researches to which that Philosophy has given birth. I have aimed, at the same time (and I hope not altogether without success,) to give somewhat more of precision to the technical phraseology of the Baconian school, and of correctness to their metaphysical ideas.

Before concluding these speculations, it may not be improper to caution my readers against supposing, that when I speak of the Baconian school, or of the Baconian logic, I mean to ascribe entirely to the Novum Organon, the advances made in physical science, since the period of its publication. The singular effects of this, and of the other inestimable writings of the same author, in forwarding the subsequent progress of scientific discovery, certainly entitle his name, far more than that of any other individual, to be applied as a distinguishing epithet to the modern rules of philosophizing; but (as I have elsewhere observed)" the genius and writings of Bacon "himself were powerfully influenced by the circumstances and cha"racter of his age: Nor can there be a doubt, that he only accele"rated a revolution which was already prepared by many concur"rent causes."*-My reasons for thinking so, which rest chiefly on historical retrospects, altogether foreign to my present design, I must delay stating, till another opportunity.

To this observation it is of still greater importance to add, that, in contrasting the spirit and the utility of the new logic with those of the old, I have no wish to see the former substituted, in our universities, in room of the latter. By a strange inversion in the order of instruction, Logic, instead of occupying its natural place at the close of the academical course, has always been considered as an introduction to the study of the sciences; and has, accordingly, been obtruded on the uninformed minds of youth, at their first entrance into the schools. While the syllogistic art maintained its reputation, this inversion was probably attended with little practical inconvenience; the trite, and puerile examples commonly resorted to for the illustration of its rules, presupposing a very slender stock of scientific attainments; but now, when the word Logic is universally understood in a more extensive sense, as comprehending, along with an outline of Aristotle's Organon, some account of the doctrines of Bacon, of Locke, and of their successors, it seems indispensably necessary, that this branch of education should be delayed till the understanding has acquired a wider and more varied range of ideas, and till the power of reflection (the last of our faculties which nature unfolds) begins to solicit its appropriate nourishment. What notions can be annexed to such words as analysis, synthesis, induction, experience, analogy, hypothetical and legitimate theories, demonstrative and moral certainty, by those whose attention has hitherto been exclusively devoted to the pursuits of classical learning? A fluent command, indeed, of this technical phraseology may be easily communicated; but it would be difficult to devise a more effectual expedient for misleading, at the very outset of life, the inexperienced and un

* Outlines of Moral Philosophy, first printed in 1793.

assured judgment. The perusal of Bacon's writings, in particular, disfigured as they are by the frequent use of quaint and barbarous expressions, suited to the scholastic taste of his contemporaries, ought to be carefully reserved for a riper age.*

In confirmation of this last remark, many additional arguments might be drawn from the peculiar circumstances in which Bacon wrote. At the period when he entered on his literary career, various branches of physical science were already beginning to exhibit the most favourable presages of future improvement; strongly inviting his original and powerful mind to co-operate in the reformation of philosophy. The turn of his genius fortunately led him to employ himself chiefly in general suggestions for the advancement of learning; and, leaving to others the task of inductive investigation, to aim rather at stating such rules as might direct and systematize their exertions. In his own experimental researches he was not very fortunate; nor is much reliance to be placed on the facts recorded in his Histories. Perhaps the comprehensiveness of his views diminished his curiosity with respect to the particular objects of science; or, perhaps, he found the multiplicity of his engagements in active life, more consistent with speculations, in which the chief materials of his reasonings were to be drawn from his own reflections, than with inquiries which demanded an accurate observation of external phenomena, or a minute attention to experimental processes. In this respect, he has been compared to the Legislator of the Jews, who conducted his followers within sight of their destined inheritance; and enjoyed, in distant prospect, that promised land which he himself was not permitted to enter.f

The effect of this prophetic imagination in clothing his ideas, to a greater degree than a severe logician may approve, with the glowing colours of a poetical diction, was unavoidable. The wonder is, that his style is so seldom chargeable with vagueness and obscurity; and that he has been able to bequeath to posterity so many cardinal and eternal truths, to which the progressive light of science is every

* Haller mentions, in his Elements of Physiology, that he was forced to enter on the study of logic in the tenth year of his age. "Memini me annum natum decimum, quo avidus historiam et poesia devorassem, ad logicam, et ad Claubergianam logicam ediscen dam coactum fuisse, quâ nihil poterat esse, pro hujusinodi homuncione, sterilius." (To mus VIII. Pars Secunda, p. 24. Lausannae, 1778.) It seems difficult to imagine any attempt more extravagant, than that of instructing a child, only ten years old, in the logic of the schools; and yet it is by no means a task so completely impracticable, as to convey to a pupil, altogether uninitiated in the Elements of Physics, a distinct idea of the object and rules of the Novum Organon.

