But the question follows, Can processes of inference end in a mystery? that is, not only in what is incomprehensible, that the stars are billions of miles from each other, but in what is inconceivable, in the co-existence of (seeming) incompatibilities? For how, it may be asked, can reason carry out notions into their contradictories? since all the developments of a truth must from the nature of the case be consistent both with it and with each other. I answer, certainly processes of inference, however accurate, can end in mystery; and I solve the objection to such a doctrine thus:—our notion of a thing may be only partially faithful to the original; it may be in excess of the thing, or it may represent it incompletely, and, in consequence, it may serve for it, it may stand for it, only to a certain point, in certain cases, but no further. After that point is reached, the [pg 047] notion and the thing part company; and then the notion, if still used as the representative of the thing, will work out conclusions, not inconsistent with itself, but with the thing to which it no longer corresponds.
This is seen most familiarly in the use of metaphors. Thus, in an Oxford satire, which deservedly made a sensation in its day, it is said that Vice “from its hardness takes a polish too.”1 Whence we might argue, that, whereas Caliban was vicious, he was therefore polished; but politeness and Caliban are incompatible notions. Or again, when some one said, perhaps to Dr. Johnson, that a certain writer (say Hume) was a clear thinker, he made answer, “All shallows are clear.” But supposing Hume to be in fact both a clear and a deep thinker, yet supposing clearness and depth are incompatible in their literal sense, which the objection seems to imply, and still in their full literal sense were to be ascribed to Hume, then our reasoning about his intellect has ended in the mystery, “Deep Hume is shallow;” whereas the contradiction lies, not in the reasoning, but in the fancying that inadequate notions can be taken as the exact representations of things.
Hence in science we sometimes use a definition or a formula, not as exact, but as being sufficient for our purpose, for working out certain conclusions, for a practical approximation, the error being small, till a certain point is reached. This is what in theological investigations I should call an economy.
A like contrast between notions and the things which [pg 048] they represent is the principle of suspense and curiosity in those enigmatical sayings which were frequent in the early stage of human society. In them the problem proposed to the acuteness of the hearers, is to find some real thing which may unite in itself certain conflicting notions which in the question are attributed to it: “Out of the eater came forth meat, and out of the strong came forth sweetness;” or, “What creature is that, which in the morning goes on four legs, at noon on two, and on three in the evening?” The answer, which names the thing, interprets and thereby limits the notions under which it has been represented.
Let us take an example in algebra. Its calculus is commonly used to investigate, not only the relations of quantity generally, but geometrical facts in particular. Now it is at once too wide and too narrow for such a purpose, fitting on to the doctrine of lines and angles with a bad fit, as the coat of a short and stout man might serve the needs of one who was tall and slim. Certainly it works well for geometrical purposes up to a certain point, as when it enables us to dispense with the cumbrous method of proof in questions of ratio and proportion, which is adopted in the fifth book of Euclid; but what are we to make of the fourth power of a, when it is to be translated into geometrical language? If from this algebraical expression we determined that space admitted of four dimensions, we should be enunciating a mystery, because we should be applying to space a notion which belongs to quantity. In this case algebra is in excess of geometrical truth. Now let us take an instance in which it falls short of geometry—What [pg 049] is the meaning of the square root of minus a? Here the mystery is on the side of algebra; and, in accordance with the principle which I am illustrating, it has sometimes been considered as an abortive effort to express, what is really beyond the capacity of algebraical notation, the direction and position of lines in the third dimension of space, as well as their length upon a plane. When the calculus is urged on by the inevitable course of the working to do what it cannot do, it stops short as if in resistance, and protests by an absurdity.
Our notions of things are never simply commensurate with the things themselves; they are aspects of them, more or less exact, and sometimes a mistake ab initio. Take an instance from arithmetic:—We are accustomed to subject all that exists to numeration; but, to be correct, we are bound first to reduce to some level of possible comparison the things which we wish to number. We must be able to say, not only that they are ten, twenty, or a hundred, but so many definite somethings. For instance, we could not without extravagance throw together Napoleon's brain, ambition, hand, soul, smile, height, and age at Marengo, and say that there were seven of them, though there are seven words; nor will it even be enough to content ourselves with what may be called a negative level, viz. that these seven were an un-English or are a departed seven. Unless numeration is to issue in nonsense, it must be conducted on conditions. This being the case, there are, for what we know, collections of beings, to whom the notion of number cannot be attached, except catachrestically, because, [pg 050] taken individually, no positive point of real agreement can be found between them, by which to call them. If indeed we can denote them by a plural noun, then we can measure that plurality; but if they agree in nothing, they cannot agree in bearing a common name, and to say that they amount to a thousand these or those, is not to number them, but to count up a certain number of names or words which we have written down.
Thus, the Angels have been considered by divines to have each of them a species to himself; and we may fancy each of them so absolutely sui similis as to be like nothing else, so that it would be as untrue to speak of a thousand Angels as of a thousand Hannibals or Ciceros. It will be said, indeed, that all beings but One at least will come under the notion of creatures, and are dependent upon that One; but that is true of the brain, smile, and height of Napoleon, which no one would call three creatures. But, if all this be so, much more does it apply to our speculations concerning the Supreme Being, whom it may be unmeaning, not only to number with other beings, but to subject to number in regard to His own intrinsic characteristics. That is, to apply arithmetical notions to Him may be as unphilosophical as it is profane. Though He is at once Father, Son, and Holy Ghost, the word “Trinity” belongs to those notions of Him which are forced on us by the necessity of our finite conceptions, the real and immutable distinction which exists between Person and Person implying in itself no infringement of His real and numerical Unity. And if it be asked how, [pg 051] if we cannot properly speak of Him as Three, we can speak of Him as One, I reply that He is not One in the way in which created things are severally units; for one, as applied to ourselves, is used in contrast to two or three and a whole series of numbers; but of the Supreme Being it is safer to use the word “monad” than unit, for He has not even such relation to His creatures as to allow, philosophically speaking, of our contrasting Him with them.
Coming back to the main subject, which I have illustrated at the risk of digression, I observe, that an alleged fact is not therefore impossible because it is inconceivable; for the incompatible notions, in which consists its inconceivableness, need not each of them really belong to it in that fulness which involves their being incompatible with each other. It is true indeed that I deny the possibility of two straight lines enclosing a space, on the ground of its being inconceivable; but I do so because a straight line is a notion and nothing more, and not a thing, to which I may have attached a notion more or less unfaithful. I have defined a straight line in my own way at my own pleasure; the question is not one of facts at all, but of the consistency with each other of definitions and of their logical consequences.
“Space is not infinite, for nothing but the Creator is such:”—starting from this thesis as a theological information, to be assumed as a fact, though not one of experience, we arrive at once at an insoluble mystery; for, if space be not infinite, it is finite, and finite