[OBJECTIVE SCIENCE.COM] [As I explained in Part 2 of this series,] the projection of the mathematical laws of nature into a higher or prior existence is an obvious expression of Platonism -- and a major source of the Primacy of Mathematics in contemporary physics. It is part of the reason why causal sequences involving the material world are scorned in favor of "elegant" mathematical formalism.

There is, however, a second major version of the Primacy of Mathematics, expressed by those physicists who reject the implicit religious mysticism of the Platonic approach. As in the usual case of subjectivism reacting against intrinsicism, they accept the basic premise of the intrinsicists, but reject the supernatural aspect of the intrinsicist theory. In the present context, this means accepting the Platonic idea of the material world as inherently passive or chaotic, but rejecting the existence of a supernatural world which imposes order.

The result is a world which simply remains chaotic -- an unfortunate theoretical result, since the fact of an orderly world is too obvious even for the best skeptic to ignore.

Thus a dilemma is set up: How can science explain the orderliness of the physical world, if it rejects the religious notion of a supernatural orderer?

Immanuel Kant provided a way out of this dilemma which has had tremendous influence on twentieth century physics. His solution was that we are the orderer: perceptual awareness is not a direct grasp of the external world, but a distortion -- it consists of sense data that have been processed by our conceptual consciousness, twisted to fit certain innate conceptual "categories" which order the chaotic data of the senses.

This unavoidable processing means that we do not perceive reality as it really is, but rather only reality as it appears after processing. This idea was the basis of Kant's splitting between the world "as it really is" (which we can never know) and the world "as it appears to us," that is, as filtered through the distorting lens of our conceptual consciousness.

In Kant's view, certain very basic features of the physical world of perception are not inherent in reality as such, but are imposed by human consciousness. Spatial relationships, for example, are not relationships of actual entities in physical space -- the three-dimensional spatial world is a "category" that sense data are pigeonholed into, and does not represent a fact about reality "in itself". The same is true for time relationships, cause and effect relationships, and even the existence of stable discrete entities (as opposed to chaotic whirling flux of sensation). Thus Kant came to reject as "tainted" the very notion of a physical world of entities.

In this view what we would normally think of as a causal picture of material objects moving and interacting in space and time, becomes a subjective projection. That may be the way our consciousness organizes various sense data, Kant says, but that tells us nothing about what physical objects are in themselves. The "true nature" of physical objects is therefore, in principle, forever unknowable to us because of the inescapable distortion involved in our consciousness's processing of sense data.

Physicists, then, are relegated to looking at experimental data, formulating mathematical principles to describe and quantify it, and making calculations and predictions on that basis -- without ever having a chance to discover the true nature of the entities they are studying, i.e., without ever understanding the underlying causes of the observed mathematical relationships. In short, physics for Kant consists of categorizing and cataloging mere appearances -- which physicists can never truly understand, since the underlying causal processes are inaccessible to human consciousness. The best we can hope for is some mathematical equation which relates one appearance to the next.

Note that in Kant's view, the referent of this equation is not a supernatural Form, as it was in Plato's theory, but our own conceptual consciousness. It is, after all, one's own consciousness that imposes structure on the initial chaos of sense data. Thus, for Kant, physics becomes, in essence, a branch of psychology -- it studies the internal processes of our consciousness, and not any external physical world. Kant explicitly shuns the idea that knowledge of physics should come from observation of the physical world, instead suggesting that it must be derived without observation or experiment: "A rational doctrine of nature deserves the name of natural science only when the natural laws at its foundation are cognized a priori, and are not mere laws of experience". That is, the fundamental laws at the root of physics must be "taken from the essential nature of the thinking faculty itself." [6]

The basic upshot of the Kantian development is that the true nature of the real world is forever inaccessible to physics and all thought. Physics cannot penetrate beyond a mere mathematical description of appearances, a description which refers ultimately to our own conceptual processing, and not to the real world. Thus, like Platonic mysticism, Kantian skepticism also leads to a version of the Primacy of Mathematics -- a version which has had tremendous influence on physics in the twentieth century.

***

Quantum mechanics is the most obvious and most important example. The quantum theory consists of an elaborate mathematical formalism that allows physicists to calculate atomic energy levels, scattering cross sections, and nearly any conceivable process involving microscopic particles. Yet the theory itself gives no physical account of the motion or evolution of the microscopic system. For example, in the famous double-slit experiment, the theory allows one to calculate the exact distribution of particles at the detecting screen, but gives no account of how that distribution arises, how the particles actually move from source to screen.

Indeed, the standard view of physicists is that such an account is impossible, that one simply can not, as a matter of principle, understand how the particles move from one location to another. Under the influence of Kant, physicists have rejected as meaningless the question of what reality is like "in itself." The causal evolution of physical objects between observations is tantamount to Kant's noumenal reality: it is forever unknowable, inherently off-limits to theoretical science.

Niels Bohr, one of the founding fathers of quantum mechanics and the man who is almost single-handedly responsible for the standard interpretation of its formalism, summarized this Kantian perspective eloquently: "There is no quantum world. There is only an abstract quantum mechanical description. It is wrong to think that the task of physics is to find out how Nature is. Physics concerns what we can say about Nature." [7]

Thus, under the grip of a Kantian rejection of "true reality", quantum physicists abandoned the goal of understanding the causal evolution of microscopic systems. As physicist John Bell writes, "...many came to hold not only that it is difficult to find a coherent picture but that it is wrong to look for one.... Some asserted that atomic and subatomic particles do not have any definite properties in advance of observation. ... Indeed, even the particles are not really there." [8]

Finally, Sir James Jeans summarizes the relationship between Kantian philosophy and the Primacy of Mathematics: "[W]e can never understand what events are, but must limit ourselves to describing the patterns of events in mathematical terms; no other aim is possible. Physicists who are trying to understand nature may work in many different fields and by many different methods; one may dig, one may sow, one may reap. But the final harvest will always be a sheaf of mathematical formulae. These will never describe nature itself... Thus our studies can never put us into contact with reality." [9]

The influence of Kantian skepticism on physics is not limited to quantum mechanics. The standard interpretation of relativity theory is also thoroughly Kantian.

The theory consists of a set of mathematical equations that describe how length and time measurements transform between different frames of reference in relative motion -- that is, how appearances change depending on one's frame of reference. As mentioned before, the mathematics of the theory is simply deduced from the axiom of the universal constancy of the speed of light, with no physical or causal explanation of this surprising fact. The standard interpretation of the theory is that it deals with mere appearances: the question of whether moving objects "really" contract or not, is regarded as meaningless. All we can say is that it is necessary to regard them as contracting in order to maintain the consistency of our description.

To be continued in Part 4. 

References:

[6] Kant, Metaphysical Foundations of Nat. Sci., 138, 142.

[7] Quoted in Bell, 142.

[8] Bell, Speakable and Unspeakable in Quantum Mechanics, 142.

[9] Ken Wilbur, ed., Quantum Questions, page 7.

Copyright 2001 Travis Norsen/ Objective Science. All rights reserved. Permission granted to link to this article only; but, permission is not granted to republish it. 

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