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.
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 (ὅτι ἔστι), and when we are unable to comprehend through a higher notion or belief Why or How it is (διότι ἔστι).”—(Reid’s Works, p. 754.) We would distinguish between why and how, between διότι, and πῶς. 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]
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?”
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.