Ideas from 'On 'Insolubilia' and their solution' by Bertrand Russell [1906], by Theme Structure

[found in 'Essays in Analysis' by Russell,Bertrand (ed/tr Lackey,Douglas) [George Braziller 1973,0-8076-0699-5]].

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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / c. Logical sets
The 'no classes' theory says the propositions just refer to the members
                        Full Idea: The contention of the 'no classes' theory is that all significant propositions concerning classes can be regarded as propositions about all or some of their members.
                        From: Bertrand Russell (On 'Insolubilia' and their solution [1906], p.200)
                        A reaction: Apparently this theory has not found favour with later generations of theorists. I see it in terms of Russell trying to get ontology down to the minimum, in the spirit of Goodman and Quine.
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / d. Richard's paradox
Richard's puzzle uses the notion of 'definition' - but that cannot be defined
                        Full Idea: In Richard's puzzle, we use the notion of 'definition', and this, oddly enough, is not definable, and is indeed not a definite notion at all.
                        From: Bertrand Russell (On 'Insolubilia' and their solution [1906], p.209)
                        A reaction: The background for this claim is his type theory, which renders certain forms of circular reference meaningless.
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
Vicious Circle: what involves ALL must not be one of those ALL
                        Full Idea: The 'vicious-circle principle' says 'whatever involves an apparent variable must not be among the possible values of that variable', or (less exactly) 'whatever involves ALL must not be one of ALL which it involves.
                        From: Bertrand Russell (On 'Insolubilia' and their solution [1906], p.204)
                        A reaction: He offers this as a parallel to his 'no classes' principle. That referred to classes, but this refers to propositions, and specifically the Liar Paradox (which he calls the 'Epimenedes').