John C. Wright (johncwright) wrote,
John C. Wright
johncwright

Infinite Regress

In reference to the Scholastic argument about an uncaused first cause, I have heard it claimed that infinite regression (while it may offend the laws of physics) does not violate the laws of logic.

In rebuttal, I would argue that infinite regress does indeed violate the laws of logic, on the grounds that it postulates, first, that every cause in the chain of cause and effect was set in motion by a prior cause, and then, second, that no first cause set the chain of cause and effect in motion.

If it is moving when nothing set it in motion, this contradicts the first sentence, which says every cause has a prior cause. But if it was at one time set in motion, then there is a first cause for which there is no prior cause, in which case, again, the first sentence, which says every cause has a prior cause, is contradicted.

In either case, the principle that every cause has a prior cause contradicts itself. There is no third possibility.

Let me use an analogy. We see a line of dominoes falling. We deduce that the fact that a domino falls is defined by the impact of the previous domino. A domino topples when struck by a previous domino and lies on the ground: it does not explode nor fly up into orbit. The position in which it lays is defined by the impulse of the previous domino, nothing else.

If we say that there is no first domino, then we assume a line of infinite dominoes, already fallen, stretching off to the left of us. No matter how long we trek, miles, light-years, infinities, we still see more and more toppled dominoes, laying precisely where they would have fallen had then been toppled by the fall of the previous domino.

But by definition, there is no first domino. It never fell. Ergo there is no second domino, whose fall was defined by the fall of the first. Ergo there is no third, fourth nor fifth dominoes, whose falls were defined each by the previous.

Therefore there is no domino of any number. No tenth domino, no hundredth, no thousandth, no millionth, no billionth. None.

Therefore any given domino we see lying down as if it had once been struck by the previous falling domino in fact is not the product of a previous series of domino strikes. If the toppling of the row of dominoes had no beginning, THEN IT NEVER BEGAN.

Our imaginations can be confused by picturing a number line, particularly  a negative number line, and saying that each event prior to each other is listed by simply subtracting one digit. Event 0 was caused by event -1, which was caused by -2, and so on. Since was can never run out of negative numbers, why must we conclude that we run out of causes?

The analogy is misleading. Numbers exist in an eternal realm of mathematical concepts. An infinite string of numbers is no more impossible or absurd than an infinite number of words or logical relations. A=A=A=A=A=... et cetera and ad nauseum and ad infinitum.

But causes are not numbers. In order for a cause to be a cause it has to actually have acted: it was at one time one thing, and it moved another thing. It has to be set in motion. Something pushed it. If you see a push-ee you know there must be a push-er.

The infinite number line is not in motion. The number x, let is be howsoever far on the number line, is adjacent to the number "x+1" no matter what "x" may be. But x never was brought into existence by x+1, and there is no point in time when x existed and x+1 did not. They are both simultaneous and eternal.

On the other hand event x, happening soever far in the past, DID NOT EXIST unless and until event x-1 existed, and pushed it. x-1 did not exist until and unless x-2 existed, and so on. They are not simultaneous. They are not eternal. They exist in time.

If an event exists in time, it is defined by the previous event. If there was no first event, there is no definition for any successive events thereafter. To say the row of dominoes was toppled by an infinitely old infinite impulse is merely word-play: what established the magnitude of the impulse? What make it so that the dominoes are acting as if toppled by a previous domino rather than acting as if they were shot from a cannon?

N.B: The question of the law of physics, I will mention in passing: the Second Law of Thermodynamics forbids an infinite chain of dominoes in motion. Any given chain of dominoes eventually runs out of energy, due to waste heat, the clattering noise, and so on, in a finite amount of time: an infinitely old and infinitely long chain of dominoes, by definition, is longer than this maximum length.
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