Combining Philosophers

All the ideas for Anaxarchus, Wilfrid Hodges and Hugh LaFollette

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23 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]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
3061 Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius]
20. Action / C. Motives for Action / 5. Action Dilemmas / a. Dilemmas
20877 Errors in moral practice might be inconsistent or inappropriate principles, or inappropriate application [LaFollette]
20878 We can discuss the criteria of a judgment, or the weight given to them, or their application [LaFollette]
20. Action / C. Motives for Action / 5. Action Dilemmas / c. Omissions
20881 The act/omission distinction is important for duties, but less so for consequences [LaFollette]
23. Ethics / D. Deontological Ethics / 2. Duty
20886 Are we only obligated by agreement, or should we always help the weak? [LaFollette]
25. Social Practice / C. Rights / 2. Moral rights
20879 Too many options may open us to unwanted pressures, like being paid very little [LaFollette]
20880 Should people be forced to make choices? [LaFollette]