Combining Philosophers
Ideas for William S. Jevons, George Engelbretsen and Feferman / Feferman
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11 ideas
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
18912
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Was logic a branch of mathematics, or mathematics a branch of logic? [Engelbretsen]
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5. Theory of Logic / E. Structures of Logic / 1. Logical Form
18905
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Propositions can be analysed as pairs of terms glued together by predication [Engelbretsen]
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18922
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Logical syntax is actually close to surface linguistic form [Engelbretsen]
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5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
18908
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Standard logic only negates sentences, even via negated general terms or predicates [Engelbretsen]
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5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10158
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A structure is a 'model' when the axioms are true. So which of the structures are models? [Feferman/Feferman]
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10162
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Tarski and Vaught established the equivalence relations between first-order structures [Feferman/Feferman]
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5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10160
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Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman]
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10159
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Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman]
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5. Theory of Logic / K. Features of Logics / 4. Completeness
10161
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If a sentence holds in every model of a theory, then it is logically derivable from the theory [Feferman/Feferman]
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5. Theory of Logic / K. Features of Logics / 7. Decidability
10156
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'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman]
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10155
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Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman]
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