NOTES AND ILLUSTRATIONS.

Note (A.) page 27.

Or the fault in Euclid's arrangement which I have here remarked, some of the ancient editors were plainly aware, as they removed the two theorems in question from the class of axioms, and placed them, with at least an equal impropriety, in that of postulates. "In quibusdam codicibus," says Dr. Gregory," Axiomata 10 ot 11 inter postulata numerantur."-Euclidis quae supersunt omnia. Ex Recens. Dav. Gregorii. Oxon. 1703. p. 3.

66

The 8th Axiom too in Euclid's enumeration is evidently out of its proper place. Καὶ τὰ ἐφαρμόζοντα ἐπ' ἄλληλα ἶσα ἀλλήλοις ἐστί :—thus translated by Dr. Minimon Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another." This, in truth, is not an axiom, but a definition. It is the definition of geometrical equality; the fundamental principle upon which the comparison of all geometrical magnitudes will be found ultimately to depend. For some of these slight logical defects in the arrangement of Euclid's definitions and axioms, an ingenious, and, I think, a solid apology, has been offered by M. Pr vost, in his Essais de Philosophie. According to this author, (if I rightly under stand his meaning,) Euclid was himself fully aware of the objections to which this part of his work is liable: but found it impossible to obviate them, without incuning the still greater inconvenience of either departing from those modes of proof which he had resolved to employ exclusively in the composition of his Elements; or of revolting the student, at his first outset, by prolix and circuitous demonstrations of manifest and indisputable truths. I shall distinguish by Italics, in the following quotation, the clauses to which I wish more particularly to direct the attention of my readers.

"C'est donc l'imperfection (peut-être inévitable) de nos conceptione, qui wen gagé à faire entrer les axiomes pour quelque chose dans les principes dan melan das raisonnement pur. Et ils y font un double office. Les una remplace des déf tions. Les autres remplacent des propositions asceptibles d'été démonikem. J'en donnerai des exemples tirés des Elémena d'Euclide

"Les axiomes remplacent quelquefois des définitions tres facilesa Vaire, comme celle du mot tout. (El. Ax. 9.) Intres suppléent a certaines définitions difficiles et qu'on évite, comme celles de la ligne droite et de l'angle.

"Quelques axiomes remplacent dex theinkmes. Vigung (Not to pr d'Euclide) Faxiome 11 peut-être nast, (como Vina con

tres anciens et modemes.) il peut être, cet anime supplée a une démonstra tion probablement laborienas

théorèmes, on demanders poté 1. Colla bandent souvent des longueurs indile. 2. Cor da trauchend lex disputex téporis mm* la science est imparfade. 2. 6x tot, esegués, be a pow*** *** er (ce que je affirme point, ext das mina vige, et met me, edenpotentia,

être sorti, pour ainsi dire, du champ des définitions pour être mis en vue sous forme d'axiome. Tel me paroit être en géométrie le principe de congruence contenu dans le 8 axiome d'Euclide."-Essais de Philosophie Tom. II. pp. 30, 31, 32.

These remarks go far in my opinion, towards a justification of Euclid for the latiAs in treating, tude with which he has used the word axiom in his Elements. however, of the fundamental laws of human belief, the utmost possible precision of language is indispensably necessary, I must beg leave once more to remind my readers, that, in denying Axioms to be the first principles of reasoning in mathematics, I restrict the meaning of that word to such as are analogous to the first seven in Euclid's list. Locke, in what he has written on the subject, has plainly understood the word in the same limited sense.

Note (B.) page 49.

The prevalence in India of an opinion bearing some resemblance to the Berkeleian Theory may be urged as an objection to the reasoning in the text; but the fact is, that this resemblance is much slighter than has been generally apprehended. (See Philosophical Essays, pp. 81, 82, et seq.) On this point the following passage from Sir William Jones is decisive; and the more so, as he himself has fallen into the common mistake of identifying the Hindu belief with the conclusions of Berkeley and Hume.

