The Mathematics of Cognition - pt. 2 .A Grammar Lesson We have mathematics, physics, psychology and the cosmic mind. We know something about all of these subjects. We would like to know more, particularly about the relation between the human and cosmic mind.
Given the existence of the human mind and a relational, immaterial reality it is quite reasonable to suppose that the human mind is patterned upon and has access to, or may be contained within a more encompassing intelligence.
The mind has a demonstrated capacity to fragment itself into subcomponents and even into sub-personalities. It would be metaphysically economical to suppose that we are the products of some such process. It would be helpful to have a model of this process.
We know that the human mind is able to discover deep mathematical structures within the patterns of natural phenomena. This suggests that similar structures may be latent in our own minds. The challenge is to further probe the structure of our psyches. Any progress in this regard would lend further credence to an immaterial cosmology, and would be of utmost importance in the working out of our destiny.
A major conceptual obstacle is the ambiguity between the objective and subjective aspect of any mental structure. How could one structure be cognizant of another? When we do mathematics are we working from the inside or the outside of the structures? Are there any analogs of cognition?
The presently favored theory of cognition is that it is equivalent to a verbal competence with respect to the object in question. My knowledge of a circle is the same as my ability to speak cogently about it. This would include the proper manipulation of the symbols referring to it. In computer terms, circle knowledge is equivalent to the portion of a geometry database relevant to circles, along with a modicum of linguistic capacity. Similar reasoning might suggest that we are happy because we smile, rather than the other way around.
Platonists would argue that our knowledge of a circle has to do with our ability to access the universal property of circularity, but this says nothing about the nature of that existence. Do the existences of goodness and circularity have any common features? I am suggesting universals have structural properties well beyond any superficial structure they might entail.
Consider Chomsky’s idea that beneath our superficial grammatical ability lies a deeper universal grammar that we must employ to communicate our thoughts. Most of the work on universal grammar has been directed toward computer language applications, and so has been computational rather than mathematical in its focus. I believe that we will discover a mathematical structure associated with the grammar, which is integral to the larger structure involved with cognition, sensation and emotion.
It may be that mathematicians have not yet intuited the nature of the mathematical structure that will eventually allow us to comprehend the cosmos. Undoubtedly it will include those structures that are necessary to the unification of math and physics. This will not be a closed system. There will rather be an open-ended hierarchy of structures that will include the ability to generate novel systems. Such structures may also be anticipated in the design of advanced digital systems. The advent of quantum system design will bring us another step closer to understanding.
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rev. 10/28/98