Mr. Mill calls this argument "a curiosity of dialectics," and answers, "Perfect wisdom would have begun to will the new state at the precise moment when it began to be better than the old." Hamilton is not speaking of states of things, but of states of the Divine nature, as creative or not creative; and Mr.
Mill"s argument, to refute Hamilton, must suppose a time when the new nature of G.o.d begins to be better than the old! Mr. Mill would perhaps have spoken of Hamilton"s argument with more respect had he known that it is taken from Plato.
On this we would remark, _en pa.s.sant_, that this is precisely Hamilton"s own doctrine, that the sphere of our belief is more extensive than that of our knowledge. The purport of Hamilton"s argument is to show that the Absolute, as conceived by Cousin, is not a true Absolute (_Infinito-Absolute_), and therefore does not represent the real nature of G.o.d. His argument is this: "Cousin"s Absolute exists merely as a cause: G.o.d does not exist merely as a cause: therefore Cousin"s Absolute is not G.o.d." Mr. Mill actually mistakes the position which Hamilton is opposing for that which he is maintaining. Such an error does not lead us to expect much from his subsequent refutation.
His first criticism is a curious specimen of his reading in philosophy.
He says:--
"When the True or the Beautiful are spoken of, the phrase is meant to include all things whatever that are true, or all things whatever that are beautiful. If this rule is good for other abstractions, it is good for the Absolute. The word is devoid of meaning unless in reference to predicates of some sort.... If we are told, therefore, that there is some Being who is, or which is, the Absolute,--not something absolute, but the Absolute itself,--the proposition can be understood in no other sense than that the supposed Being possesses in absolute completeness _all_ predicates; is absolutely good and absolutely bad; absolutely wise and absolutely stupid; and so forth."[AO]--(P. 43.)
[AO] In support of this position, Mr. Mill cites Hegel--"What kind of an absolute Being is that which does not contain in itself all that is actual, even evil included?" We are not concerned to defend Hegel"s position; but he was not quite so absurd as to mean what Mr. Mill supposes him to have meant. Does not Mr. Mill know that it was one of Hegel"s fundamental positions, that the Divine nature cannot be expressed by a plurality of predicates?
Plato expressly distinguishes between "the beautiful" and "things that are beautiful," as the One in contrast to the Many--the Real in contrast to the Apparent.[AP] It is, of course, quite possible that Plato may be wrong, and Mr. Mill right; but the mere fact of their antagonism is sufficient to show that the meaning of "the phrase" need not be what Mr.
Mill supposes it must be. In fact, "the Absolute" in philosophy always has meant the One as distinguished from the Many, not the One as including the Many. But, as applied to Sir W. Hamilton, Mr. Mill"s remarks on "the Absolute," and his subsequent remarks on "the Infinite,"
not only misrepresent Hamilton"s position, but exactly reverse it.
Hamilton maintains that the terms "absolute" and "infinite" are perfectly intelligible as abstractions, as much so as "relative" and "finite;" for "correlatives suggest each other," and the "knowledge of contradictories is one;" but he denies that a concrete thing or object can be positively conceived as absolute or infinite. Mr. Mill represents him as only proving that the "unmeaning abstractions are unknowable,"--abstractions which Hamilton does not a.s.sert to be unmeaning; and which he regards as knowable in the only sense in which such abstractions can be known, viz., by understanding the meaning of their names.[AQ]
[AP] _Republic_, book v., p. 479.
[AQ] This confusion between conceiving a concrete thing and knowing the meaning of abstract terms is as old as Toland"s _Christianity not Mysterious_, and, indeed, has its germ, though not its development, in the teaching of his a.s.sumed master, Locke. Locke taught that all our knowledge is founded on simple ideas, and that a complex idea is merely an acc.u.mulation of simple ones. Hence Toland maintained that no object could be mysterious or inconceivable if the terms in which its several attributes are expressed have ideas corresponding to them. But, in point of fact, no simple idea can be conceived as an object by itself, though the word by which it is signified has a perfectly intelligible meaning. I cannot, _e.g._, conceive whiteness by itself, though I can conceive a white wall, _i.e._, whiteness in combination with other attributes in a concrete object.
