Combining Texts

All the ideas for 'On Plural Reference and Set Theory', 'Toward a Philosophy of History' and 'First-order Logic, 2nd-order, Completeness'

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13 ideas

5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10751 Second-order logic needs the sets, and its consequence has epistemological problems [Rossberg]
10757 Henkin semantics has a second domain of predicates and relations (in upper case) [Rossberg]
10759 There are at least seven possible systems of semantics for second-order logic [Rossberg]
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
10753 Logical consequence is intuitively semantic, and captured by model theory [Rossberg]
5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
10752 Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true [Rossberg]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
10754 In proof-theory, logical form is shown by the logical constants [Rossberg]
5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
10670 A 'singulariser' converts a plural like 'number of' to a syntactically neutral form [Cartwright,H, by Hossack]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10756 A model is a domain, and an interpretation assigning objects, predicates, relations etc. [Rossberg]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
10758 If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model [Rossberg]
5. Theory of Logic / K. Features of Logics / 4. Completeness
10761 Completeness can always be achieved by cunning model-design [Rossberg]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
10755 A deductive system is only incomplete with respect to a formal semantics [Rossberg]
7. Existence / A. Nature of Existence / 3. Being / h. Dasein (being human)
20752 For man, being is not what he is, but what he is going to be [Ortega y Gassett]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
20756 Instead of having a nature, man only has a history [Ortega y Gassett]