to which the body rises is the whole effect of the impulse, and ought to be the whole measure of it. Secondly, His reasoning serves as well against him as for him: for may I not plead with, as good reason at least thus? The velocity given by an impressed force is the whole effect of that impressed force; and therefore the force must be as the velocity. Thirdly, Supposing the height to which the body is raised to be the measure of the force, this principle overturns the conclusion he would establish by it, as well as that which he opposes. For, supposing the first velocity of the body to be still the same, the height to which it rises will be increased, if the power of gravity is diminished; and diminished, if the power of gravity is increased. Bodies descend slower at the equator, and faster towards the poles, as is found by experiments made on pendulums. If then a body is driven upwards at the equator with a given velocity, and the same body is afterwards driven upwards at Leipsic with the same velocity, the height to which it rises in the former case will be greater than in the latter; and therefore, according to his reasoning, its force was greater in the former case; but the velocity in both was the same; consequently the force is not as the square of the velocity any more than as the velocity.

Reflections on this Controversy.-On the whole, I cannot but think the controvertists on both sides have had a very hard task; the one to prove, by mathematical reasoning and experiment, what ought to be taken for granted; the other by the same means to prove what might be granted, making some allowance for impropriety of expression, but can never be proved.

If some mathematician should take it in his head to affirm, that the velocity of a body is not as the space it passes over in a given time, but as the square of that space; you might bring mathematical arguments and experiments to confute him; but you would never by these force him to yield, if he was ingenious in his way; because you have no common principles left you to argue from, and you differ from each other, not in a mathematical proposition, but in a mathematical definition.

Suppose a philosopher has considered only that measure of centripetal force which is proportional to the velocity generated by it in a given time, and from this measure deduces several propositions. Another philosopher in a distant country, who has the same general notion of centripetal force, takes the velocity generated by it, and the quantity of matter together, as the measure of it. From this he deduces several conclusions, that seem directly contrary to those of the other. Thereupon a serious controversy is begun, whether centripetal force be as the velocity, or as the velocity and quantity of matter taken together. Much mathematical and experimental dust is raised, and yet neither party can ever be brought to yield; for they are both in the right, only they have been unlucky in giving the same name to different mathematical conceptions. Had they distinguished these measures of centripetal force as Newton has done, calling the one vis centripetæ quantitatis acceleratrix, the other quantitatis motrix; all appearance of contradiction had ceased, and their propositions, which seem so contrary, had exactly tallied.

DD

ANALYSIS.

OF

ARISTOTLE'S LOGIC,

WITH REMARKS *.

CHAPTER I.

OF THE FIRST THREE TREATISES.

SECTION 1.-OF THE AUTHOR.

ARISTOTLE had very uncommon advantages: born in an age when the philosophical spirit in Greece had long flourished, and was in its greatest vigour; brought up in the court of Macedon, where his father was the king's physician; twenty years a favourite scholar of Plato, and tutor to Alexander the Great, who both honoured him with his friendship, and supplied him with every thing necessary for the prosecution of his inquiries. These advantages he improved by indefatigable study, and immense reading. He was the first we know, says Strabo, who composed a libraryAnd in this the Egyptian and Pergamenian kings copied his example. As to his genius, it would be disrespectful to mankind not to allow an uncommon share to a man who governed the opinions of the most enlightened part of the species near two thousand years.

If his talents had been laid out solely for the discovery of truth and the good of mankind, his laurels would have remained for ever fresh; but he seems to have had a greater passion for fame than for truth, and to have wanted rather to be admired as the prince of philosophers than to be useful; so that it is dubious, whether there be in his character most of the philosopher or of the sophist. The opinion of lord Bacon is not without probability, That his ambition was as boundless as that of his royal pupil; the one aspiring at universal monarchy over the bodies and fortunes of men, the other over their opinions. If this was the case, it cannot be said that the philosopher pursued his aim with less industry, less ability, or less success than the hero.

His writings carry too evident marks of that philosophical pride, vanity, and envy, which have often sullied the character of the learned. He determines boldly things above all human knowledge; and enters upon the most difficult questions, as his pupil entered upon a battle, with full assurance of success. He delivers his decisions oracularly, and without any fear of mistake. Rather than confess his ignorance, he hides it under hard words and ambiguous expressions, of which his interpreters can make what they please. There is even reason to suspect, that he wrote often with affected obscurity, either that the air of mystery might procure great veneration, or that his books might be understood only by the adepts who had been initiated in his philosophy.

*This Analysis originally appeared in lord Kames's Sketches of the History of Man, published in 1773, and is esteemed the best analysis yet given of that philosopher's writings.

His conduct towards the writers that went before him has been much censured. After the manner of the Ottoman princes, says lord Verulam, he thought his throne could not be secure unless he killed all his brethren. Ludovicus Vives charges him with detracting from all philosophers, that he might derive that glory to himself, of which he robbed them. He rarely quotes an author but with a view to censure, and is not very fair in representing the opinions which he censures.

The faults we have mentioned are such as might be expected in a man, who had the daring ambition to be transmitted to all future ages as the prince of philosophers, as one who had carried every branch of human knowledge to its utmost limit, and who was not very scrupulous about the means he took to obtain his end.

We ought, however, to do him the justice to observe, that although the pride and vanity of the sophist appear too much in his writings in abstract philosophy, yet, in natural history, the fidelity of his narrations seems to be equal to his industry; and he always distinguishes between what he knew and what he had by report. And, even in abstract philosophy, it would be unfair to impute to Aristotle all the faults, all the obscurities and all the contradictions, that are to be found in his writings. The greatest part, and perhaps the best part, of his writings is lost. There is reason to doubt whether some of those we ascribe to him be really his; and whether what are his be not much vitiated and interpolated. These suspicions are justified by the fate of Aristotle's writings, which is judiciously related from the best authorities, in Bayle's Dictionary, under the article Tyrannion, to which I refer.

His books in logic, which remain, are, 1. One book of the Categories. 2. One of Interpretation. 3. First Analytics, two books. 4. Last Analytics, two books. 5. Topics, eight books. 6. Of Sophisms, one book. Diogenes Laertius mentions many others that are lost. Those I have mentioned have commonly been published together under the name of Aristotle's Organon, or his Logic; and, for many ages, Porphyry's Introduction to the Categories has been prefixed to them.

SECT. II. OF PORPHYRY'S INTRODUCTION.

In this introduction, which is addressed to Chrysoarius, the author observes, That, in order to understand Aristotle's doctrine concerning the categories, it is necessary to know what a genus is, what a species, what a specific difference, what a property, and what an accident; that the knowledge of these is also very useful in definition, in division, and even in demonstration: therefore he proposes, in this little tract to deliver shortly and simply the doctrine of the ancients, and chiefly of the Peripatetics, concerning these five predicables; avoiding the more intricate questions. concerning them; such as, Whether genera and species do really exist in nature? or, Whether they are only conceptions of the human mind? If they exist in nature, Whether they are corporeal or incorporeal? and, Whether they are inherent in the objects of sense, or disjoined from them? These, he says, are very difficult questions, and require accurate discussion; but that he is not to meddle with them.

After this preface he explains very minutely each of the five words above mentioned, divides and subdivides each of them, and then pursues all the agreements and differences between one and another through sixteen chapters.

horse runs.

SECT. III.-OF THE CATEGORIES.

man may

THE book begins with an explication of what is meant by univocal words, what by equivocal, and what by denominative. Then it is observed, that what we say is either simple, without composition or structure, as man, horse; or it has composition and structure, as a man fights, the Next comes a distinction between a subject of predication; that is, a subject of which any thing is affirmed or denied, and a subject of inhesion. These things are said to be inherent in a subject, which, although they are not a part of the subject, cannot possibly exist without it, as figure in the thing figured. Of things that are, says Aristotle, some may be predicated of a subject, but are in no subject: as be predicated of James or John, but is not in any subject. Some again are in a subject, but can be predicated of no subject. Thus my knowledge in grammar is in me as its subject; but it can be predicated of no subject; because it is an individual thing. Some are both in a subject, and may be predicated of a subject, as science; which is in the mind as its subject, and may be predicated of geometry. Lastly, Some things can neither be in a subject, nor be predicated of any subject. Such are all individual substances, which cannot be predicated, because they are individuals; and cannot be in a subject, because they are substances. After some other subtleties about predicates and subjects, we come to the categories themselves; the things above-mentioned being called by the schoolmen the anteprædicamenta. It may be observed, however, that, notwithstanding the distinction now explained, the being a subject, and the being predicated truly of a subject, are, in the Analytics, used as synonymous phrases; and this variation of style has led some persons to think that the Categories were not written by Aristotle.

Things that may be expressed without composition or structure are, says the author, reducible to the following heads: They are either substance, or quantity, or quality, or relatives, or place, or time, or having, or doing, or suffering. These are the predicaments or categories. The first four are largely treated of in four chapters; the others are slightly passed over, as sufficiently clear of themselves. As a specimen, I shall give a summary of what he says on the category of substance

Substances are either primary, to wit, individual substances, or secondary, to wit, the genera, and species of substances. Primary substances neither are in a subject, nor can be predicated of a subject; but all other things that exist, either are in primary substances, or may be predicated of them. For whatever can be predicated of that which is in a subject, may also be predicated of the subject itself. Primary substances are more substances than the secondary; and of the secondary, the species is more a substance than the genus. If there were no primary, there could be no secondary substances. The properties of substance are these: 1. No substance is capable of intention or remission. 2. No substance can be in any other thing as its subject of inhesion. 3. No substance has a contrary; for one substance cannot be contrary to another; nor can there be contrariety between, a substance and that which is no substance. 4. The most remarkable property of substance is, that one and the same substance may, by some change in itself, become the subject of things that are contrary. 'Thus the same body may be at one time hot, at another cold.

Let this serve as a specimen of Aristotle's manner of treating the categories. After them we have some chapters, which the schoolmen call post prædicamenta; wherein, first, the four kinds of opposition of terms

are explained; to wit, relative, privative, of contrariety, and of contradiction. This is repeated in all systems of logic. Last of all, we have distinctions of the four Greek words which answer to the Latin ones, prius, simul, motus, and habere.

SECT. IV.-OF THE BOOK CONCERNING INTERPRETATION.

WE are to consider, says Aristotle, what a noun is, what a verb, what affirmation, what negation, what speech. Words are the signs of what passeth in the mind; writing is the sign of words. The signs both of writings and of words are different in different nations, but the operations of mind signified by them are the same. There are some operations of thought which are neither true nor false. These are expressed by nouns or verbs singly, and without composition.

A noun is a sound, which by compact signifies something without respect to time, and of which no part has signification by itself. The cries of beasts may have a natural signification, but they are not nouns; we give that name only to sounds which have their signification by compact. Non homo is The cases of a noun, as the genitive, dative, are not nouns. not a noun, but, for distinction's sake, may be called a nomen infinitum. A verb signifies something by compact with relation to time. Thus valet is a verb; but valetudo is a noun, because its signification has no relation to time. It is only the present tense of the indicative that is properly called a verb: the other tenses and moods are variations of the verb. Non valet may be called a verbum infinitum.

Speech is sound significant by compact, of which some part is also significant. And it is either enunciative, or not enunciative. Enunciative speech is that which affirms or denies. As to speech which is not enunciative, such as a prayer or wish, the consideration of it belongs to oratory or poetry. Every enunciative speech must have a verb, or some variation of a verb. Affirmation is the enunciation of one thing concerning another. Negation is the enunciation of one thing from another. Contradiction is an affirmation and negation that are opposite. This is a summary of the first six chapters.

The seventh and eighth treat of the various kinds of enunciations or propositions, universal, particular, indefinite, and singular and of the various kinds of opposition in propositions, and the axioms concerning them. These things are repeated in every system of logic. In the ninth chapter he endeavours to prove, by a long metaphysical reasoning, that propositions respecting future contingencies are not, determinately, either true or false; and that, if they were, it would follow that all things happen necessarily, and could not have been otherwise than as they are. The remaining chapters contain many minute observations concerning the equipollency of propositions both pure and modal.

CHAPTER II.

REMARKS.

SECT. I.-ON THE FIVE PREDICABLES.

THE writers on logic have borrowed their materials almost entirely from Aristotle's Organon, and Porphyry's Introduction. The Organon,