The example of Mr. Smith, during the short time he held the Professorship of Logic at Glasgow, is worthy of imitation in those universities which admit of similar deviations from old practices. For an account of his plan, see Biographical Memoirs of Smith, Robertson, and Reid, p. 12; where I have inserted a slight but masterly sketch of his academical labours, communicated to me by his pupil and friend, the late Mr. Millar.

+ See Cowley's Ode, prefixed to Sprat's History of the Royal Society. Nor does Bacon himself seem to have been at all disposed to overrate the value of his own contributions to Experimental Science. "In rebus quibuscunque difficilioribus," he has observed on one occasion, "non expectandum est ut quis simul et serat et metat; sed

I remember that in my tenth year, when I could have eagerly devoured poetry and history, I was compelled to study logic, and that the logic of Claubergius; than which nothing, to a boy of that age, could possibly be more useless.]

day adding a new accession of lustre. Of these truths, however, (invaluable in themselves as heads or texts, pregnant with thought) many, to borrow the expression of a Greek poet-sound only to the intelligent; while others present those confident but indefinite anticipations of intellectual regions yet undiscovered, which, though admirably calculated to keep alive and to nourish the man of science, are more fitted to awaken the enthusiasm, than to direct the studies of youth. Some of them, at the same time (and these, I apprehend, cannot be too early impressed on the memory) are singularly adapted to enlarge and to elevate the conceptions; exhibiting those magnificent views of knowledge, which, by identifying its progress with the enlargement of human power and of human happiness, ennoble the humblest exertions of literary industry, and annihilate, before the triumphs of genius, the most dazzling objects of vulgar ambition. A judicious selection of such passages, and of some general and striking aphorisms from the Novum Organon, would form a useful manual for animating the academical tasks of the student; and for gradually conducting him from the level of the subordinate sciences, to the vantage-ground of a higher philosophy.

Unwilling as I am to touch on a topic so hopeless as that of Academical Reform, I cannot dismiss this subject, without remarking, as a fact which, at some future period will figure in literary history, that two hundred years after the date of Bacon's philosophical works, the antiquated routine of study, originally prescribed in times of scholastic barbarism and of popish superstition, should, in so many Universities, be still suffered to stand in the way of improvements, recommended at once by the present state of the sciences, and by the order which nature follows in developing the intellectual faculties. On this subject, however, I forbear to enlarge.-Obstacles of which I am not aware may perhaps render any considerable innovations impracticable; and, in the mean time, it would be vain to speculate on ideal projects, while the prospect of realizing them. is so distant and uncertain.

praeparatione opus est, ut per gradus maturescant."* But the most remarkable passage of this sort, which I recollect in his writings, occurs towards the close of his great work, De Augmentis Scientiarum :-Tandem igirur paululum respirantes, atque ad ea, quae prae tervecti sumus, oculos reflectentes, hunc tractatum nostrum non absimilem esse censemus sonis illis et praeludiis quae praetentant Musici, dum fides ad modulationem concinnant: Quae ipsa quidem auribus ingratum quiddain et asperum exhibent; at in causa sunt, ut quae sequuntur omnia sint suaviora: Sic nimirum nos in animum induximus, ut in cithara Musarum conciunanda, et ad harmoniam veram redigenda, operam navaremus, quo ab aliis postea pulsentur chordae, meliore digito, aut plectro."+-Bacon.

[In difficult pursuits, it ought not to be expected, that any one should both sow and reap together. There is a necessity for previous labour, that the fruits may gradually reach maturity.]

