The Method of Circulation Analysis; Brief Item #94

A first step is to offer some definition of the positive integers, 1, 2, 3, 4…. … Further, let us suppose as too familiar to be defined, the notions of ‘one’, ‘plus’, ‘equals’…. As the acute reader will see, the one important element in the above series of definitions, is the etc., etc., etc…It means that an insight should have occurred.  If one has had the relevant insight, if one has caught on, if one can see how the defining can go on indefinitely, no more need be said … in defining the positive integers there is no alternative to insight. … a single insight is expressed in many concepts.  In the present instance, a single insight grounds an infinity of concepts.  (CWL 3, 13-14/38-39)

The method of circulation analysis resembles more the method of arithmetic than the method of botany.  It involves a minimum of description and classification, a maximum of interconnections and functional relations.  … only a few of the integral numbers in the indefinite number series are classes derived from descriptive similarity; by definition, the whole series is a progression in which each successive term is a function of its predecessor.  It is this procedure that gives arithmetic its endless possibilities of accurate deduction; and … it is an essentially analogous procedure that underlies all effective theory. … (CWL 21, 111)

For example, the positive integers are an infinite series of intelligibly related terms. … But besides the terms and their relations there is the generative principle of the series; inasmuch as that generative principle is grasped, one grasps the ground of an infinity of distinct concepts.  Still, what is the generative principle?  It is intelligible, for it is grasped, understood.  But it cannot be conceived without conceiving what an insight is, for the real generative principle of the series is the insight; and only those ready to speak about the insight are capable of asking and answering the question, How does one know the infinite remainder of positive integers denoted by the ‘and so forth’? … (CWL 3, 647/670) (#94) (Click here for previous Brief Items)

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