanasia'

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16 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory
13451 The two best understood conceptions of set are the Iterative and the Limitation of Size [Rayo/Uzquiano]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / m. Axiom of Separation
13452 Some set theories give up Separation in exchange for a universal set [Rayo/Uzquiano]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
13449 We could have unrestricted quantification without having an all-inclusive domain [Rayo/Uzquiano]
13450 Absolute generality is impossible, if there are indefinitely extensible concepts like sets and ordinals [Rayo/Uzquiano]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
13453 Perhaps second-order quantifications cover concepts of objects, rather than plain objects [Rayo/Uzquiano]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17963 The facts of geometry, arithmetic or statics order themselves into theories [Hilbert]
17966 Axioms must reveal their dependence (or not), and must be consistent [Hilbert]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
17967 To decide some questions, we must study the essence of mathematical proof itself [Hilbert]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
17965 The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
17964 Number theory just needs calculation laws and rules for integers [Hilbert]
19. Language / F. Communication / 5. Pragmatics / a. Contextual meaning
13448 The domain of an assertion is restricted by context, either semantically or pragmatically [Rayo/Uzquiano]
23. Ethics / E. Utilitarianism / 2. Ideal of Pleasure
20883 Modern utilitarians value knowledge, friendship, autonomy, and achievement, as well as pleasure [Hooker,B]
23. Ethics / E. Utilitarianism / 5. Rule Utilitarianism
20884 Rule-utilitarians prevent things like torture, even on rare occasions when it seems best [Hooker,B]
25. Social Practice / F. Life Issues / 2. Euthanasia
20885 Euthanasia is active or passive, and voluntary, non-voluntary or involuntary [Hooker,B]
20882 Euthanasia may not involve killing, so it is 'killing or not saving, out of concern for that person' [Hooker,B]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / d. Knowing essences
17968 By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert]