a term made use of by mathematicians when they demonstrate any truth, by showing that its contrary is impossible, or involves an absurdity. Thus, Euclid demonstrates the truth of the fourth proposition of the first book of his Elements, by showing that its contrary implies this obvious absurdity—“that two straight lines may inclose a space.”

This mode of demonstration is called *reductio ad absurdum*, and is every whit as conclusive as the direct method; because the contrary of every falsehood must be truth, and of every truth, falsehood.

The young geometrician, however, does not, we believe, feel himself so perfectly satisfied with a demonstration of this kind, as with those which, proceeding from a few self-evident truths, conduct him directly, by necessary consequences, to the truth of the proposition to be proved. The reason is, that he has not yet learned to distinguish accurately between the words *false* and *impossible*, *different* and *contrary*. Many different assertions may be made relating to the same thing, and yet be all true or all false; but it is impossible to make two assertions directly contrary to each other, of which the one shall not be true and the other false. Thus, “snow is white,” “snow is cold,” are different assertions relating to the same thing; and both true; as, “snow is black,” “snow is red,” are both false; but let it be remembered, that of the first and second, and of the third and fourth of these assertions, neither is directly contrary to the other; nor is any one of them, abstractly considered, impossible, or such as a blind man, who had never felt nor heard of snow, might not believe upon ordinary testimony. But were all the men in Europe to tell a native of the interior parts of Africa that snow is a thing at once *white* and *not white*, *cold* and *not cold*, the woolly-headed savage would know as well as the most sagacious philosopher, that of these contrary assertions the one must be true and the other must be false. Just so it is with respect to Euclid’s fourth proposition. Had he proved its truth by showing that its contrary involves this proposition, that “the diagonal of a square is commensurate with its side,” the skilful geometrician would indeed have admitted the demonstration, because he knows well that the diagonal of a square is not commensurate with its side; but the tyro in geometry would have been no wiser than before. He knew from the beginning, that the proposition and its contrary cannot both be true; but which of them is true, and which false, such a demonstration could not have taught him, because he is ignorant of the incommensurability of the diagonal and side of a square. No man, however, is ignorant, that two straight lines cannot inclose a space; and since Euclid shows that the contrary of his proposition implies this absurdity, no man of common sense can entertain a doubt but that the proposition itself must be true.

**ACCELERATED MOTION.** See (Encycl.) ACCELERATING FORCE; CELEBRATION; and MECHANICS, Sect. VI.—and (this Supplement) DYNAMICS.

**ACTION** is a term which has been sufficiently explained in the Encyclopedia; but since that article was written, questions have been agitated respecting agents, agency, and action, which, as they have employed some of the most eminent philosophers of the age, and are connected with the dearest interests of man, are certainly entitled to notice in this place.

It is the opinion of Dr Reid, and we have adopted it (see METAPHYSICS, no. 129, &c. Encycl.), that no being can be an agent, or perform an action, in the proper sense of the word, which does not possess, in some degree, the powers of will and understanding. If this opinion be just, it is obvious, that what are called the powers of nature, such as impulse, attraction, repulsion, elasticity, &c. are not, strictly speaking, powers or causes, but the effects of the agency of some active and intelligent being; and that physical causes, to make use of common language, are nothing more than laws or rules, according to which the agent produces the effect.

This doctrine has been controverted by a writer whose acuteness is equalled only by his virtues; and we shall consider some of his objections to it in another place (see CAUSE); but a question of a different kind falls under our present consideration; and perhaps the answer which we must give to it, may go far to remove the objections to which we allude.

Can an agent operate where, either by itself or by an instrument, it is not present? We think not; because agency, or the exertion of power, must be the agency of something. The constitution of the human mind compels us to attribute every action to some being; but if a being could act in one place from which it is absent, it might do the same in a second, in a third, and in all places; and thus we should have action without an agent; for to be absent from all places is a phrase of the same import as not to exist. But if a living and intelligent being cannot act but where it is either immediately or instrumentally present, much less surely can we attribute events of any kind to the agency of an absent and inanimated body. Yet it has been said, that “we have every reason, which the nature of the subject and of our own faculties can admit of, to believe, that there are among things inanimate such relations, that they may be mutually causes or principles of change to one another, without any exertion of power, or any operation of an agent, strictly so called.” Such relations, for aught that we know, may take place among bodies at great distances from one another, as well as among bodies bodies really or seemingly in actual contact; and they may vary both in degree and in kind, according to the distances between the bodies."

