Induction. fcience knows that phyfical truths cannot be compared with moral truths, nor the truths of pure mathematics with either. That the method of induction is a juft logic, has been fufficiently evinced elfewhere (fee Logic, Part III. chap. V. and PHILOSOPHY, n° 73-78. Encycl.), and is now indeed generally admitted. It is even admitted by British philofophers to be the only method of reafoning by which any progrefs can be made in the phyfical sciences; for the laws of Nature can be difcover ed only by accurate experiments, and by carefully noting the agreements and the differences, however minute, which are thus found among the phenomena apparently fimilar. It is not, however, commonly faid that induction is the method of reafoning employed by the mathematicians; and the writer of this article long thought, with others, that in pure geometry the reafoning is ftrictly fyllogiflical. Mature reflection, however, has Appendix led him to doubt, with Doctor Reid *, the truth of the to Vol. III- generally received opinion, to donbt even whether by of the Hifto. categorical fyllogifms any thing whatever can be proved. ty of Man. To the idolaters of Ariftotle we are perfectly aware that this will appear an extravagant paradox; but to the votaries of truth, we do not defpair of making it very evident, that for fuch doubts there is fome foundation. of Sketches We are led into this difquifition to counteract, in some degree, what we think the pernicious tendency of the philofophy of Kant, which attempts have been lately made to introduce into this country. Of this philofophy we shall endeavour to give fomething like a diftinct view in the proper place. It is fufficient to obferve here, that it refts upon the hypothefis, that "we are in poffeffion of certain notions à priori, which are abfolutely independent of all experience, although the objects of experience correfpond with them; and which are diftinguifhed by neceffity and ftrict univerfality." Thefe innate and univerfal notions, Kant confiders as a fet of categories, from which is to be deduced all fuch knowledge as deferves the name of feience; and he talks, of courfe, or at least his English tranflators reprefent him talking, with great contempt, of inductive reafoning, and fubftituting fyllogiftic demonftration in its ftead. As his categories are not familiar to our readers, we fhall, in this place, examine fyllogifms connected with the categories of Ariftotle, which are at leaft more intelligible than thofe of Kant, and which, being likewife general notions, muft, in argument, be managed in the fame way. Now the fundamental axiom upon which every categorical fyllogifm refts, is the well known propofition, which affirms, that "whatever may be predi cated of a whole genus, may be predicated of every fpecies and of every individual comprehended under that genus." This is indeed an undoubted truth; but it cannot conftitute a foundation for reafoning from the genus to the fpecies or the individual; because we cannot poffibly know what can be predicated of the genus till we know what can be predicated of all the individuals ranged under it.. Indeed it is only by afcertaining, through the medium of induction, what can be predicated, and what not, of a number of individuals, that we come to form fuch notions as thofe of genera and Species; and therefore, in a fyllogifm ftrictly categorical, the propofitions, which conftitute the premises, and are taken for granted, are thofe alone which are capable of proof; whilft the conclufion, which the logician pre or tends to demonftrate, must be evident to intuition experience, otherwife the premises could not be known to be true. The analyfis of a few fyllogifms will make this apparent to every reader. Dr Wallis, who, to an intimate acquaintance with the Ariftotelian logic, added much mathematical and phyfical knowledge, gives the following fyllogifm as a perfect example of this mode of reafoning in the firit figure, to which it is known that all the other figures may be reduced :- Omne animal eft fenfu præditum. Here the propofition to be demonftrated is, that Socrates is endowed with fenfe; and the propofitions af fumed as felf-evident truths, upon which the demonftration is to be built, are, that "every animal is endowed with fenfe;" and that" Socrates is an animal." But how comes the demonftrator to know that “ every ani mal is endowed with fenfe?" To this queftion we are not aware of any anfwer which can be given, except this, that mankind have agreed to call every being, which they perceive to be endowed with fenfe, an animal. Let this, then, be supposed the true answer: the next queftion to be put to the demonftrator is, How he comes to know that Socrates is an animal? If we have anfwered the former question properly, or, in other words, if it be effential to this genus of beings to be endowed with fenfe, it is obvious that he can know that Socrates is an animal only by perceiving him to be endowed with fenfe; and therefore, in this fyllogifm, the propofition to be proved is the very firft of the