" Herr Meinong ...regards zero as the contradictory opposite of each magnitude of its kind." Russell in 'The Principles of Mathematics ' .
The book written as early as 1903 mentions Meinong. It was because I have read ' The Principles of Mathemaics ' that I asked Prof. Reicher-Marek how it came to Russell-Meinong encounter, did Russell understand German or Meinong English . She praised my question. But biography aside, the ontological status of zero is as fascinating as some of Alice's questions in Wonderland.
We hear Russell talk of null-class ( p. 186 ibid) We hear David Lewis talk of 'The Null Set ' ( David Lewis Parts of Classes )
Will Zero bring Cantors theory of the continuum in disarray ? How ? Well... if r is <b and b is not the infintessimal r cannot be less than zero . r<0 ? ( leaving out for the moment negative numbers which are less than zero )
Herr Meinongs Zero as the contradictory opposite of each magnitude...say, 7 , its contradictory opposite ' Not-7 )=Zero and so on for each magnitude, its contradictory opposite is zero. Russell finds this solution not free from ambiguity. Because 'opposite' can be anything when we talk of a class with infinite members. Any cardinal number is a class by itself. It is The Limit...where the fraction 0... ,... 1/32, 1/16, 1/8, 1/4, 1/2,...1 must stop, must end . 1 as a limit. 0-1. The lower Limit 0 and the upper Limit 1. The infinite series 0-1 . Russell's solution of defining class by virtue of meaning and not by enumeration is the key here , I guess. If we rely on enumeration , how do we proceed from zero to one ? We will never come to an end. Never to the silence we cherish. But if we come to 1 and still go on , it is because we want to play a language game called philosophy...ein Sprachspiel a la Wittgenstein. Because we are all children at heart as we see it when we do sports and art and music and painting and philosophy. Jesus told us to be like children if we want to enter the kingdom of heaven.