*

"The fundamental tenet of the Védánti school consisted, not in denying the existence of matter, that is, of solidity, impenetrability, and extended figure, (to deny which would be lunacy) but in correcting the popular notion of it, and in contending, that it has no essence independent of mental perception, that existence and perceptibility are convertible terms, that external appearances and sensations are illusory, and would vanish into nothing, if the divine energy, which alone sustains them, were suspended but for a moment; an opinion which Epicharmus and Plato seem to have adopted, and which has been maintained in the present century with great elegance, but with little public applause; partly because it has been misunderstood, and partly because it has been misapplied by the false reasoning of some unpopular writers, who are said to have disbelieved in the moral attributes of God, whose omnipresence, wisdom, and goodness, are the basis of the Indian philosophy. I have not sufficient evidence on the subject to profess a belief in the doctrine of the Védánta, which human reason alone could, perhaps, neither fully demonstrate, nor fully disprove; but it is manifest, that nothing can be farther removed from impiety than a system wholly built on the purest devotion."-Works of Sir William Jones, Vol. I. pp. 165, 166.

From these observations, (in some of which, I must be permitted to say, there is a good deal of indistinctness, and even of contradiction,) it may on the whole be inferred, 1. That in the tenets of the Védánti school, however different from the first apprehensions of the unreflecting mind, there was nothing inconsistent with the fundamental laws of human belief, any more than in the doctrine of Copernicus concerning the earth's motion. 2. That these tenets were rather articles of a theological creed, than of a philosophical system; or at least, that the two were so blended together, as sufficiently to account for the hold which, independently of any refined reasoning, they had taken of the popular belief.

In this last conclusion I am strongly confirmed, by a letter which I had the pleasure of receiving, a few years ago, from my friend Sir James Mackintosh, then Recorder of Bombay. His good nature will, I trust, pardon the liberty I take in mentioning his name upon the present occasion, as I wish to add to the following very curious extract, the authority of so enlightened and philosophical an observer. Amidst the variety of his other important engagements, it is to be hoped that the results of his literary researches and speculations, while in the East, will not be lost to the world.

"I had yesterday a conversation with a young Bramin of no great learning, the son of the Pundit (or assessor for Hindu law) of my court. He told

*Sir William Jones here evidently confounds the system which represents the material universe as not only at first created, but as every moment upheld by the agency of Divine Power, with that of Berkeley and Hume, which, denying the distinction between primary and secondary qualities, asserts, that extension, figure, and impenetrability are not less inconceivable, without a percipient mind, than our sensations of heat and cold, sounds and odors. According to both systems, it may undoubtedly be said, that the material universe has no existence independent of mind; but it ought not to be overlooked, that in the one, this word refers to the Crest, and in the other, to the created percipient.

me, that besides the myriads of gods whom their creed admits, there was one whom they know by the name of BRIM, or the great one, without form or limits, whom no created intellect could make any approach towards conceiving; that, in reality, there were no trees, no houses, no land, no sea, but all without was Maia, or illusion, the act of BRIM; that whatever we saw or felt was only a dream, or, as he expressed it in his imperfect English, thinking in one's sleep, and that the reunion of the soul to BRIM, from whom it originally sprung, was the awakening from the long sleep of finite existence. All this you have heard and read before as Hindu speculation. What struck me was, that speculations so refined and abstruse should, in a long course of ages, have fallen through so great a space as that which separates the genius of their original inventor from the mind of this weak and unlettered man. The names of these inventors have perished; but their ingenious and beautiful theories, blended with the most monstrous superstitions have descended to men very little exalted above the most ignorant populace, and are adopted by them as a sort of articles of faith, without a suspicion of their philosophical origin, and without the possibility of comprehending any part of the premises from which they were deduced. I intend to investigate a little the history of these opinions, for I am not altogether without apprehension, that we may all the while be mistaking the hyperbolical effusions of mystical piety, for the technical language of a philosophical system. Nothing is more usual, than for fervent devotion to dwell so long and so warmly on the meanness and worthlessness of created things, and on the all-sufficiency of the Supreme Being, that it slides insensibly from comparative to absolute language, and, in the eagerness of its zeal to magnify the Deity, seems to annihilate every thing else. To distinguish between the very different import of the same words in the mouth of a mystic and of a sceptic, requires more philosophical discrimination than most of our Sanscrit investigators have hitherto shown."

Note (C.) page 57.

The private correspondence here alluded to, was between Mr. Hume and the late Sir Gilbert Elliott; a gentleman who seems to have united, with his other wellknown talents and accomplishments, a taste for abstract disquisitions, which rarely occurs in men of the world; accompanied with that soundness and temperance of judgment which, in such researches, are so indispensably necessary to guard the mind against the illusions engendered by its own subtilty. In one of his letters (of which the original draft in his own hand-writing was communicated to me by the Earl of Minto) he expresses himself thus : *

"I admit, that there is no writing or talking of any subject which is of importance enough to become the object of reasoning, without having recourse to some degree of subtilty and refinement. The only question is, where to stop, how far we can go, and why no farther? To this question I should be extremely happy to receive a satisfactory answer. I can't tell if I shall rightly express what I have just now in my mind; but I often imagine to myself, that I perceive within me a certain instinctive feeling, which shoves away at once all over subtile refinements, and tells me, with authority, that these air-built notions are inconsistent with life and experience, and by consequence cannot be true or solid. From this I am led to think, that the speculative principles of our nature ought to go hand in hand with the practical ones; and, for my own part, when the former are so far pushed, as to leave the latter quite out of sight, I am always apt to suspect that we have transgressed our limits. If it should be asked, how far will these practical principles go? I can only answer, that the former difficulty will recur, unless it be found, that there is something in the intellectual part of our nature, resembling the moral sentiment in the moral part of our nature, which determines this, as it were, instinctively. Very possibly, I have wrote nonsense: however, this notion first occurred to me at London, in conversation with a man of some depth of thinking; and talking of it since to your friend Henry Home,t I found that he seemed to entertain some notions nearly of the same kind, and to have pushed them much farther."

The practical principles referred to in this extract, seem to me to correspond very nearly with what I have called fundamental laws of belief, or first elements of hu man reason; and the SOMETHING in the intellectual part of our nature, resem bling the moral sentiment in the moral part of our nature, is plainly descriptive of

what Reid and others have since called common sense; coinciding, too, in substance with the philosophy of Lord Kames, who refers our belief of the existence of the Deity, and of various other primary truths, to particular senses, forming a constituent part of our intellectual frame. I do not take upon me to defend the forms of expression which Mr. Hume's very ingenious correspondent has employed to convey his ideas; and which, it is probable, he did not think it necessary for him, in addressing a confidential friend, to weigh with critical exactness: but his doctrine must be allowed to approximate remarkably to those parts of the works of Reid, where he appeals from the paradoxical conclusions of metaphysicians, to the principles on which men are compelled, by the constitution of their nature, to judge and to act in the ordinary concerns of life;-as well as to various appeals of the same kind, which occur in Lord Kames's writings. My principal object, however, in introducing it here, was to show, that this doctrine was the natural result of the state of science at the period when Reid appeared; and, consequently, that no argument against his originality in adopting it can reasonably be founded on a coincidence between his views concerning it and those of any preceding author.

Of Mr. Hume's respect for the literary attainments of this correspondent, so strong a proof occurs in a letter, (dated Ninewells, March 10, 1751,) that I am tempted to subjoin to the foregoing quotation the passage to which I allude.

"You would perceive, by the sample I have given you, that I make Cleanthes the hero of the dialogue. Whatever you can think of to strengthen that side of the argument, will be most acceptable to me. Any propensity you imagine I have to the other side crept in upon me against my will; and 'tis not long ago that I burned an old manuscript book, wrote before I was twenty, which contained, page after page, the gradual progress of my thoughts on that head. It began with an anxious search after arguments to confirm the common opinion: Doubts stole in,-dissipated,-returned, were again dissipated,-returned again: And it was a perpetual struggle of a restless imagination against inclination, perhaps against reason.

"I have often thought, that the best way of composing a dialogue would be, for two persons that are of different opinions about any question of importance, to write alternately the different parts of the discourse, and reply to each other. By this means that vulgar error would be avoided, of putting nothing but nonsense into the mouth of the adversary; and, at the same time, a variety of character and genius being upheld, would make the whole look more natural and unaffected. Had it been my good fortune to live near you, I should have taken upon me the character of Philo in the dialogue, which you 'll own I could have supported naturally enough : and you would not have been averse to that of Cleanthes."

In a postscript to this letter, Mr. Hume recurs to the same idea. "If you'll be persuaded to assist me in supporting Cleanthes, I fancy you need not take the matter any higher than Part 3. He allows, indeed, in Part 2d, that all our inference is founded on the similitude of the works of nature to the usual effects of mind: otherwise they must appear a mere chaos. The only difficulty is, why the other dissimilitudes do not weaken the argument: And, indeed, it would seem from experience and feeling, that they do not weaken it so much as we might reasonably expect. A theory to solve this would be very acceptable."*

Note (D.) page 62.

