Virtual Logic-Number and Imagination

This column consists in a dialogue (sections 2 and 3) between Cookie and Parabel, protagonists from an earlier column called “Fragments of the Void” (Kauffman, 2004). The dialogue is about the nature of number and the emergence of form and number from the void. In this discussion the void is not empty. It is quite full. The void consists in what is given prior to any distinction. Thus in the void there is no distinction between the observer and the observed or between concept and reality. There are no distinctions in the void, and all that we are familiar with and all that we are not familiar with is right there, but there is no there there. This property of everything and nothing (but the void does not even have this property) makes the void maximally unstable, ready to exfoliate form (we take the form of distinction for the form) at an instant if there were such a spark as an instant. Cookie and Parabel show how number arises from the void and how it is our imagination, our reflexivity that produces and maintains the apparent infinity of entities. In taking this point of view on cognition and form we see that mathematics and indeed the arising of all forms and worlds is reflexive and must include the observer, for it is only with the imagination of an observer that these worlds come to life. In the absence of an observer, the apparent worlds fall back into the potentiality of the void. At the end of the column a reference list forms a background to the dialogue. These include previous papers of the author (Kauffman, 1987, 2004, 2005, 2009, 2010); Laws of Form by G. Spencer-Brown (1969); a paper on Number by Warren McCulloch (1965); a warning by the mathematician Edward Nelson (2006); and the Tractatus Logicus Philosophicus by Ludwig Wittgenstein (1922).