To conceive attributes as coexisting, however, we must conceive them as coexisting in a certain manner; for an object of conception is not a mere heap of ideas, but an organized whole, whose const.i.tuent ideas exist in a particular combination with and relation to each other.
To conceive, therefore, we must not only be able to apprehend each idea separately in the abstract, but also the manner in which they may possibly exist in combination with each other.
"Something infinite," says Mr. Mill, "is a conception which, like most of our complex ideas, contains a negative element, but which contains positive elements also. Infinite s.p.a.ce, for instance; is there nothing positive in that? The negative part of this conception is the absence of bounds. The positive are, the idea of s.p.a.ce, and of s.p.a.ce greater than any finite s.p.a.ce."--(P. 45.)
This definition of _infinite s.p.a.ce_ is exactly that which Descartes gives us of _indefinite extension_,--"Ita quia non possumus imaginari extensionem tam magnam, quin intelligamus adhuc majorem esse posse, dicemus magnitudinem rerum possibilium esse indefinitam."[AR] So too, Cudworth,--"There appeareth no sufficient ground for this positive infinity of s.p.a.ce; we being certain of no more than this, that be the world or any figurative body never so great, it is not impossible but that it might be still greater and greater without end. Which _indefinite increasableness_ of body and s.p.a.ce seems to be mistaken for a _positive infinity_ thereof."[AS] And Locke, a philosopher for whom Mr. Mill will probably have more respect than for Descartes or Cudworth, writes more plainly: "To have actually in the mind the idea of a s.p.a.ce infinite, is to suppose the mind already pa.s.sed over, and actually to have a view of all those repeated ideas of s.p.a.ce, which an endless repet.i.tion can never totally represent to it,--which carries in it a plain contradiction."[AT] Mr. Mill thus unwittingly ill.u.s.trates, in his own person, the truth of Hamilton"s remark, "If we dream of effecting this [conceiving the infinite in time or s.p.a.ce], we only deceive ourselves by subst.i.tuting the _indefinite_ for the infinite, than which no two notions can be more opposed." In fact, Mr. Mill does not seem to be aware that what the mathematician calls _infinite_, the metaphysician calls _indefinite_, and that arguments drawn from the mathematical use of the term _infinite_ are wholly irrelevant to the metaphysical. How, indeed, could it be otherwise? Can any man suppose that, when the Divine attributes are spoken of as infinite, it is meant that they are indefinitely increasable?[AU]
[AR] _Principia_, i., 26.
[AS] _Intellectual System_, ed. Harrison, vol. iii., p. 131.
[AT] _Essay_, ii., 17, 7.
[AU] One of the ablest mathematicians, and the most persevering Hamiltono-mastix of the day, maintains the applicability of the metaphysical notion of infinity to mathematical magnitudes; but with an a.s.sumption which unintentionally vindicates Hamilton"s position more fully than could have been done by a professed disciple.
"I shall a.s.sume," says Professor De Morgan, in a paper recently printed among the _Transactions of the Cambridge Philosophical Society_, "the notion of infinity and of its reciprocal infinitesimal: that a line can be conceived infinite, and therefore having points at an infinite distance. Image apart, which we cannot have, it seems to me clear that a line of infinite length, without points at an infinite distance, is a contradiction." Now it is easy to show, by mere reasoning, without any image, that this a.s.sumption is equally a contradiction. For if s.p.a.ce is finite, every line in s.p.a.ce must be finite also; and if s.p.a.ce is infinite, every point in s.p.a.ce must have infinite s.p.a.ce beyond it in every direction, and therefore cannot be at the greatest possible distance from another point. Or thus: Any two points in s.p.a.ce are the extremities of the line connecting them; but an infinite line has no extremities; therefore no two points in s.p.a.ce can be connected together by an infinite line.
