Single Value Logic

Consider a pattern of synapse events in the brain, which we may here take to represent the active event of thought. As these synapses are physical events, we can imagine a least action principle corresponding to a line of thought. Suppose, for example, that we wish to consider a synaptic connection between a neural plance A and a neural place B. Then among the various possible courses of events represented by all of the synapses occurring in the neural sets underlying these thoughts, there may be one shortes actually occurring connected causal sequence of synapses connecting A and B. This is the shortest sequence in terms of action. Note that all other sequences connecting A and B are somewhat irrelevant, if we accept the unity of thought, (note: I would not now agree with the unity of thought, FJS, 2000AD) since having already thought, by the shortest sequence, from A to B, we then continue to think from B on.

Whatever the psychophysical validity of the above presentation, it provides an intuitive conceptual background for a new element of neomathematics, called single value logic, or 'svl' for short, which may also be denoted by an arrow.

The present is always connected by svl with the past (if the past is singular, fjs, 2000AD). Whatever actually occurs is just one situation (but consider the Everett interpretatin of quantum mechanics for an alternative) not a choice of multiplicities. Thus svl is the logic of reality.

Now, 2000AD, I must interject some text. I had much more confidence in the stability and singularity of reality 20 years ago than I do now. Nevertheless, svl is a useful representation of a point of view, one that we might perhaps call physical, or just classical. Such a perspective is still useful as a model, a boundary or a limiting form. Now we return to the original discussion in the Neomathematicon.

We always come to the present by svl. Although it may appear that we leave the present by multivalued logic, when going toward the future, the future does not actually exist. Thus svl is the logic of being.

Referring back to our psychophysiological model for svl, consider that we perceive, imagine, or draw a straight line between two points. each ofthese occurrences of a straight line requires additional synaptic events to the svl path between a pair of neurons associated with thoughts containing the consciousness of each of the two points, in order to consider or produce the straightness or the line. Thus the svl connection between the two points is shorter than the linear connection. We might call svl the shortest path between two points.

We are not conceptually limited to pure, absolute svl. If we can accept a little traditional logic, consider two alternate pathways from the present. Then suppose, by our knowledge of similar events, that we have an equal expectation for the occurrence of each of the paths. Now it is quite easy to imagine a logical continuum between the equal probability prediction and the case where one of the paths is actually chosen (collapse of the wave vector). This will provide logical values between single valued and two valued logic.

For our purposes in doing neomathematics we will use an arrow to mean anapproximation to svl, an intent towards svl, a transformation from multiple valued towards single valued logic. A little reflection on the matter may convince the reader that logically pure svl cannot really be mentioned, since it is going faster than any medium which might be used to mention it. We can mention the name svl, which is not single valued since it may either exist, 'svl' or not.

There are few paved roads in unexplored territory.

Exercise: Axiomatize svl.

Joe Staley

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