Combining Texts
Ideas for
'The Problem of Empty Names', 'Set Theory and Its Philosophy' 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
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Henkin semantics has a second domain of predicates and relations (in upper case) [Rossberg]
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10759
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There are at least seven possible systems of semantics for second-order logic [Rossberg]
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10751
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Second-order logic needs the sets, and its consequence has epistemological problems [Rossberg]
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10704
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We can formalize second-order formation rules, but not inference rules [Potter]
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5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
10753
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Logical consequence is intuitively semantic, and captured by model theory [Rossberg]
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5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
10752
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Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true [Rossberg]
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5. Theory of Logic / E. Structures of Logic / 1. Logical Form
10754
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In proof-theory, logical form is shown by the logical constants [Rossberg]
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5. Theory of Logic / F. Referring in Logic / 1. Naming / e. Empty names
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Unreflectively, we all assume there are nonexistents, and we can refer to them [Reimer]
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5. Theory of Logic / H. Proof Systems / 3. Proof from Assumptions
10703
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Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter]
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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10756
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A model is a domain, and an interpretation assigning objects, predicates, relations etc. [Rossberg]
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5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
10758
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If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model [Rossberg]
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5. Theory of Logic / K. Features of Logics / 4. Completeness
10761
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Completeness can always be achieved by cunning model-design [Rossberg]
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5. Theory of Logic / K. Features of Logics / 5. Incompleteness
10755
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A deductive system is only incomplete with respect to a formal semantics [Rossberg]
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