MR. URBAN, Bath, May 11. THAT there is much of needless complexity, and a useless effort at a sort of mechanical certitude, in the differences of mood and figure appertaining to the Aristotelian logic, will be denied, I think, by few. The objections to the system, however, as a whole, must chiefly have arisen from the misuse and the abuse of logical forms in ages of ignorance and barbarism, for they seem to proceed on the supposition that, if we give any place to the logic of the schools, all converse should be turned into debate, and every reason be stated syllogistically. The objections first started have been continued by the fashion to run down what has been once depreciated, and in some quarters, I suspect, by the lurkings of envy toward literary rivals. Thus, even that eminent man Dr. George Campbell '(Rhetoric, b. 1, ch. 6) amid a heap of words inveighs against syllogism as if designed for an instrument of original discovery, rather than of detection of pretended truths, and confirmation of real truths already known. The following is the first example at which he carps: "All animals feel; all horses are animals; therefore all horses feel." Hereupon he remarks, "It is impossible that any reasonable man, who really doubts whether a horse has feeling or is a mere automaton, should be convinced by this argument, for," &c. &c. But what reasonable opponent of so strange a notion would not first inquire of the doubter whether he did or did not believe that animals are sentient beings. If he admitted their power of sensation, the syllogism conclusively shows the folly of his doubt. If he denied the existence of that power, no such syllogism could ever be formed against him; but he

would be addressed from other topics, tending to show that animality and sensibility are invariably associated. If, indeed, he made an exception of horses, while allowing sensation to others similarly made and moving creatures, the reasonable course would be no longer to argue with him. And this last remark I think a sufficient answer to Dr. Campbell's further objection," It is possible that one may believe the conclusion who denies the major." But men begin to see the folly of pretending to discard that without which they can no more reason than they can talk without air.

Your correspondent who signs D. S. (May, p. 481,) has done that • justice to logic which Dr. Whateley, its professed expositor, has failed to do. If, to quote your correspondent's words, the archbishop asserts of a certain problem, that "a logical demonstration of it is impossible," assuredly the master himself would have disclaimed such an exposition, and have authoritatively pronounced that his rules are universally true or utterly fallacious. Professor Newman also (late of Bristol College), in his instructive lectures on logic, article Syllogism, speaks of the right reverend logician as under a mistake, observing of the celebrated argument against infinite divisibility, that it was Dr. Whateley's.... business to reduce (the sophism to syllogistic) form, and to show us that, when reduced, it offended some of the Aristotelic rules (whereas, says Mr. Newman, it depends) on a false premiss suppressed." This premiss, a mathematical one, he adds mathematical also is the solution by De Crousaz given us by your correspondent. But mathematics, I confess, are beyond my ken. Conceiting, too, that mathematics rest on logic, that consequently there must be some plain mode of treating every question, not purely one of computation, I submit to you, sir, what I have never yet seen, and in the hope of its being acceptable and satisfactory to many merely literary readers like myself, a simply logical arrangement and solution of this far-famed sophism, here veiled under the form of a little apologue.

;

It happened in heroic times that swift-footed Achilles once thought to catch a tortoise which was crawling

off as fast as its little legs could carry it from the sight of man, that common foe of bird and beast and every creeping thing. The tortoise, however, having the start of his pursuer on the ground, and ground, as ancient sages say, being infinitely divisible, and infinite divisibility, as deeper investigators show, compelling all beings to mince their movements infinitely, it came to pass that Achilles, hindmost at setting out, could never, with all his striving, overtake the tortoise first ahead, thus verifying the adage, slow and sure!

A single perusal I imagine, sir, of .this tale-told Sorites, will enable any intelligent man to perceive the falsehood of the second intermediate premiss, since, allowing even the truth and applicability of the first, it is manifest that nothing hinders the swifter at his earliest very near approximation to the slower from making at one effort so much way as either to reach the slower or leave it far behind. But, though matter be infinitely divisible, it is false incontrovertibly that either Achilles or the tortoise, either man or beast, can infinitely divide; the very dimensions of their instruments of motion soon bring them to a stand-still; and only an eternal power is adequate to an endless operation. The first intermediate premiss, therefore, is altogether dubious, the second is a false assumption based upon a doubtful medium, the conclusion contradicts reality, and the design would limit the power of the Almighty.

Before concluding this paper, suffer

me to remark on the unfortunate use of the term infinite in questions of various science, occasioning a vast confusion of ideas; without an end is the simple meaning of the word; but because the word may also signify without any bounds either of beginning or of end, and is thus constantly applied to the Deity, it sounds, indeed, most marvellous to men to hear of infinitesimals and infinite division. Yet are they apt to think even this may be effected as they believe in the existence of a God. But an actually infinite division is a thing impossible, since every division must have a beginning, and on the supposition is never terminated; continue it through countless ages, and it will still have two extremes,

and must be finite; for, though endlessly divisible, no quantity can ever have been infinitely divided. Let infinite, therefore, and its derivation, be confined to their proper subjects; to God, to space, and to duration; and the terms indefinite, interminate, immeasurable, innumerable, and so forth, take their place in questions falling under human comprehension or investigation. The change could at least not injure truth, and would aid the unscientific. Yours, &c.

