the room which succession and change require; they can lay no claim to Eternity.

6. We now, as it must appear, find ourselves shut up to the theory within which religious belief respecting the origin of the universe confines its dogmas and its speculations. The whole phenomenal world, an endless succession of changes, belongs to Time; but its existence presupposes that of another kind of Being (äλλo 7ɩ, or more explicitly, érépa ovcía), namely, one that differs from it in being Immutable and Eternal.

7. In the process of becoming acquainted with the ever-changing scene laws of sequence and association are ascertained by the method of Induction, and discovery is preceded by observation, experiment, and research. A priori determinations, however specious their claim to be received as axioms, are but an ignis fatuus if they tempt us to forsake this well-defined highway in the hope of finding a shorter cut. But, beyond the frontier of the finite and the phenomenal, Induction can have no place; nor indeed are we indebted to it in any degree, if we pass the boundary but by one hair's breadth. The Infinite is not the interconcept, quite distinct; and

e

minable; it is another

• The recognition of inability to reach in thought a fixed and necessary limit is liable to be confounded with the conception of the absolutely unlimited. It is when the interminable is thus mistaken for the Infinite that those bewildering contradictions are encountered, which have seemed to justify the assertion that the latter is inconceivable. As specimens of the kind of seeming contradictions to which I allude, I select the following from a fragmentary paper published in the Appendix to the second volume of Sir W. Hamilton's "Lectures on Metaphysics" (p. 527):

"I. Finite cannot comprehend, contain the Infinite.-Yet an inch or minute, say, are finites, and are divisible ad infinitum, that is, their terminated division incogitable.

although, whenever applied in its proper signification, the word always points to something which transcends compre

"2. Infinite cannot be terminated or begun.-Yet eternity ab ante ends now; and eternity a post begins now. So apply to space.

"3. There cannot be two infinite maxima.-Yet eternity ab ante and a post are two infinite maxima of time.

4. Infinite maximum if cut into two, the halves cannot be each infinite, for nothing can be greater than infinite, and thus they could not be parts; nor finite, for thus two finite halves would make an infinite whole.

“7. An infinite number of quantities must make up either an infinite or a finite whole. I. The former.-But an inch, a minute, a degree, contain each an infinite number of quantities; therefore an inch, a minute, a degree, are each infinite wholes; which is absurd. II. The latter.—An infinite number of quantities would thus make up a finite quantity; which is equally absurd. . . ."

Remarks that may serve for the elucidation of these and similar metaphysical puzzles will be found in the preceding note and in note on pp. 18-20. Here it may suffice to comment briefly on certain statements to which, as it appears to me, exception may be taken. I review them seriatim.

1. The inch or the minute may of course be conceived as interminably divisible; but terminated division is a phrase which cannot be admitted in relation to a process which, ex hypothesi, never ceases. If, however, it should seem allowable at some time or other to represent by no definite number, but by absolute infinity, the numerator of the fraction thus obtained, the denominator must have precisely the same value. The infinite minimum would be = o; that is to say, it would be non-existent. But that which is non-existent cannot be considered as comprehended or contained in any quantity or value.

I

∞

2. As regards duration, nothing has its end in the present, but the ever lengthening, yet still at each moment finite, track which the mind makes for itself as it runs back through the moments, years, and ages which constitute the past. Absolute Eternity is never reached by the imagination; it is apprehended by a higher faculty of cognition, and by this it is perceived to comprehend at once the past, the present, and the future. The Infinite is thus discovered, and is understood to account for all things that subsist in subjection to limitations,—all things whose duration may be measured, and whose presence and powers are circumscribed.

There is no such extent of duration as eternity a post, strictly speaking. The interval between the present moment and the most

hension, it is perfectly intelligible. But no enlargement of view obtained by repetition of experiences, no advance in

distant point of future time that will ever be reached cannot be otherwise than finite.

3. I have already shown that there is but one infinite maximum relative to duration, namely, the all-comprehending Eternity.

4. Nothing admits of being halved, or may be conceived as comprising portions that bear to one another any ratio whatever, but a conceivably measurable quantity. An infinite maximum is no such quantity: therefore no question arising from the supposition that it is cut in two can for a moment be entertained.

7. An infinite number is an impossibility; and even if it were permissible to regard as infinite the number of parts of which a finite whole consists, this could only be, as already intimated, on condition that each part shall equal nothing. The fraction thus obtained would be which gives us still a finite quantity. In this result there is no absurdity, for the imaginary parts which are here supposed to be infinite in number are no quantities at all; they are mere nonentities.