three of which the truth is perceived; and it is perceived intui tively, and not inferred from others by a process of rea foning. Though there are ten categories and five predi cables, there are but two kinds of categorical propofitions, viz Thofe in which the property or accident is predicated of the fubftance to which it belongs, and thofe in which the genus is predicated of the Species or individual. Of the former kind is the propofition pretended to be proved by the fyllogifm which we have confidered; of the latter, is that which is proved by the following: Quicquid fenfu præditum, eft animal. That this is a categorical fyllogifm, legitimate in mode and figure, will be denied by no man who is not an abfolute ftranger to the very firft principles of the Ariftotelian logic; but it requires little attention indeed to perceive that it proves nothing. The impofition of names is a thing fo perfectly arbitrary, that the being, or clafs of beings, which in Latin and English is called animal, is with equal propriety in Greek called wor, and in Hebrew w55. To a native of Greece, therefore, and to an ancient Hebrew, the major propofition of this fyllogifm would have been wholly unintelligible; but had either of those perfons been told by a man of known veracity, and acquainted with the Latin tongue, that every thing endowed with fenfe was, by the Romans, called animal, he would then have understood the propofition, admitted its truth without hesitation, and have henceforth Inductions Induction, henceforth known that Socrates and Mofes, and every thing else which he perceived to be endowed with fenfe, would at Rome be called animal. This knowledge, however, would not have refted upon demonftrative reafoning of any kind, but upon the credibility of his informer, and the intuitive evidence of his own fenfes. It will perhaps be faid, that the two fyllogifms which we have examined are improper examples, because the truth to be proved by the former is felf-evident, whilft that which is meant to be established by the latter is merely verbal, and therefore arbitrary. But the follow ing is liable to neither of these objections: All animals are mortal. Man is an animal; therefore Here it would be proper to ask the demonftrator, up- Yet by a concatenation of fyllogifms have logicians pretended that a long feries of important truths may be discovered and demonftrated; and even Wallis himfelf feems to think, that this is the inftrument by which the mathematicians have deduced, from a few poftulates, accurate definitions, and undeniable axioms, all the truths of their demonftrative fcience. Let us try the truth of this opinion by analyfing fome of Euclid's demonftrations. In the fhort article PRINCIPLE (Encycl.), it has been fhewn, that all our firft truths are particular, and that it is by applying to them the rules of induction that we form general truths or axioms-even the axioms of pure geometry. As this fcience treats not of real external things, but merely of ideas or conceptions, the creatures of our minds, it is obvious, that its definitions may be perfectly accurate, the induction by which its axioms are formed complete, and therefore the axioms themfelves univerfal propofitions. The ufe of thefe axioms is merely to fhorten the different proceffes of geometri- Indu Won Thus in the 47th propofition of the firft book of A 2 that Induction. that the triangles on the bafts of the parallelograms are precifely equal to the triangles on the bafes of the fquares, he perceives at once that the two parallelo. grams, of which the largeft fquare is compofed, mut be equal to the fum of the two leffer fquares; and the truth of the propofition is demonftrated. In the courfe of this demonftration, there is not fo much as one truth inferred from another by fyllogifm, but all are perceived in fucceffion by a feries of fimple apprehenfions. Euclid, indeed, after finding the triangle conftructed on the bafe of one of the parallelograms to be equal to the triangle conftructed on the bafe of one of the fquares, introduces an axiom, and fays, "but the doubles of equals are equal to one another; therefore the parallelogram is equal to the fquare." But if from this mode of expreffion any man conceive the axiom or univerfal truth to be the cause of the truth more particular, or fuppofe that the latter could not be apprehended without a previous knowledge of the former, he is a ftranger to the nature of evidence, and to the process of generalization, by which axioms are form ed. If we examine the problems of this ancient geome. trician, we fhall find that the truth of them is proved by the very fame means which he makes ufe of to point out the truth of his theorems. Thus, the fit problem of his immortal work is, " to defcribe an equi lateral triangle on a given finite ftraight line;" and not only is this to be done, but the method by which it is done must be fuch as can be fhewn to be incontroverti bly juft. The fides of a triangle, however, cannot be ap. plied to each other fo as to be immediately compared; for they are