2. Before, however, coming to the conclusion that the ultimate region of mystery is absolutely impenetrable, we may be permitted to entertain the question whether the conditions of rational thought restrict us to those methods whereby we investigate the inter-relations of phenomena. So momentous, indeed, are the interests which must needs engage attention in the course of inquiry thus indicated, that it is not easy to set out with a mind free from prepossessions unfavourable to the attainment of truth; but an examination of the subject is not for that reason to be deprecated. If it be conducted in a truly scientific spirit, its issue, as I believe, will be a Science, and one that may be properly and distinctively termed Fundamental."

3. Having proposed to myself to attempt the inquiry, I start from the supposition that, in tracing backward into past time a chain of successive phenomena, we have reached the remotest link at present discovered. Here, if we are

a “Verum in experientiæ vero curriculo, eoque ad nova opera producendo, Divina Sapientia omnino et ordo pro exemplari sumenda sunt. Deus autem primo die creationis lucem tantum creavit eique operi diem integrum attribuit; nec aliquid materiati operis eo die creavit. Similiter et ex omnimoda experientia, primum inventio causarum et axiomatum verorum elicienda est; et lucifera experimenta, non fructifera quærenda. Axiomata autem recte inventa et constituta praxin non strictim sed confertim instruunt, et operum agmina ac turmas post se trahunt” (Bacon, “Nov. Org.,” Aph. LXX.).

The process contemplated by the author of this aphorism is simply the inductive discovery of determinate antecedents or conditions within the phenomenal world. But if rational creatures investigate with a view to fruit worthy of their labours, they must ascend to the Original Cause. We are not concerned to show that any immediate practical results are due to the process of discovery, but it fulfils the preliminary condition of all true fruitfulness; it lets in upon the mind a quickening light. To facilitate illumination, to aid in dispersing such mists as are liable to be generated by an exclusive and absorbing devotion to the physical sciences, and tend to bewilderment in metaphysical inquiry, is the aim of this treatise.

not disposed to rest, we find ourselves in face of two alternative hypotheses: (1) the phenomenon we are contemplating had an antecedent; or (2) it had no antecedent. Of these, the latter, if it be adopted, necessitates a similar choice: (a) the phenomenon had no beginning; or (b), having had a beginning, it was self-originated. Now, to account for anything by asserting that it is self-originated is to use a phrase the absurdity of which at once exposes itself; for it assumes the necessity of a cause, but nullifies

In wording this hypothesis I have rhetorically assumed that it is inadmissible; but my argument will lose nothing of its force if I say, “it originated uncaused," or "there was nothing to account for it." I do not know whether any one would insist upon my admitting the possibility of uncaused origination; but if, on the supposition that existence or action has had a beginning, our reason is under no obligation to demand that it shall have also had a conditioning antecedent, then, as regards existence and action, our reason is clearly without function: no discoveries can be established; induction is an imaginary process. There being no ground for assuming that the phenomena of consciousness owe their origin to anything, and that their changes and successions are in any way determined, we have no warrant for the persuasion that they have any significance; and, as regards reason, the subject of consciousness must rest satisfied with the conviction that as such he exists, and that the thoughts of which he is conscious, and the sensations which he feels, are his own thoughts and sensations. In no way can reason escape from this prison, and exercise its powers upon objective existence, except by proceeding on the assumption that nothing ever originates, or takes place, or stirs, but there is a cause for what has happened. But, indeed, even if restricted within the limits of the pure mathematics, the reason cannot exert its activity without thereby illustrating causal origination. The subject of consciousness cannot put two and two together otherwise than as a conditioning antecedent. Ignore altogether volitional agency; still, he cannot reason without being in some way concerned in projecting into his consciousness the thoughts which he thus associates: they are severally linked to him as to a cause; he is more than a mere subject of affections; he sets in motion certain mental processes, and therefore (whether subordinately or not, would be an irrelevant consideration) he is an author.

• To prevent confusion, I think it advisable to define the sense in which I use the word cause. I mean the obviously proper correlative

It

the assumption by identifying the cause with the effect. is prompted by the impossibility of conceiving a beginning without a cause, but this impossibility it obviously fails to disguise. On the other hand, by assuming that the phenomenon had an end, we clearly render inadmissible the hypothesis that it had no beginning. An eternal condition can be no otherwise conceived than as being in its nature immutable. Our minds refuse to ascribe existence to any

to effect. I assume that what we want to know is, how a given change has been brought about (To őbev ʼn kívnois). I do not include matter, or form, or end. To represent these, in any admissible sense, as being severally causes of anything, is only another way of saying that the existence of the thing presupposes the matter of which it consists, the form by which it is characterized, and the end for which it exists; that these are essential conditions, and that in fulfilling them the thing is neither more nor less than what it is. To require that it shall have an efficient cause is to assume that it cannot have arisen from nothing, but, as having had a beginning, must be the effect of something. When an original efficient cause is taken into account, this of necessity is regarded as being, not a determinate condition instrumentally antecedent, but an author.

