(esoteric / exoteric 2)

             Contrary to Pythagoras, number does not exist in nature, if, by ‘nature’, we mean the world external to consciousness. But, at the same time, when Russell and Whitehead tried to prove that all mathematics can be logically derived, not only the philosophers, but the theoretical and speculative mathematicians concluded that the ‘project’ was a failure; and the mathematical thinkers concluded that mathematics is, in fact, an empirical science. But the question then arises as to precisely where this empirical field subsists. Not only do their conclusions overturn the last Humean presumption of a standpoint – an absolutely necessary condition for Humean skepticism, since analysis itself becomes meaningless without a stable ground or point of origin, if only in process – but it also controverts the Humean assumption that ‘empirical’ is necessarily based in ‘sensory’, since number is not only very nearly the defining condition for ‘abstraction’, all of its expression in form is a human invention in signs; and therefore mathematics itself is essentially symbolic in both content and expression. The Symbol itself has somehow become a pure, discursive empirical content, a field that is not in any sense automatically self-defining.

             When Einstein insisted that ‘God does not roll dice’, he perhaps expressed the final Pythagorean viewpoint. Insisting that causality is discrete and not probabilistic is basically an assertion that the universe is essentially numerical, obeying an implicit law of cogency or number. But, of course, Einstein was literally a neo-Kantian. Most of the Humean progeny refuse – or at least fail – to confront the core issue of solipsism and hence the peculiar necessities of the Kantian solution. It is not enough to deny the synthetic apriori to obviate the residual forces of the Copernican Revolution which sap the Humean half measures. Isolating ourselves in immediacy simply denies the abstracting forces which allow us to assess validity. Neither ‘number’ nor ‘matter of fact’ suffices, in itself, to establish validity, as much as validity may be undeniable in experience. Somehow, it is experience itself which establishes validity, and establishes it by a process requiring abstraction.
             It is this necessity for abstraction which, in fact, Einstein is pointing toward, however indirectly. If we ask, where does abstraction arise? Kant supplies the first answer. Abstraction is the function of awareness that isolates the witness, thus allowing us to view witness and experience simultaneously. But, of course, Kant is approaching the issue from the perspective of idea and the presumption that ideation itself is a logical act. Therefore, he can equate logical ideation and experience – his ‘transcendental dialectic’. The transcendental dialectic is necessary because, if we assume with Kant that experience is based in ideation as logical, then the idea that the witness can witness the witness is inherently logically absurd. The problem, of course, is that, however absurd, self-witnessing is an empirical fact. Not only is it an empirical fact; it is also empirically arrived at. We have become self-aware; and this self-awareness, being an empirical process, is also empirically accessible.
             Einsteinian physics opens this accessibility by providing an objective mirror – an empirical mirroring of objectivity itself – by which we can access this grounding experience of abstraction. When we enter this mirror moment, we begin to recognize that it is the basis of the inferential moment which is perception. The recognition of an object is simply the corollary for the recognition of the self. But as the Kantian logic shows by contrary, on the subjective side this involves the same kinds of paradoxes as Einsteinian physics. The inferential basis of experience is the preclusive corollary for analysis. And both are subject to this non-logical – not to say anti-logical – process of experience. Abstraction itself is the product of the non-logical but fully empirical process of self-awareness.
             If Einstein insists that ‘God does not roll dice’, he is tacitly expressing the cogency necessary for self-awareness. The reflective process is the root nature of cogency because it is root condition for ‘form’. While formal abstraction is a secondary reflective process after ‘perception’, as we understand it, nevertheless, the reflective process underlies ‘perception’ as we experience it. The fact that we recognize that we are experiencing a form means that abstraction and reflection are already present, even before we ‘name’ the ‘object’. The witness itself has already been abstracted.

             In other words, number is not only inherent in reflection; in some sense, number is reflection. Number is the abstractive definition of the reflective field.