Tuesday, October 20, 2009

An infinitely thin knife cuts no ice…

How we know infinity, and thus eternity, is not a natural concept. Or a reductio of Spinoza.

[The following link HERE presents an earlier stab at this same point.]

AXIOM 1: A characteristic which cannot be instantiated in nature should not be presumed to hold for nature as such.

POSTULATE 1: An object A cannot be in more than one place P at one time T. If A were in more than one place P at T, it would eo ipso cease to be a single object A. That is just what we mean by A being an object as opposed to two objects B and C. This is a basic characteristic of what it means to be a physically delimited (and thus quantifiable) object. A's objective unity allows for compossible, internal margins, but not noncontiguous, external boundaries.

CONSEQUENT 1 from AXIOM 1 + POSTULATE 1: Nature as a whole cannot be in two places at once, if for no other reason that there is no larger “space” in which nature can exist at this or that location. A further reason why nature as a whole can no more be in one place P than A can at a single T, is that A's objective existence in a presumed whole-nature at T would require A to be as objectively existent in some other whole-nature* at T, which, again, violates POSTULATE 1 and the unity of corporeal objects.

OBJECTION 1: Perhaps nature is infinite (and eternal) and therefore at all places (and all times) at once.

REPLY 1: An infinite quantity is a contradiction in terms, since a quantity is only possible by being physically, or even just conceptually, distinct from and delimited by some other quantity.

CONSEQUENT 2 from REPLY 1: Nature as a whole is not infinite and eternal. If it is, then it is no longer a physical reality, subject to quantification-mensuration.

POSTULATE 2: An infinitely thin surface cannot exist in nature. In our normal experience, the thinner something is, the sharper it is and the more easily and deeply it can cut into something else. But if we extend our mind along an infinitely thinner and thinner blade, we can quickly see that something goes wrong, as it were, in natural terms. For, while any surface asymptotically on its way towards infinity with indeed cut magnificently into physical reality, once it so to speak “reaches infinite thinness,” it will no longer cut anything, since an infinitely thin cut into something is physically equivalent to no cut at all. An infinitely small gap between two objects is actually no gap at all. When infinity is applied to nature as a presumably physical reality, we see that, to put it mildly, funny things happen.

CONSEQUENT 3 from POSTULATE 2 + AXIOM 1: Therefore, again, infinitely great––or minor––measures do not pertain to nature and natural objects, nor to nature as a whole. As such, it is illegitimate to refer to nature as a whole as both physical and infinite-eternal.

Someone can certainly refer to nature as "eternal," "infinite," and the like, but then it no longer seems the referent is nature, but supernature. The price, then, of naturalizing God is that of rendering nature incoherent for scientific, let alone naive exploratory, purposes.

6 comments:

Agellius said...

"REPLY 1: An infinite quantity is a contradiction in terms, since a quantity is only possible by being physically, or even just conceptually, distinct from and delimited by some other quantity."

Does this also explain why the material universe can't be eternal, i.e. infintely old?

The Cogitator said...

Agellius:

Yes. And especially so according to Einsteinian general relativity, wherein matter is quasi-synonymous with time. An infinite quantity of matter would then be an infinite amount of time. But my point is that an infinite quantity of matter is incoherent, is no longer a *quantitative* reality. An infinitely old "amount" of time is, in turn, incoherent.

One could argue for an eternal and infinite universe, but it would no longer be a quantitative reality, but some something infinitely transcending the nature (i.e., limits) of quantitative reality. It would, moreover, cease to be amenable to scientific analysis qua quantitative analysis.

Best,

Agellius said...

I guess it behooves the Church, and individual Catholics, to learn to understand science!

The Cogitator said...

Agellius:

You are right. But I would add two qualifications.

1. "Science" is not, traditionally, synonymous with "exact science" as we understand it now. Scientia meant knowledge based on relevant causes. It so happens, however, that some causes transcend (or 'subscend') the grasp of "exact physical science" as we now refer to "Science!". So we should always maintain "Science's" place in the larger pantheon of scientia, not simply collapse all knowledge into scientism. Indeed, as the work of Pierre Duhem, Stanley Jaki, Reijer Hookyas (sp?), Thomas Woods, Christopher Dawson, et al., indicates, the Church is behooved to engage science as but one of its genuine historical fruits. Science was born in the Church and it generally seems to die too far outside the worldview of the Church. It is, I admit, a much too neglected "family heirloom" in contemporary Catholicism. Look for John Farrell's essay from last year on the question: http://www.faith.org.uk/Publications/Magazines/Jul08/Jul08HasTheChurchMissedTheImportOfScience.html

2. It behooves Catholics to understand science if they feel called to engage it. Otherwise, as St. Augustine said, we would be laughed at by those with actual knowledge of the subject in question. It is not, however, a "spiritual necessity" to engage "Science." If it's not your intellectual or spiritual cup of tea, big deal; God loves the professional scientist no more and no less than the most science-ignorant laborer. It happens to be my cup of tea. ;)

Best,

The Cogitator said...

I should add that even if my argument fails to refute the eternality and infinity of the cosmos, it still falls within Catholic reason to allow for such a cosmos. St. Thomas d'Aquino granted that the finitude of the cosmos is only known by Revelation. He could "tolerate" an eternal cosmos, whereas St. Bonaventura could not, because he recognized that its structure qua Creation would still be contingent on God. The "actus essendi" of an eternal creature is still ontologically separate in itself from such an essence. Only in God is existence one with essence, even if the divide in creatures persists eternally.

Best,

The Cogitator said...

_____ says:

"two notes so far 1) spacetime is the context in which material has a state. So it would be wrong to say my brain is a configuration of spacetime, so much as my brain is a configuration of matter in spacetime... it's like the canvas on which matter goes (and of course 4dst is changed by relative presence or absence of matter.) 2) Measurements within a "rest frame" are consistent. So there is a "true yardstick" of the speed of light (for instance) so long as you're measuring it a) within a vacuum and b) in a rest frame... if you do those two things, you'll get the same "truth" every time... *I retract sub-point "b", light is the same speed in all frames of reference."