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intelligible, to a result uniformly correct. Now, what is the objection?-briefly and substantially it is this,—the conclusion is not attained by any known process of logic. This would be fair enough if any known process of logic could, from the same conditions fairly used, prove the possible fallacy of the conclusion: to do this, however, we have to observe, not only the ascertained process must be tried by this test, but the secret condition must be included. This is, by the hypothesis, impossible. Next, it is to be considered that if Berkeley's view be correct, the true result is obtained by a compensation of errors. It is evident that there can be no fallacy in the reasoning of the process, unless this compensation can be shown also to be accidentalthis is not alleged, and the argument correctly stated on his view would be this, there is a certain method of reasoning which discovers truth by the compensation of opposite errors. The fact is this, the initial statement makes an omission, which the conclusion rectifies by a necessity arising from the hypothesis itself. But if the compensation is just, and the uniform result of a process, there is no fallacy; it is simply one of the processes of reason in the discovery of truth. It is either a new law, or reducible to an old law of logic; but the argument, which when correctly used leads to a true conclusion, is not a sophism. It is curious enough that Berkeley's objection to the calculus is, in fact, the principle into which Carnot resolves it.

But indeed it is not difficult to perceive that the errors supposed are merely resources of calculation-the actual logic contains no contradiction, which is really to be found in Berkeley's mistake as to the intent and real process of the argument. Berkeley's main objection, may, for clearness, be resolved into two. That the reader, who is not conversant with such questions, may understand these, a simple statement of the nature of the reasoning to which he objects will be necessary. If certain variable quantities are so related to each other, that as one of them is taken greater or less, the other will also increase or diminish according to some ascertained law, and that it is desired to ascertain the state which is the limit of those changes. A statement of the known conditions is made in a form called an equation, which is supposed to represent the variable quantities, together with their supposed increments and decrements. This equation is not, as in common algebra, a statement in which all the values are supposed fixed, and serving to ascertain the precise value of the unknown from the given quantities. It is, in fact, the statement of a hypothesis essentially implying the contrary, and made for the purpose of reasoning on a state of continued change; consequently, it represents an initial state, from which a final state is to be deduced: therefore, it is evident that the very law of reason to which Berkeley objects, is the accurate logic of the question; for, a hypothesis must be made in the first equation, which must disappear in the last. The question is,-if such increments go on continually lessening, and may be assumed therefore indefinitely small or nothing, what will be the consequence i But there is in the objection, to which this is the answer, another sophism: Berkeley attempts to show that the equation is false, and, strictly speaking, it is so, according to the laws of common algebra; tried by the assumed test it would be found to want certain quantities. But these are the very quantities which must necessarily go out by the very principle above stated_terms which would add much complication in the reasoning, and have no effect in the conclusion, and have, therefore, by a universal rule of reason, been omitted in a compendious process, which does better without them. Now, one of Berkeley's arguments consists in a calculation by which he makes these quantities appear,—which the ordinary method of fluxions does not exhibit, He thus appears to falsify the ordinary process. But the reply to this objection is, that the omission of certain considerations, for the convenience of an argument, in which it is essentially implied that they are unimportant, is not a fallacy. The equation, in its first form, is a statement of the effective conditions of a question; and all Berkeley's objections could be met by simply adding et cetera. So far relates to the algebraic method: the answer is, however, completed by a consideration which will lead to the other point. The reason why the omission is of no importance is this: that the variables being supposed to pass through all the successive states of magnitude, while the incre. ments, or decrements, diminish to a certain state, in which they cease to exist--the question is, to determine or prove this state. And this is determined by assuming the symbol expressing the increment to be = 0, the equation must then be such as to indicate the sought limit; and the quantities which were involved in the omitted part of the difference, must have ceased to exist. If the question were, what would be the result, supposing the variables to stop half wayall Berkeley's reasoning would be conclusive, so far as it applies. Against the conclusion itself, he offers another curious cavil. But the mathematical reader does not require this exposition; and for the reader unversed in such considerations, we have perhaps gone to the utmost limit of clearness. Berkeley's objection to any conclusion being founded on a ratio, of which the quantities are evanescent, has been anticipated by Newton, in a scholium, contained in the first section of the first book of his Principia. We shall, therefore, here conclude with the observation, that Newton's own statement of the intent of his method should have set Berkeley on a juster course of reasoning. " But because the hypothesis of indivisibles appears more hard, and, therefore, that method has been considered less geometrical, I have thought fit rather to found the demonstrations of the following propositions upon the first and last sums and ratios of nascent and evanescent quantities; that is, to the limits of those sums and ratios."* It is, if just, curious enough, that Berkeley's objection, to what he calls an erroneous equation, might be obviated by the addition of an “ &c.

If the reader should desire to see Berkeley's powers to advantage, he must look for them in his attacks upon the sophistry of others,-in the Minute Philosopher, and in portions of his Theory of Vision.

We have, in this memoir, sufficiently noticed the first of these excellent compositions.

*“Sed quoniam durior est indivisibilium hypothesis, et propterea minus geometricæ censetur ; malui demonstrationes rerum sequentium ad ultimas quantitatum evanescentium summas et rationes, primasque nascentium, id est, ad limites summarum et rationum deducere.

His new theory of vision is curious for the mixed evidence it gives of the disposition of his understanding to the illusions of his own subtlety, and the clearness of his apprehension when judging of the fallacies of others. It indeed seems not a little curious how much of the sounder portion of his conclusions appears to be the result of his more unsound reasonings. In his disproof of the external world, he dissipates the erroneous doctrines of abstract ideas. His Theory of Vision, evidently composed for the same purpose, in the same manner draws from him the most admirable details, and the rectification of old fallacies. But the subject occupies much of the attention of the present time, and would lead us too far for any purpose connected with these memoirs.

