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jects are present and have produced a certain affection of our sensorial organ, we are instantly affected with the primary elementary feelings of perception; and, I may add, that, as our sensations or perceptions are of various species, so are there various species of relations ;-the number of relations, indeed, even of external things, being almost infinite, while the number of perceptions is, necessarily, limited by that of the objects which have the power of producing some affection of our organs of sensation.
The more numerous these relations may be, however, the more necessary does some arrangement of them become. Let us now proceed, then, to the consideration of some order, according to which their varieties may be arranged.
In my Lectures on the objects of physical enquiry, in the early part of the Course, I illustrated very fully the division which I made of these objects, as relating to space or time; or, in other words, as coexisting or successive : our enquiry, in the one case, having regard to the elementary composition of external things; in the other case, to their sequences, as causes and effects; and in mind, in like manner, having regard in the one case, to the analysis of our complex feelings ; in the other, to the mere order of succession of our feelings of every kind, considered as mental phenomena. The same great line of distinction appears to me to be the most precise which can be employed in classing our relations. They are the relations either of external objects, or of the feelings of our mind, considered without reference to time, as coexisting; or considered with reference to time, as successive. To take an example of each kind, I feel that the one half of four is to twelve, as twelve to seventy-two; and I feel this, merely by considering the numbers together, without any regard to time. No notion of change or succession is involved in it. The relation was and is, and will forever be the same, as often as the numbers may be distinctly conceived and compared. I think of summer, I consider the warmth of its sky, and the profusion of flowers that seem crowding to the surface of the earth, as if hastening to meet and enjoy the temporary sunshine. I think of the cold of winter, and of our flowerless fields and frozen rivulets; and the warmth and the cold of the different seasons, I regard as the causes of the different appearances. this case as in the former, I feel a rela
Sa tion; but it is a relation of antecedence and consequence, to which the notion of time, or change, or succession, is so essential, that without it the relation could not be felt.
It is not wonderful, indeed, that the classes of relations should be found to correspond with the objects of physical inquiry; since the results of all physical inquiry must consist in the knowledge of these relations. To see many objects,-or I may say even to see all the objects in nature, and all the elements of every object-and to remember these distinctly as individuals, without regard to their mutual relations, either in space or time-would not be to have science. To have what can be called science is to know these objects, as coexisting in space, or as successive in time,-as involving certain proportions, or proximities, or resemblances, or certain aptitudes to precede or follow. Without that susceptibility of the mind, by which it has the feeling of relation, our consciousness would be as truly limited to a single point, as our body would become, were it possible to fetter it to a single atom. The feeling of the present moment would be every thing; and all beside, from the infinitely great to the infinitely little, would be as nothing. We could not know the existence of our Creator ; for it is by reasoning from effects to causes, that is to say, by the feeling of the relation of antecedence and consequence, that we discover his existence, as the great cause or antecedent of all the wonders of the universe. We could not know the existence of the universe itself ; for it is as I have shewn, by the consideraation of certain successions of our feelings only, that we believe things to be external, and independent of our mind. We could not, even in memory, know the existence of our own mind, as the subject of our various feelings ; for this very knowledge implies the relation of these transient feelings to one permanent subject. We might still have had a variety of momentary feelings, indeed, but this would have been all ;--and, though we should have differed from them in our capacity of pleasure and pain, we should scarcely have been raised, in intellectual and moral dignity, above the organized beings around us, of a different class, that rise from the earth in spring, to flourish in summer, and wither at the close of autunn--and whose life is a brief chronicle of the still briefer seasons in which they rise, and flourish, and fade.
The relations of phenomena may, as I have already said,
be reduced to two orders ;—those of coexistence and succession ; -the former of which orders is to be considered by us in the first place.
The relations of this order, are either of objects believed by us to coexist withont, or of feelings that are considered by us as if coexisting in one simple state of mind.
