Combining Philosophers

All the ideas for Hermarchus, Daniel Statman and Wilfrid Hodges

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27 ideas

2. Reason / D. Definition / 7. Contextual Definition
10476 The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
10282 Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [Hodges,W]
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 / 1. Semantics of Logic
10283 A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables [Hodges,W]
10284 There are three different standard presentations of semantics [Hodges,W]
10285 I |= φ means that the formula φ is true in the interpretation I [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
10473 Model theory studies formal or natural language-interpretation using set-theory [Hodges,W]
10475 A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W]
10481 Models in model theory are structures, not sets of descriptions [Hodges,W]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10288 Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [Hodges,W]
10289 Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W]
5. Theory of Logic / K. Features of Logics / 6. Compactness
10287 If a first-order theory entails a sentence, there is a finite subset of the theory which entails it [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]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10286 A 'set' is a mathematically well-behaved class [Hodges,W]
20. Action / C. Motives for Action / 4. Responsibility for Actions
7096 We may still admire a person's character even if the traits are involuntary [Statman]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / d. Ethical theory
7098 There is a new sort of moral scepticism, about the possibility of moral theories [Statman]
22. Metaethics / C. The Good / 2. Happiness / b. Eudaimonia
7099 With a broad concept of flourishing, it might be possible without the virtues [Statman]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / d. Virtue theory critique
7100 Virtue theory isn't a genuine ethical theory, because it doesn't have universal application [Statman]
7102 Promises create moral duties that have nothing to do with character [Statman]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / d. Teaching virtue
7095 Moral education is better by concrete example than abstract principle [Statman]
23. Ethics / C. Virtue Theory / 4. External Goods / d. Friendship
7094 Friends express friendship even when no utility is involved [Statman]
23. Ethics / D. Deontological Ethics / 2. Duty
7093 Behaviour may be disgusting or inhumane, but violate no duty [Statman]
7104 The ancients recognised imperfect duties, but we have added perfect duties like justice [Statman]
25. Social Practice / F. Life Issues / 3. Abortion
7103 Abortion issues focus on the mother's right over her body, and the status of the foetus [Statman]
25. Social Practice / F. Life Issues / 6. Animal Rights
6005 Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley]