On The Idea Of An Infinite Series, As Applicable To Natural Theology -- By: Joseph Tracy
BSac 7:28 (Oct 1850) p. 613
On The Idea Of An Infinite Series, As Applicable To Natural Theology
There was no first man, say some atheists. The human race, they assert, has been from eternity, and each of us has an infinite series of ancestors.
The answer is old, that this hypothesis is self-contradictory. It assumes, concerning each and every individual of this infinite series, that there was a time when he had not yet come into existence; and if this is true of every one of them, it must be true of all of them. There must, therefore, have been a time when none of them existed; which is contrary to the supposition.
This reasoning has usually been met, we believe, by the naked assertion, that it is unsatisfactory, a mere dialectical subtilty; that, as eternity runs back without limit, it is evident that the same may be true of the human race; and that the argument which pretends to prove the contrary, must contain some sophism. It would be more satisfactory, could we be told precisely what that sophism is, and where it lies.
But we will not insist upon that. For the sake of honest minds, to whom the atheists’ reply seems plausible and embarrassing, we will take up the question anew, and endeavor to ascertain whether any series of finite terms, or of individuals, can be infinite, except in theory. If we succeed in showing that the actual completion of an infinite series of finite terms is an absurdity, it will follow of necessity that the series of fathers and sons, to which we belong, is not infinite, but must have had a beginning.
BSac 7:28 (Oct 1850) p. 614
Every scholar knows that there are theories which, though demonstrably true as theories, are yet demonstrably incapable of being reduced to practice. A mathematical point, for example, can exist only in theory — only as an idea; for if it exist otherwise, it must occupy space, — must have extension, and is therefore not a mathematical point. The same is true of a mathematical line, which is only the imagined path of a moving point. Lines and points are what some old logicians call entia rationalia, entities for the reason, in distinction from entia realia, entities which have an existence of their own, whether thought of or not. They are ideas, evolved by the mind itself, and by a right use of which we are enabled to reason on the subjects to which they pertain, with perfect accuracy; though things answering to those ideas, cannot possibly exist. Our task is, to show that an Infinite Series, like a mathematical point, is one of these entia rationalia; a mere fiction of the mind, for its own convenience in arithmetical calculation; and that no series of actually existing terms can possibly be infinite. The infinity of a...
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