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Of MICHAEL CLEARY very little is satisfactorily known, and we should, for this reason, consider ourselves absolved from any notice of him, but for the place which he occupies in the history of our Irish literature. This topic, so far as relates to the commencement of the present division of these memoirs, must be regarded as rather belonging to the antiquarian than to the historical biographer. But it is necessary, as briefly as we may, to account for our neglect of the very numerous poets who lived in the earlier half of the 17th century, and whose writings are yet extant. For this there are sufficient reasons: there are no materials for their personal histories, and their writings are not extant in any published form. The great celebrity of a renowned author of unpublished poetry might impose it upon us to give some account of his works; but great indeed must be the importance of the writings to which such a tribute would be excusable here, and whatever may be the collective worth of the bards and historians of the period included in these remarks, there are, individually, few instances which demand the distinction of a memoir. We might, by the help of some very accessible authorities, easily continue in this period the barren list of unknown poets, which helped to fill the vacuity of our previous period; but, on looking very carefully over those materials, we are unable to perceive what purpose would be served by such a waste of our space, already contracting too fast for the important matter yet before us.*

In that portion of the introductory observations allotted to the gene

• We should here apprize the reader that the seeming disproportion, between the space which we have given to the ecclesiastics and the literary persons belong. ing to this period, is to be explained by the fact, that the most respectable of our writers hold also a prominent rank among our ecclesiastical dignitaries of the same period.

ral consideration of Irish literature, we have endeavoured to give some general notices of the character and importance of this unknown but numerous class of writings, which lie concealed, though not inaccessible, in the archives of colleges, and in public and private libraries. The individual whose name affords us occasion for these remarks, was a native of Ulster, and a Franciscan friar. He was early in life known as learned in the antiquities of his country, and as having a critical acquaintance with the Irish tongue. These qualifications recommended him to Mr Hugh Ward as a fit person to collect information for his projected history of the Irish saints, for which purpose he was sent to the Irish college in Louvain. The materials which he collected in the course of fifteen years passed into the hands of Colgan, by the death of Ward.

Cleary at the same time collected materials, which he reduced into three volumes of Irish history, of which the letters are mentioned by Ware.

He was one of the compilers of the “ Annals of Donegal”—a MS. of the greatest authority in the antiquities of Ireland. His last work was a Dictionary of the obsolete words in the Irish Language, published in 1643, the year of his death.

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COLGAN was a Franciscan in the Irish convent of St Anthony of Padua, in Louvain, where he was professor of divinity. He collected and compiled a well-known work of great authority among antiquarians, and of considerable use in some of the earlier memoirs of this work.

His writings were numerous; and all, we believe, on the ecclesiastical antiquities of Ireland. His death, in 1658, prevented the publication of many of them.

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KEATING, well known as the writer of an antiquarian history of Ireland—of great authority for the general fulness with which it preserves the traditionary accounts of the earliest times, though liable to some rather hasty censures for the indiscriminate combination of the probable and improbable into one digested narrative, and in the language of implicit belief. Such a work is, nevertheless, the most certain and authentic record of the ancient belief of the learned and unlearned of the land; and if the facts be not true in themselves, they evidently characterize the mind of a period, while, generally speaking, there is every reason to give credit to the more important parts of the narrative; and, above all, to the genealogical traditions of the ancient families of chiefs and kings. It is by no means a just inference that

they who entertain superstitious notions, and believe the absurdest mythological fables and traditions, are, therefore, to be discredited in their statements of the ordinary facts of history; in the former, both the senses which observe, and the faithfulness which records, are wholly uninvolved the facts belong to a different class of things, and a man may believe a fable, yet speak truth in the concerns of life. When a historian's authority, or the authorities on which he writes, are to be questioned, the question must be,-is the relation honest, and are the facts such as to admit of natural error? Now, in Keating's history, the line of demarcation between truth and error will, in the main, be easily seen. It will be at once observed, that the mere fact of the existence of a large body of ancient literature, with all the extant remains and traditions of Ireland, undeniably prove the existence of some old state of civil order different from anything now existing, and as far removed from the savage state. Such a state of things must needs have left some record stamped with the form, and having at least all the main outlines of the truth; and it may be asked where this record of which the absence would be more improbable than any part of Irish history-can be found, if not in those very traditions which are the genuine remains of Irish literature, and the authorities of old Keating. The facts are, it is true, often strangely involved with fable; but there is no instance in which the discrimination of an unbiassed intellect cannot at once make the due allowance.

Keating studied for twenty-three years in the college of Salamanca. On his return to Ireland he was appointed to the parish of Tybrid, which he soon resigned. He is said to have been driven into concealment by the hostility of a person whose mistress he excommunicated.

This person having threatened to murder him, he took refuge in a wood between the Galty mountains and the town of Tipperary; and in this retirement he wrote his history in the Irish language.

He was buried in the church of Tybrid, founded by himself and his successor, in 1644.

His history was translated into English by a Mr Dermod O'Conor, whose version is considered to have many inaccuracies. Another translation was since commenced by a Mr William Halliday, an Irish scholar of great reputation. His task was cut short by an early death. He had proceeded so far as the Christian era, and published a thin octavo, which has induced much regret among antiquarians that he did not live to complete his undertaking.

Keating's other writings are of slight importance they are a few poems and professional treatises.

The Hon. Robert Boyle.

BORN A.D. 1626.-DIED A.D. 1691. The account of the early infancy of this most illustrious Irishman has been written by himself under the title of Philalethes. This period of his life was subject to more casualties and changes than are often knowu to occur in the maturer age of the generality of men; and this,

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