On Diagonal Quantifiers; 1 of 9

          On Diagonal Quantifiers

1.    Variation and Constancy

          The science-fiction writer Robert Anton Wilson invented a word, sumbunol, meaning “some but not all”. He did so to combat the temptation to over-generalize. Sumbunol’s formal definitions are:        

                             Sumbunol things have property P

                    =       Exists(x)(P(x))  and  Exists(y)(not P(y))

                   =       Exists(x,y)( P(x) xor P(y) )

          The last equation says; “sumbunol things are P” is equivalent to “P differs on some two things”. Sumbunol is the variation quantifier; so the symbol for sumbunol is “Var”: Var(x)(P(x))  =  P varies.

          The negation of sumbunol is ollerno, meaning “all or no”, with these formal definitions:

                             Ollerno things have property P

                    =       All(x)(P(x))  or  All(y)(not P(y))

                   =       All(x,y)( P(x) iff P(y) )

          The last equation says; “ollerno things are P” is equivalent to “P is the same for any two things”.  Ollerno is the constancy quantifier; so the symbol for ollerno is “Con”: Con(x)(P(x)) = P is constant.

          I call variation and constancy diagonal quantifiers. I also call them Wilsonian quantifiers, in honor of Robert Anton Wilson.