J. P. BARTRUM.

MR. URBAN, Northampton, Feb. 27. IN the report of the proceedings of the Numismatic Society in your January number, p. 78, I observe a slight mistake relative to the coin belonging to Mr. Alfred Beesley of Banbury. It is stated that on the obverse is an ear of corn, and on the reverse a horse, wheel, &c. with the letters QVANTEO. I have in my possession a gold British coin of similar fabric, with the horse, wheel, &c. on the concave side, and the reverse or convex side quite plain. Respecting the inscription on Mr. Beesley's coin, I find, from a very careful perusal of it, that it reads QVANTE, and the symbolic mark resembles one on my coin, which is without an inscription. In the plate of Symbols on British Coins, given in the Numismatic Chronicle, Nos. 26 and 27 are similar. A coin belonging to Mr. Cuff, and probably from the same die, has been engraved in the 1st vol. of the Numismatic Journal, and described in page 223, No. 8. And in the last edition of Ruding the same coin is again engraved. In both works the reverse is described as bearing a fern-leaf, and not an ear of corn; from the probable imperfection of the coin they differ so far as regards the legend. In the latter publication it is given CAIII, and what has been conjectured to be o, or the symbolic mark, on Mr. Beesley's coin, forms part of the neck of the horse. In the Numismatic Journal they give the inscription CATTI. Two of my antiquarian friends have suggested that QVANTE may probably be intended for CANTI or Kent.

Yours, &c. .

not have remained satisfied with myself had I not published the result of my trying but gratifying labours, which very few, if any, may have the opportunity, if they possess the inclination, to undertake.

Since writing the above your June No. has come to hand. I am induced, from its perusal, to trespass somewhat more upon your patience with a few further remarks.

The mystical rubbish about Noah, and the arkite deities, Mithraic caves, helio-arkite theology engrafted on Druidic rites! the belly of Kúd, and such like stuff, which has really no intelligible meaning, and only serves to nauseate the subject of Celtic antiquities and philology, but is so flippantly put forth by persons who know but little of what they are speaking, and merely follow up the mystification which has so long imposed upon the world and rendered the inquiry contemptible,-should no longer be tolerated. No sooner, however, is an attempt made to give from actual examination a rational and probable definition of ancient languages, manners, and customs, from the remains of a people who are admitted by all to have existed, than a general cry is raised like that of "great is Diana of the Ephesians," glorious is the humbug which has kept the world in the dark, mighty the dreams and conceptions of fanciful men, who have without premises formed the most ridiculous systems, imagined the existence of nations, and, assuming falsehood for fact, deceived themselves and others for ages, by gravely postulating as theorems systems repugnant to common

This is a curiously constructed sentence of negatives, not one of which can S. T. P. prove. The learned Welsh are not Celtic scholars, and S. T. P. probably does not know one. Notwithstanding the tenacity with which most Welsh writers adhere to the idea, it has been repudiated by the learned and eminent Welsh authors and philologists, Edward Llwyd and the Rev. Peter Roberts. The former confesses that he failed to find more than a few hundred words common to both languages, which may be accounted for by neighbourhood and consequent intercourse. Roberts, who compared the two languages, is still more explicit, and says:

"The Irish and Welsh languages are of no more use to the knowledge of each other, than the mere knowledge of the Latin would be to understand the Greek.

"The grammatical structure is radically different. Having formed his opinion from comparison of the two languages, he felt less hesitation in stating the fact which (Welsh) antiquaries had mistaken.'

Bishop Percy, who, although not a Welshman, was an eminent philologist, says, "I cannot think they (the Irish and Welsh) are derived from one Celtic stock."

Professor D. Forbes, eminent as a Gaelic scholar, in your pages, Mr. Urban, clearly demonstrated that there was no affinity, and he is borne out by every sound Gaelic scholar.

I am, therefore, justified in the opinion I have myself formed from actual comparison, and have no hesitation in declaring that such evidence shows the Cymbri and the Gael to be altogether different in origin; that the latter being Celts, the former were of Teutonic or northern origin.

From the positive language in which S. T. P. asserts that it can be shown that the Irish tongue did not exist before the Christian era, we have a right to assume that he is prepared to show it; if not, he has been most indiscreet in making the assertion. Negatives are always difficult of proof; no prudent man will attempt to prove them. Proof here, except by an affirmative showing the period of the origin of the Irish, is impossible.

If S. T. P. would take an Irish dictionary and grammar, and make a