Re: Jan Burse gives support that godels use of impredicative s
- From: "elsiemelsi" <cyprinsam@xxxxxxxxxxxxxxx>
- Date: Sun, 27 Jan 2008 14:01:35 -0600
It seems that the vicious circle principle [: : : ]
applies only if the entities involved are constructed by ourselves. In
this case there must clearly exist a definition (namely the description
of the construction) which does not refer to a totality to which the
object defined belongs,
this just repeats what russell said
'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 of
Certainty"
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