Explosion and Cut Necessary

Joseph Vidal-Rosset joseph.vidal.rosset at gmail.com
Wed May 25 15:19:20 EDT 2022

Le   mer.   05/25/22   mai   2022   à   06:53:59   ,   "Tennant,   Neil"
<tennant.9 at osu.edu> a envoyé ce message:
> Gosh, Jo, you  must therefore have proved that  Classical Logic itself
> is  inconsistent.  (Core Logic  is  a  proper subsystem  of  Classical
> Logic.)

Hello Neil,

Thank you for this nice email, both informative and obviously full of
consideration for my work.

But you forget to say  that neither Classical Logic, nor intuitionitic
logic    are     paraconsistent,    by    contrast     with    minimal
logic. Paraconsistency i.e. the antisequent

\(\lnot A, A \nvdash B\)

doest not entail a contradiction in minimal logic, by contrast with Core
logic.  (In  /Core  Logic/,  p.156,  you  wrote  that  Core  logic  is
paraconsistent. Me at least, I read you with attention.)

So, I am afraid  that, if my argument is correct, and  I believe that it
is, Core logic is not a proper subsystem of Classical logic, because, if
it  is paraconsistent,  then  it  is simply  /not/  a  logic, logic  being
consistency, /pace/ Priest.

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