It would perhaps be difficult to mention another phrase in our language, which admits of so great a variety of interpretations as common sense; and to which, of consequence, it could have been equally dangerous to annex a new technical meaning in stating a controversial argument. Dr. Beattie has enumerated some of these in the beginning of his Essay, but he has by no means exhausted the subject: nor is his enumeration altogether unexceptionable in poin cal distinctness. On this point, however, I must allow my readers to judge ves.-See F Nature and Immutability of Truth, p. 37, et seq.

The Latin phrase sensus communis has also b various passages of Cicero it may be perfectly tra mon sense; and, in the same acceptation, it is of this (not to mention other authorities) many exam

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ematica of Dr. Barrow; a work not more distinguished by originality and depth of thought, than by a logical precision of expression. In one of these, he appeals to common sense, (sensus communis,) in proof of the circumference of the circle being less than the perimeter of the circumscribed square.-Lect. 1.

On other occasions, the sensus communis of classical writers plainly means something widely different; as in those noted lines of Juvenal, so ingeniously illustrated by Lord Shaftesbury in his Essay on the Freedom of Wit and Humor.

"Hæc satis ad juvenem, quem nobis fama superbum
Tradit, et inflatum, plenumque Nerone propinquo.
Rarus enim ferme sensus communis in illa
Fortuna.".

"Some commentators," says Shaftesbury, "interpret this very differently from what is generally apprehended. They make this common sense of the poet, by a Greek derivation, to signify sense of public weal, and of the common interest; love of the community or society, natural affection, humanity, obligingness, or that sort of civility which rises from a just sense of the common rights of mankind, and the natural equality there is among those of the same species.

"And, indeed, if we consider the thing nicely, it must seem somewhat hard in the poet to have deny'd wit or ability to a court such as that of Rome, even under a Tiberius or a Nero. But for humanity or sense of public good, and the common interest of mankind, 't was no such deep satire to question whether this was properly the spirit of a court. 'T was difficult to apprehend what Community subsisted among courtiers; or what Public among an absolute Prince and his slave-subjects. And for real society, there could be none between such as had no other sense than that of private good.

"Our poet, therefore, seems not so immoderate in his censure; if we consider it is the heart, rather than the head, he takes to task: when reflecting on a court education, he thinks it unapt to raise any affection towards a country; and looks upon young Princes and Lords as the young masters of the world; who, being indulged in all their passions, and trained up in all manner of licentiousness, have that thorough contempt and disregard of Mankind, which Mankind in a manner deserves, where arbitrary power is permitted, and a tyranny adored."

While I entirely agree with the general scope of these observations, I am inclined to think, that the sensus communis of Juvenal might be still more precisely rendered by sympathy; understanding this word (in the appropriate acceptation annexed to it by Mr. Smith) as synonymous with that fellow-feeling which disposes a man, in the discharge of his social duties, to place himself in the situation of others, and to regulate his conduct accordingly. Upon this supposition, the reflection in question coincides nearly with one of Mr. Smith's own maxims, that "the great never look upon their inferiors as their fellow-creatures; ""-a maxim which, although sufficiently founded in fact to justify the sarcasm of the satirical poet, must (it is to be hoped for the honor of human nature) be understood with considerable limitations, when stated as a correct enunciation of philosophical truth.

It yet remains for me to take some notice of the sensus communis of the schoolmen; an expression which is perfectly synonymous with the word conception, as defined in the first volume of this work. It denotes the power whereby the mind is enabled to represent to itself any absent object of perception, or any sensation which it has formerly experienced. Its seat was supposed to be that part of the brain (hence called the sensorium, or the sensorium commune) where the nerves from all the organs of perception terminate. Of the peculiar function allotted to it in the scale of our intellectual faculties, the following account is given by Hobbes: "Some say the senses receive the species of things, and deliver them to the Common Sense; and the Common Sense delivers them over to the Fancy; and the Fancy to the Memory, and the Memory to the Judgment; like handing of things from one to another, with many words making nothing understood."-Of Man, Part I. Chap. 2.

Sir John Davis, in his poem on the Immortality of the Soul, (published in the reign of Queen Elizabeth, gives the name of common sense to the power of imagin Mon; (See Sections XIX, and XX.) and the very same phraseology occurs, at a period, in the Philosophy of Descartes: (ece, in particular, his Second Med.

*Theory of Moral Kentimente, Vol. 1. p. 136, kela od