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selves. The American painters have only been waiting for the criticism of this country. They will do better now: they will be more encouraged. May it be so among their men of literature.- We know not if this report be true; because the picture, we know, was not finished a few weeks ago. But we have it, on pretty good authority. The Philadelphians, too, are wide awake. They have employed Sully to paint a full-length of LA FAYETTE. But for what? Why for 300 dollars (60 guineas by subscription, of 100 persons, at 3 dollars

head (136. 6d.)—which money he is to collect; and out of which, (before he gets it) he is to disburse the enses of a visit to-a residence in Washington city, where the picture is to be painted.--So much for Athens! So much for the ATHENIANS !



We trust that the contents of the present paper will not be deemed irrelevant, if by means of them we are enabled the better to explain the nature of the evidence on which Political Economy must rest. To this topic, and the causes that have rendered the science so obscure and unsatisfactory, one more preliminary Essay will be devoted ; and then we shall be fully prepared to raise, on a clear and unoccupied foundation, a structure, solid, and permanent, and symmetrical in all its parts.

Essay III.-Part III.

On the sources of human knowledge, and the nature of the evidence on which it rests ; with a particular reference to Political Economy.

Homo, nataræ minister, et interpres, tantum facit et intelligit, quantum, de naturæ ordine, re vel mente observaverit : nec amplius scit aut potest. --Novum OrganUM, aphorism.-I.

As the object and contents of this not such a system as is usually taught, division of the third Essay may appear which scarcely ever penetrates through not necessarily and immediately con- mere words, so as to reach to facts on nected with Political Economy, it may which we may reason, or to the faculbe proper to premise a few observa- ties by which we must reason ; but a tions tending to prove that they are system which should be confined to connected, and thus justify the line of an explanation of the nature and deinvestigation we are about to pursue. gree of evidence of which each branch From whatever sources and causes, of human knowledge is susceptible, error, and difference of opinion, which and of the best mode of applying the implies error, may arise, there can be human faculties, so as to attain that no doubt that one of the most fer- evidence. tile sources, and most powerful and We have not the vanity to imagine general causes, must be sought in our that we could supply such a desideramisapprehension of the peculiar nature tum ; as it would be a most valuable of the different branches of human gift to man, so it would require a mest knowledge, and of the particular kind vigorous, clear, and comprehensive of evidence of which each is suscepti- intellect, that had long and deeply ble, and on which, if solid and perma- studied the subject. But there are a nent, it must rest.

few hints that we can suggest-scatPerhaps no higher or more valua- tered and unconnected, we are sensible gift could be bestowed on the in- ble, but which we shall not hesitate to tellect, and, through it, on the mental offer, both on account of the importand moral improvement and the hap- ance of the subject, and because these piness of man, than a system of logic: hints, few and imperfect as they are,

will serve to guide us to the real na- duce to human labour and skill ; and ture of Political Economy, and of the that that produce continued to afford evidence of which alone it is suscepti an agreeable and wholesome nutrible, and on which it must rest, before ment to man: all these things reit can be rendered a clear, solid, and main exactly in every respect as they permanent science.

were. The constitution of the human There are two circumstances essen- mind alone undergoes an essential tially and indispensably necessary to change ; all things that surround us, the acquisition of knowledge, and indeed, all that we see, and do, or by even the continuance of the human which we are acted upon, remain as race; if both, or either of these cir- formerly; our senses perform their cumstances were annihilated, or were functions as usual ; but the associaconstituted differently from what they tion of our ideas is destroyed. What are, we could know nothing, and man- would be the result? as we are constikind would speedily become extinct. tuted, the sun and the idea of warınth One is the permanence or stability of are so indissolubly connected in our the appearances and operations of na- mind, that the appearance of the one, ture: the other is, that fundamental immediately, without an effort of the law of the human mind, on which mind, or process of reasoning, calls up rests the association of our ideas. the expectation of the other; and on

Let us imagine, for an instant, that this expectation, we act and calculate. the permanence of the appearances Suppose our ideas no longer to be asand operations of nature were destroy- sociated, that every impression in our ed; that the food which when tirst mind was single and insulated : the eaten pleased our palates, and supplied sun, though it warmed us the first a wholesome and nutritious aliment, time we felt its rays play upon us, the next time we used it, was bitter would raise no expectation of future and disagreeable, and afforded no warmth. In short, if our ideas were nourishment, or absolutely proved poi- not associated, we could have no know. sonous; let us extend this supposi- ledge of any kind; for if we attend to tion to every other thing surrounding what passes in our own minds, we shall us, which we observed, or did, or used, be convinced that knowledge is nothing on which we acted, or which acted else but the association of ideas, by upon us ;—and whence could our whatever means this association takes knowledge be derived, or how could we place, whether from what we are continue to exist? So far as regards taught and accustomed to do, or from our knowledge—the point to which at our own observation and experience. present we must exclusively direct our If our ideas were no longer subject to attention the experience or observa- the law of association, we could no tion of this moment would be contra- longer be taught anything: habits dicted by the experience or observa- could no longer be formed : and nature tion of the next: and it is too evident would in vain exhibit a permanence to require illustration or proof, that in and stability in her appearances and such a state of things, we could antie operations. cipate nothing-we could know no But this very law of association on thing, we could believe nothing, but which depends the whole fabric of huwhat would deceive us.

man intellect, happiness, and even exThe other circumstance, not being istence, is itself the source of our preso obvious and direct, may not appear judices, errors, and misery. No apat first sight so absolutely necessary to pearance manifests itself, no operation the acquisition of knowledge, or an or event takes place in the three deindispensable and essential instrument partments of the universe in which we even to the obtaining of its simplest have an opportunity of seeing the rerudiments. But let us suppose, that gular order of nature displayed, viz. the fundamental law of the mind, by the phenomena of inanimate matter, which our ideas are associated, were the phenomena of the lower animals, annihilated: that the course of nature and the phenomena exhibited by the in her appearances and operations con- human race, which is not surrounded tinued, as it is, permanent and stable ; by a variety of circumstances. It may - that the sun continued to rise, and be that the phenomena depend on set, and give heat, and fertility, and one alone of all these circumstances; health ; that the earth yielded its pro or on several, or possibly on the whole

of them; and it may be, that, from ture-a fact whith has been found to some simple circumstance making a hold uniformly in our past experience, strong impression on our senses or feel- and on the continuance of which, in ings at the time the phenomena were future, the constitution of our mind, witnessed, they become associated in as exhibited in the association of our our minds with it, though in no re- ideas, determines us confidently to spect its cause. Hence, error in our rely. thoughts, and mistakes in our conduct, But it is evident that the general arising from the very law of associa- fact, or permanent principle, on which tion on which human intellect and nature proceeds, cannot be determihappiness essentially depend. But the ned, unless after a great number and phenomena of the order of nature, variety of observations and experiaided by this law of association, cor- ments, so as to enable us to separate rect the error, and remove the mis those circumstances that are accidentake which the latter has occasioned. tal from those that are necessary : by We observe and experiment again and necessary, all that we can really mean again : at every time, some circum- or understand, except in the case of stances preceding, attending, or follow- mathematics-amounts to this, that ing the phenomenon, change, and some with them, the result takes place ;remain unaltered:-iftheone which we without them, it does not. This seat first connected with it, as its cause, paration is indispensable in order to disappears while the phenomenon con- destroy erroneous associations, and to tinues, or continues while the pheno- establish those that in all respects cormenon disappears,-in either case, the respond with the general laws of naassociation in our minds between them ture. is destroyed, and a new association be The first object, therefore, is to attween those circumstances that uni- tend to what is passing around and formly precede, attend, and follow within us; the next, to separate accithe phenomenon, and the phenomenon dental from necessary circumstances. itself, is formed. Hence the utility, or It must be obvious, that those generather the absolute necessity, of repeat- ral facts will be ascertained with the ed observations and experiments, if least trouble, and in the shortest time, we wish to avoid error or wrong asso which are attended with the smallest ciations, and to attain truth, or an as number and variety of circumstances; sociation of ideas in our minds, exactly as the circumstances increase in eithroughout similar to the regular or ther or both these respects, the diffider displayed in the three departments culty of separating the accidental from of the universe, already particulari. the necessary proportionally increases, zed.

