Combining Texts

All the ideas for 'fragments/reports', 'First-Order Logic' and 'Truth by Convention'

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20 ideas

1. Philosophy / F. Analytic Philosophy / 6. Logical Analysis
8996 If if time is money then if time is not money then time is money then if if if time is not money... [Quine]
2. Reason / D. Definition / 7. Contextual Definition
8995 Definition by words is determinate but relative; fixing contexts could make it absolute [Quine]
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 / C. Ontology of Logic / 3. If-Thenism
10064 Quine quickly dismisses If-thenism [Quine, by Musgrave]
5. Theory of Logic / C. Ontology of Logic / 4. Logic by Convention
20296 Logic needs general conventions, but that needs logic to apply them to individual cases [Quine, by Rey]
8998 Claims that logic and mathematics are conventional are either empty, uninteresting, or false [Quine]
8999 Logic isn't conventional, because logic is needed to infer logic from conventions [Quine]
9000 If a convention cannot be communicated until after its adoption, what is its role? [Quine]
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 / A. Nature of Mathematics / 2. Geometry
8994 If analytic geometry identifies figures with arithmetical relations, logicism can include geometry [Quine]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
8997 There are four different possible conventional accounts of geometry [Quine]
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]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
8993 If mathematics follows from definitions, then it is conventional, and part of logic [Quine]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
1748 Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]