conceived to be immoveable among them felves. A common measure, therefore, or fomething equivalent to a common measure, mult be found, by which the triangle may be conftructed, and the equality of its three fides afterwards evinced; and this equivalent Euclid finds in the circle. By contemplating the properties of the circle, it was eafy to perceive that all its radii must be equal to one another. He therefore directs two circles to be defcribed from the oppofite extremities of the given finite ftraight line, fo as that it may be the radius of each of them; and from the point in which the circles interfe&t one another, he orders lines to be drawn to the extreme points of the given line, affirming that thefe three lines conftitute an equilateral triangle. To convince his reader of the truth of this affirmation, he has only to put him in mind, that from the properties of the circle, the lines which he has drawn must be each equal to the given line, and of courfe all the three equal to one another; and this mutual equality is per ceived by fimple apprehenfion, and not inferred by fyl logiftic reafening. Euclid, indeed, by introducing into the demonftration his firft axiom, gives to it the form of a fyllogifm: but that fyllogifm proves nothing; for if the equality of the three fides of the triangle were not intuitively perceived in their pofition and the properties of the circle, the firft axiom would itfelf be a falfehood. So true it is that categorical fyllogifms have no place in geometrical reafoning; which is as ftrictly experimental and inductive as the reafoning em ployed in the various branches of phyfics. But if this be fo, how come the truths of pure geometry to be neceffary, so that the contrary of any one of them is clearly perceived to be impoffible; whilft Inductions That there is not one phyfical truth, of which the The objects of pure geometry, as we have already ob. He fame Inertia, faine in both, or at least equally removed from categorical fyllogifins. Jnflammation. INERTIA. See DYNAMICS and IMPULSION in this Supplement INFLAMMATION has been fufficiently explain. ed in the Encyclopedia, and in the article CHEMISTRY in this Supplement; but it cannot be improper, in this place, to give an account of fome remarkable Spontaneous INFLAMMATIONS, which, as different fubftances, are liable to them, have been, and may again be, the cause of many and great misfortunes. The fpontaneous inflammation of effential oils, and that of fome fat oils, when mixed with nitrous acid, are well known to philofophers; fo alfo is that of pow dered charcoal with the fame acid (lately discovered by M. Prouft), and those of phosphorus, of pyrophorus, and of fulminating gold. Thefe fubftances are generally to be found only in the laboratories of chemilts, who are perfectly well acquainted with the precautions which it is neceffary to take to prevent the unhappy accidents which may be occafioned by them. The burning of a ftore house of fails, which happened at Breft in the year 17,7, was caused by the fpontaneous inflammation of fome oiled cloths, which, after having been painted on one fide and dried in the fun, were towed away while yet warm; as was fhewn by See Me fubfequent experiments *. moires de PAcademie de Paris, 1760. + Fournal de Phyfique, 1784. Vegetables boiled in oil or fat, and left to themfelves, after having been preffed, inflame in the open air. This inflammation always takes place when the vegetabl. s retain a certain degree of humidity; if they are firit thoroughly dried, they are reduced to afhes, without the appearance of flame. We owe the obfer. vation of thefe facts to MM. Saladin and Carette f. The heaps of linen rags which are thrown together in paper manufactories, the preparation of which is hailened by means of fermentation, often take fire, if not carefully attended to. The fpontaneous inflammation of hay has been known for many centuries; by its means houfes, barns, &c. have been often reduced to afhes. When the hay is laid up damp, the inflammation often happens; for the fermentation is then very great. This accident very feldom occurs to the first hay (according to the obfervation of M. de Bomare), but is much more common to the second; and if, through inattention, a piece of iron should be left in a stalk of hay in fermentation, the inflammation of that ftalk is almoft a certain confequence. Corn heaped up has alfo fometimes produced inflammations of this nature. Vanieri, in his Prædium Rufticum, fays, Que vero (gramina) nondum fatis infolata recondens Imprudens, fubitis pariunt incendia flammis. Dung alfo, under certain circumstances, inflames fpontaneously. In a paper, publifhed in the Repertory of Arts and Manufactures, by the Rev. William Tooke, F. R. S. &c. we have the following remarkable inftances of fpontaneous inflammation. A perfon of the name of Rüde, an apothecary at Bautzen, had prepared a pyrophorus from rye-bran and alum. Not long after he had made the discovery, there broke out, in the next village of Nauflitz, a great fire, which did much mif. chief, and was