Combining Philosophers

Ideas for Rescher,N/Oppenheim,P, Susan A. Gelman and Bertrand Russell

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22 ideas

4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
14113 The null class is a fiction [Russell]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
6103 Normally a class with only one member is a problem, because the class and the member are identical [Russell]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
14427 We can enumerate finite classes, but an intensional definition is needed for infinite classes [Russell]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
14428 Members define a unique class, whereas defining characteristics are numerous [Russell]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
14440 We may assume that there are infinite collections, as there is no logical reason against them [Russell]
14447 Infinity says 'for any inductive cardinal, there is a class having that many terms' [Russell]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
14443 The British parliament has one representative selected from each constituency [Russell]
14445 Choice shows that if any two cardinals are not equal, one must be the greater [Russell]
14444 Choice is equivalent to the proposition that every class is well-ordered [Russell]
14446 We can pick all the right or left boots, but socks need Choice to insure the representative class [Russell]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
18130 Axiom of Reducibility: there is always a function of the lowest possible order in a given level [Russell, by Bostock]
14459 Reducibility: a family of functions is equivalent to a single type of function [Russell]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / c. Logical sets
21563 The 'no classes' theory says the propositions just refer to the members [Russell]
14461 Propositions about classes can be reduced to propositions about their defining functions [Russell]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
15894 Russell invented the naïve set theory usually attributed to Cantor [Russell, by Lavine]
4. Formal Logic / F. Set Theory ST / 6. Ordering in Sets
14126 Order rests on 'between' and 'separation' [Russell]
14127 Order depends on transitive asymmetrical relations [Russell]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
8469 Russell's proposal was that only meaningful predicates have sets as their extensions [Russell, by Orenstein]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
11064 Classes can be reduced to propositional functions [Russell, by Hanna]
7548 Classes, grouped by a convenient property, are logical constructions [Russell]
8745 Classes are logical fictions, and are not part of the ultimate furniture of the world [Russell]
6436 I gradually replaced classes with properties, and they ended as a symbolic convenience [Russell]