=1953.= The Infinite is often confounded with the Indefinite, but the two conceptions are diametrically opposed. Instead of being a quantity with unassigned yet assignable limits, the Infinite is not a quantity at all, since it neither admits of augmentation nor diminution, having no assignable limits; it is the operation of continuously _withdrawing_ any limits that may have been assigned: the endless addition of new quantities to the old: the flux of continuity. The Infinite is no more a quantity than Zero is a quantity. If Zero is the sign of a vanished quantity, the Infinite is a sign of that continuity of Existence which has been ideally divided into discrete parts in the affixing of limits. --LEWES, G. H. _Problems of Life and Mind (Boston, 1875), Vol. 2, p. 384._ =1954.= A great deal of misunderstanding is avoided if it be remembered that the terms _infinity_, _infinite_, _zero_, _infinitesimal_ must be interpreted in connexion with their context, and admit a variety of meanings according to the way in which they are defined.--MATHEWS, G. B. _Theory of Numbers (Cambridge, 1892), Part 1, sect. 104._ =1955.= This further is observable in number, that it is that which the mind makes use of in measuring all things that by us are measurable, which principally are _expansion_ and _duration_; and our idea of infinity, even when applied to those, seems to be nothing but the infinity of number. For what else are our ideas of Eternity and Immensity, but the repeated additions of certain ideas of imagined parts of duration and expansion, with the infinity of number; in which we can come to no end of addition? --LOCKE, JOHN. _An Essay concerning Human Understanding, Bk. 2, chap. 16, sect. 8._ =1956.= But of all other ideas, it is number, which I think furnishes us with the clearest and most distinct idea of infinity we are capable of.--LOCKE, JOHN. _An Essay concerning Human Understanding, Bk. 2, chap. 17, sect. 9._ =1957.= Willst du ins Unendliche schreiten? Geh nur im Endlichen nach allen Seiten! Willst du dich am Ganzen erquicken, So musst du das Ganze im Kleinsten erblicken. --GOETHE. _Gott, Gemüt und Welt (1815)._ [Would’st thou the infinite essay? The finite but traverse in every way. Would’st in the whole delight thy heart? Learn to discern the whole in its minutest part.] =1958.=