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Results tagged with paradox
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user 34276
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Avoiding reflexive paradox in set theory
I've just read an interesting paper that addresses the question of how best to remove paradoxes from the naive abstraction axiom. Reference is:
Goldstein, L. 2013. Paradoxical partners: semantical br …
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Avoiding reflexive paradox in set theory
I am an amateur mathematician, and certainly not a set theorist, but there seems to me to be an easy way around the reflexive paradox: Add to set theory the primitive $A(x,y)$, which we may think of as … \wedge \phi(y)$
Then if we try to construct the set $B$ of all sets not belonging to themselves, we get
$\forall x, x\in B \leftrightarrow A(x,B) \wedge x\notin x$
Then, instead of the reflexive paradox …