Re: Jan Burse gives support that godels use of impredicative s

*Nowadays* we would consider the use of the Vicious Circle Principle too
strict.

Russell and Whitehead did not make a distinction betweens syntax and
semantics in the Principia. Therefore they had to interpret the Vicious
Circle Principle in the strict way above.

Or in short: PM is foobar.

this sounds semantic to me
'Whatever involves all of a collection must not be one of the
collection.'Put otherwise, if to define a collection of objects one must
use the total
collection itself, then the definition is meaningless. This explanation
given by Russell in 1905 was accepted by Poincare' in 1906, who coined the
term impredicative definition, (Kline's "Mathematics: The Loss ofCertainty"



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