Combining Philosophers

All the ideas for Anaxarchus, Wilfrid Hodges and Stephen Boulter

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25 ideas

1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science
22138 Science rests on scholastic metaphysics, not on Hume, Kant or Carnap [Boulter]
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]
8. Modes of Existence / D. Universals / 2. Need for Universals
22134 Thoughts are general, but the world isn't, so how can we think accurately? [Boulter]
10. Modality / A. Necessity / 6. Logical Necessity
22150 Logical possibility needs the concepts of the proposition to be adequate [Boulter]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
3061 Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius]
14. Science / A. Basis of Science / 3. Experiment
22139 Experiments don't just observe; they look to see what interventions change the natural order [Boulter]
14. Science / B. Scientific Theories / 1. Scientific Theory
22136 Science begins with sufficient reason, de-animation, and the importance of nature [Boulter]
15. Nature of Minds / C. Capacities of Minds / 1. Faculties
22135 Our concepts can never fully capture reality, but simplification does not falsify [Boulter]
19. Language / E. Analyticity / 3. Analytic and Synthetic
22152 Aristotelians accept the analytic-synthetic distinction [Boulter]
22. Metaethics / B. Value / 1. Nature of Value / b. Fact and value
22156 The facts about human health are the measure of the values in our lives [Boulter]