'A great change has been effected at Oxford of late years, and almost solely through the labours of Dr. Whately. The logical systems taught in King's College, and University College, London, since their respective establishment about twenty years ago, have been of an eclectic character, partly philosophical, and partly formal or syllogistic.'

In the last chapter of the volume, we have very brief notices (too brief indeed, generally, for the purpose) of a number of modern logical publications. Among the rest is Mr. John Mill's 'System of Logic.' Our author gives no definite opinion on the views of this talented writer, respecting the principle on which we reason; this (Mr. Mill) holds to be-not from generals to particulars, but from particulars to particulars, without passing through generals. Thus, he says, that we do not argue that the Duke of Wellington is mortal, because this is a general law, i. e., because all men are mortal, but the mortality of John, Thomas and Company, is the whole evidence we have for the mortality of the Duke of Wellington. Nor does the professor give any judgment on Mr. Mill's application of his doctrine to mathematical evidence, which he pronounces to be by no means necessary or intuitive. Axioms,' (mathematical) says Mr. Mill, are experimental truths, generalizations from observation. Two straight lines cannot inclose a space, is an induction from experience.' We cannot now stay to controvert these positions of Mr. Mill. We must content ourselves with simply recording our dissent from them. Mr. Mill's theory of causation, however, our author speaks decidedly; and we must say that, on reading the book when it came out, we thought it faulty. We venture to affirm,' says Mr. Blakey, that this is a very unsound part of his system. It is ill reasoned, and presents flagrant inconsistencies and contradictions at every turn. We feel confident that when the question as to causation is dispassionately examined, and upon strictly philosophical grounds, it will be found that there is a principle implanted in human nature, of steady and unerring operation, that refers every true cause to some power, faculty, or mental influence. This position, we conceive, is as susceptible of complete demonstration, as anything in the whole circle of human knowledge can manifest."

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Mr. Blakey enumerates some more recent logical treatises, and among them those of Mr. Thomson, Mr. Boole, Mr. Baynes, and Mr. De Morgan. Of the latter, all he says is, that it is a treatise of acknowledged ability, and the chapters on probabilities and fallacies are the two most interesting in the book;' from which the reader would not know that it is based on the principle of every term having its negative, and that its

object is to reduce logic decidedly to a mathematical calculus. A passing notice of the works of Hedge, True, and Tappan, published in the United States, closes Mr. Blakey's volume; which, though it certainly will not furnish the student with that close and critical information on systems which he might expect from such a work, may at least serve in some measure to introduce the subject of logic to the general reader. If not remarkable for learning on a branch of study which presents a field for the most varied attainments in literature and science, the book is marked by a considerable amount of good sense and moderation, and it is always on the side of morality and religion.

The last work announced in our heading, is by Mr. Baynes. It extends to but eighty pages, with an Appendix; but it is the only one of the three which can be regarded as at all a scientific treatise. The author is known to the public as the translator of the Port Royal Logic.' His work, 'An Essay on the New Analytic of Logical Forms,' was exclusively composed, he informs us, from his notes of Professor Sir William Hamilton's lectures, at Edinburgh, in the session 1845-6; and it is published as originally written, with a very slight exception or two, and the addition of some foot-notes, and some historical details in the Appendix. It is the essay which gained the prize proposed by Sir William, in the year 1846, for the best exposition of the new doctrine propounded in his lectures, and it has his express sanction for its publication. As the volume is by no means of a popular character, and deals with the subject in a very condensed and technical manner, our notice of it must necessarily be brief.

The main principle of the treatise, as an exhibition of a new analysis of logical forms, is the thorough-going quantification of the predicate,' a principle quite opposed to the old orthodox Aristotelian doctrine of the schools. Thus Stahl, an Oxford writer of the 17th century, says that, if you add a universal sign to the predicate, your proposition will be false.' The requirements for the essay, it appears, included a statement of 'what logic postulates as a condition of its applicability;' and accordingly our author very properly chooses to begin with this essential element in the theory. He states that the fundamental postulate of logic is, That we be allowed to state in language what is contained in thought.' Logicians allow that the subject of a proposition has a determinate quantity in thought, and this is expressed in language accordingly: It is to the predicate,' says Mr. Baynes, that we have to vindicate an interest in the postulate coequal with that of the subject.' But we must let the author speak for himself:

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The predicate has always a determinate quantity in thought. A notion of holding the place of predicate in a proposition has always such determinate quantity. This will appear from what a notion is. It is the cognition or idea of the general attribute or attributes in which a plurality of objects coincide. This involves the perception of a number of objects, their agreement the recognition of their points of similarity, and their subjective union by this common attribute. When we bring an object under a notion, or predicate of it that it belongs to such a class, we must know that it occupies a certain place in that class. In other words, if we comprehend what we utter, every notion holding the place of predicate in a proposition must have a determinate quantity in thought. This is always involved in predication, which is the expression of the relation in which a notion stands to an individual, or two notions to each other. this relation were indeterminate, if we were uncertain whether it was of part, or whole, or none, there could be no predication. The very fact of predication is thus always evidence that the predicate notion holds a relation of determinate quantity to the subject. In other words, we think only as we think under some determinate quantity, for all thought is comparison of less and more, of part and whole. All predication is but the utterance of thought. All predication must, therefore, have a determinate quantity.'

