Combining Texts

All the ideas for 'Rechnungsmethoden (dissertation)', 'First-Order Logic' and 'Metaphysics: contemporary introduction'

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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 / 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 / 3. Nature of Numbers / c. Priority of numbers
18256 Quantity is inconceivable without the idea of addition [Frege]
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 / 2. Intuition of Mathematics
9831 Geometry appeals to intuition as the source of its axioms [Frege]
8. Modes of Existence / B. Properties / 13. Tropes / b. Critique of tropes
4483 If abstract terms are sets of tropes, 'being a unicorn' and 'being a griffin' turn out identical [Loux]
8. Modes of Existence / D. Universals / 1. Universals
4481 Austere nominalists insist that the realist's universals lack the requisite independent identifiability [Loux]
4477 Universals come in hierarchies of generality [Loux]
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
4482 Austere nominalism has to take a host of things (like being red, or human) as primitive [Loux]
8. Modes of Existence / E. Nominalism / 1. Nominalism / c. Nominalism about abstracta
4478 Nominalism needs to account for abstract singular terms like 'circularity'. [Loux]
9. Objects / A. Existence of Objects / 5. Individuation / c. Individuation by location
4480 Times and places are identified by objects, so cannot be used in a theory of object-identity [Loux]