The Limitations of
Formal Models of Measurement, Control, and Cognition
Howard H. Pattee
Applied Mathematics and Computation
July 1993, Vol. 56, pp. 111-130.
The question of the adequacy, or lack of it, of formal or syntactic (i.e. non-interpreted symbolic manipulation) treatments of biological and cognitive phenomena in terms of
physical law is taken up. It is argued that such pure-syntax treatments in terms of physical law are not adequate, even though biology and cognition admit of such treatments (though, not in the functional form that we know them) because their material substrate are assuredly subject to the laws of physics. The reason for such inadequacy is the fact that the affinity of biological and cognitive phenomena is with
Measurement and Control processes, not physical laws.
Measurement
processes (which involve subject systems exercising selective effects upon object systems) assign initial conditions (i.e. specific values of variables) to the equations of motion constituting physical laws. (Prior to the measurement process, physical laws are in a sort of timeless limbo and are without actual contact with the observable universe.) Control processes change those initial conditions. These processes only operate in instances in which physical laws are in suspension because such laws are, by definition, universal and inexorable whenever they are in effect. Accordingly, physical laws are independent of our hopes, feelings, and actions.
It is because living things and cognition are essentially measure and control processes that they are able to exercise any choice at all that would otherwise be denied them if they were under the continuous restraint of physical law. Considerations resonant with the foregoing discussion are what led J. B. S. Haldane to consider
physics a degenerate form of biology and caused Ernst Mayr to argue that biology is an autonomous subject from physics (the attitude being, since we have all the facts, what do we care about theory?!)
The complementary relations between physical law, on the one hand, and measure and control processes, on the other, disclosed by the foregoing discussion, transpire, the article argues, because of our insistence (through the exemplar of physics) in syntactic, formal descriptions of nature. In other words, physical laws; and measure and control processes are simply syntactically incompatible, thus necessitating separate, logically irreducible descriptions.
If we are to avoid this complementarity, to achieve a more unified and deeper understanding of nature, the article argues that we shall have to dispense with purely syntactic treatments of nature and adopt non-formal models that make
functional as opposed to
formal distinctions. The possibility of such non-formal models, the article argues, is disclosed by the image processing and pattern-recognition capabilities of the brain that are able to accommodate syntactically incompatible descriptions (e.g. reversible dynamical descriptions and irreversible statistical descriptions).
The fact that the brain is possessed of such capacities argues that complementarity is an artifact of the language we use to describe nature rather than an objective feature of nature. This conclusion echoes the verdict of von Neumann who articulated that mathematics was a secondary language derived from the primary language of the nervous system.
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