Combining Texts

Ideas for 'works', 'Scientific Objectivity' and 'Philosophy of Logic'

expand these ideas     |    start again     |     choose another area for these texts

display all the ideas for this combination of texts

12 ideas

4. Formal Logic / A. Syllogistic Logic / 1. Aristotelian Logic
18953 Modern notation frees us from Aristotle's restriction of only using two class-names in premises [Putnam]
4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
18949 The universal syllogism is now expressed as the transitivity of subclasses [Putnam]
4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / a. Symbols of PC
18952 '⊃' ('if...then') is used with the definition 'Px ⊃ Qx' is short for '¬(Px & ¬Qx)' [Putnam]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
15901 Trying to represent curves, we study arbitrary functions, leading to the ordinals, which produces set theory [Cantor, by Lavine]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / c. Basic theorems of ST
13444 Cantor's Theorem: for any set x, its power set P(x) has more members than x [Cantor, by Hart,WD]
18098 Cantor proved that all sets have more subsets than they have members [Cantor, by Bostock]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / a. Types of set
18958 In type theory, 'x ∈ y' is well defined only if x and y are of the appropriate type [Putnam]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
15505 If a set is 'a many thought of as one', beginners should protest against singleton sets [Cantor, by Lewis]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
10701 Cantor showed that supposed contradictions in infinity were just a lack of clarity [Cantor, by Potter]
10865 The continuum is the powerset of the integers, which moves up a level [Cantor, by Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / d. Axiom of Unions III
13016 The Axiom of Union dates from 1899, and seems fairly obvious [Cantor, by Maddy]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / b. Combinatorial sets
14199 Cantor's sets were just collections, but Dedekind's were containers [Cantor, by Oliver/Smiley]