Physics, especially mathematical physics, Vaihinger explains in detail, has been based, and fruitfully based, on fictions. The infinite, infinitely little or infinitely great, while helpful in lightening our mental operations, is a fiction. The Greeks disliked and avoided it, and “the gradual formation of this conception is one of the most charming and instructive themes in the history of science,” indeed, one of the most noteworthy spectacles in the history of the human spirit; we see the working of a logical impulse first feeling in the dark, gradually constructing ideas fitted to yield precious service, yet full of hopeless contradictions, without any relation to the real world. That absolute space is a fiction, Vaihinger points out, is no new idea. Hobbes had declared it was only a _phantasma_; Leibnitz, who agreed, added that it was merely “the idolum of a few modern Englishmen,” and called time, extension, and movement “_choses idéales_.” Berkeley, in attacking the defective conceptions of the mathematicians, failed to see that it was by means of, and not in spite of, these logically defective conceptions that they attained logically valuable results. All the marks of fiction were set up on the mathematician’s pure space; it was impossible and unthinkable: yet it proved useful and fruitful. The tautological fiction of “Force”—an empty reduplication of the fact of a succession of relationships—is one that we constantly fall back on with immense satisfaction and with the feeling of having achieved something; it has been a highly convenient fiction which has aided representation and experience. It is one of the most famous, and also, it must be added, one of the most fatal of fantasies. For when we talk of, for instance, a “life-force” and its _élan_, or whatever other dainty term we like to apply to it, we are not only summarily mingling together many separate phenomena, but we are running the risk that our conception may be taken for something that really exists. There is always temptation, when two processes tend to follow each other, to call the property of the first to be followed by the other its “force,” and to measure that force by the magnitude of the result. In reality we only have succession and coexistence, and the “force” is something that we imagine.