Combining Texts

All the ideas for 'Space and Time', 'First-Order Logic' and 'The New Organon'

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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]
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
16639 Only individual bodies exist [Bacon]
9. Objects / C. Structure of Objects / 2. Hylomorphism / c. Form as causal
16033 There are only individual bodies containing law-based powers, and the Forms are these laws [Bacon]
14. Science / B. Scientific Theories / 2. Aim of Science
21950 Science must clear away the idols of the mind if they are ever going to find the truth [Bacon]
27. Natural Reality / C. Space / 6. Space-Time
14014 Space alone, and time alone, will fade away, and only their union has an independent reality [Minkowski]