Ontology

I will describe some of the ontologies which are entwining in the Neomathematicon. Primary, perhaps, is the denotational ontology of the symbols, the core of which is their occurrence on the page, embedded in the language of explanation. In the case of web moduli they are strictly mathematical symbols, with a direct correspondence to both simple finite graphs (many-one) and a physical realization as parts of the neural system (one-many). The twists become slightly more neomathematical; their particular representation as the twist diagrams requires some interaction with the neomathematical core of twist, the hypernumber. On the other hand, their purely algebraic and formal realization could be developed mathematically. Triadic dualism is both mathematical and neomathematical; the symmetry is obviously existent both in the world around us and in the written symbols; and it is not difficult to find appropriate symbols for observed triadic dualisms, or to find material world examples of given symbolic forms. To these two levels of triadic dualism I wish to add a third, more fundamental, if it is real.

Suppose we have a triangular modulus of neurons; one neuron connects to another which connects to a third which itself connects to the first neuron. Suppose we try to look at the synaptic causal directivity and sequentiation of action in the modulus, intrinsically to itself, without reference to exterior reference. Call the neurons A, B and C and call their lines of connection (axon:dendritic:synaptic connection) AB, BC, and CA. Suppose we have a synapse along AB and another synapse at another place in the modulus. Does the other synapse occur before or after AB? Imagine the synapses are causal, in that one synapse initiates another in the modulus. If the other synapse occurs before AB then it can be considered causal of AB, but if the other synapse occurs after AB then AB can be considered causal of the other synapse.

If we associate our consciousness with AB, then, in the modulus, we have our own point of reference there and one exterior point of reference, CA, because CA can give input to and thus be observed by, AB. We cannot observe BC directly and so, in particular, we cannot know whether BC precedes CA or not. And neither can we observe whether CB is other than CA or not; we cannot detect C. Thus the whole triangular structure is intrinsically ambiguous; it is only externally observable as to direction and sequentiation. If we hypothesize that consciousness is organized by synapse action and the causal and otherwise connections between synapse actions, then each triangular modulus as described above would present an ambiguity, or symmetry, of consciousness. Furthermore, since we cannot observe C, we have no reference to distinguish A from B; if we take consciousness as directed by the flash of the synapse, then in the triangular modulus we do not know the direction of causal action nor the triangular structure. So every instance of triangular connectivity is both triangularly and dualistically ambiguous; and this I take to be another ontology for triadic dualism. Although the argument seems very hypothetical, it was in fact the original source for the conception of triadic dualism which, once conceived, can be observed and constructed so variously.

Single value logic is a neomathematical usage of an approximate concept, or direction of intent which, in its limit of true single valuedness, is the most fundamental logic available for both the physical world and the mind, whichever of these is taken as primary.

Superintegers have the same ontology as written triadic dualisms, as symbols, as collections of formed ink on the page. Hypernumbers occupy a larger and more indefinite ontological realm than just as symbols. The hypernumber is the name of a conceptual entity, which is observed as its multiple levels of intersection with physical, mental and symbolic realities.

K-space is postulated to have a more fundamental existence than the causal world and probably lies deeper than space and time. The causal laws of physics themselves would be examples of the intersection of the K-space hypernumber with language, professional actions and assumptions (of, for example, physicists and engineers) and also as the equations on the page expressing the laws.

Joe Staley