If

Our author goes on to show that as the quantity exists in thought, it must be expressed in logic by language, and that the predicate notion will be definite (universal or individual), or indefinite (particular), as the subject notion is greater, equal to, or less than the predicate. We fear that some of Mr. Baynes's illustrations will sound rather odd in unlogical ears; but we will venture to give specimens:- All man is some mortal, then, is a case in which the subject notion is less than the predicate, as mortal includes much more than man. If we say

all man is all rational,' we make the subject equal to the predicate. Again, in some mortal is all man,' the subject mortal is greater than the predicate man, and we attribute the whole predicate to the subject as a part only of its extension. Our readers, if they chance to have the slightest tincture of logic, will now see by the application of the universal and particular signs to the predicate what is meant by its quantification.' They need to have chopped very little logic to understand this mystery.

Mr. Baynes next asks why the quantity of the predicate is not expressed in common language? And he replies that the reason is to be sought in the end which language proposes, namely, to render at once intelligible by signs the thing signified. When we say 'every horse is an animal,' it is not necessary to say that there are other animals besides horses, for the extension of the general term is understood by all men. All know that the predicate here is affirmed of its subject only in some part of its (the predicate's), extension. Hence the quantifica

tion, not being necessary, is usually omitted. But in logic the case is different from that of common language, for logic seeks perfection.

Our readers must pardon us for dosing out to them a little more logic. Our author (whose book is really written with great clearness and ability) goes on to apply this said principle of the formal and expressed quantification of the predicate,' to propositions, and to the doctrine of their conversion-having first, however, condemned the ordinary orthodox doctrine of illative conversion, whether simple, accidental, or contrapository, or what not. If you quantify the predicate, you at once bring two notions of different extension into equality; for 'all predication is an equation of subject and predicate.' By quantification the sphere of an individual object in a notion is marked out, and that sphere becomes absolutely convertible with the object; thus, all man is some animal, is simply converted, without reducing the quantity of the proposition, to some animal is all man. Barbarous and outlandish as this language will seem to those of our readers who are not initiated, others will at once see in these examples at least a lucid exposition of the principles of the New Analytic.'

Next follows the consideration of the influence of the principle of the quantification of the predicate on the doctrine of categorical syllogisms; in short, it reduces their general laws to one, abolishes their special laws, and amplifies the valid forms of reasoning. After stating a variety of objections to the common doctrine of syllogistic mood, figure, and reduction, our author proceeds to give the 'one supreme canon of the new analytic which potentially contains the whole doctrine of categorical syllogisms.' The canon is: Whatever relation of subject to predicate subsists between either of two terms and a common third term, with which both are related, and one at least positively so that relation subsists between these two terms themselves.' This canon involves the whole doctrine of categorical syllogisms; and is to them an all-sufficient and exhaustive code of law, observing which none can be formally invalid.' Here follow a variety of examples by way of illustrating this reduction of syllogistic rules to this single canon, the special laws which govern particular classes of such syllogisms being first dealt with, but for the study of which we must, for brevity's sake, refer our logical readers to the book itself. By the way, it may be remarked that the fourth logical figure, or model figuration (Galen's), is rejected, the three first figures being to be regarded as exclusively competent in logic. The syllogistic form of expression in the New Analytic' may be seen from an example or two. Thus the second figure is made to have either an affirmative or a negative conclusion, while in the common logic

it only has the latter. All A is all B; all C is some B; all C is some A. Again :-All A is all B; no C is any B; no C is any A. In the third figure, also, we have here both universal and particular conclusions, contrarily to the ordinary doctrine of modal figuration.

Our author goes on to show that the Analytic' doubles the number of propositions, making them eight instead of four. The old notation A, E, I, O, however, is retained, the new forms being indicated by certain combinations of these letters. The work closes with a new symbolical notation, in the form of a table, which is exemplified by syllogisms in the first figure. The following is the author's recapitulation :

'We set out with the principle of a quantified predicate. We have noticed some things by the way not immediately connected therewith; but recurring to it we have endeavoured to vindicate that principle. We have indicated its influence on propositions in abolishing the complex doctrine of conversion; its influence on categorical syllogisms, in reducing their laws to a higher simplicity, and amplifying their valid forms,-in short, by correcting what was false, and supplying what was wanting; and thus securing to logic a higher degree of formal exactness, realizing for it a higher degree of scientific perfection. The new analytic accomplishes this by being true to its office, and fully investigating the form of thought. The form, the whole form, and nothing but the form of thought, is indeed the bannered motto which it bears on its triumphant way. True to its purpose it advances over the whole region of formal thought, conquering and to conquer; destroying the false landmarks which had been set up by the early discoverers of that territory; repressing the incursions which were continually made into neighbouring kingdoms; destroying the border ground by determining for ever the frontier line; dethroning the potentates who had intrenched themselves in its high places, and long there exercised a usurped authority; recalling from their long exile the true lords of the soil; re-establishing the laws on which their rights were founded, and enforcing strict obedience to these in every province of the empire. Thus, though its path is in some respects as the path of the destroyer, in a higher and truer sense it is the path of peace; for through its instrumentality there breaks at length upon this long distracted region the golden age of simplicity and order. And anarchy, the result of laws neglected and rights ignored, is for ever abolished in the establishment of perfect harmony-a harmony, the result of law clearly expounded and rigidly obeyed throughout the entire empire of formal thought.'

Our readers will think this passage rather florid from a cool-headed logician-a sort of man who is generally looked on as an abstraction of humanity, a being all head and no soul. It reminds us of some very occasional passages of Kant, who had an imagination when he chose to use it. Mr. Baynes is sanguine enough, it seems, of the speedy triumph of the New