faid to have been occafioned by the treat I tion. ing of a fick cow in the cow-houfe. Mr Rüde knew, Inflamma that the countrymen were used to lay an application of parched rye bran to their cattle for curing the thick neck; he knew alfo, that alum and rye bran, by a pro. per procefs, yielded a pyrophorus; and now he withed to try whether parched rye bran alone would have the fame effect. Accordingly, he roafted a quantity of rye. bran by the fire, till it had acquired the colour of roasted coffee. This roafted bran he wrapped up in a linen cloth; in the space of a few minutes there arose a strong fmoke through the cloth, accompanied by a fmell of burning. Not long afterwards the rag grew as black as tinder, and the bran, now become hot, fell through it on the ground in little balls. Mr Rüde repeated the experiment at various times, and always with the fame refult. Who now will any longer doubt, that the frequency of fires in cow-houfes, which in those parts are mottly wooden buildings, may not be occafioned by this common practice, of binding roafted bran about the necks of the cattle? The fire, after confuming the cattle and the fhed, communicates itfelf to the adjoining buildings; great damage enfues; and the ignorant look for the caufe in wilful and malicious firing, confequently in a capital crime." The fame author informs us, that in the spring of the year 178, a fire was difcovered on board a Ruffian frigate lying in the road of Cronstadt; which, if it had not been timely extinguifhed, would have endangered the whole fleet. After the fevereft fcrutiny, no caufe of the fire was to be found; and the matter was forced to remain without explanation, but with ftrong furmifes of fome wicked incendiary being at the bottom of it. In the month of Augutt, in the fame year, a fire broke out at the hemp-magazine at St Petersburgh, by which feveral hundred thousand poods of hemp and flax were t A pood confumed. The walls of the magazine are of brick, confifts of the floors of ftone, and the rafters and covering of iron; + pounds it ftands alone on an ifland in the Neva, on which, as Rufs, or 36 English. well as on board the fhips lying in the Neva, no fire is permitted. In St Petersburgh, in the fame year, a fire was discovered in the vaulted fhop of a furrier. In thefe fhops, which are all vaults, neither fire nor candle is allowed, and the doors of them are all of iron. At length the probable caufe was found to be, that the furrier, the evening before the fire, had got a roll of new cere-cloth (much in ufe here for covering tables, counters, &c. being eatly wiped and kept clean), and had left it in his vault, where it was found almoit confumed. In the night between the 20th and 21ft of April 1781, a fire was feen on board the frigate Maria, which lay at anchor, with feveral other fhis, in the road off the island of Cronftadt; the fire was, however, foon extinguished; and, by the feverett examination, little or nothing could be extorted corcerning the manner in which it had arifen. The gariifon was threatened with a fcrutiny that fhould coft them dear; and while they were in this cruel ftate of fulpence, an order came from the fovereign, which quieted their minds, and gave rife to fome very fatisfactory experiments. It having been found, upon juridical examination, as well as private inquiry, that in the fhip's cabin, when the fmoke appeared, there lay a bundle of matting, containing Ruffian lamp black prepared from tir foot, moiftened with hemp oil varnith, which was perceived to Inflamma to have fparks of fire in it at the time of the extinction, tion. the Ruffian admiralty gave orders to make various experiments, in order to fee whether a mixture of hempoil varnish and the forementioned Ruffian black, folded up in a mat and bound together, would kindle of itself. They hook 40 pounds of fir-wood foot into a tub, and poured about 35 pounds of hemp oil varnish upon it; this they let ftand for an hour, after which they poured off the oil. The remaining mixture they now wrapped up in a mat, and the bundle was laid clofe to the cabin, where the midshipmen had their birth. To avoid all fufpicion of treachery, two officers fealed both the mat and the door with their own feals, and ftationed a watch of four fea officers, to take notice of all that paffed the whole night through; and as foon as uny fmoke fhould appear, immediately to give information to the commandant of the port. The experiment was made the 26th of April, about 11 o'clock A. M. in prefence of all the officers named in the commiffion. Early on the following day, about fix o'clock A. M. a smoke appeared, of which the chief commandant was immediately informed by an officer: he came with all poffible fpeed, and through a small hole in the door faw the mat fmoking. Without opening the door, he dispatched a meffenger to the members of the commiffion; but as the fmoke became ftronger, and fire began to appear, the chief commandant found it neceflary, without waiting for the members of the commiffion, to break the feals and open the door. No