Points, lines, and all that...

[I have revised and expanded this post, so I'm redating it into the present.]

[Also, the posts {as of 4 Nov 09} just below this one that are {currently} in blue, are all redated posts dealing with rationality and faith.]

A point is defined as a geometric 'position' without extension or depth. Do points actually exist in material nature? If so, where? Occupying no extended space, they seem to have no 'foothold' in material reality. By analogy, imagine a wave of zero wavelength: it wouldn't be a wave and therefore wouldn't be. A spatial "location" that lacked any extension whatsoever would not exist in space and would therefore not be a spatial location at all. If geometric points actually exist in material spacetime, then our entire sense of "existence" must be radically overhauled. A Pyrrhic victory, methinks.

On the other hand, if points do not exist in material spacetime, then neither do lines exist in material reality, since a line is but the shortest distance between two points. If one point cannot actually exist, far less can two or more. Nature, being devoid of actual material points, is also devoid of actual material lines. Consequently, material nature is also devoid of perfect triangles, circles, curves, ellipses, squares, parabolas, etc. As such, the perfect, ideal geometric laws of motion do not obtain in material reality. This is basically what Nancy Cartwright means by explaining "how the laws of physics lie." For example, as Lawrence Gage notes, "the Law of Inertia talks about bodies unaffected by outside forces: when was the last time you saw a body isolated from all forces?"

As Maxwell knew all too well, his system of electromagnetic equation was unable to account for heat and motion--a fact which indicates once more that such equations, otherwise perfect in their inner consistency, are idealized out of actual nature. I would suggest that only if reality is understood as being more than a material-energetic system, and recognized to possess a dimension of 'pure formal' functionality qualitatively different from material nature, can such equations obtain in nature. The formal dimensions of nature as I am proposing here do not remove the well known 'signal loss' created by the indeterminateness of matter (i.e., the numerous experimental discrepancies between gritty fact and pristine theory), a loss which Galileo recognized, grudgingly, time and again in order to account for the discrepancies between his equations and observed results.

[I have transcribed most of what I think are the pertinent quotations from my reading of The Relevance of Physics thus far, but rather than inserting them all nice and perty in the body of this post at this juncture (and hour), I'm just presenting them in raw form in another post with prefatory and concluding glosses.]

I should also mention that the extremely counterintuitive nature of this "thought experiment"--remember, FCA is my cognitive palette/lab--depends for any of its validity on two things: 1. the claim that there are no actual geometric points in material space, and 2. just how well natural phenomena obey pure laws of motion. The best move of some objector would be to refute my presentation of the immaterial existence of geometric forms. Failing (or following) that, an objector should refute my claim that nature does not perfectly obey its own laws.

I'd love to be corrected about the second point, but it seems that the entire progress of science has stemmed, in large part, from a theoretic "leap" from the jumble of data to a "perfect" formula which "makes sense of" the otherwise senseless data. In other words, the reason a formula is not just a spare-nothing synthesis of all data, but rather a selective conformation (for want of a better term right now) of the theoretically relevant data, is because numerous cases of observation do not conform to the formal purity of the theory. Indeed, it only makes sense to speak of relevant as opposed to irrelevant (or aberrant) data based on a knowledge--or, rather, an intuition--of how they should "hang together." (I.e., Relevant with respect to what?) Certainly, there are instances of material phenomena which emulate, apparently perfectly, a formula (notably, Newton's inverse square ratio of gravitation), but these are literally the exceptions that prove the rule. If every instance of phenomena conformed exactly to the ideal formula behind it, scientists would only need a handful of empirical cases to "just read off" the law from a formally exhaustive material world. But, as scientists know all too well, the practice of science is riddled with skewed observations and off-the-mark instances of phenomena.

The fact that we can transcend the imperfect emulations observed in physical nature in order to grasp the "ideal" to which they are "striving," suggests two things in line with the Aristhomistic tradition. First, humans possess an organ capable of "manipulating" or "grasping" immaterial, ideal reality in a way not confined to the purely physical. This we call the intellect. Second, nature itself displays a striving for perfection from the indeterminate potentiality of matter towards the determinate actuality of form. This is really all that is meant by "final causality": natural causes tend towards actual effects based on some coherent inner principle (viz., ratio naturae) as a specific class of the broader act-potency dynamic in Creation. These rationes naturae are not self-actualizers--i.e., their actus essendi is crucially distinct from their rationalis essentia, and therefore contingent on some agent in possession of existence not subject to the same "cleft in being"--which accounts for why they cannot always, and perhaps not ever perfectly, overcome the "interference" posed by the potency of their matter, a tendency called "caducity" by the Scholastics.