and we are the more exposed to error The order of nature, therefore, being and prejudice in our opinions, and permanent and stable, and the assoa to hurtful mistakes in our conduct. ciation of ideas being a fundamental The general law, which we call gravi. law of the human intellect, which is tation, is one of the simplest and most the source at once of all our errors and obvious in nature: the circumstances all our knowledge, it becomes a ques which seem to suspend or modify it tion of infinite importance, how we are few, and may be easily ascertained, should proceed, in order to render this accounted and allowed for. On the law as little injurious, and as highly other hand, the law which nature folbeneficial, as possible.

lows in proportioning the births of the There are two grand and paramount sexes, and in regulating the duration objects to which we must direct our of human life, appears, even after long attention and researches, if we wish to and close attention to the facts from attain the truth, and to render it, when which it must be drawn, so varying attained, useful and valuable: we must, and contradictory, that we are dispoin the first place, find out what the sed to regard it as beyond the limit of general laws of nature are, and, in the human knowledge, or as having no next place, learn to apply them with real existence. And yet how wonderpropriety and effect to the extension fully shall we find the balance between of our knowledge and regulation of the sexes preserved in the case of a our conduct. By a law of nature is numerous society, and in a long list of meant a statement of some general persons of the same age, and placed in fact with respect to the order of na the same circumstances ! the mean du.

ration of life, too, is found to vary with- competent judge, and cannot be susin very narrow limits. It is a just re pected of a wish to bring down Mathe. mark, that how accidental soever cir matics to the level of an experimental cuinstances, and how much soever science-expressly states, that the funthey may be placed, when individu- damental principles of Geometry may ally considered, beyond the reach of be reduced to two: the measurement our calculations, experience shews that of angles by circular arches, and the they are, somehow or other, mutually principle of superposition. After adjusted, so as to produce a certain de- wards, however, he maintains, and ingree of uniforinity in the result; and deed proves, that the measurement of this uniformity is the more complete, angles by circular arches, is, itself, the greater is the number of circum- dependent on the principle of superstances combined.

position. On this latter principle, This separating of those circumstan- therefore, according to D'Aleinbert, ces which uniformly precede a result, the whole structure of Geometry rests. from those which are accidental and in- The attempt of this author, and, long operative, as well as from those that pre- prior to him, of Barrow, to rescue Mavent the result from taking place, or al- thematics from the character of being ter and modify it, is, in fact, the induc an experimental science, we cannot tion which Bacon recommends; and think happy or successful.

The suwhere the mind is not powerfully warp- perposition, it is contended, not being ed by prejudice,and the necessary obser- actual—not the applying of one figure vations and experiments are made with to another, to judge by the eyes if care and attention, is a natural conse there is really a difference, as a workquence of that law of association, to man applies his foot-measure to a line which we have already alluded. to measure it ;-but an imaginary or

There is only one branch of know- ideal superposition, consisting in supledge which does not require induc- posing one figure placed on the other tion or the association of ideas for its -the evidence is addressed to the unattainment, though it may rest on derstanding alone, and cannot fairly these :—this is Mathematics. There be characterized as nothing but an ulhas been much controversy on the timate appeal to external observation. nature of mathematical evidence; by But, if the whole structure of Geomost it is represented as something ab- metry is grounded on the principle of stract, and entirely independent of superposition, will not the basis of experiment, or even of the senses; or, this structure be more stable and perto use the expression of M. Prevost, manent, if that superposition is actuin his Philosophical Essays, Mathe- ally performed, than if it is only supmatics is a science of pure reasoning. posed or imagined to be so? Others, on the contrary, and particu Mr Stewart, who coincides with the larly Dr Beddoes, maintain that ma opinion of D'Alembert, that the whole thematical truths, like allother truths, structure of Geometry rests on this must be drawn entirely and exclusive- principle ; repels the inference that it is ly from observation and experiment; a mechanical science. Alluding to the and that so they ought to be taught fourth proposition of the first book, and communicated. This is an im- he says, that the reasoning employed portant and interesting topic; but it rests solely on hypotheses and definiwould lead us far beyond our limits, as tions; and therefore possesses the pewell as our special subject, to enter on culiar characteristic which distinit here: a few remarks, however, may guishes mathematical evidence from be made.

