Combining Texts

All the ideas for 'Subjectivist's Guide to Objective Chance', 'Outline of a Theory of Truth' and 'Higher-Order Logic'

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18 ideas

3. Truth / F. Semantic Truth / 2. Semantic Truth
15327 Kripke's semantic theory has actually inspired promising axiomatic theories [Kripke, by Horsten]
15343 Kripke offers a semantic theory of truth (involving models) [Kripke, by Horsten]
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
14966 The Tarskian move to a metalanguage may not be essential for truth theories [Kripke, by Gupta]
14967 Certain three-valued languages can contain their own truth predicates [Kripke, by Gupta]
3. Truth / G. Axiomatic Truth / 3. KF Truth Axioms
16328 Kripke classified fixed points, and illuminated their use for clarifications [Kripke, by Halbach]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
10301 The axiom of choice is controversial, but it could be replaced [Shapiro]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
10588 First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10298 Some say that second-order logic is mathematics, not logic [Shapiro]
10299 If the aim of logic is to codify inferences, second-order logic is useless [Shapiro]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
10300 Logical consequence can be defined in terms of the logical terminology [Shapiro]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
10290 Second-order variables also range over properties, sets, relations or functions [Shapiro]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10590 Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro]
10296 The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro]
10297 The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro]
10292 Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10294 Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro]
8. Modes of Existence / B. Properties / 11. Properties as Sets
10591 Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro]
26. Natural Theory / D. Laws of Nature / 4. Regularities / b. Best system theory
9425 Lewis later proposed the axioms at the intersection of the best theories (which may be few) [Mumford on Lewis]