In fact, it is the "concrete reality," the "something infinite," and not the mere abstraction of infinity, which is only conceivable as a negation. Every "something" that has ever been intuitively present to my consciousness is a something finite. When, therefore, I speak of a "something infinite," I mean a something existing in a different manner from all the "somethings" of which I have had experience in intuition.
Thus it is apprehended, not positively, but negatively--not directly by what it is, but indirectly by what it is not. A negative idea is not negative because it is expressed by a negative term, but because it has never been realised in intuition. If infinity, as applied to s.p.a.ce, means the same thing as being greater than any finite s.p.a.ce, both conceptions are equally positive or equally negative. If it does not mean the same thing, then, in conceiving a s.p.a.ce greater than any finite s.p.a.ce, we do not conceive an infinite s.p.a.ce.
Mr. Mill"s next string of criticisms may be very briefly dismissed.
First, Hamilton does _not_, as Mr. Mill a.s.serts, say that "the Unconditioned is inconceivable, because it includes both the Infinite and the Absolute, and these are contradictory of one another." His argument is a common disjunctive syllogism. The unconditioned, if conceivable at all, must be conceived _either_ as the absolute _or_ as the infinite; neither of these is possible; therefore the unconditioned is not conceivable at all. Nor, secondly, is Sir W. Hamilton guilty of the "strange confusion of ideas" which Mr. Mill ascribes to him, when he says that the Absolute, as being absolutely One, cannot be known under the conditions of plurality and difference. The absolute, as such, must be out of all relation, and consequently cannot be conceived in the relation of plurality. "The plurality required," says Mr. Mill, "is not within the thing itself, but is made up between itself and other things." It is, in fact, both; but even granting Mr. Mill"s a.s.sumption, what is a "plurality between a thing and other things" but a relation between them? There is undoubtedly a "strange confusion of ideas" in this paragraph; but the confusion is not on the part of Sir W. Hamilton. "Again," continues Mr.
Mill, "even if we concede that a thing cannot be known at all unless known as plural, does it follow that it cannot be known as plural because it is also One? Since when have the One and the Many been incompatible things, instead of different aspects of the same thing?... If there is any meaning in the words, must not Absolute Unity be Absolute Plurality likewise?" Mr. Mill"s "since when?" may be answered in the words of Plato:--"[Greek: Ouden emoige atopon dokei heinai ei hen hapanta apophainei tis to metechein tou henos kai tauta tauta polla to plethous au metechein; all" ei ho estin hen, auto touto polla apodeixei, kai au ta polla de hen, touto ede thaumasomai.]"[AV] Here we are expressly told that "absolute unity" cannot be "absolute plurality." Mr.
Mill may say that Plato is wrong; but he will hardly go so far as to say that there is no meaning in his words. In point of fact, however, it is Mr. Mill who is in error, and not Plato. In different relations, no doubt, the same concrete object may be regarded as one or as many. The same measure is one foot or twelve inches; the same sum is one shilling or twelve pence; but it no more follows that "absolute unity must be absolute plurality likewise," than it follows from the above instances that one is equal to twelve. And, thirdly, when Mr. Mill accuses Sir W.
Hamilton of departing from his own meaning of the term _absolute_, in maintaining that the Absolute cannot be a Cause, he only shows that he does not himself know what Hamilton"s meaning is. "If Absolute," he says, "means finished, perfected, completed, may there not be a finished, perfected, and completed Cause?" Hamilton"s Absolute is that which is "_out of relation_, as finished, perfect, complete;" and a Cause, as such, is both in relation and incomplete. It is in relation to its effect; and it is incomplete without its effect. Finally, when Mr. Mill charges Sir W. Hamilton with maintaining "that extension and figure are of the essence of matter, and perceived as such by intuition," we must briefly reply that Hamilton does no such thing. He is not speaking of the essence of matter _per se_, but only of matter as apprehended in relation to us.
[AV] _Parmenides_, p. 129.
Mr. Mill concludes this chapter with an attempt to discover the meaning of Hamilton"s a.s.sertion, "to think is to condition." We have already explained what Hamilton meant by this expression; and we recur to the subject now, only to show the easy manner in which Mr. Mill manages to miss the point of an argument with the clue lying straight before him.