fooner was the air thus admitted, than the mat began to burn with greater force, and prefently it burft into a flame. The Ruffian admiralty, being now fully convinced of the self-enkindling property of this compofition, tranfmitted their experiment to the Imperial Academy of Sciences; who appointed Mr Georgi, a very learned and able adjunct of the academy, to make farther experiments on the subject. Previous to the relation of thefe experiments, it is neceffary to obferve, that the Ruffian fir-black is three or four times more heavy, thick, and unctuous, than that kind of painters black which the Germans call kien-rahm. The former is gathered at Ochta, near St Petersburgh, at Mofco, at Archangel, and other places, in little wooden huts, from refinous fir-wood, and the unctuous bark of birch, by means of an apparatus uncommonly fimple, confifting of pots without bottoms fet one upon the other; and is fold very cheap. The famous fine German kien-rahm is cal led in Ruffia Holland's black. In what follows, when raw oil is fpoken of, it is to be understood of linfeed. oil or hemp oil; but most commonly the latter. The varnish is made of five pounds of hemp oil boiled with two ounces and a half of minium. For wrapping up the compofition, Mr Georgi made ufe of coarfe hemplinen, and always fingle, never double. The impregna tions and commixtures were made in a large wooden bowl, in which they flood open till they were wrapped up in linen. Three pounds of Ruffian fir-black were flowly impregnated with five pounds of hemp-oil varnish; and when the mixture had flood open five hours, it was bound up in linen. By this process it became clotted; but fome of the black remained dry. When the bundle had lain fixteen hours in a cheft, it was obferved to emit a very nauseous, and rather putrid, fmell, not quite unlike that of boiling oil. Some parts of it became Inflanıma. warm, and fteamed much; this fteam was watery, and tion. by no means inflammable. Eighteen hours after the mixture was wrapped up, one place became brown, emitted smoke, and directly afterwards glowing fire appeared. The fame thing happened in a second and a third place, though other places were fcarcely warm. The fire crept flowly around, and gave a thick, grey, ftinking fmoke. Mr Georgi took the bundle out of the cheft, and laid it on a ftone pavement; when, on being exposed to the free air, there arose a flow burning flame, a fpan high, with a strong body of smoke. Not long afterwards there appeared, here and there, feveral chaps or clefts, as from a little volcano, the va pour iffuing from which burit into flame. On his breaking the lump, it burst into a very violent fiame, full three feet high, which foon grew lefs, and then went out. The fmoking and glowing fire lafted for the space of fix hours; and afterwards the remainder continued to glow without fioke for two hours longer. The grey earthy afhes, when cold, weighed five ounces and a half. In another experiment, perfectly fimilar to the foregoing, as far as relates to the compofition and quantities, the enkindling did not ensue till 41 hours after the impregnation: the beat kept increasing for three hours, and then the accenfion followed. It is worthy of remark, that thefe experiments fucceeded better on bright days than on fuch as were rainy; and the accension came on more rapidly. In another experiment, three pounds of Ruffian firblack were flowly impregnated with three pounds of raw hemp-oil; and the accenfion enfued after nine hours. Three quarters of a pound of German rahm were flowly impregnated with a pound and a half of hempoil varnish. The mixture remained 70 hours before it became hot and reeking: it then gradually became hotter, and emitted a ftrong exhalation; the effluvia were moift, and not inflammable. The reaction lasted 36 hours, during which the heat was one while ftronger, and then weaker, and at length quite ceased. Stove or chimney foot, moftly formed from birchwood fmoke, was mingled with the above-mentioned fubftances and tied up; the compound remained cold and quiet. Ruffian fir-black, mixed with equal parts of oil of turpentine, and bound up, exhibited not the least reaction or warmth. Birch oil, mixed with equal parts of Ruffian firblack, and bound up, began to grow warm and to emit a volatile fmell; but the warmth foon went off again. From the experiments of the admiralty and of Mr Georgi, we learn, not only the decifive certainty of the felf-accenfion of foot and oil, when the two fubftances are mixed under certain circumftances, but also the following particulars : Of the various kinds of foot, or lamp-black, the experiments fucceeded more frequently and furely with the coarfer, more unctuous, and heavier, like Ruffian painters black, than with fine light German rahm, or with coarse chimney-foot. In regard to oils, only thofe experiments fucceeded which were inade with drying oils, either raw or boiled. The proportions of the foots to the oils were, in the fuccefsful experiments, very vari ous; the mixture kindled with a tenth, a fifth, a third, |