ranked in this class, because they "exist only as properties of some intelligent being."

Here seems to be some confusion of thought, and we do not know whether to ascribe it to Dr. Wilson, or to some other author from whom his language seems to imply that he has cited it. But at any rate, it is his by adoption. In the first place, time and space are not properly classed with lines, surfaces, and other abstractions of the mathematicians; for time and space are real and independent existences. They are not, indeed, "substantial existences," if "substantial" here means "material." But their existence is independent and necessary, inasmuch as we not only conceive of their separate existence, but we believe it, and cannot help believing it. The reality of pure space, extending without limitation be yond the bounds of our existing universe, is as clear a belief as any that can be present to the mind; it is even a necessary belief, which that in the reality of the universe is not, for I can conceive of the non-existence of matter, but I cannot conceive of the non-existence of space. And so of time. On the other hand, lines, surfaces, and angles are mere abstractions, which we can indeed conceive separately, but which we cannot conceive as existing separately, their independent existence wholly transcending the power of thought. Exist ence cannot be affirmed of them, but only of the bodies, or of the pure space, to which they belong.

Accordingly, we should rank time and space, along with minds and bodies, as realities of being. Lines, angles, &c. should be classed with justice, virtue, and the like, as abstractions, or, if such phraseology be preferred, as realities of truth; while the axioms of knowledge certainly should not be ranked under either of these heads, but should form a third class. These are not realities of either sort, but they are truths; they are not conceptions, but judgments.

The distinction here adopted by Dr. Wilson seems to coincide very nearly with that proposed by Hume, but to be less definite, and to be expressed in language far more ambiguous. Hume divides all things knowable into two classes, relations of ideas and matters of fact; all abstractions come under the former denomination, all actually existing objects and all

events, under the latter. This distinction is at once precise and unambiguous, while a volume would be needed to expose all the ambiguities which lurk under the terms real, actual, reality, &c. Reality can be affirmed of a tree, a government, a virtue, or an angle, but of each in a different sense; and the confusion surely will not be cleared up by trying to reduce all the different kinds of reality to two.

It is only in the Preface, and in a brief introduction to his work, that our author enters into any discussion of the nature of logic, of the limitations of its province, and of the common objections to the study of it which are founded upon misconceptions of these two points. Because these objections and misconceptions are so common, and are sanctioned by so high authority as that of Locke, Reid, Stewart, and John S. Mill, we should have been glad to see them considered at greater length; for science cannot advance, nor can the portion of it which is already determined be successfully taught, unless its objects are defined with the utmost precision, so that it can be relieved from the unjust reproach of failing to accomplish what it never even professed to perform. Having already touched upon this portion of the subject, we cannot resume it at length; but there is one objection, more frequently and pressingly urged than any other, which merits some comment.

"It must be granted," says Mr. Mill, "that in every syllogism, considered as an argument to prove the conclusion, there is a petitio principii." For, he argues, we cannot syllogistically prove that the Duke of Wellington is mortal, except by previously assuming that all men (the Duke of Wellington himself included) are mortal; and having assumed thus much in the major premise, the conclusion is no proper inference, no affirmation of a new truth, but only a repetition of what we have just taken for granted. Hence, it is argued, "no reasoning from generals to particulars can, as such, prove anything; since from a general principle you cannot infer any particulars, but those which the principle itself assumes as foreknown."

De Morgan answers this sophistry by saying: "Inference does not give us more than there was before; but it may

make us see more than we saw before." And again: "It is not that the consequence follows from the premises, but that our perception of the consequence follows our perception of the premises," which makes the reasoning valid and useful. Thus, the whole science of geometry, which contains so many and so recondite truths, that very few even of the professed mathematicians are acquainted with all of them, is certainly contained in, that is, is necessarily deducible from a very few axioms and definitions, which are so simple and obvious, that the learner often smiles contemptuously when he first hears them announced. De Morgan adds: "Persons not spoiled by sophistry will smile when they are told, that, knowing two straight lines cannot enclose a space, the whole is greater than its part, &c., they as good as knew that the three intersections of opposite sides of a hexagon inscribed in a circle must be in the same straight line. Many of my readers will learn this now for the first time"; and, he continues, with his customary insufferable air of smartness and triumph: "It will comfort them much to be assured, on many high authorities, that they virtually knew it ever since their childhood. They can now ponder upon the distinction, as to the state of their own minds, between virtual knowledge and absolute ignorance."