"Did any," he says (of those who say that the Absolute is thinkable), "profess to think it in any other manner than by distinguishing it from other things?" Now this is the very thing which, according to Hamilton, Sch.e.l.ling actually did. Mr. Mill does not attempt to show that Hamilton is wrong in his interpretation of Sch.e.l.ling, nor, if he is right, what were the reasons which led Sch.e.l.ling to so paradoxical a position: he simply a.s.sumes that no man could hold Sch.e.l.ling"s view, and there is an end of it.[AW] Hamilton"s purpose is to rea.s.sert in substance the doctrine which Kant maintained, and which Sch.e.l.ling denied; and the natural way to ascertain his meaning would be by reference to these two philosophers. But this is not the method of Mr. Mill, here or elsewhere.
He generally endeavours to ascertain Hamilton"s meaning by ranging the wide field of possibilities. He tells us what a phrase means in certain authors of whom Hamilton is not thinking, or in reference to certain matters which Hamilton is not discussing; but he hardly ever attempts to trace the history of Hamilton"s own view, or the train of thought by which it suggested itself to his mind. And the result of this is, that Mr. Mill"s interpretations are generally in the potential mood. He wastes a good deal of conjecture in discovering what Hamilton might have meant, when a little attention in the right quarter would have shown what he did mean.
[AW] Mr. Mill does not expressly name Sch.e.l.ling in this sentence: but he does so shortly afterwards; and his remark is of the same character with the previous one.
"Even Sch.e.l.ling," he says, "was not so gratuitously absurd as to deny that the Absolute must be known according to the capacities of that which knows it--though he was forced to invent a special capacity for the purpose." But if this capacity is an "invention"
of Sch.e.l.ling"s, and if he was "forced" to invent it, Hamilton"s point is proved. To think, according to all the real operations of thought which consciousness makes known to us, is to condition. And the faculty of the unconditioned is an invention of Sch.e.l.ling"s, not known to consciousness. In other words: all our real faculties bear witness to the truth of Hamilton"s statement; and the only way of controverting it is to invent an imaginary faculty for the purpose.
The third feature of Hamilton"s philosophy which we charged Mr. Mill with misunderstanding, is the distinction between Knowledge and Belief. In the early part of this article, we endeavoured to explain the true nature of this distinction; we have now only a very limited s.p.a.ce to notice Mr.
Mill"s criticisms on it. Hamilton, he says, admitted "a second source of intellectual conviction called Belief." Now Belief is not a "source" of any conviction, but the conviction itself. No man would say that he is convinced of the truth of a proposition _because_ he believes it; his belief in its truth is the same thing as his conviction of its truth.
Belief, then, is not a source of conviction, but a conviction having sources of its own. The question is, have we legitimate sources of conviction, distinct from those which const.i.tute Knowledge properly so called? Now here it should be remembered that the distinction is not one invented by Hamilton to meet the exigencies of his own system. He enumerates as many as twenty-two authors, of the most various schools of philosophy, who all acknowledged it before him. Such a concurrence is no slight argument in favour of the reality of the distinction. We do not say that these writers, or Hamilton himself, have always expressed this distinction in the best language, or applied it in the best manner; but we say that it is a true distinction, and that it is valid for the princ.i.p.al purpose to which Hamilton applied it.
We do not agree with all the details of Hamilton"s application. We do not agree with him, though he is supported by very eminent authorities, in cla.s.sifying our conviction of axiomatic principles as _belief_, and not as _knowledge_.[AX] But this question does not directly bear on Mr.
Mill"s criticism. The point of that criticism is, that Hamilton, by admitting a _belief_ in the infinite and unrelated, nullifies his own doctrine, that all _knowledge_ is of the finite and relative. Let us see.
