It must be admitted, however, that the axiom by which we are enabled to deduce a cause with specific attributes from any definite facts, such as we know by previous experience to be the natural consequents of that particular efficient, must be restricted to the special case where we have no acquaintance with any other cause competent for the production of the given phenomena. And this is precisely the condition of the case in our present argument. We have the most abundant and perfect experience that intelligence is adequate to produce the harmonious regularity and beautiful order of nature; but we are altogether destitute of scientific, or even superficial, knowledge as to the reality of any different cause which might yield those results.
As I have already observed, the most advanced schools of modern sensist philosophy entirely ignore the investigation of efficient or producing causes, as removed beyond the sphere of the human senses. On this point the Scotch metaphysicians speak as decidedly as the disciples of Locke and Hume, or the more profound and intensely critical Kant. Indeed, Dr. Thomas Brown has clearly demonstrated that in the physical world we can never hope to discover by sensation anything save phenomena, either antecedents or consequents, with their invariable laws of simultaneity and succession; while the deepest as the most laborious thinker of all, M. Auguste Comte, refuses even so much as to use the term cause in his Course of Positive Philosophy.
On the other hand, those who aver the existence of imperceptible powers and occult qualities as the actual efficients of phenomena do not attempt to define their character, nor pretend that they fall within the limits of sensible or intellectual cognition. A member of that sect, like the pedant in the old play, may explain “that opium produces sleep because it has a soporific property”; but if you ask him how he knows it to possess such a property, he can only answer, from the fog of his vicious circle, “because it produces sleep.” And such must ever be the virtual avowal of utter ignorance as to the nature of causation by the adherents of this obsolete school. And could they thus solve, even to their own satisfaction, the question of secondary causes, they leave the question of the First Cause untouched.
It therefore follows, in accordance with all the rules of the most rigid and thorough induction, that the mathematical harmonies of the universe furnish conclusive proofs of an intelligent cause; and if we reject this inference there is not, and cannot be, the faintest shadow of a possible hypothesis for the explanation of natural phenomena.
I will next proceed to state my second proposition: All natural phenomena have the characteristics of mathematical order and harmony to the exclusion of chance.
Now, it is evident that a generalization so sweeping and universal as the above could only be made good by an immense, an almost infinite series of inductions. Nevertheless, we are not bound to assume an onus of such overpowering magnitude. For as the syllogism of our argument belongs to the first figure, and we have to deal at present with the minor premise, that may well be particular; and the conclusion will be valid as to everything embraced within its terms, and that will be found sufficient to warrant our conclusion.
As a preliminary, however, it becomes necessary to explain the logical process for the exclusion or mathematical elimination of chance. Suppose there be two dice in a box, what are the chances of our turning an ace at a single throw? Obviously one-sixth, leaving six chances minus one against the probability; while the chances against our throwing two aces, or any other equation, may be set down, with sufficient accuracy for the purpose of this argument, as the square of the last number, or thirty-six. The chances against an equation of four dice are 1,296; while against eight they amount to the enormous sum of 1,679,616—an impossible throw, unless the cubes have been loaded. And it is manifest from this example how very soon the multiplication of coincidences indicative of order must demonstrate causation to the utter elimination of chance. I will now commence with the particular cases of the general law announced in my second premise.
INSTANCE I.—MYSELF.
I survey my right hand: it has five fingers; I look at my left: it has five also—the other member of an algebraic equation. I then turn to my feet, and behold a similar equation of five toes on each. I next turn to my bodily senses, and again find the mystic five. The wonder is increasing. And now all the incalculable millions of my fellow-men rise up and sweep before the eye of the mind, in all the rich and radiant, or coarse and unseemly, varieties of humanity; and all these, too, present the identical God-announcing miracle, the quintuple equation of fives.
Let us, however, apply the rigorous rules for the calculation of chances, not forgetting the judicious remark of Whately: “That the probability of any given supposition must be estimated by means of a comparison with each of its alternatives.”