Combining Philosophers

All the ideas for Hermarchus, Wilfrid Hodges and Andrew Dobson

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26 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
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]
24. Political Theory / C. Ruling a State / 4. Changing the State / b. Devolution
23429 The environment needs localised politics, with its care for the land [Dobson]
24. Political Theory / D. Ideologies / 1. Ideology
23424 An ideology judges things now, and offers an ideal, with a strategy for reaching it [Dobson]
24. Political Theory / D. Ideologies / 6. Liberalism / g. Liberalism critique
23426 Ecologism is often non-liberal, by claiming to know other people's best interests [Dobson]
24. Political Theory / D. Ideologies / 8. Socialism
23427 Socialism can be productive and centralised, or less productive and decentralised [Dobson]
24. Political Theory / D. Ideologies / 12. Feminism
23428 Difference feminists say women differ fundamentally from men [Dobson]
24. Political Theory / D. Ideologies / 13. Green Politics
23430 A million years is a proper unit of political time [Dobson]
23425 Ecologism says growth must be reduced, and efficiency is not enough [Dobson]
23422 For the environment, affluence and technology matter as much as population size [Dobson]
23423 We currently value the present fourteen times more highly than the future [Dobson]
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]