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Published online by Cambridge University Press: 12 March 2014
The usual logical paradoxes, which stem from Russell's class R0 (i.e.,  and its relatives R1, R2, and so on (i.e.,
 and its relatives R1, R2, and so on (i.e.,  ,
,  , and so on, correspondingly), are contradictions (Ri ϵ Ri) ≡ ~(Ri ϵ Ri), derivable under unrestricted rules of inference. No contradiction
, and so on, correspondingly), are contradictions (Ri ϵ Ri) ≡ ~(Ri ϵ Ri), derivable under unrestricted rules of inference. No contradiction  appears to obtain.
 appears to obtain.