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Ideas for 'Nietzsche and Philosophy', 'The Evolution of Logic' and 'Ontology and the Ambitions of Metaphysics'

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14 ideas

5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Since properties can have properties, some theorists rank them in 'types' [Hofweber]
5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
Maybe not even names are referential, but are just by used by speakers to refer [Hofweber]
5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
'Singular terms' are not found in modern linguistics, and are not the same as noun phrases [Hofweber]
If two processes are said to be identical, that doesn't make their terms refer to entities [Hofweber]
5. Theory of Logic / G. Quantification / 1. Quantification
The inferential quantifier focuses on truth; the domain quantifier focuses on reality [Hofweber]
5. Theory of Logic / G. Quantification / 3. Objectual Quantification
The universal quantifier can't really mean 'all', because there is no universal set [Hart,WD]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
Modern model theory begins with the proof of Los's Conjecture in 1962 [Hart,WD]
Model theory studies how set theory can model sets of sentences [Hart,WD]
Model theory is mostly confined to first-order theories [Hart,WD]
Models are ways the world might be from a first-order point of view [Hart,WD]
5. Theory of Logic / K. Features of Logics / 6. Compactness
First-order logic is 'compact': consequences of a set are consequences of a finite subset [Hart,WD]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / c. Berry's paradox
Berry's Paradox: we succeed in referring to a number, with a term which says we can't do that [Hart,WD]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / c. Burali-Forti's paradox
The Burali-Forti paradox is a crisis for Cantor's ordinals [Hart,WD]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
The machinery used to solve the Liar can be rejigged to produce a new Liar [Hart,WD]