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.