Combining Texts

All the ideas for 'Physiologia', 'First-Order Logic' and 'Letters to Fichte'

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11 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]
9. Objects / C. Structure of Objects / 4. Quantity of an Object
16674 The quantity is just the matter, in that it has extended parts and is diffuse [Charleton]
23. Ethics / C. Virtue Theory / 3. Virtues / g. Contemplation
7071 Life and rationality are pointless if we can only contemplate the freedom of our own ego [Jacobi]
23. Ethics / F. Existentialism / 2. Nihilism
7072 Jacobi was the first philosopher to talk of nihilism [Jacobi, by Critchley]