Combining Texts

All the ideas for 'Semantics for Propositional Attitudes', 'First-Order Logic' and 'The Problem of Consciousness'

expand these ideas     |    start again     |     specify just one area for these texts

12 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]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
15785 Our commitments are to an 'ontology', but also to an 'ideology', or conceptual system [Hintikka]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
15786 Commitment to possible worlds is part of our ideology, not part of our ontology [Hintikka]
17. Mind and Body / D. Property Dualism / 6. Mysterianism
7388 McGinn invites surrender, by saying it is hopeless trying to imagine conscious machines [Dennett on McGinn]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / b. Multiple realisability
3185 Multiple realisability rules out hidden essences and experts as the source of water- and gold-concepts [McGinn]