Combining Philosophers

All the ideas for Thrasymachus, H. Paul Grice and Wilfrid Hodges

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31 ideas

1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
22140 The greatest philosophers are methodical; it is what makes them great [Grice]
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
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]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10289 Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W]
10288 Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [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]
10. Modality / B. Possibility / 8. Conditionals / c. Truth-function conditionals
13856 Conditionals are truth-functional, but we must take care with misleading ones [Grice, by Edgington]
8948 The odd truth table for material conditionals is explained by conversational conventions [Grice, by Fisher]
13767 Conditionals might remain truth-functional, despite inappropriate conversational remarks [Edgington on Grice]
10. Modality / B. Possibility / 8. Conditionals / f. Pragmatics of conditionals
10990 Conditionals are truth-functional, but unassertable in tricky cases? [Grice, by Read]
14277 A person can be justified in believing a proposition, though it is unreasonable to actually say it [Grice, by Edgington]
19. Language / A. Nature of Meaning / 3. Meaning as Speaker's Intention
7752 Only the utterer's primary intention is relevant to the meaning [Grice]
7751 Meaning needs an intention to induce a belief, and a recognition that this is the speaker's intention [Grice]
7753 We judge linguistic intentions rather as we judge non-linguistic intentions, so they are alike [Grice]
19. Language / A. Nature of Meaning / 6. Meaning as Use
22330 Grice said patterns of use are often semantically irrelevant, because it is a pragmatic matter [Grice, by Glock]
19. Language / F. Communication / 5. Pragmatics / b. Implicature
18045 Grice's maxim of quality says do not assert what you believe to be false [Grice, by Magidor]
18044 Grice's maxim of manner requires one to be as brief as possible [Grice, by Magidor]
10991 Key conversational maxims are 'quality' (assert truth) and 'quantity' (leave nothing out) [Grice, by Read]
18046 Grice's maxim of quantity says be sufficiently informative [Grice, by Magidor]
28. God / C. Attitudes to God / 3. Deism
1558 Clearly the gods ignore human affairs, or they would have given us justice [Thrasymachus]