[AX] Hamilton"s distinction is in principle the same as that which we have given in our previous remarks (pp. 18, 19). He says, "A conviction is incomprehensible when there is merely given to us in consciousness--_That its object is_ ([Greek: hoti esti]), and when we are unable to comprehend through a higher notion or belief _Why or How it is_ ([Greek: dioti esti])."--(Reid"s Works, p.
754.) We would distinguish between _why_ and _how_, between [Greek: dioti], and [Greek: pos]. We can give no reason _why_ two straight lines cannot enclose a s.p.a.ce; but we can comprehend _how_ they cannot. We have only to form the corresponding image, to see the manner in which the two attributes coexist in one object. But when I say that I believe in the existence of a spiritual being who sees without eyes, I cannot conceive the _manner_ in which seeing coexists with the absence of the bodily organ of sight. We believe that the true distinction between knowledge and belief may ultimately be referred to the presence or absence of the corresponding intuition; but to show this in the various instances would require a longer dissertation than our present limits will allow.
We may believe _that_ a thing is, without being able to conceive _how_ it is. I believe _that_ G.o.d is a person, and also _that_ He is infinite; though I cannot conceive _how_ the attributes of personality and infinity exist together. All my knowledge of personality is derived from my consciousness of my own finite personality. I therefore believe in the coexistence of attributes in G.o.d, in some manner different from that in which they coexist in me as limiting each other: and thus I believe in the fact, though I am unable to conceive the manner. So, again, Kant brings certain counter arguments, to prove, on the one side, that the world has a beginning in time, and, on the other side, that it has not a beginning. Now suppose I am unable to refute either of these courses of argument, am I therefore compelled to have no belief at all? May I not say, I believe, in spite of Kant, _that_ the world has a beginning in time, though I am unable to conceive _how_ it can have so begun? What is this, again, but a belief in an absolute reality beyond the sphere of my relative knowledge?
"I am not now considering," says Mr. Mill, "what it is that, in our author"s opinion, we are bound to believe concerning the unknowable."
Why, this was the very thing he ought to have considered, before p.r.o.nouncing the position to be untenable, or to be irreconcilable with something else. Meanwhile, it is instructive to observe that Mr. Mill himself believes, or requires his readers to believe, something concerning the unknown. He does not know, or at any rate he does not tell his readers, what Hamilton requires them to believe concerning the unknowable; but he himself believes, and requires them to believe, that this unknown something is incompatible with the doctrine that knowledge is relative. We cannot regard this as a very satisfactory mode of refuting Hamilton"s thesis.[AY]
[AY] In a subsequent chapter (p. 120), Mr. Mill endeavours to overthrow this distinction between Knowledge and Belief, by means of Hamilton"s own theory of Consciousness.
Hamilton maintains that we cannot be conscious of a mental operation without being conscious of its object.
On this Mr. Mill retorts that if, as Hamilton admits, we are conscious of a belief in the Infinite and the Absolute, we must be conscious of the Infinite and the Absolute themselves; and such consciousness is Knowledge. The fallacy of this retort is transparent.
The immediate object of Belief is a _proposition_ which I hold to be true, not a _thing_ apprehended in an act of conception. I believe in an infinite G.o.d; _i.e._, I believe _that_ G.o.d is infinite: I believe that the attributes which I ascribe to G.o.d exist in Him in an infinite degree. Now, to believe this proposition, I must, of course, be conscious of its meaning; but I am not therefore conscious of the Infinite G.o.d as an object of conception; for this would require further an apprehension of the manner in which these infinite attributes coexist so as to form one object. The whole argument of this eighth chapter is confused, owing to Mr. Mill not having distinguished between those pa.s.sages in which Sir W. Hamilton is merely using an _argumentum ad hominem_ in relation to Reid, and those in which he is reasoning from general principles.
But if Mr. Mill is unjust towards the distinction between Knowledge and Belief, as held by Sir W. Hamilton, he makes ample amends to the injured theory in the next chapter, by enlarging the province of credibility far beyond any extent which Hamilton would have dreamed of claiming for it.
