Combining Texts

All the ideas for 'The Sign of Four', 'First-Order Logic' and 'Ontological Relativity'

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16 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 / G. Quantification / 4. Substitutional Quantification
21642 If quantification is all substitutional, there is no ontology [Quine]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
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]
10283 A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables [Hodges,W]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10289 Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W]
10288 Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [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 / A. Nature of Existence / 6. Criterion for Existence
1633 Absolute ontological questions are meaningless, because the answers are circular definitions [Quine]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / d. Commitment of theories
18964 Ontology is relative to both a background theory and a translation manual [Quine]
9. Objects / F. Identity among Objects / 1. Concept of Identity
18965 We know what things are by distinguishing them, so identity is part of ontology [Quine]
13. Knowledge Criteria / E. Relativism / 5. Language Relativism
1634 Two things are relative - the background theory, and translating the object theory into the background theory [Quine]
14. Science / C. Induction / 1. Induction
22200 If you eliminate the impossible, the truth will remain, even if it is weird [Conan Doyle]
19. Language / B. Reference / 1. Reference theories
8470 Reference is inscrutable, because we cannot choose between theories of numbers [Quine, by Orenstein]
19. Language / F. Communication / 6. Interpreting Language / b. Indeterminate translation
18963 Indeterminacy translating 'rabbit' depends on translating individuation terms [Quine]