constituted with its own fundamental laws of thought, which will inevitably cause it to develope only to certain effects-that is, by which it will develope thus and thus, and no otherwise,— and that at the same time a certain external influence, a contact with the outward world, is absolutely necessary,—without which it would never develope at all. On the one hand, as Professor De Morgan well puts it, Either we have ideas which we do not acquire from or by means of communication with the ' external world (experience, trial of our senses), or there is a power in the mind of acquiring a certainty and a generality which experience alone could not properly give;' and on the other hand, without that experience, the mind, for aught we know, would remain in perpetual slumber; this experience being, as far as either facts or consciousness can teach us, an invariable condition of the very first germination of thought. The external world presents us with abundant illustrations of an analogous union of similarly diverse conditions of development. Thus the internal structure of the flower is such that it will develope only to a certain colour, form, fragrance, and no other; yet without the sun, the wind, the dew, the rain, the soil, it will remain in the germ. In like manner, the eye, were it otherwise constructed than it is, would not see, whatever the abundance of light; and were it constructed as it is, could see just as little if there were no light at all.

But in that complex result which flows from this perpetual, reciprocal, and inveterately entangled interaction of the diverse components of thought, it is almost hopeless to estimate the precise portion of effect due to either alone. The result itself becomes an insoluble compound. As in a product of chemical affinities, the separate elements have disappeared; the acid and alkali have alike vanished; the silica and the potash are no longer visible in the transparent crystal. And of the hopelessness which must probably attend every attempt at complete analysis, we may see proof in the fact that two such philosophers, even in our own day, as Dr. Whewell, and Mr. J. S. Mill, can yet come to such opposite conclusions as to the elements contributed severally by the internal constitution of the mind and its external experience, in the formation of our ideas of that class of truths which have been deemed (inasmuch as their contraries appear impossible) necessary. Dr. Whewell contends that even such a principle as the equal pressure of fluids in all directions which, at first sight, seems so little self-evident, that the curious fact which it alone explains is still called the Hydrostatic Paradox was not derived from experience in

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Dr. Whecell and Mr.J. S. Mill.

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'any exam sense of that phrase,'* but that the mind can pronounce on its à priori certainty. Similarly, he contends that the first law of motion which was at first regarded as an enoriços paradox—and even the law of definite proportions in chemistry a fact fully established only in our own age), though historically collected from experience, yet have an evidence far beyond it; the mind, in virtue of its own laws of thought, being competent to pronounce not only that these facts are, but must have been; that it attains a point of view from which it can pronounce that the first might certainly have been discovered independently of experience, and the contrary of the second 'inconceiva Mr. Mill, on the other hand, contends, and with great force and ingenuity of argument, that even axioms themselves are experimental truths, generalisations from ex'perience;" that however the mind may and does transmute into general truth the facts of experience, its constitution is not such that, except as taught by uniform experience, it would be entitled to pronounce even the proposition that_two_straight 'lines inclose a space' inconceivable! From no single instance, or a few instances, but from the universality of the experience, can the mind, it seems, in any case legitimately establish an axiom; in other words, that axioms are generalisations from experience.

We have said that Mr. Mill has argued with great force and ingenuity, but we cannot say with complete success. While Dr. Whewell seems to us to have gone much too far, on the one hand, in reducing to necessary truths what assuredly the generality of mankind will not feel to be such, we are equally impressed with the conviction that Mr. Mill has gone too far on the other in exploding all 'necessary truths' whatsoever. But, at all events, whether Dr. Whewell or Mr. Mill be nearer the truth, their disputes are certainly most instructive; for when we find such men thus at variance, at this late period of metaphysical history, and in relation to truths so far from elementary, it may well seem an insuperable difficulty to separate, by any exact analysis, the precise degrees in which the mind itself and the outward conditions of its development have co-operated; and, least of all, in the earliest and most elementary products of thought.

The reasons for which we cannot help suspecting Mr. Mill's extreme view to be a paradox, we will take the liberty of briefly stating. He maintains that experience alone gives us even such a notion as that two straight lines, which intersect, will never † Ibid. p. 213.

* Phil Ind. Sciences, vol. i. p. 203.

meet again; on the other hand, mankind have certainly been disposed to call such propositions as these necessary truths, and to distinguish them from the undoubted lessons. of experience, where that experience has been quite as universal and uniform. We have always seen a cloudless sky blue, and the grass green; our experience of this has been equally early and unvarying with that which tells us that intersecting straight lines meet not again. Our feelings, therefore, in the two cases ought to be the same, if experience were all; but are they? Surely we all feel there is a totally different state of mind in the two cases: we can conceive the sky might have been green and the grass blue without difficulty; not so in the other case: we feel that there is a difference not only in the intensity, but in the nature, of the conviction. Without any experience, indeed, we should have no thoughts of any of these things,-lines, clouds, sky, or grass; but the experience being equally invariable and uniform in all the supposed cases, we feel that the results are totally different. Why is this? unless it be that the mind by its very constitution, has been able to do something in the one case which it could not do in the others, to transform the one fact into something more than a generalisation from experience, which something it calls a necessary truth?-Again: unless the mind, from the peculiarity of its own constitution, could thus deal with some of the materials submitted to it from without, how came it to separate some of the propositions among the many thus supposed to be wholly (and certainly equally) verified by experience into these so-called necessary and contingent truths. How came it to make any distinction between them? It is not sufficient, we think, to say that the experience in all the former cases was more uniform and unvarying; for it cannot be more than perfectly uniform and unvarying and such it often is in what we persist in regarding as what might possibly have been otherwise; the phenomena of gravitation, for example. Now in all those cases in which the mind says, 'this is a necessary truth, it cannot be otherwise;' and this is a generalisation of an equally uniform experience, but it might have been other'wise;' how is it that the mind comes to make this distinction at all, and to feel it yet more strongly than it can express it? The very classification of truths into two such divisions (experience in either case being the same) is, we think, proof that the mind has the power of acquiring from experience what experience alone could never give.Again: that the mind, at all events, is so constituted as that its laws, to a certain extent, are superior to experience, and can transform it, is, we think, evident from this very notion that there are propositions neces

