furnish one of these; the likeness of their relations (which I must not yet call analogy) supplies the other, I should assert, but that you disallow the independent existence of the latter, in morals, which is confessedly the widest field of exercise for the human judgment. In morals, I say, for you admit that there may be, elsewhere, a comparison of bare proportions,' founded on a mere likeness of relations *.' I should have conjectured, that you meant here to except the case of Mathematics, (Euclid having defined mathematical analogy to consist in the similitude of ratios,') but that you have formally argued against such excep In fact, this argument is the principal weapon with which you combat the propriety of Dr. C.'s definition; a circumstance which surprised me at first, because he has not used one inference arising from mathematical investigations' in support of it. But I perceive that you have inadvertently restricted the import of the symbols A, B, C, D, employed by him, to mathematical quantities, whereas they are (as you will acknowledge, on re-consideration) intended to designate any four things capable of constituting an analogy. With this observation, I, who confine myself to the task of replying to your objections, might wave all farther comment on what you have alleged, on the assumption of his having been swayed in framing his account of the nature of analogy, by a regard to the ordinary use of the word' by geometers §. But since you have, on this occasion, exhibited in detail the principle, to which, without much farther demonstration, you afterwards refer invariably for confutation of Dr. C.'s position-I should do you wrong, were I not to consider what you have thus urged, attentively. To save time, I will borrow the term which you have adopted, in stating this principle; viz. congeniality. From your context I gather that you mean by it-sameness of kind, indicated by the possession of common properties . And I conjecture that you have preferred it to homogeneity, because the latter is, in general, strictly construed, and you have need of a term which shall apply both to perfect and imperfect sameness of kind ¶. This is fair and convenient. "Now the principle itself is, that it is this very congeniality pervading the subjects of every definite science, which furnishes the substratum of analogy ** And herein resides the likeness, which you afterward declare essential to ' any two or more moral subjects ++,' in order that they should enter into an analogy, and which you instance forthwith in the case of those which are geometrical: viz. lines, surfaces, and solids. These are, I understand you to say, alike, inasmuch as they are congenial; and con * "Letter, p. 33." "Ibid. p. 4. 1. 19-25.". + "Ibid. p. 3-8." ++Ibid. p. 24." "Ibid. p. 6. (and Note,) p. 9. 24, &c." ** Ibid. p. 7." genial, inasmuch as they are magnitudes. There is, you allow, a subordinate distinction between perfectly homogeneous magnitudes, (as line to line,) and partly heterogeneous magnitudes, (as, line to solid.) Still, you contend, that both these classes. are ultimately congenial. And so they are, by your own definition of the word. And so are, by parity of reasoning in morals, judgment and imagination, for they are both mental faculties, or revenge and mercy, for they are both passions, or, to go one step farther, bodily strength and cunning, for they are both human qualities. The very same process of abstraction, by which the common notion of magnitude is elicited from line, surface, and solid, presents us with the genus passion, when it is applied to revenge and mercy, and so on with the rest. Are they therefore, like each other, in any recognized sense of the word? Surely not. But, to confine ourselves a little while longer to the mathematician's province, does he ever admit that a line is like a surface, or talk of the resemblance of either of these to a solid? I may venture to say that he does not, scanty as my knowledge is of his operations. Suppose, however, that he did. This would not establish your position at all. For, would he, or could he, employ, this fact, in any shape, to demonstrate an analogy to subsist among any of them? If so, Euclid has forgotten himself, in having made no mention of the likeness of congeniality, in his somewhat prolix enunciation of a test for the ascertaining geometrical analogies, Should you urge that the definition referred to implies the mon quality of extension' in the subjects of these analogies; I grant the fact as readily as I have granted that they are magnitudes,' and have still to ask whether mathematicians call lines and surfaces like, (or similar,) because they are extended, or even whether they ever infer such likeness or similarity from that fact. On the contrary, it is well known that they would uno ore, pronounce any such fashion a solecism in language, and a fundamental error of conception. com "If these observations are just, they invalidate (I conceive) your assertion of a similarity of subjects necessarily implied in the expression of a similarity of geometrical ratios. For you will readily allow the geometer to have a better right than any one else to determine where any proposed term, as similarity,' or likeness,' can, or cannot, be applied with propriety to the things which fall within his province." (Dalby's Defence, p. 38.) Dr. Copleston has briefly suggested his opinion, that Mr. Grinfield was betrayed into his mathematical disquisition by the same error of conception to which it is attributed by Mr. Dalby; and he distinctly declares, that the general signa used in his statement, which Mr. Grinfield has regarded as appropriate to geometry, have no connexion with geometry as such, but are used merely to represent any four terms, between which there is, a sameness or a similitude of rela tion. After this clear disclaimer, we were, we will own, beyond measure astonished to find Mr. Grinfield, in his second pamphlet, hazarding such an assertion as this: "Your definition of analogy was confessedly mathematical." (Vind. Anal. Part II. p. 22.) It has been observed of some legal advocates, that the confidence of their language and manner always increases in proportion to their knowledge of the real weakness of their cause. We will not undertake to say, that this is Mr. Grinfield's policy; but we cannot help suspecting, that he is not quite satisfied that the public will consider his error to be so extremely natural as he chuses to represent it to be. And though, with an allowable attachment to a new study, he cannot altogether refrain, even in his second publication, from referring to Euclid (p. 40), and mathematical proportions (p. 42); and from expressions of his kope, that the pains he bestowed upon this part of his reasoning have not been lost, we are of opinion, that he would willingly have been spared the trouble in which this unfortunate misconception has involved him. Especially as Mr. Dalby has shewn, that he is not yet competent to the management of a mathematical argument; and Dr. Copleston has informed him of a fact which he would have known had he been better acquainted with the science; viz. that the definition prefixed to the fifth book of Euclid, which states analogy, or proportion, to be the similitude of ratios, "is justly rejected as spurious; because it exceeds the province of geometry, being, in fact, a metaphysical, not a mathematical definition.' (Remarks, p. 58.) Mr. Grinfield's logic meets with no better reception from Mr. Dalby than his mathematics. 