The Nature of Number

Many learned people chortle at the superstitions that some have regarding numbers like 13 and 666. But the theory of Number that those superstitions entail is not that far removed from a more intellectually respectable one. Magical powers are attributed to those numbers, which means that they exist, that they exist in a sphere that is removed from ordinary reality, and that they have causal efficacy upon the latter. Pythagoras, and the Idealist ancient Greeks that he influenced, likewise held Number in the same esteem, the difference being that, according to them, the qualities that they manifest in reality are expressive of their numerality--Oneness is Unity, Twoness is Opposition, Threeness is Balance, etc. Later Rationalist theories continued to hold that Numbers are non-sensible, but that their qualities are strictly quantitative. Empiricists inverted that scheme, maintaining that Numbers are merely abstractions from quantities given in sensory experience. Kant explained how they actively structure that experience. More recently, Numbers have been treated as mere symbols on a piece of paper. Now, one premise common to all these theories is that Number is fundamentally cardinal, namely 1, 2, 3, 4, etc. Rarely, if ever, has it been suggested that Number is fundamentally ordinal, namely, that the essence of Numbers is Firstness, Secondness, Thirdness, etc. One indication of the primacy of Ordinality is that while 1, 2, 3, 4, etc. can be abstracted from 1st, 2nd, 3rd, 4th, etc., the converse derivation seems more problematic. As the perhaps most influential Mathematical theory of recent times, Whitehead and Russell's, demonstrates, the transition from one number to the next requires a recursive 'successor' function, which entails an ordered progressive generation of each number. What this means in non-technical terms is that the essence of Number is given in the activity of counting, not in the occult, rational, or, otherwise.