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Origination of Mathematical Definitions.

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sarily true, and not generalisations from experience. This is a very general, not to say universal, notion of the human mind. This notion is itself either derived from experience or not. If so derived, and the notion itself is true, then experience has contradicted itself; if so derived, and the notion is false, then experience has taught us falsehood, and not truth; if not so derived, and the notion be false, the human mind is yet so constituted as to subordinate objective experience to its own subjective laws; if not so derived, and the notion be true, the argument, of course, is fully decided.-Once more: since this notion has certainly been a necessary notion of the majority of minds (that is, they cannot help forming it), it appears that, if false, such minds, though they cannot attain necessary truth, are so constituted as necessarily to transform the truths of experience into falsehoods.

Again: according to Mr. Mill's theory, the definitions of mathematics are not mere abstractions, but are approximately true in fact, and have been derived from actual figure and magnitude. This and this alone, he says, enables us to apply mathematical reasonings to the actual world. It is no doubt true that what we must call abstractions have been thus derived; and that we can apply mathematical reasoning to physics only because material forms indefinitely approximate to the definitions; so that in the application we may omit the inappreciable or unimportant difference between the definition and the reality. Yet, as he concedes that there are in fact no mathematical lines or surfaces, no exact triangles, rectangles, or circles, it seems as natural to say that these notions are formed as much in contradiction to experience as in conformity with it*; they are notions which experience suggested, but

* As to the origination of mathematical definitions, Mr. Hallam, in a long note inserted in the last edition of his valuable History of European Literature, has made a strenuous endeavour to rescue them from being mere creations of the mind, and contends that the generally admitted doctrine - admitted alike by Dr. Whewell and Mr. Millthat there are and can be no such things in nature as perfect triangles, rectangles, or circles, is altogether an illusion: he affirms that if this were true, it would reduce the most certain of the sciences to a mere play of fancy; he therefore contends that its conclusions are true only because its definitions are perfectly capable of being realised as actual existences in the relations of pure space. Whether this be so or not, we cannot feel convinced that it applies to the point here in dispute; since it seems to us tolerably certain that it was not in this way that the mind arrived at the definitions of perfect mathematical figures; it was not because it chose to imagine them as really existing-it cer

which experience never realised; and surely this very tendency of the mind to separate from experience all that in fact interferes with the theoretic perfection of its definitions and ratiocination, affords an indication that, by its very constitution, it is so framed as to modify by its own peculiar laws the conceptions derived from experience.

Once more: we should like (we submit it without pretending more than a doubt) to have an intelligent solution of the following dilemma: Taking the case of the 'intersecting right lines which, when produced, never meet,' we would ask, is it possible that minds should ever be constructed, such that they would not infer that, though produced ever so far, these lines would never meet? Either such minds could be constructed, or not; if they could, then that we form different notions is owing to the peculiar structure of our minds by which we arrive at a different conclusion from theirs; for the experience itself we suppose to be the same. If no such minds could be formed, then it appears that it is a universal condition of all minds that they must conclude some inferences from some facts of universal experience which they do not from others equally universal; that is, the laws of thought are such that we are necessarily led to believe that such and such things could not have been otherwise.-If Mr. Mill's reasoning be correct, then, for aught we know, we fear we must be warranted to say that there may be a number x, such that it cannot be increased, and a world in which two intersecting right lines may possibly meet again; for assuredly experience can disprove neither. We are also left to wonder at the universal presumption and inconsistency of the human race, not one of whom but would stake his life that there is no spot in the universe where two straight lines would inclose a space;

tainly saw none such-but because it was capable of framing them from the rude approximations which experience supplied. If Mr. Hallam had gone one step further- to the definitions, namely, of mathematical physics-we think that he would have seen that the solution (possible or not) was not needed. Not even he, we presume, will contend that the lever or the pulley of mechanical science; the rod perfectly inflexible, the cord perfectly flexible, and both imponderable, ever had an existence, or in a material world can be even conceivable. But we venture to recommend the entire note to the attention of our readers. It is a striking example, at all events, of the 'viridis senectus' which the venerable critic is enjoying; of the strenuous manner in which his mind still feels disposed to revolve problems which are usually dismissed at a much earlier period of life. We congratulate him on this verdant aftermath of thought so late in the autumn of his days.