6 "I will here summarily avow my belief, says he, to be, that you have supposed a logical denomination capable of producing a prac tical conviction, in morals, as well as in mathematics. For instance, you have called a line and a solid, reason' and 'instinct,' congenial; you have justified the propriety of this appellation, by your circumstantial definition of the term; and, then, have required us to admit, on the strength of it, that a line is like a solid, reason like instinct; and, afterward, by extension of the same principle, that human wisdom is like that ineffable attribute of God, by which he hath made the heavens t,' and 'founded the earth + Whereas the writer whom you criticise has not attempted to refine on the vulgar notion of likeness, or to demand that it be invariably attached to any abstract idea, (as that of con "I adopt this term in the wish to combine brevity with fairness." Psal. cxxxvi. 5." geniality, but has merely admonished men not to confound it, es pecially in their aspirations after the knowledge of things above,' with another notion, of distinct character and different application, viz. that of correspondence, (or homology.) He has reminded us, that we have no reason, a priori, to predicate likeness of the correspondent terms of an analogy, moral or mathematical. He does not deny that they may be like; he only contends that they are not so necessarily (Dalby's Defence, p. 45.) Again, "You have supposed the question to be put, How do we discover any such common possession of properties in two subjects?' And you answer, By judging from the similarity of their effects +." You must mean here in morals, for in mathematics you have not, surely, discovered lines, surfaces and solids, to be magnitudes by the similarity of their effects. In morals, then. All that I shall remark is, that judgment formed on such observed similarity of two effects not altogether identical, (suppose the hut of the beaver, and the dwelling-house of man,) be they ever so much alike, presupposes the exercise of abstraction, (i. e. the collecting their features of agreement, exclusively of the points in which they differ.) And this process (abstraction) was the way in which, as I endeavoured to shew, you must proceed in all cases to arrive at congeniality, or community of properties, simply because they are abstract ideas. Wherefore I object to your theory of analogy, which rests exclusively on this basis, that it will often require long conduct of an operation hard to pursue far, and in the course of which thousands lose their way every day. [Dr. C. shews a less hazardous, a broader road, without absolutely shutting up this.] To your theory, I say, for the practice which you should institute on it is as much too narrow, (as it appears to me,) as the theory itself is too operose. Many of the most sublime discoveries in natural philosophy, (for example,) even of an identity of causes, have been derived from the observation of effects prima facie, altogether dissimilar, nay, directly opposed to each other. Besides, similarity of effect does not always accompany, and thus indicate similarity of rank among things related to each other (e. g. revenge occupies a place in the bad man's heart similar to that of forgiveness in the good Christian's; yet their effects are opposite.) Now you would not exclude similarity of rank from furnishing a basis of analogy, I am sure. Do we not frequently speak of titles and offices, in ancient governments, analogous to those which exist in modern constitutions? Yet the effects of the former and of the latter could not strike us as similar, if they presented themselves to us fully. The materials on which they wrought were very different; the circumstances under which, equally so. To take one example in illustration of what has been suggested in these few last sentences. The sense of honour, ac * "See p. 4." "Letter, p. 10." cording to Montesquieu*, is the chief motive of personal feeling by which a monarchical government is upheld; and the fear of violent death &c. serves the some office in a despot's state. Here is an analogy, if any where; sense of honour is to the monarchy what fear is to the despotism-where is the observable similarity of effects between sense of honour and fear, or between monarchy and despotism? "In fine, analogy does not imply (any more than it excludes) resemblance of its subjects, but it does imply, and is suggested by, correspondence in rank, of the first with the third, the second with the fourth, numbered according to the order in which we think of them. Mathematicians call this correspondence, homology, and regulate all their statements of proportions by it." (Dalby's Defence, p. 53.) We might, perhaps, be inclined to smile at the laboured errors of Mr. Grinfield's argument, did we not find it leading him to such conclusions as these: that Dr. Copleston is "lending the weight of his name and character to delusive speculations, which must inevitably lead to the increase of Atheism and Infidelity:" (Vind. Anal. Part I. p. 14.) that "his theology is heterodox and his logic unsound:" and that he has laboured to establish conclusions which a good man should have hesitated to avow." (Vind. Anal. Part II. p. 90.) This, to say the least of it, is harsh and unbecoming language, and not likely to conciliate the favour of his readers towards his own inaccuracies. Before he ventured upon bringing forward so grave a charge, it surely behoved him to be especially careful that he never mistook the scope of the author's reasoning, or the meaning of his words; that he never imputed to him what he had not said, or derived consequences from his expressions which he disavowed. But Mr. Dalby shews, we think most satisfactorily, that Mr. Grinfield "combats views no where to be found in Dr. Copleston's book, nor deducible by sound inference from any thing which is found there." And this he does in a manner against which no exception can be justly taken; by contrasting the passages on which Mr. G. has raised so lively an alarm, with the representation which he has given of their import. Following this course, he discusses separately every charge which Mr. Grinfield has brought against Dr. Copleston's "Esprit des Loix, b. i. c. 6. 9. I quote this sentiment of his for illustration's sake only, of course. Like many others of his ingenious positions, it exhibits a materially defective view of the subject which he is handling. Still it is an analogical view of two relations." C |