Combining Philosophers

Ideas for Anaxarchus, Gottlob Frege and Kurt Gdel

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20 ideas

4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
18806 Frege thought traditional categories had psychological and linguistic impurities [Frege, by Rumfitt]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
9154 Frege agreed with Euclid that the axioms of logic and mathematics are known through self-evidence [Frege, by Burge]
9585 Since every definition is an equation, one cannot define equality itself [Frege]
4. Formal Logic / C. Predicate Calculus PC / 1. Predicate Calculus PC
4971 I don't use 'subject' and 'predicate' in my way of representing a judgement [Frege]
4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / d. Universal quantifier ∀
17745 For Frege, 'All A's are B's' means that the concept A implies the concept B [Frege, by Walicki]
4. Formal Logic / C. Predicate Calculus PC / 3. Completeness of PC
17751 Gödel proved the completeness of first order predicate logic in 1930 [Gödel, by Walicki]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
13455 Frege did not think of himself as working with sets [Frege, by Hart,WD]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
9157 The null set is only defensible if it is the extension of an empty concept [Frege, by Burge]
9835 It is because a concept can be empty that there is such a thing as the empty class [Frege, by Dummett]
16895 The null set is indefensible, because it collects nothing [Frege, by Burge]
14238 A class is an aggregate of objects; if you destroy them, you destroy the class; there is no empty class [Frege]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / e. Equivalence classes
9854 We can introduce new objects, as equivalence classes of objects already known [Frege, by Dummett]
9883 Frege introduced the standard device, of defining logical objects with equivalence classes [Frege, by Dummett]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
17835 Gödel show that the incompleteness of set theory was a necessity [Gödel, by Hallett,M]
8679 We perceive the objects of set theory, just as we perceive with our senses [Gödel]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
18104 Frege, unlike Russell, has infinite individuals because numbers are individuals [Frege, by Bostock]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
9942 Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
21716 In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / c. Logical sets
9834 A class is, for Frege, the extension of a concept [Frege, by Dummett]
3328 Frege proposed a realist concept of a set, as the extension of a predicate or concept or function [Frege, by Benardete,JA]