[And now respiring, and casting my eyes backwards to those things which I have left behind, I cannot help thinking that this treatise of mine resembles, in some degree, those notes and preludes, which Musicians are wont to produce, while they try their instruments and cause them to harmonize Such sounds are indeed harsh and unfeeling to the ear, yet are necessary to the sweetness of the concert which follows; so I have been induced to bestow my labour in tuning the lyre to the Muses, and reducing it to an exact har. mony, that others may hereafter strike the chords with a more skilful hand.]

NOTES AND ILLUSTRATIONS.

Note (A.) page 29.

OF 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 et "11 inter postulata numerantur." (Euclidis quae supersunt omnia. Ex Recens. Dav. Gregorii. Oxon. 1703. p. 3.)

The 8th Axiom too in Euclid's enumeration is evidently out of its proper place. Και τα εφαρμοζοντα επ' άλληλα ισα αλληλοις εστι :—thus translated by Dr. Simson ; "Magnitudes which coincide with one another, that is, which exactly fill the same 66 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. Prevost, in his Essais de Philosophie. According to this author (if I rightly understand 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 incurring 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 Italicks, 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 conceptions, qui a en"gagé à faire entrer les axiomes pour quelque chose dans les principes des sciences "de raisonnement pur. Et ils y font un double office. Les uns remplacent des "définitions. Les autres remplacent dés propositions susceptibles d'être démon"trées. J'en donnerai des exemples tirés des Elemens d' Euclide.

"Les axiomes remplacent quelquefois des définitions très faciles à faire comme "celle du mot tout. (El. Ax. 9.) D'autres suppléent à certaines définitions diffi"ciles et qu'on évite, comme celles de la ligne droite et de l'angle.

"Quelques axiomes remplacent des théorèmes. J'ignore si (dans les principes "d'Euclide) l'axiome 11. peut-être démontré (comme l'ont cru Proclus et tant d'au"tres anciens et modernes.) S'il peut l'être, cet axiome supplée à une démonstration "probablement laborieuse.

"Puisque les axiomes ne font autre office que suppléer à des definitions et à des "théorèmes, on demandera peut-être qu'on s'en passe. Observons 1. Qu'ils evi"tent souvent des longueurs inutiles. 2. Qu'ils tranchent les disputes à l'epoque "même ou la science est imparfaite. 3. Que s'il est un état, auquel la science puisse “ s'en passer (ce que je n'affirme point) il est du moins sage et même indispensable,

* By introducing, for example, the idea of Motion, which he has studied to avoid, as much as possible, in delivering the Elements of Plane Geometry.

"de les employer, tant que quelque insuffisance, dans ce degré de perfection où l'on "tend, interdit un ordre absolument irréprochable. Ajoutons 4. Que dans "chaque science il y a ordinairement un principe qu'on pourroit appeller dominant, "et qui par cette raison seule (et indépendamment de celles que je viens d'allé"guer) a paru devoir 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 prin"cipe 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 latitude with which he has used the word, Axiom, in his Elements. As in treating, 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 45.

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 Védanti school consisted, not in denying the ex"istence 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 exis"tence 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,

[It is then the imperfection, perhaps inevitable, of our conceptions, which has occasioned the introduction of axioms, for certain purposes, into the beginning 'of sciences of pure reasoning. They serve here a double purpose. Some supply the place of definitions, others of propositions, susceptible of demonstration. I shall give examples of these drawn from the Elements of Euclid.

Some axioms stand in the stead of easy definitions, as of the word, all. Others of definitions which are difficult and which we prefer to avoid; as those of a right line and of an angle. Some axioms supply the place of theorems. I know not if the eleventh axiom of Euclid can be demonstrated, as supposed by Proclus and so many others both ancient and modern. If so, this axiom stands in place of a demonstration probably difficult.

Since axioms serve no other purpose than to supply the place of definitions and theorems, some perhaps will think it better wholly to omit them; I reply, 1. They often enable us to avoid a long and useless process. 2. They cut short disputes which arise in the infancy of a science. 3. If there be a period when a science can do with out them, which I do not assert, it is yet wise, and even necessary, to make use of them so long as any falling short of the perfection which we attempt, prevents the series of reasoning from being perfect. I add, 4. In every science there commonly exists some one principle which we may consider as more important than any other, and which for this reason only, independent of others which I shall point out, ought to be chosen from amidst the crowd of definitions, and presented as an axiom. Such appears to me, in geometry, the principle of coincidence in the 8th axiom of Euclid.]

† 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