Combining Texts

All the ideas for 'Law and Causality', 'Brainchildren' and 'First-Order Logic'

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21 ideas

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 / 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 / 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 / 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 / d. Non-truthfunction conditionals
10993 Ramsey's Test: believe the consequent if you believe the antecedent [Ramsey, by Read]
10. Modality / B. Possibility / 8. Conditionals / e. Supposition conditionals
14279 Asking 'If p, will q?' when p is uncertain, then first add p hypothetically to your knowledge [Ramsey]
10. Modality / D. Knowledge of Modality / 1. A Priori Necessary
2526 Philosophers regularly confuse failures of imagination with insights into necessity [Dennett]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / f. Foundationalism critique
2523 That every mammal has a mother is a secure reality, but without foundations [Dennett]
14. Science / B. Scientific Theories / 8. Ramsey Sentences
6894 Mental terms can be replaced in a sentence by a variable and an existential quantifier [Ramsey]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / a. Consciousness
2528 Does consciousness need the concept of consciousness? [Dennett]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / c. Parts of consciousness
2525 Maybe language is crucial to consciousness [Dennett]
15. Nature of Minds / B. Features of Minds / 4. Intentionality / b. Intentionality theories
2527 Unconscious intentionality is the foundation of the mind [Dennett]
17. Mind and Body / C. Functionalism / 1. Functionalism
2530 Could a robot be made conscious just by software? [Dennett]
18. Thought / B. Mechanics of Thought / 4. Language of Thought
2524 A language of thought doesn't explain content [Dennett]
18. Thought / D. Concepts / 5. Concepts and Language / c. Concepts without language
2529 Maybe there can be non-conscious concepts (e.g. in bees) [Dennett]
26. Natural Theory / D. Laws of Nature / 4. Regularities / b. Best system theory
9418 All knowledge needs systematizing, and the axioms would be the laws of nature [Ramsey]
9420 Causal laws result from the simplest axioms of a complete deductive system [Ramsey]