relations of ideas; the other showed us the theory of reasoning inductively from matters of fact.

The extraordinary success of physical inquiry after Bacon's time tended naturally to the depression, and somewhat to the injury or corruption, of abstract science. The undue extension of the inductive method to the region of pure ideas produced the ethical system of Hobbes, himself a friend and disciple of the great master, but whose philosophy is now a byword from its degrading principles, and its tendencies to selfishness in morals, to materialism in philosophy, and to despotism in politics. Among his successors may be counted Mandeville, "the buffoon and sophister of the ale-house," and the English school of deists of the early part of the last century, including Bolingbroke, the friend and philosophical instructor of Pope. From him his satirical pupil learned to sneer at the metaphysicians of the older school, who, in the Universities or the Church, distrustful of the tendencies of modern physical science, and perhaps ignorant alike of its principles and its practice, still kept up their fondness for ancient and abstract learning. Prophesying the triumph of dulness and obscurity, the poet exclaims,

"As Argus' eyes, by Hermes' wand oppressed,

Closed one by one to everlasting rest,

Thus, at her felt approach and secret might,

Art after art goes out, and all is night.

See skulking Truth to her old cavern fled,
Mountains of casuistry heaped o'er her head;
Philosophy, that leaned on heaven before,
Shrinks to her hidden cause, and is no more.

Physic of Metaphysic begs defence,

And Metaphysic calls for aid to Sense:

See Mystery to Mathematics fly;

In vain; they gaze, turn giddy, rave, and die."

A later instance of the erroneous application of the method of physical inquiry to metaphysical subjects may be found in the writings of the celebrated David Hartley, who endeavoured to account for the course and association of our ideas by vibrations and vibratiuncles in the medullary substance of the brain. Of

the same school was Dr. Priestley, whose just fame for his bril-
liant discoveries in natural science inclines one to speak tenderly
of his philosophical speculations, though his habits, formed in the
laboratory and other schools of experimental investigation, be-
trayed him into the avowed support of materialism, and of what
he calls the doctrine of "philosophical necessity." The influ-
ence of the same cause of error may be traced in the works of
the French philosophers, so called, of the last century, especially
in those of Helvetius, Volney, D'Holbach, and Condillac. Hel-
vetius, for instance, refusing to receive any other evidence than
that of the senses, tracing all ideas to this source, and assuming
the inductive method to be the only guide to knowledge, can find
no cause for the superiority of man over the brute, except that
the human hand is a more convenient instrument than the foot of
a quadruped, which terminates in horn, nails, or claws.
"The
life of animals, in general," he observes, "being of a shorter
duration than that of man, does not permit them to make so
many observations, or to acquire so many ideas; and animals,
being better armed and better clothed by nature than the human
species, have fewer wants, and consequently fewer motives to
stimulate or exercise their invention. Who can doubt, then,'
he triumphantly asks, "that if the wrist of a man had been ter-
minated by the hoof of a horse, the species would still have
been wandering in the forest?"

Such vagaries of speculation are not a whit more respectable than the opposite errors of the schoolmen, who sought to interpret nature by the relations of abstract ideas, or, in other words, to ascertain facts by the aid of a transcendental logic. It would be very unjust to accuse the inductive method of leading to these gross blunders, which have arisen solely from a misapplication of that method, from an extension of it to a province which it was never formed to govern, namely, the region of pure mental conceptions. We shall be likely to avoid both causes of error by keeping constantly in view the axiom, that the methods as well as the objects of physical and of metaphysical inquiry are radically different. We never can demonstrate a matter of fact; we

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can have no sensible evidence of the relations of abstract ideas. There is no question of dignity between the two methods; each is sovereign in its own sphere. There is no superiority of the one kind of evidence over the other, when considered as a foundation of belief; both lead to positive and well-founded convictions.

