[FOM] Use of Ex Falso Quodlibet (EFQ)

[Tennant, Neil]

Paul Levy wrote
__________

I was referring to natural deduction, where n-ary or-elimination is

                      [A_1]    [A_n]
                        :  ...  :
A1 or ... or A_n      B        B
------------------------------------
                B

The case n=0 is

False
----------------------------------
  B

which is Ex Falso Quodlibet.
__________

I'm afraid I don't have any idea how one might extrapolate from a rule governing an *n-fold disjunction for n greater than 1* to a so-called "case n=0".  What if one were to say "Oh no, the case n=0 is not False/B; rather, it is True/B" ?

Strangely enough, I do (sort of) get the idea of what the case n=1 would be:

        X       Y, [A1]
         :        :
       A1      B
      _________
            B

(Some would call this the cut rule.)

But that there so much as exists a case for n=0 baffles me. What is a disjunction with no disjuncts? I should imagine it is a passing-over-in-silence, because it cannot be said. But isn't that a very far cry from saying something absurd (#) ? And how would the B be obtained in the 'case proof' using no case-assumption at all? It seems that the closest thing to a 'case n=0' would be

       Y, [ ]
         :
        B
     ______
        B

(Some might make what in the USA would euphemistically be called a 'disability allowance' for such a rule of logical stuttering.)


Neil Tennant
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