Chapter 6

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 space 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 constitute 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 principal 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 classifying 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 space; 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_ God 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 God, 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 pronouncing 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 God; _i.e._, I believe _that_ God is infinite: I believe that the attributes which I ascribe to God 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 God 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 passages 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 association; and it is quite possible that, under other associations, 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 space, 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 assert that the Philosophy of the Conditioned is entirely founded on a mistake, inasmuch as infinite space on the one hand, and, on the other, both an absolute minimum and an infinite divisibility of space, are perfectly conceivable. With regard to the former of these two assertions, 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 assertion, that infinite space 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 passage, "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 masses. 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 space, 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 space 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 circumstances 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 circumstances, 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 assign 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 assertion 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 Space as cognisable by our senses, but Space 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. "Space as it is in itself!" the Noumenon Space! 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 _Space_;" that he accepts Kant's analysis of time and space as formal necessities of thought, but pronounces no opinion whatever as to whether time and space can exist as Noumena or not? It is the phenomenal space, "space as cognisable by our senses," which Sir W. Hamilton says must be either limited or unlimited: concerning the Noumenon Space, 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 Identity, 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 classifies Space 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.

We have now examined the first six chapters of Mr. Mill's book, containing his remarks on that portion of Sir W. Hamilton's philosophy which he justly regards as comprising the most important of the doctrines which specially belong to Hamilton himself. The next chapter is an episode, in which Mr. Mill turns aside from Sir W. Hamilton to criticise Mr. Mansel's _Bampton Lectures_. As our limits do not permit us to carry on the argument at present through the remainder of Mr. Mill's remarks on Hamilton himself, we shall conclude our notice with a few words on this chapter, as closing the properly metaphysical portion of Mr. Mill's book, and as affording ample proof that, in this department of philosophy at least, Mr. Mill's powers of misapprehension do not cease when Sir W. Hamilton is no longer their object.

Mr. Mill's method of criticism makes it generally necessary to commence with a statement of the criticised theory as it really is, before proceeding to his exposition of it as it is not. The present instance offers no exception to this rule. Mr. Mansel's argument may be briefly stated as follows. The primary and essential conception of God, imperatively demanded by our moral and religious consciousness, is that of a _person_. But personality implies intellectual and moral attributes; and the only direct and immediate knowledge which we have of such attributes is derived from the testimony of self-consciousness, bearing witness to their existence in a certain manner in ourselves. But when we endeavour to transfer the conception of personality, thus obtained, to the domain of theology, we meet with certain difficulties, which, while they are not sufficient to hinder us from _believing_ in the Divine Personality as a fact, yet hinder us from _conceiving_ the manner of its existence, and prevent us from exhibiting our belief as a philosophical conclusion, proved by irrefragable reasoning and secured against all objections. These difficulties are occasioned, on the one hand, by the so-called Philosophy of the Unconditioned, which in all ages has shown a tendency towards Pantheism, and which, in one of its latest and most finished manifestations, announces itself as the exhibition of God as He is in His eternal nature before creation; and, on the other hand, by the limitations and conditions to which our own personality is subject, and which, as we have pointed out in the earlier part of this article, have, from the very beginning of Christian theology, prevented theologians from accepting the limited personality of man as an exact image and counterpart of the unlimited personality of God. These difficulties Mr. Mansel endeavours to meet in two ways. On the one side, he maintains, in common with Sir W. Hamilton, that the Philosophy of the Unconditioned, by reason of its own incongruities and self-contradictions, has no claim to be accepted as a competent witness in the matter; and on the other side, he maintains, in common with many theologians before him, that human personality cannot be assumed as an exact copy of the Divine, but only as that which is most nearly analogous to it among finite things. But these two positions, if admitted, involve a corresponding practical conclusion as regards the criterion of religious truth or falsehood. Were we capable, either, on the one hand, of a clear conception of the Unconditioned, or, on the other, of a direct intuition of the Divine Attributes as objects of consciousness, we might be able to construct, deductively or inductively, an exact science of Theology. As it is, we are compelled to reason by analogy; and analogy furnishes only probabilities, varying, it may be, from slight presumptions up to moral certainties, but whose weight, in any given case, can only be determined by comparison with other evidences. There are three distinct sources from which we may form a judgment about the ways of God--first, from our own moral and intellectual consciousness, by which we judge _a priori_ of what God ought to do in a given case, by determining what we should think it wise or right for ourselves to do in a similar case; secondly, from the constitution and course of nature, from which we may learn by experience what God's providence in certain cases actually is; and thirdly, from revelation, attested by its proper evidences. Where these three agree in their testimony (as in the great majority of cases they do) we have the moral certainty which results from the harmony of all accessible evidences: where they appear to differ, we have no right at once to conclude that the second or the third must give way to the first, and not _vice versa_; because we have no right to assume that the first alone is infallible. In the author's own words: "The lesson to be learnt from an examination of the Limits of Religious Thought is not that man's judgments are _worthless_ in relation to Divine things, but that they are _fallible_: and the probability of error in any particular case can never be fairly estimated without giving their full weight to all collateral considerations. We are indeed bound to believe that a Revelation given by God can never contain anything that is really unwise or unrighteous; but we are not always capable of estimating exactly the wisdom or righteousness of particular doctrines or precepts. And we are bound to bear in mind that _exactly in proportion to the strength of the remaining evidence for the Divine origin of a religion, is the probability that we may be mistaken in supposing this or that portion of its contents to be unworthy of God._ Taken in conjunction, the two arguments may confirm or correct each other: taken singly and absolutely, each may vitiate the result which should follow from their joint application."[BD]

[BD] _Bampton Lectures_, p. 156, 4th edition.