Of the nature of this latter species of virtual, but not absolute coexistence, I have already spoken too often to require again to caution you against a mistake, into which, I must confess, that the terms, which the poverty of our language obliges us to use, might, of themselves very naturally lead you ;—the mistake of supposing, that the most complex states of mind are not truly, in their very essence, as much one and indivisible, as those which we term simple--the complexity and seeming coexistence which they involve, being relative to our feeling only, not to their own absolute nature. I trust I need not repeat to you, that, in itself, every notion, however seemingly complex, is, and must be, truly simplebeing one state or affection, of one simple substance, mind. Our conception of a whole army, for example, is as truly this one mind existing in this one state, as our conception of any of the individuals that compose an army. Our notion of the abstract numbers, eight, four, two, as truly ope feeling of the mind, as our notion of simple unity. But, by the very nature or original tendency of the mind, it is impossible for us not to regard the notion of eight as involving, or having the relation of equality to two of four, four of two, eight of one; and it is in consequence merely of this feeling of the virtual equivalence of one state of mind, which we therefore term complex, to many other states of mind, which we term simple, that we are able to perceive various relations of equality, or proportion, in the complex feeling which seems to us to embrace them all in one joint conception-not in consequence of any real coexistence of separate parts, in a feeling that is necessarily and essentially indivisible. It is, as I before stated to you, on this virtual complexity alone that the mathematical sciences are founded; since these are only forms of expressing the relations of proportion, which we feel of one seeming part of a complex conception, to other seeming parts of that complex conception, which appear to us as if mentally separable from the rest.
1 proceed, then, now, to the consideration of the first of our classes of relations,—those of which the subjects are regarded, without reference to time. To this order of real coexistence, as in matter, or of seeming coexistence, as in the complex phenomepa of the mind, belong the relations of position, resemblance or difference, proportion, degree, comprehension. I am aware, that some of these might, by a little refinement of analysis, be made to coincide,—that, for example, both proportion and degree might, by a little effort, be forced to find a place in that division which L have termed comprehension, or the relation of a whole to the separate parts included in it; but I am aware, at the same time, that this could not be done without an effort,—and an effort too, in some cases, of very subtile reasoning; and I prefer, therefore, the division which I have now made, as sufficiently distinct, for every purpose of arrangement.
I look at a number of men, as they stand together. If I merely perceived each individually, or the whole as one complex group, I should not have the feeling of relation ; but I remark one, and I observe who is next to him, who second, who third ; who stands on the summit of a little eminence above all the rest; who on the declivity; who on the plain beneath; that is to say, my mind exists in the states which constitute the various feelings of the relation of position.
I see two flowers, of the same tints and form, in my path. I lift my eye to two cliffs of corresponding outline, that hang above my head. I look at a picture, and I think of the well known face which it represents ;-or, I listen to a ballad, and seem almost to hear again some kindred melody, which it wakes in my remembrance. In each of these cases, if the relative suggestion take place, my mind, after existing in the states which constitute the perception, or the remembrance of the two similar objects, exists immediately in that state which constitutes the feeling of resemblance, as it exists in the state which constitutes the feeling of difference, when I think of certain circumstances, in which objects, though similar, perhaps, in other respects, have no correspondence or similarity whatever.
I think of the vertical angles formed by two straight lines, which cut one another; of the pairs of numbers, four and sixteen, five and twenty,—of the dimensions of the columns, and their bas
es and entablatures, in the different orders; and my mind exists immediately in that state, which constitutes the feeling of proportion.
I hear one voice, and then a voice which is louder. I take up some flowers, and smell first one, and then another, more or less fragrant. I remember many days of happiness, spent with friends who are far distant,—and I look forward to the day of still greater happiness, when we are to meet again. In these instances of spontaneous comparison, my mind exists in that state, which constitutes the feeling of degree.
I consider a house, and its different apartments,-a tree, and its branches, and stems, and foliage,-a horse, and its limbs, and trunk, and head. My mind, which had existed in the states that constituted the simple perception of these objects, begins immediately to exist in that different state, which constitutes the feeling of the relation of parts to one comprehensive whole.
In these varieties of relative suggestion, some one of which, as you will find, is all that constitutes each individual judgment, even in the longest series of our ratiocination --nothing more is necessary to the suggestion, or rise of the feeling of relation, than the simple previous perceptions or conceptions, between the objects of which the relation is felt to subsist. When I look at two flowers, it is not necessary that I should have formed any intentional comparison. But the similitude strikes me, before any desire of discovering resemblance can have arisen. I may, indeed, resolve to trace, as far as I am able, the resemblances of particular objects, and may study them accordingly; but this very desire presupposes, in the mind, a capacity of relative suggestion, of which it avails itself, in the same manner, as the intention of climbing a bill, or traversing a meadow, implies the power of muscular motion as a part of our physical constitution.
The susceptibility of the feeling of relation, in considering objects together, is as easy to be conceived in the mind, as its primary susceptibility of sensation, when these objects were originally perceived, whether separately or together; and, if nothing had before been written on the subject, I might very safely leave you to trace, for yourselves, the modifications of relative suggestion, in all the simple or consecutive judgments which we form ;-but so much mystery has been supposed to hang about it; and the art