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Ideas for 'Thinking About Mathematics', 'New Essays on Human Understanding' and 'Alfred Tarski: life and logic'

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12 ideas

5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
12992 Logic teaches us how to order and connect our thoughts [Leibniz]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
10056 At bottom eternal truths are all conditional [Leibniz]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
8729 Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro]
5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
12974 People who can't apply names usually don't understand the thing to which it applies [Leibniz]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10158 A structure is a 'model' when the axioms are true. So which of the structures are models? [Feferman/Feferman]
10162 Tarski and Vaught established the equivalence relations between first-order structures [Feferman/Feferman]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10160 Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman]
10159 Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
13002 It is always good to reduce the number of axioms [Leibniz]
5. Theory of Logic / K. Features of Logics / 4. Completeness
10161 If a sentence holds in every model of a theory, then it is logically derivable from the theory [Feferman/Feferman]
5. Theory of Logic / K. Features of Logics / 7. Decidability
10156 'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman]
10155 Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman]