It is an obvious remark, that infinity was a symbol of evil in Hellenic speculation, whereas to Christian and modern thought it is identified with good. Much idle talk has arisen on this account, as to the limitation of the Hellenic mind. For in fact, the Finite ascribed to Pythagoras, and the idea of limit and proportion in Plato or in Aristotle, are far more nearly akin to true infinity than is the Infinite of modern popular philosophy. Infinite means the negation of limit. Now, common infinity, which may be identified in general with enumeration _ad infinitum_,--the _false_ infinity of Hegel--is the attempt to negate or transcend a limit which inevitably recurs. It arises from attempting a task or problem in the wrong way, so that we may go on for ever without making any advance towards its achievement. All quantitative infinity--which of course has its definite uses, subject to proper reservations--is of this nature. A process does not change its character by mere continuance, and the aggregate of a million units is no more free from limitation than the aggregate of ten. A defect in kind cannot be compensated by mere quantity. We see the fallacious attempt in savage, barbaric, or vulgar art. Meaningless iteration, objectless labour, enormous size, extravagant costliness, indicate the effort to satisfy man's need of expression by the mere accumulation of work without adequate idea or purpose. But such efforts, however stupendous, never attain their goal. They constitute a recurrent failure to transcend a recurrent limit, precisely analogous to enumeration _ad infinitum_. A hundred thousand pounds' worth of bricks and mortar comes no nearer to the embodiment of mind than a thousand pounds' worth. To attempt adequate expression by mere aggregation of cost or size is therefore to fall into the infinite process or the false infinity.
Another well-known instance is the pursuit of happiness in the form of "pleasure for pleasure's sake." The recurrence of unchanging units leaves us where we were. A process which does not change remains the same, and if it did not bring satisfaction at first, will not do so at last.[9] We might as well go on producing parallels to infinity, in the hope that somehow or somewhere they may meet. An infinite straight line may serve as a type of the kind of infinity we are considering.