Conceivability or inconceivability, he tells us, are usually dependent on a.s.sociation; and it is quite possible that, under other a.s.sociations, we might be able to conceive, and therefore to believe, anything short of the direct contradiction that the same thing is and is not. It is not in itself incredible, that a square may at the same time be round, that two straight lines may enclose a s.p.a.ce, or even that two and two may make five.[AZ] But whatever concessions Mr. Mill may make on this point, he is at least fully determined that Sir W. Hamilton shall derive no benefit from them; for he forthwith proceeds to charge Sir William with confusing three distinct senses of the term _conception_--a confusion which exists solely in his own imagination,[BA]--and to a.s.sert that the Philosophy of the Conditioned is entirely founded on a mistake, inasmuch as infinite s.p.a.ce on the one hand, and, on the other, both an absolute minimum and an infinite divisibility of s.p.a.ce, are perfectly conceivable. With regard to the former of these two a.s.sertions, Mr. Mill"s whole argument is vitiated, as we have already shown, by his confusion between _infinite_ and _indefinite_; but it is worth while to quote one of his special instances in this chapter, as a specimen of the kind of reasoning which an eminent writer on logic can sometimes employ. In reference to Sir W.
Hamilton"s a.s.sertion, that infinite s.p.a.ce would require infinite time to conceive it, he says, "Let us try the doctrine upon a complex whole, short of infinite, such as the number 695,788. Sir W. Hamilton would not, I suppose, have maintained that this number is inconceivable. How long did he think it would take to go over every separate unit of this whole, so as to obtain a perfect knowledge of the exact sum, as different from all other sums, either greater or less?"
[AZ] In reference to this last paradox, Mr. Mill quotes from _Essays by a Barrister_: "There is a world in which, whenever two pairs of things are either placed in proximity or are contemplated together, a fifth thing is immediately created and brought within the contemplation of the mind engaged in putting two and two together....
In such a world surely two and two would make five. That is, the result to the mind of contemplating two twos would be to count five." The answer to this reasoning has been already given by Archdeacon Lee in his Essay on Miracles. The "five" in this case is not the sum of two and two, but of two and two _plus_ the new creature, _i.e._, of two and two _plus_ one.
[BA] The sense in which Sir W. Hamilton himself uses the word _conception_ is explained in a note to _Reid"s Works_, p. 377--namely, the combination of two or more attributes in a _unity of representation_. The second sense which Mr. Mill imagines is simply a mistake of his own. When Hamilton speaks of being "unable to conceive as possible," he does not mean, as Mr. Mill supposes, physically possible under the law of gravitation or some other law of matter, but mentally possible as a representation or image; and thus the supposed second sense is identical with the first. The third sense may also be reduced to the first; for to conceive two attributes as combined in one representation is to form a notion subordinate to those of each attribute separately. We do not say that Sir W. Hamilton has been uniformly accurate in his application of the test of conceivability; but we say that his inaccuracies, such as they are, do not affect the theory of the conditioned, and that in all the long extracts which Mr.
Mill quotes, with footnotes, indicating "first sense,"
"second sense," "third sense," the author"s meaning may be more accurately explained in the first sense only.
It is marvellous that it should not have occurred to Mr. Mill, while he was writing this pa.s.sage, "How comes this large number to be a "whole" at all; and how comes it that "this whole," with all its units, can be written down by means of six digits?" Simply because of a conventional arrangement, by which a single digit, according to its position, can express, by one mark, tens, hundreds, thousands, &c., of units; and thus can exhaust the sum by dealing with its items in large ma.s.ses. But how can such a process exhaust the infinite? We should like to know how long Mr. Mill thinks it would take to work out the following problem:--"If two figures can represent ten, three a hundred, four a thousand, five ten thousand, &c., find the number of figures required to represent infinity."[BB]
[BB] Precisely the same misconception of Hamilton"s position occurs in Professor De Morgan"s paper in the _Cambridge Transactions_, to which we have previously referred. He speaks (p. 13) of the "notion, which runs through many writers, from Descartes to Hamilton, that the mind must be big enough to _hold_ all it can conceive." This notion is certainly not maintained by Hamilton, nor yet by Descartes in the paragraph quoted by Mr. De Morgan; nor, as far as we are aware, in any other part of his works.
