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All the ideas for 'Precis of 'Limits of Abstraction'', 'Higher-Order Logic' and 'The Mengzi (Mencius)'

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26 ideas

2. Reason / D. Definition / 2. Aims of Definition
10528 Definitions concern how we should speak, not how things are [Fine,K]
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]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
10529 If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K]
10530 Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K]
8. Modes of Existence / B. Properties / 11. Properties as Sets
10591 Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
10527 An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
8239 If the King likes music then there is hope for the state [Mengzi (Mencius)]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
23398 Human nature is naturally compassionate and good (as a 'sprout'), but people may not be good [Mengzi (Mencius), by Norden]
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
23400 Righteousness is extending the unthinkable, to reveal what must be done [Mengzi (Mencius)]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
23399 Each correct feeling relies on an underlying virtue [Mengzi (Mencius)]
23. Ethics / C. Virtue Theory / 3. Virtues / e. Honour
8235 Should a coward who ran fifty paces from a battle laugh at another who ran a hundred? [Mengzi (Mencius)]
24. Political Theory / C. Ruling a State / 2. Leaders / b. Monarchy
8240 A true king shares his pleasure with the people [Mengzi (Mencius)]
24. Political Theory / D. Ideologies / 7. Communitarianism / a. Communitarianism
8237 Extend the treatment of the old and young in your family to the rest of society [Mengzi (Mencius)]
25. Social Practice / D. Justice / 3. Punishment / b. Retribution for crime
8241 Only put someone to death if the whole population believes it is deserved [Mengzi (Mencius)]
25. Social Practice / E. Policies / 1. War / e. Peace
8238 Seeking peace through war is like looking for fish up a tree [Mengzi (Mencius)]
25. Social Practice / F. Life Issues / 6. Animal Rights
8236 Avoid the animals you are going to eat, as it is hard once you have got to know them [Mengzi (Mencius)]