Being apart from Form (ovoía otherwise than as involving eldos) must of course be admitted to be inconceivable. But to be assured of this is not our object, when we inquire into the cause of anything; what we wish to know is, how it came into existence, or, if it be an occurrence, how it came to pass. What we desire is not a metaphysical exposition, which, be it ever so luminous, leaves our minds still within the limits of the conception we had to form of the thing itself; but information that may lift them above it, at least one step.

To promote Matter and Form to the rank of first causes is of course to assume them to be eternal, and so to confound the phenomenal with its Source. As regards such kinds of nexus as are merely phenomenal, it should be observed that in point of time the so-called cause, or concurrence of causes, is not of necessity antecedent to the effect; they may be simultaneous; thus the alternation of day and night is accounted for by the revolution of the earth on its axis. But wherever investigation is pursued until the first link of the causal nexus is reached, this must be acknowledged to be something which had existed before any of the others appeared, and, being uncaused, was without beginning.

thing which unites in itself the characteristics of time and of eternity. No less abhorrent to the Infinite is an end than a beginning: the negation of one is the negation of the other.

4. There remains then the hypothesis that the phenomenon had an antecedent. Was this also of limited duration ? So far as we know, nothing forbids the supposition, or indeed precludes the conjecture that the antecedent thus assumed may have had an antecedent similar to it in the same respect. But to what length is our imagination at liberty to extend the chain? May we conceive that it had no beginning, no first link? In at once answering this question in the negative, I am uttering a conviction of a kind which steadfastly refuses to allow the legitimacy of any appeal to the future decisions of a deepened and enlarged experience. I am forced to conceive a limit to the phenomenal chain.

5. But the conviction in question admits, I think, of some elucidation. A succession without beginning presupposes the possibility of an infinite number; but an infinite number is a contradiction in terms. The numerable can never be the infinite. Our intellect finds of necessity that it limits whatever it represents to itself as a result that may be arrived at by the process of counting. It cannot allow that there is any such thing as an aliquot part of infinity. We may imagine that we go on counting for

d

a As bearing upon this point two passages which I here quote may perhaps be found suggestive.

“Οτι μὲν τοίνυν ἄπειρον οὐκ ἐνδέχεται, δῆλον· οὔτε γὰρ περιττὸς ὁ ἀπειρός ἐστιν οὔτε ἄρτιος, ἡ δε γένεσις τῶν ἀριθμῶν ἢ περιττοῦ ἀριθμοῦ ἢ ἀρτίου ἀεί or."-Aristotle, " Metaphys.," XII. viii. 15.

“ Δέδεικται δὲ καὶ ὅτι μέγεθος οὐθὲν ἔχειν ἐνδέχεται ταύτην τὴν οὐσίαν, ἀλλ ἀμερὴς καὶ ἀδιαίρετός ἐστιν. Κινεῖ γὰρ τὸν ἄπειρον χρόνον, οὐθὲν δ ̓ ἔχει δύναμιν ἄπειρον πεπερασμένον. Ἐπεὶ δὲ πᾶν μέγεθος ἢ ἄπειρον ἢ πεπερασμένον, πεπε

ever and ever; but never at any time would the duration thus occupied reach the measure of the infinite. Time is

ρασμένον μὲν διὰ τοῦτο οὐκ ἂν ἔχοι μέγεθος, ἄπειρον δ ̓ ὅτι ὅλως οὐκ ἔστιν οὐθὲν ἄπειρον μέγεθος.”—Id., XI. vii. 12, 13.

Nothing may be regarded as divisible and at the same time conceived of as infinite. Nor are size or magnitude and infinity compatible concepts; for a magnitude cannot be given― cannot be represented to the mind, except as something determinate in respect

to measure.

Space, as it pictures itself to our imagination, although illimitable, is always a magnitude, and as such divisible and finite, and in it objects represent themselves to us as holding definite relations in respect to size and distance. Of Infinity we have no adequate idea, no true concept, until we have conceived of it as transcending both Space and Time.

There is no arithmetical conception of infinity; that which Algebra admits is analogical: o: a (any given quantity) :: a: ∞o, i.e. '∞ = a2

a

The relation which nothing bears to quantity is not arithmetical, neither is the relation which quantity bears to infinity. The expression of an algebraical magnitude in a so-called infinite series (a suggestive, but necessarily imperfect expression) implies that a number may be conceived of as infinite on condition that a quantity may be nothing. The possibility assumed is purely conditional: it is only on the understanding that shall represent absolutely nothing that n is allowed to signify infinity. Thus the term to which n belongs expresses, when the latter is said to be infinite, an algebraical fiction. As belonging, however, to a series of quantities successively diminishing, and as involving a quantity that goes on increasing, it conveniently indicates that as soon as one of them disappears from the category of quantity at one pole of thought, the other must needs vanish at the opposite.

x

The meaningless dogma of the Pythagoreans, that Number is the origin of all things, affords singularly striking proof that the intellect does but dream when it expatiates in the emptiness it has made by persistent abstraction, and fancies that here it has found escape from the tyranny of sense; for, of all the shadows it strives to grasp, none is less fitted than Number to represent the ineffable Cause which accounts for all things. Of the fundamental error to which the theory may be traced, Aristotle had, I think, a dim perception; but he perceived it perhaps even more clearly than he succeeded in pointing it out.