If often happens that infinity is marshaled to prop up the notion that evolution can work via random mutations, no matter how heavily the odds are stacked against that possibility. If the finiteness of our universe limits the effectiveness of randomness in producing wonders, then infinity is offered as the handy solution. Our universe was preceded by an infinite number of other universes which rolled the dice an infinite number of times until finally our own time-bound universe happened to get it “just right.” An infinite number of universes of course entails infinite time, a concept tossed blithely into discussion as if it were no more problematic than booking a meal at a restaurant.
Here is one of several proofs that Spitzer offers to show the impossibility of infinite past time. I find it rather elegant:
Infinities within an aggregating succession imply “unoccurrable,” “unachievable,” and “unactualizable,” for an aggregating succession occurs one step at a time (that is, one step after another), and can therefore only be increased a finite amount. No matter how fast and how long the succession occurs, the “one step at a time” or “one step after another” character of the succession necessitates that only a finite amount is occurrable, achievable, or actualizable. Now, if “infinity” is applied to an aggregating succession, and it is to be kept analytically distinct from (indeed, contrary to) “finitude,” then “infinity” must always be more than can ever occur, be achieved or be actualized through an aggregating succession. Any other definition would make “infinity” analytically indistinguishable from “finitude” in its application to an aggregating succession. Therefore, in order to maintain the analytical distinction between “finitude” and “infinity” in an aggregating succession, “infinity” must be consider unoccurrable (as distinct from finitude which is occurrable), unachievable (as distinct from finitude which is achievable), and unactualizable (as distinct from finitude which is actualizable). We are now ready to combine the two parts of our expression through our three common conceptual bases:
“Infinite Past Time”
“(The) unoccurrable (has) occurred.”
“(The) unachievable (has been) achieved.”
“(The) unactualizable (has been) actualized.”
Failures of human imagination may deceive one into thinking that the above analytical contradictions can be overcome, but further scrutiny reveals their inescapability. For example, it might be easier to detect the unachievability of an infinite series when one views an infinite succession as having a beginning point without an ending point, for if a series has no end, then, a priori, it can never be achieved. However, when one looks at the infinite series as having an ending point but no beginning point (as with infinite past time reaching the present), one is tempted to think that the presence of the ending point must signify achievement, and, therefore, the infinite series was achieved. This conjecture does not avoid the contradiction of “infinite past time” being “an achieved unachievable.” It simply manifests a failure of our imagination. Since we conjecture that the ending point has been reached, we think that an infinite number of steps has really been traversed, but this does not help, because we are still contending that unachievability has been achieved, and are therefore still asserting an analytical contradiction. ( – New Proofs for the Existence of God, Robert J. Spitzer, p. 181 )
See also: Arrow of time points to missing dark matter
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