That any thing should be a cause or principle of change to another, without the exertion of power or the operation of an agent, appears to us a palpable contradiction; and we could as easily conceive any two sides of a triangle to be not greater than the third side, as reconcile such a proposition to that faculty of our minds by which we distinguish truth from falsehood. When we see one body the apparent cause of change in another body, we cannot possibly entertain a doubt of the exertion of power; but whether that power be in the body apparently producing the change, or in a distinct agent, is a question to which an answer will not so readily be found. That it is in a distinct agent, we are strongly inclined to believe, not only by the received doctrine concerning the inertia of matter, which, though it has been frequently controverted, we have never seen disproved, but much more by considering the import of an observation frequently introduced to prove the direct contrary of our belief. "We cannot be charged (says the writer whom we have just quoted) with maintaining the absurdity, that there may be an effect without a cause, when we refer the fall of a stone to the ground, and the ebbing and flowing of the sea, to the influence of the earth on the stone, and of the sun and moon on the ocean, according to the principle of general gravitation."

We admit the truth of this observation, provided the influence of the sun and moon on the ocean be possible; but, to us at least, it appears impossible, and is certainly inconceivable. The influence of the sun and moon can here mean nothing but the action or operation of the sun and moon; but if these two bodies be inanimate, they cannot act at all, in the proper sense of the word; and whatever they be, it is obvious that they cannot act immediately on an object at such a distance from them as the earth and the ocean. If they be the agents, they must operate by an instrument, as we do when moving objects to which our hands cannot reach; but as it has been shown elsewhere (see Metaphysics, no. 199, and Optics, no. 63, Encyc.), that neither air, nor ether, nor any other material instrument which has yet been thought of, is sufficient to account for the phenomena of attraction and repulsion, it is surely much more rational to conclude, that the ebbing and flowing of the sea are produced, not by the influence of the sun and moon, but by the power of some distinct agent or agents.

What those agents are, we pretend not to say. If the Supreme Being himself be the immediate author of every change which takes place in the corporeal world, it is obvious that he acts by fixed rules, of which many are apparent to the most heedless observer, whilst the discovery of others is reserved for the reward of the judicious application of the faculties which he has given us. If he employs inferior agents to carry on the great operations of nature, it is surely not difficult to conceive that the powers of those agents which were derived from him, may by him be restrained within certain limits, and their exercise regulated by determined laws, in such a manner as to make them produce the greatest benefit to the whole creation. Nor let it be thought an objection to this theory, that the changes which take place among bodies at great distances from each other, vary both in degree and in kind according to the distances; for this variation, which we acknowledge to be a fact, appears to us wholly unaccountable upon any other hypothesis than that which attributes the different changes to agents distinct from the bodies themselves. Did we perceive all the particles of matter, at all distances, tending towards each other by a fixed law, we might be led to consider mutual attraction as an essential property of that substance, and think no more of inquiring into its cause, than we think of inquiring into the cause of extension. But when we find that the same particles, which at one distance seem to attract each other, are at a different distance kept asunder by a power of repulsion, which no force, with which we are acquainted, is able to overcome, we cannot attribute the principle or cause of these changes to brute matter, but must refer it to some other agent exerting power according to a fixed law.

It is the fashion at present to despise all metaphysical enquiries as absurd and useless; and on this account we doubt not but some of our readers will turn away from this disquisition with affected disgust, whilst the petulant and unthinking chemist, proud of possessing the secrets of his science, will deem it superfluous to inquire after any other natural agents than those of which he has been accustomed to talk. But with the utmost respect for the discoveries made by modern chemists, which we acknowledge to be both numerous and important, we beg leave to observe, that though these gentlemen have brought to light many events and operations of nature formerly unknown, and have shown that those operations are carried on by established laws, none of them can say with certainty that he has discovered a fugitive agent. The most enlightened of them indeed pretend not to have discovered in one department of science more than Newton discovered in another; for they well know that agents and agency cannot be subjected to any kind of physical experiments. Our very notions of these things are derived wholly from our own consciousness and reflection; and when it is considered what dreadful consequences have in another country resulted from that pretended philosophy which excludes the agency of mind from the universe, it is surely time to inquire whether our consciousness and reflection do not lead us to refer real agency to mind alone. Let this be our apology both to the real and to the affected enemies of metaphysics for endeavouring to draw their attention to the present question. It is a question of the utmost importance, as well to science as to religion; and if the laws of human thought decide it, as we have endeavoured to show that they do, we may without hesitation affirm, that the impious philosophy of France can never gain ground but among men incapable of patient thinking.