Combining Texts

All the ideas for 'Reference and Modality', 'Elements of Set Theory' and 'The Prince'

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24 ideas

4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
10928 Maybe we can quantify modally if the objects are intensional, but it seems unlikely [Quine]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
13201 ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton]
13204 The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton]
13206 A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
13200 Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton]
13199 The empty set may look pointless, but many sets can be constructed from it [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
13203 The singleton is defined using the pairing axiom (as {x,x}) [Enderton]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
13202 Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13205 We can only define functions if Choice tells us which items are involved [Enderton]
5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
10925 Failure of substitutivity shows that a personal name is not purely referential [Quine]
5. Theory of Logic / G. Quantification / 1. Quantification
10926 Quantifying into referentially opaque contexts often produces nonsense [Quine]
9. Objects / D. Essence of Objects / 15. Against Essentialism
10930 Quantification into modal contexts requires objects to have an essence [Quine]
10. Modality / A. Necessity / 4. De re / De dicto modality
14645 To be necessarily greater than 7 is not a trait of 7, but depends on how 7 is referred to [Quine]
10. Modality / A. Necessity / 11. Denial of Necessity
9201 Whether 9 is necessarily greater than 7 depends on how '9' is described [Quine, by Fine,K]
10927 Necessity only applies to objects if they are distinctively specified [Quine]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
9203 We can't quantify in modal contexts, because the modality depends on descriptions, not objects [Quine, by Fine,K]
23. Ethics / B. Contract Ethics / 3. Promise Keeping
7127 If men are good you should keep promises, but they aren't, so you needn't [Machiavelli]
24. Political Theory / B. Nature of a State / 3. Constitutions
6309 The principle foundations of all states are good laws and good armies [Machiavelli]
24. Political Theory / C. Ruling a State / 2. Leaders / c. Despotism
6306 People are vengeful, so be generous to them, or destroy them [Machiavelli]
6305 To retain a conquered state, wipe out the ruling family, and preserve everything else [Machiavelli]
6308 A sensible conqueror does all his harmful deeds immediately, because people soon forget [Machiavelli]
25. Social Practice / E. Policies / 1. War / a. Just wars
6307 A desire to conquer, and men who do it, are always praised, or not blamed [Machiavelli]
25. Social Practice / E. Policies / 2. Religion in Society
7486 Machiavelli emancipated politics from religion [Machiavelli, by Watson]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / e. Anti scientific essentialism
10931 We can't say 'necessarily if x is in water then x dissolves' if we can't quantify modally [Quine]