Combining Texts

All the ideas for 'Classical Cosmology (frags)', 'Concerning the Author' and 'First-Order Logic'

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14 ideas

1. Philosophy / E. Nature of Metaphysics / 7. Against Metaphysics
14767 The demonstrations of the metaphysicians are all moonshine [Peirce]
1. Philosophy / G. Scientific Philosophy / 3. Scientism
14764 I am saturated with the spirit of physical science [Peirce]
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]
11. Knowledge Aims / B. Certain Knowledge / 3. Fallibilism
14768 Infallibility in science is just a joke [Peirce]
12. Knowledge Sources / D. Empiricism / 2. Associationism
14765 Association of ideas is the best philosophical idea of the prescientific age [Peirce]
14. Science / B. Scientific Theories / 1. Scientific Theory
14766 Duns Scotus offers perhaps the best logic and metaphysics for modern physical science [Peirce]
27. Natural Reality / E. Cosmology / 1. Cosmology
5994 Is the cosmos open or closed, mechanical or teleological, alive or inanimate, and created or eternal? [Robinson,TM, by PG]