Combining Philosophers

All the ideas for Lynch,MP/Glasgow,JM, Wilfrid Hodges and Ori Simchen

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24 ideas

2. Reason / D. Definition / 7. Contextual Definition
10476 The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W]
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
16186 The Barcan Formulas express how to combine modal operators with classical quantifiers [Simchen]
16187 The Barcan Formulas are orthodox, but clash with the attractive Actualist view [Simchen]
16190 BF implies that if W possibly had a child, then something is possibly W's child [Simchen]
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 / 3. Levels of Reality
16062 A necessary relation between fact-levels seems to be a further irreducible fact [Lynch/Glasgow]
7. Existence / C. Structure of Existence / 5. Supervenience / c. Significance of supervenience
16061 If some facts 'logically supervene' on some others, they just redescribe them, adding nothing [Lynch/Glasgow]
7. Existence / D. Theories of Reality / 6. Physicalism
16060 Nonreductive materialism says upper 'levels' depend on lower, but don't 'reduce' [Lynch/Glasgow]
16064 The hallmark of physicalism is that each causal power has a base causal power under it [Lynch/Glasgow]
10. Modality / E. Possible worlds / 1. Possible Worlds / d. Possible worlds actualism
16188 Serious Actualism says there are no facts at all about something which doesn't exist [Simchen]