[FOM] 481:Complementation and Incompleteness

Arnon Avron aa at tau.ac.il
Tue Feb 21 03:25:33 EST 2012

Quoting "Michael Lee Finney" <michael.finney at metachaos.net>:

> However, there is a great deal of literature. For instance, recently
> there is Ross Brady's book Universal Logic which is an excellent
> attempt to solve the problem using depth relevant logic and naive set
> theory. There is Peter Aczel's book "Non-Well-Founded Sets" and
> Vicious Circles by Jon Barwise and Lawrence Moss. As well as Anderson
> and Belnap's "Entailment I & II", the "Frontiers of Paraconsistent
> Logic" and many more.

As someone who has made some contributions to the study of
paraconsistent logics and relevance logics, I can assure you
that none of them even begins to provide an alternative
to classical logic for FOM.

 In fact, every serious work on any of these logics that
has even been made has used  classical logic (or at most
intuitionistic logic, in order not to start an irrelevant debate).

Arnon Avron

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