Combining Philosophers

All the ideas for Herodotus, Wilfrid Hodges and Keith T. Maslin

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27 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]
7. Existence / C. Structure of Existence / 5. Supervenience / c. Significance of supervenience
3523 Shadows are supervenient on their objects, but not reducible [Maslin]
7. Existence / D. Theories of Reality / 1. Ontologies
3517 'Ontology' means 'study of things which exist' [Maslin]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / d. Other minds by analogy
3538 Analogy to other minds is uncheckable, over-confident and chauvinistic [Maslin]
16. Persons / B. Nature of the Self / 7. Self and Body / b. Self as brain
3540 If we are brains then we never meet each other [Maslin]
16. Persons / C. Self-Awareness / 3. Limits of Introspection
3518 I'm not the final authority on my understanding of maths [Maslin]
17. Mind and Body / D. Property Dualism / 2. Anomalous Monism
3530 Denial of purely mental causation will lead to epiphenomenalism [Maslin]
17. Mind and Body / D. Property Dualism / 3. Property Dualism
3520 Token-identity removes the explanatory role of the physical [Maslin]
26. Natural Theory / C. Causation / 9. General Causation / b. Nomological causation
3528 Causality may require that a law is being followed [Maslin]
26. Natural Theory / D. Laws of Nature / 7. Strictness of Laws
3525 Strict laws make causation logically necessary [Maslin]
3527 Strict laws allow no exceptions and are part of a closed system [Maslin]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
1513 The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus]