Combining Texts

All the ideas for 'fragments/reports', 'Model Theory' and 'Intro: Theories of Vagueness'

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28 ideas

2. Reason / C. Styles of Reason / 1. Dialectic
20768 Like spiderswebs, dialectical arguments are clever but useless [Ariston, by Diog. Laertius]
2. Reason / D. Definition / 7. Contextual Definition
10476 The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
9065 S5 collapses iterated modalities (◊□P→□P, and ◊◊P→◊P) [Keefe/Smith]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
10478 Since first-order languages are complete, |= and |- have the same meaning [Hodges,W]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
10477 |= in model-theory means 'logical consequence' - it holds in all models [Hodges,W]
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
10474 |= should be read as 'is a model for' or 'satisfies' [Hodges,W]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10475 A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W]
10473 Model theory studies formal or natural language-interpretation using set-theory [Hodges,W]
10481 Models in model theory are structures, not sets of descriptions [Hodges,W]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
10480 First-order logic can't discriminate between one infinite cardinal and another [Hodges,W]
7. Existence / D. Theories of Reality / 10. Vagueness / b. Vagueness of reality
9064 Objects such as a cloud or Mount Everest seem to have fuzzy boundaries in nature [Keefe/Smith]
7. Existence / D. Theories of Reality / 10. Vagueness / c. Vagueness as ignorance
9044 If someone is borderline tall, no further information is likely to resolve the question [Keefe/Smith]
9048 The simplest approach, that vagueness is just ignorance, retains classical logic and semantics [Keefe/Smith]
9055 The epistemic view of vagueness must explain why we don't know the predicate boundary [Keefe/Smith]
7. Existence / D. Theories of Reality / 10. Vagueness / f. Supervaluation for vagueness
9049 Supervaluationism keeps true-or-false where precision can be produced, but not otherwise [Keefe/Smith]
9056 Vague statements lack truth value if attempts to make them precise fail [Keefe/Smith]
9058 Some of the principles of classical logic still fail with supervaluationism [Keefe/Smith]
9059 The semantics of supervaluation (e.g. disjunction and quantification) is not classical [Keefe/Smith]
9060 Supervaluation misunderstands vagueness, treating it as a failure to make things precise [Keefe/Smith]
7. Existence / D. Theories of Reality / 10. Vagueness / g. Degrees of vagueness
9050 A third truth-value at borderlines might be 'indeterminate', or a value somewhere between 0 and 1 [Keefe/Smith]
9061 People can't be placed in a precise order according to how 'nice' they are [Keefe/Smith]
9062 If truth-values for vagueness range from 0 to 1, there must be someone who is 'completely tall' [Keefe/Smith]
9063 How do we decide if my coat is red to degree 0.322 or 0.321? [Keefe/Smith]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
9045 Vague predicates involve uncertain properties, uncertain objects, and paradoxes of gradual change [Keefe/Smith]
9047 Many vague predicates are multi-dimensional; 'big' involves height and volume; heaps include arrangement [Keefe/Smith]
9053 If there is a precise borderline area, that is not a case of vagueness [Keefe/Smith]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / f. The Mean
3049 The chief good is indifference to what lies midway between virtue and vice [Ariston, by Diog. Laertius]
23. Ethics / D. Deontological Ethics / 1. Deontology
3549 Ariston says rules are useless for the virtuous and the non-virtuous [Ariston, by Annas]