[FOM] About Paradox Theory
Zvonimir Sikic
zvonimir.sikic at gmail.com
Mon Sep 19 13:35:10 EDT 2011
A class defined by
x el z iff (Ey)( y el x & -(x el y) )
is contradictory because
sngl(z) el z iff -( sngl(z) el z ).
But there is no logical contradiction in the defining formula because it is
satisfiable in natural numbers by interpreting "el" as "> or =" and z as 0.
This class is just the beginning of a sequence generated from Cantors
theorem by using iterated intersections, instead of identity that Russell
used to generate his class.
It is interesting that his class, but also those generated by iterated
unions (that turned out to be Quines classes), are logically contradictory.
What an unexpected difference between unions and intersections
C.f.
http://www.fsb.unizg.hr/matematika/sikic/download/ZS_cantors_theorem.pdf
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