But we go much further. It is not true that the particular truth is always affirmed, or recognized by the mind, before the general truth is admitted. In most cases, no doubt, the general maxim is the result of our previous examination of all the particulars; we affirm of all, because we have already satisfied ourselves of each. In these cases, the general truth is obtained by induction. But sometimes this process is reversed; the universal maxim is sometimes obtained, not by induction, but by general considerations, or a priori reasoning. Then, we may save ourselves the trouble of examining the particular case, and at once affirm the particular as a (logical) consequence of the universal truth. It is not by induction, by actually measuring all triangles, that the mathematician becomes convinced that "the three angles of any triangle are equal to two right-angles." But having previously established this general truth by demonstrative reasoning, he immediately affirms it of any particular triangle which

he may be considering, though he has not measured it, and though, by the nature of the case, that is, by the inaccessibility of the angles, — it is impossible that it should be measured. The astronomer erects a triangle having for its basis the diameter of the earth's orbit, and for its apex the position of the nearest fixed star; and having actually measured the two angles at the basis of this immense figure, he immediately deduces from the general proposition just mentioned the size of the angle at the apex, and the distance of that apex from the earth, two quantities which it is evidently impossible to measure directly. So, also, the skilful mathematician demonstrates the impossibility of squaring the circle, and then immediately rejects any pretended solution of the problem which is offered to him, without needing to examine and confute the fallacious reasoning adduced in its support.

The utility of the study of logic, considered as a branch of academic discipline, seems to us to depend on the fact, that it fastens the learner's attention closely upon the main points of the argument, or the logical train of thought, in everything which he reads or hears, and teaches him to subject this to a rigid process of analysis, which lays bare any sophistry that it may contain. He is thus led to neglect, or to rate at their proper value, the verbiage, the irrelevant matter, the unnecessary amplification, the appeals to the passions, and all the other arts of the sophist and tricks of the rhetorician and blunders of the sciolist. He thus has a divining-rod put into his hands, which saves him from the risk of digging where no water is to be found. Logic does not directly teach us how to reason well; it is only a generalization of the forms and a specification of the laws under which all good reasoning must exist. But indirectly this science is of the highest utility as an art; the habit acquired by the frequent practice of logical analysis and the constant application of logical rules is invaluable in all study and investigation. We do not deny that some persons reason well who have never acquired this habit, just as they often write well though they may never in their lives have opened a book on grammar. But as a general rule, the elements of a correct style are not given by inspiration, nor are long trains of consequences de

duced with precision and accuracy from a few premises, by intuition. Reasoning is not, as some worthy persons seem to imagine, merely a weapon of disputation, whose sole or chief use is in controversy. It is the only organon for the discovery of all truth which lies beyond the narrow precincts of direct observation and experiment; and even observation and experiment, as we have already shown, cannot be practised to any good purpose, or made the basis of anything except the shallowest empiricism, unless they are forearmed and guided by sagacious anticipations and correct logic. The study is not without its effects upon the style of those who are proficients in it. By fastening attention upon the matter rather than the manner, upon the evolution of thought rather than the display of words, it leads to the formation of a compact, nervous, and pointed style, which is the very opposite of the shallow diffuseness, the rambling and ill-jointed rhet oric, which is now so much in vogue. Far the most forcible and concise writers of the present day in Great Britain are Dr. Whately, Sir William Hamilton, and Professor De Morgan, all of whom are best known, in this country at least, by their contributions to logic. We are happy to add, that the style both of Mr. Tappan and Dr. Wilson is marked by the same characteristics.

ART. VI.-Works of BENJAMIN FRANKLIN. Edited by JARED SPARKS. In Ten Volumes. A New Edition. Boston: Whittemore, Niles, and Hall. 1856. 8vo.

SIXTY-SIX years have elapsed since the mortal remains of Benjamin Franklin were placed beneath a tablet in the Friends' Cemetery in Philadelphia; the granite obelisk which marks the last resting-place of his parents is a familiar object to all who walk the streets of his native city; but these graves, thus humbly designated, were, until a few days since, the only visible monuments of a name as illustrious as it is