Infinite divisibility stands or falls with infinite extension. In both cases Mr. Mill confounds infinity with indefiniteness. But with regard to an absolute minimum of s.p.a.ce, Mr. Mill"s argument requires a separate notice.
"It is not denied," he says, "that there is a portion of extension which to the naked eye appears an indivisible point; it has been called by philosophers the _minimum visibile_. This minimum we can indefinitely magnify by means of optical instruments, making visible the still smaller parts which compose it. In each successive experiment there is still a _minimum visibile_, anything less than which cannot be discovered with that instrument, but can with one of a higher power. Suppose, now, that as we increase the magnifying power of our instruments, and before we have reached the limit of possible increase, we arrive at a stage at which that which seemed the smallest visible s.p.a.ce under a given microscope, does not appear larger under one which, by its mechanical construction, is adapted to magnify more, but still remains apparently indivisible. I say, that if this happened, we should believe in a minimum of extension; or if some _a priori_ metaphysical prejudice prevented us from believing it, we should at least be enabled to conceive it."--(P. 84.)
The natural conclusion of most men under such circ.u.mstances would be, that there was some fault in the microscope. But even if this conclusion were rejected, we presume Mr. Mill would allow that, under the supposed circ.u.mstances, the exact magnitude of the minimum of extension would be calculable. We have only to measure the _minimum visibile_, and know what is the magnifying power of our microscope, to determine the exact dimensions. Suppose, then, that we a.s.sign to it some definite magnitude--say the ten billionth part of an inch,--should we then conclude that it is impossible to conceive the twenty billionth part of an inch?--in other words, that we have arrived at a definite magnitude which has no conceivable half? Surely this is a somewhat rash concession to be made by a writer who has just told us that numbers may be conceived up to infinity; and therefore, of course, down to infinitesimality.
Mr. Mill concludes this chapter with an a.s.sertion which, even by itself, is sufficient to show how very little he has attended to or understood the philosophy which he is attempting to criticise. "The law of Excluded Middle," he says, "as well as that of Contradiction, is common to all phenomena. But it is a doctrine of our author that these laws are true, and cannot but be known to be true, of Noumena likewise. It is not merely s.p.a.ce as cognisable by our senses, but s.p.a.ce as it is in itself, which he affirms must be either of unlimited or of limited extent" (p. 86). At this sentence we fairly stand aghast. "s.p.a.ce as it is in itself!" the Noumenon s.p.a.ce! Has Mr. Mill been all this while "examining" Sir William Hamilton"s philosophy, in utter ignorance that the object of that philosophy is the "Conditioned in Time and _s.p.a.ce_;" that he accepts Kant"s a.n.a.lysis of time and s.p.a.ce as formal necessities of thought, but p.r.o.nounces no opinion whatever as to whether time and s.p.a.ce can exist as Noumena or not? It is the phenomenal s.p.a.ce, "s.p.a.ce as cognisable by our senses," which Sir W. Hamilton says must be either limited or unlimited: concerning the Noumenon s.p.a.ce, he does not hazard an opinion whether such a thing exists or not. He says, indeed (and this is probably what has misled Mr. Mill), that the laws of Ident.i.ty, Contradiction, and Excluded Middle, are laws of things as well as laws of thought;[BC] but he says nothing about these laws as predicating infinite or finite extension. On the contrary, he expressly cla.s.sifies s.p.a.ce under the law of Relativity, the violation of which indicates what may exist, but what we are unable to conceive as existing. Briefly, the law of Excluded Middle (to take this instance alone) is a law of things only in its abstract form, "Everything must be A or not A" (_extended_, if you please, or _not extended_); but in its subordinate form, "Everything extended must be extended infinitely or finitely," it is only applicable, and only intended by Hamilton to be applied, to those _phenomena_ which are already given as extended in some degree.
[BC] _Discussions_, p. 603.