The latest historian of the Inductive Sciences is not satisfied with this exclusion of metaphysical ideas from the domain of physical investigation; his work upon the Philosophy of these sciences, which is an elaborate attempt to enlarge the inductive method by the doctrines, and to clothe it in the terminology, of Kantian metaphysics, is a virtual restoration of the scholastic method, or the philosophy of the Middle Ages, and must be considered as "a remarkable instance of what has been aptly called the peculiar zest which the reaction against modern tendencies gives to the revival of ancient absurdities." When Mr. Whewell, in his glowing admiration of the brilliant discoveries recently made in natural science, expresses his confident hope that the mere physical inquirer will soon pass on from a determination of the laws of phenomena to a knowledge of the efficient causes of these phenomena, and gives as a reason for this expectation the light that has recently been thrown upon the action of polar forces, one may be permitted to doubt whether he knows the meaning of the words he uses, or is able to distinguish efficient from occasional causes. A far more cautious thinker, Mr. John Stuart Mill, in his zeal for inductive logic, falls into an error of the opposite character, by boldly taking up the doctrine, that even the axioms of the mathematician are but generalizations from experience, that there is no distinction between necessary truths and facts of observation, and, consequently, that the reasonings of the geometer do not differ in kind from the inductions of the optician or the chemist. It is hardly necessary to say, that the common opinion of the scientific world lies between the extreme doctrines maintained respectively by these two theorists.

The case of the mixed sciences deserves consideration here, as it really corroborates the principles that have been advanced,

though it may appear at first sight to conflict with them. Pure logic and pure mathematics are not so much sciences as methods of scientific inquiry, or organa of investigation and proof. They are modes of reasoning, irrespective of the subjects or facts about which we reason, and therefore applicable to all subjects. In the syllogism, for instance, the conclusion follows with absolute certainty from the premises, the truth of the premises being presupposed; whether this truth rests upon sensible evidence, or intuition, or a previous demonstration, is of no consequence. The principles of the syllogism, then, are pure abstractions; and the letters of the alphabet, or purely arbitrary marks taken as signs of any ideas or facts whatsoever, are the most convenient notation for expressing them. If the premises are matters of fact, or contingent truth, the conclusion will also be a matter of fact, or contingent truth; only the relation between premises and conclusion is a metaphysical truth, and as such is made known by intuition.

The case is precisely similar with mathematics, in which we employ a notation of the same sort. In its pure form, this science proceeds from abstraction to abstraction, the truth developed by it having no foundation in fact, and never being exemplified in the external world. If an event in the physical world, or a proposition founded on experience, be taken as a datum, or point of departure for the inquiry, however long the chain of mathematical reasoning may be which proceeds from it, the result at which we arrive is a truth of the same order with the one which formed the basis of the investigation. It has lost nothing, and it has gained nothing, in point of logical certainty, through the process to which it has been subjected. Take, for instance, the most brilliant achievement that is recorded in the whole history of mathematical science, the recent discovery by Adams and Leverrier of a new orb on the farther verge of our planetary system. Its existence was long before suspected, for it was said that its influence had been felt trembling along the far-extended line of our delicate analysis. But how was this influence detected? It was through repeated observations, made

by the telescope, of certain irregularities in the motion of Uranus, - observations so delicate, and irregularities so slight, that many years elapsed before it could be said with certainty that the latter were real, or before they could be measured so nicely as to afford a basis for the calculations which were to reveal the mass and the position of the body that caused them;-I say the mass and the position, for the general fact of the existence of such a body was inferred at once, by strict induction, from the mere knowledge that there were such irregularities.

A boat, moored at night by the side of a placid stream, suddenly heaves and oscillates as a few slight ripples move over the surface of the waters; and the watcher in that little boat, though he can descry nothing in the darkness, knows at once that some large object not far off is passing up or down the river, and throwing off those waves which extend obliquely from its wake. Had he instruments nice enough to measure the exact size and force of these ripples, and the aid of an empirical law, like that of Bode, to teach him that the object could move only through a certain channel at a known distance from him, he might calculate the size and exact position of the moving mass, so as to turn his night-glass directly upon it. This is precisely what was done by Adams and Leverrier. The calculation alone was mathematical; the existence of the new planet had previously been made known by induction, and the data used by the computers were all observed facts. And it was not the mathematical process which afforded any new evidence, or added to the convictions of astronomers that a hitherto unobserved planet rolled beyond the path of Uranus. The calculations left this supposed fact precisely where it was before, with the exact measure or kind of certainty which belongs to a truth of induction. The crowning labor of the whole, the real discovery, which, in legal phrase, changed circumstantial to direct evidence, was made when Challis at Cambridge and Galle at Berlin turned their telescopes to the region indicated, and actually saw the new orb which was causing this ripple in the heavens. In what sense, or with what color of reasoning, then, can it be said that moral evidence, the