Combining Texts

All the ideas for 'fragments/reports', 'Higher-Order Logic' and 'Draft Statement of Human Obligations'

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25 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
10301 The axiom of choice is controversial, but it could be replaced [Shapiro]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
10588 First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10298 Some say that second-order logic is mathematics, not logic [Shapiro]
10299 If the aim of logic is to codify inferences, second-order logic is useless [Shapiro]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
10300 Logical consequence can be defined in terms of the logical terminology [Shapiro]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
10290 Second-order variables also range over properties, sets, relations or functions [Shapiro]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10590 Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro]
10296 The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro]
10297 The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro]
10292 Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10294 Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro]
8. Modes of Existence / B. Properties / 11. Properties as Sets
10591 Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / a. Idealistic ethics
23814 Every human yearns for an unattainable transcendent good [Weil]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
23824 Where human needs are satisfied we find happiness, friendship and beauty [Weil]
23. Ethics / C. Virtue Theory / 3. Virtues / h. Respect
23815 We cannot equally respect what is unequal, so equal respect needs a shared ground [Weil]
23. Ethics / F. Existentialism / 4. Boredom
23823 Life needs risks to avoid sickly boredom [Weil]
24. Political Theory / B. Nature of a State / 4. Citizenship
23822 We all need to partipate in public tasks, and take some initiative [Weil]
24. Political Theory / D. Ideologies / 3. Conservatism
23817 We need both equality (to attend to human needs) and hierarchy (as a scale of responsibilities) [Weil]
25. Social Practice / A. Freedoms / 3. Free speech
23819 Deliberate public lying should be punished [Weil]
25. Social Practice / A. Freedoms / 6. Political freedom
23818 We have liberty in the space between nature and accepted authority [Weil]
25. Social Practice / C. Rights / 4. Property rights
23820 People need personal and collective property, and a social class lacking property is shameful [Weil]
25. Social Practice / D. Justice / 3. Punishment / d. Reform of offenders
23821 Crime should be punished, to bring the perpetrator freely back to morality [Weil]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
1748 Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]
28. God / A. Divine Nature / 6. Divine Morality / c. God is the good
23816 Attention to a transcendent reality motivates a duty to foster the good of humanity [Weil]