mental Antithesis of Ideas and Facts, and progress ⚫consists in a constant advance of the point which separates the two elements of this Antithesis. In both, Facts are constantly won over to the domain of Ideas. But still, there is a difference in the two cases; for in the one case the Facts are beyond our control. We cannot make them other than they are; and all that we can do, if we can do that, is to shape our Ideas so that they shall coincide with the Facts, and still have the manifest connexion which belongs to them as Ideas. In the other case, the Facts are, to a certain extent, in our power. They are what we make them, for they are what we do. In this case, the Facts ought to come towards the Ideas, rather than the Ideas towards the Facts. As we called the former process the Idealization of Facts, we may call this the Realization of Ideas; and the analogy which I have here wished to bring into view may be expressed by saying, that the Progress of Physical Science consists in a constant successive Idealization of Physical Facts; and the Progress of man's Moral Being is a constant successive Realization of Moral Ideas.

8. Thus the necessary co-existence of an objective and a subjective element belongs not only to human knowledge, as was before explained, but also to human action. The objective and the subjective element are inseparable in this case as in the other. We have always the Fact of Positive Law, along with the Idea of Absolute Justice; the Facts of Gain or Loss, along with the Idea of Rights. The Idea of Justice is inseparable from historical facts, for justice gives to each his own, and history determines what that is. We cannot even conceive justice without society, or society without law, and thus in the moral and in the natural world the fundamental antithesis is inseparable, even in thought. The two elements must always subsist; for however far the moral ideas be realized in the world, there will always remain much in the world which is not conformable to moral ideas, even if it were only through its necessary dependence on an unmoral and immoral past. As in the physical world so in the

moral, however much the ideal sphere expands, it is surrounded by a region which is not conformable to the idea, although in one case the expansion takes place by educing ideas out of facts, in the other, by producing facts from ideas.

I shall hereafter venture to pursue further this train of speculation, but at present I shall make some remarks on writers who may be regarded as the successors amongst ourselves of these German schools of Philosophy.

CHAPTER XXVI.

OF THE

"PHILOSOPHY OF THE INFINITE."

IN

N the last Chapter but one I stated that Schelling propounded a Philosophy of the Absolute, the Absolute being the original basis of truth in which the two opposite elements, Ideas and Facts, are identified, and that Hegel also founded his philosophy on the Identity of these two elements. These German philosophies appear to me, as I have ventured to intimate, of small or no value in their bearing on the history of actual science. I have in the history of the sciences noted instances in which these writers seem to me to misconceive altogether the nature and meaning of the facts of scientific history; as where' Schelling condemns Newton's Opticks as a fabric of fallacies: and where Hegel says that the glory due to Kepler has been unjustly transferred to Newton. As it appears to me important that English philosophers should form a just estimate of Hegel's capacity of judging and pronouncing on this subject, I will print in the Appendix a special discussion of what he has said respecting Newton's discovery of the law of gravitation.

2

Recently attempts have been made to explain to English readers these systems of German philosophy, and in these attempts there are some points which may deserve our notice as to their bearing on the philosophy of science. I find some difficulty in discussing these attempts, for they deal much with phrases which appear to me to offer no grasp to man's power of reason. What, for instance, is the Absolute, which occupies a

1 Hist. Ind. Sc. b. ix. c. iii.

2 Ibid. b. vii. c. ii.

prominent place in these expositions? It is, as I have stated, in Schelling, the central basis of truth in which things and thoughts are united and identified. To attempt to reason about such an Absolute" appears to me to be an entire misapprehension of the power of reason. Again; one of the most eminent of the expositors has spoken of each system of this kind as a Philosophy of the Unconditioned. But what, we must ask, is the Unconditioned? That which is subject to no conditions, is subject to no conditions which distinguish it from any thing else, and so, cannot be a matter of thought. But again; this Absolute or Unconditioned is (if I rightly understand) said to be described also by various other names; unity, identity, substance, absolute cause, the infinite, pure thought, &c. As each of these terms expresses some condition on which the name fixes our thoughts, I cannot understand why they should any of them be called the Unconditioned; and as they express very different thoughts, I cannot understand why they should be called by the same name. From speculations starting from such a point, I can expect nothing but confusion and perplexity; nor can I find that anything else has come of them. They appear to me more barren, and more certain to be barren, of any results which have any place in our real knowledge, than the most barren speculations of the schoolmen of the middle ages: which indeed they much resemble in all their features their acuteness, their learning, their ambitious aim, and their actual failure.

2. But leaving the Absolute and the Unconditioned, as notions which cannot be dealt with by our reason without being something entirely different from their definitions, we may turn for a moment to another notion which is combined with them by the expositors of whom I speak, and which has some bearing upon our positive science, because it enters into the reasonings of mathematics: I mean the notion of Infinite. Some of those who hold that we can know nothing concerning

* Sir W. Hamilton's Note on the Philosophy of the Unconditioned.

Y

the Absolute and the Unconditioned, (which they pretend to prove, though concerning such words I do not conceive that anything can be true or false,) hold also that the Infinite is in the same condition;-that we can know nothing concerning what is Infinite ;therefore, I presume, nothing concerning infinite space, infinite time, infinite number, or infinite degrees.

To disprove this doctrine, it might be sufficient to point out that there is a vast mass of mathematical science which includes the notion of infinites, and leads to a great body of propositions concerning Infinites. The whole of the infitesimal calculus depends upon conceiving finite magnitudes divided into an infinite number of parts: these parts are infinitely small, and of these parts there are other infinitesimal parts infinitely smaller still, and so on, as far as we please to go. And even those methods which shun the term infinite, as Newton's method of Ultimate Ratios, the method of Indivisibles, and the method of Exhaustions of the ancient geometers, do really involve the notion of infinite; for they imply a process continued without limit.

3. But perhaps it will be more useful to point out the fallacies of the pretended proofs that we can know nothing concerning Infinity and infinite things.

The argument offered is, that of infinity we have no notion but the negation of a limit, and that from this negative notion no positive result can be deduced.

But to this I reply: It is not at all true that our notion of what is infinite is merely that it is that which has no limit. We must ask further that what? that space? that time? that number?—And if that space, that what kind of space? That line? that surface? that solid space?—And if that line, that line bounded at one end, or not? If that surface, that surface bounded on one, or on two, or on three sides? or on none? However any of these questions are answered, we may still have an infinite space. Till they are answered, we can assert nothing about the space; not because we can assert nothing about infinites; but because we are not told what kind of infinite we are talking of.