Quote: principle of abstraction--given any condition, there is a class of those members satisfying the condition

Quotation Skeleton

A fair standard [for a formal system of mathematics] is [Whitehead and Russell's Principia Mathematica]. … The system here to be presented is adequate … R3. if 'x' does not occur in .phi., … [R3] may be called the principle of abstraction; … whose members are just those objects y such … theorem: (.thereExists.x)(y)((y.in.x) .equiv. ~(y.in.y))). Now let us take … We thus have the self-contradictory theorem: (.thereExists.x)((x.in.x) .equiv. … … [p. 90] Thus a formula in our original sense … for the variables in such a way that … test will be called stratified.   Google-1   Google-2

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Additional Titles

Quote: abstraction leads to Russell's paradox, (.thereExists.x)((x.in.x).equiv. ~(x.in.x))

Quote: Russell's theory of types avoids Russell's paradox by stratified formulas; e.g., .in. only occurs in contexts of the form n .in. n+1

Related Topics

Topic: abstraction (62 items)
Topic: Liar's paradox and Russell's paradox (25 items)
Group: data type   (34 topics, 723 quotes)