that of all the other sciences. In the The demonstration of all the theo case of this proposition, the hypotherems in the elements of plane geome ses are, that the sides of two triangles try, in which different spaces are com are equal, each to each, and that the pared together, when traced back to angles included between the respecits first principles, terminates in the tively equal sides, are also equal. The fourth proposition of Euclid's first definition to which Mr Stewart alBook; and this rests entirely on a ludes, is, in fact, Euclid's eighth axsupposed application of the one tri- iom, that magnitudes which coincide angle to the other. Indeed, according with each other are equal. But we to D'Alembert, we might go farther; apprehend, that, with the help of these for this author, who certainly is a hypotheses, and this definition, or ax


iom, the sole inference that can be le three angles of a triangle to two right gitimately drawn is, that the two given angles, was the result of a previous dissides, and the given angle, which, by covery of this equality in all the kinds the hypothesis, are stated to be equal, of triangles. And there is good reason are found to be so, by their coinciding to believe, that the celebrated and most on superposition.

important binomial theorem of NewA little examination and reflection ton was entirely the result of inducwill, we think, convince us, that in tion." There is no reason to suppose," the case of this proposition, the thing observes Mr Stewart, “ that he ever proved simply amounts to this:--that attempted to prove the theorem in any where two lines have the same limits, other way; and yet there cannot be a they are equal: for two sides of the doubt, that he was as firmly satisfied triangles, and the included angles, of its being universally true, as if he being supposed equal, the limits of the had examined all the different demonthir) side, in each triangle, are, by this strations of it which have since been very supposition, positively fixed; and given.” Mr Stewart adds, that consiif we suppose that the remaining sides derable use is made of the method of are not respectively equal, we must, induction, by Dr Wallis, in his Arithat the same time, suppose that the hy- metica Infinitorum ; and this innopothesis is altered in some one respect. vation, in the established forms of Similar remarks might be made on mathematical reasoning, gave great ofthat part of the theorem which relates fence to some of his contemporaries; to the equality of the remaining an in particular to M. de Fermat, one of gles. If these observations be well the most distinguished geometers of founded, it would follow, that all ma- the 17th century. The ground of the thematical evidence resolves itself ul. objection was not any doubt of the timately into the perception of iden- conclusions obtained by Dr Wallis, tity. This opinion, we are aware, has but because Fermat was of opinion, been held by some writers, and is that this truth might have been estastrongly opposed by Mr Stewart. He blished by a more legitimate and elethinks that it is founded on the error gant process. of using the terms, identity and equa It is rather singular, that La Place lity, as synonymous and convertible should have given his sanction to interms, and he endeavours to prove that ductive reasoning, and that he should they are not. But, in the only strict have particularly noticed a striking and proper meaning which can be at- instance of its failure by that very Fertached to them in mathematical rea mat, who did not object to its em. soning, they undoubtedly are synony- ployment from any doubt of the truth mous and convertible. Let us take, of the conclusions to which it leads. for example, the fourth proposition, We allude to that passage of La and confine ourselves to the equality Place's. Essai Philosophique sur les of the third side. Mathematics is con Probabilités, where he cites, as an exversant alone with magnitude and fi- ample that induction sometimes leads gure : if, therefore, two lines are equal to inaccurate results, the theorem of in length, they are, in a strict mathe- Fermat on prime numbers. The inmatical sense, identical. Mathematics duetion on which he rested his theoknow no other identity. In every rem he had carried to a considerable sense, identity is a metaphysical idea; extent; and hence he inferred that and Mr Stewart's mistake arises from the truth of the theorem might be deinferring, that because equality is not pended upon in all cases, and to whatthe same as metaphysical identity, ever extent the induction was pushed. therefore it is not the same as mathe. In short, he maintained that his theomatical identity ; but identity is a term rem would always lead to a prime which ought not to be admitted into number, because, in all cases that he mathematical demonstration.

had tried, it had done so. Euler, howWe have remarked, that the truths ever, proved that the theorem failed in of Mathematics may be proved by in- producing a prime number, when the duction, as well as by demonstration, process was carried to a certain point, in whatever that may consist. We are and thus exhibited an instance of the indeed expressly told by Proclus, in failure of induction in mathematicshis Commentary on Euclid, that the a failure which it would not be easy to general theorem of the equality of the parallel in those sciences to which the


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