∞

I hold myself therefore entitled to conclude that the conception of the Infinite is embarrassed by no contradictions except such as the imagination necessarily creates if urged to attempt the discharge of functions which for it are ultra vires. Forms and modes of existence conditioned by Time and Space are not the materials with which we can represent to our minds an existence superior to these conditions. We find ourselves, however, thinking of Something which, as we perceive, admits of no such representation. Yet how do we know that such is its peculiarity? We confess that the language we employ respecting it is inadequate; we make an apologetic use of the purely negative term infinite. How comes it we are aware that any apology is needed? And how are we to explain the inability of minds of a reverential cast to approach the subject without feeling that they are treading upon holy ground? A conception of the Infinite is presupposed in what we thus think and feel respecting it; it must be ascribed even to those whose sense of the impotence of finite minds in relation to so incomprehensible an object of thought disposes them to deny that it is conceivable. Indeed, a knowledge of the finite as such implies a corresponding knowledge of the Infinite; for the science of contraries is one.

Sir W. Hamilton asserts that "to say that the infinite can be thought, but only inadequately thought, is a contradiction in adjecto; it is the same as saying, that the infinite can be known, but only known as finite (p. 375). My contention, however, is simply that

empirical knowledge, would suffice to account for it. If the human mind were deficient in the innate strength required for leaping up from the finite to touch the Infinite, in vain would it use this springing-board in the attempt to accomplish the feat.

8. These considerations will, I trust, render it sufficiently evident that the method by which I have sought to establish my positions has not laid me open to the charge of making à priori notions do duty for experiment and induction. In accommodating my reasonings to what I believe to be innate exigencies and irrepressible demands of the

the infinite, although no mental picture, nor diagram, nor arithmetical expression of quantity can represent it, except conventionally, is nevertheless, as the contrary of the finite, distinctly apprehended, is thus known as something sui generis, and has a tendency to evoke feelings such as indicate for it a rank which can be claimed for nothing supposed to be finite, however imposing on account of magnitude or antiquity. That it becomes known even to finite minds when they exchange this mortal life for a higher state of existence is an opinion he no less decisively holds. "The Scriptures," he says, "explicitly declare that the infinite is for us now incognizable; they declare that the finite, and the finite alone, is within our reach. It is said (to cite one text out of many) that, 'now I know in part' (i.e. the finite); ‘but then' (i.e. in the life to come)' shall I know even as I am known' (¿.e. without limitation)." I cannot, however, believe that the Apostle is here predicting for himself equality with the Eternal Being in respect to comprehension of the infinite. Rather, as it seems to me, he is intimating, not only that he will attain to a full knowledge of the Saviour, but that, when from his life of future glory he looks back upon the interests with which his mind was conversant while as yet within the horizon of a mortal life, his view of them will no longer be partial and imperfect, as it is at present, but, taking in vastly more than he now sees, will be adequate and complete. “Aptı yivάokw èk μέρους, τότε δὲ ἐπιγνώσομαι καθὼς καὶ ἐπεγνώσθην” (Ι Cor. xiii. 12).

I subjoin Alford's unquestionably correct rendering and suggestive comments: "I SHALL THOROUGHLY KNOW EVEN AS I WAS (during this life he places himself in that state, and uses the aor.: as of a thing gone by) THOROUGHLY KNOWN.""

human intellect, I am but after all following the example of those inquirers who are devoting their energies to an examination of the external world-those learned guides who are conducting us through the galleries of Nature, and pointing out what is to be seen. For how do I know that there is anything real to be seen-how can I be sure that there is an external world, if the conditions under which my reason is exercised allow it to do no more than determine by observation of sequence and association the multifarious relations which my mental pictures and my sensations bear to one another? I perceive, indeed, that these pictures and sensations admit of classification. In particular, some of them come and go at my pleasure; others are independent of my will; in obtaining some I am conscious more or less of volitional action and effort; in the experience of others I seem to myself to be simply passive; some are such as to lead me to believe that they represent objects immediately impressing me from without; others, of a fainter kind in respect to certain features, whether they come unbidden or not, I dissociate from all such producing causes. But what if I imagine myself to have discovered that the impressions involved in muscular action give me cognition of distance and space—what more do I know of muscular action, or of distance and space, than the mere sensations, which I conceive myself to have rightly interpreted when I accept their suggestion that I have an organized body, and that I occupy space, and that I measure distances? Who or what has authorized me to do more than map out, and, as far as I am able, determine my impressions? What warrant have I for proceeding farther and assuming things of which I neither have nor can have an immediate intuition? If I suppose myself to recognize no canons in reasoning other than those which the exigencies of Induction, pure and proper, justify, what