On the Philosophy of Discovery, Chapters Historical and Critical

CHAPTER XXV.
The Fundamental Antithesis as it exists in the Moral World

1. WE HAVE hitherto spoken of the Fundamental Antithesis as the ground of our speculations concerning the material world, at least mainly. We have indeed been led by the physical sciences, and especially by Biology, to the borders of Psychology. We have had to consider not only the mechanical effects of muscular contraction, but the sensations which the nerves receive and convey:—the way in which sensations become perceptions; the way in which perceptions determine actions. In this manner we have been led to the subject of volition or will²⁹⁷, and this brings us to a new field of speculation, the moral nature of man; and this moral nature is a matter not only of speculative but of practical interest. On this subject I shall make only a few brief remarks.

2. Even in the most purely speculative view, the moral aspect of man's nature differs from the aspect of the material universe, in this respect, that in the moral world, external events are governed in some measure by the human will. When we speculate concerning the laws of material nature, we suppose that the phenomena of nature follow a course and order which we may perhaps, in some measure, discover and understand, but which we cannot change or control. But when we consider man as an agent, we suppose him able to determine some at least of the events of the external world; and thus, able to determine the actions of other men, and to lay down laws for them. He cannot alter the properties of fire and metals, stones and fluids, air and light; but he can use fire and steel so as to compel other men's actions; stone-walls and ocean-shores so as to control other men's motions; gold and gems so as to have a hold on other men's desires; articulate sounds and intelligible symbols so as to direct other men's thoughts and move their will. There is an external world of Facts; and in this, the Facts are such as he makes them by his Acts.

3. But besides this, there is also, standing over against this external world of Facts, an internal world of Ideas. The Moral Acts without are the results of Moral Ideas within. Men have an Idea of Justice, for instance, according to which they are led to external acts, as to use force, to make a promise, to perform a contract, as individuals; or to make war and peace, to enact laws and to execute them, as a nation.

4. Some such internal moral Idea necessarily exists, along with all properly human actions. Man feels not only pain and anger, but indignation and the sentiment of wrong, which feelings imply a moral idea of right and wrong. Again, what he thinks of as wrong, he tries to prevent; what he deems right, he attempts to realize. The Idea gives a character to the Act; the Act embodies the Idea. In the moral world as in the natural world, the Antithesis is universal and inseparable. It is an Antithesis of inseparable elements. In human action, there is ever involved the Idea of what is right, and the external Act in which this idea is in some measure embodied.

5. But the moral Ideas, such as that of Justice, of Rightness, and the like, are always embodied incompletely in the world of external action. Although men's actions are to a great extent governed by the Ideas of Justice, Rightness and the like; (for it must be recollected that we include in their actions, laws, and the enforcement of laws;) yet there is a large portion of human actions which is not governed by such ideas: (actions which result from mere desire, and violations of law). There is a perpetual Antithesis of Ideas and Facts, which is the fundamental basis of moral as of natural philosophy. In the former as in the latter subject, besides what is ideal, there is an Actual which the ideal does not include. This Actual is the region in which the results of mere desire, of caprice, of apparent accident, are found. It is the region of history, as opposed to justice; it is the region of what is, as distinct from what ought to be.

6. Now what I especially wish here to remark, is this;—that the progress of man as a moral being consists in a constant extension of the Idea into the region of Facts. This progress consists in making human actions conform more and more to the moral Ideas of Justice, Rightness, and the like; including in human actions, as we have said, Laws, the enforcement of Laws, and other collective acts of bodies of men. The History of Man as Man consists in this extension of moral Ideas into the region of Facts. It is not that the actual history of what men do has always consisted in such an extension of moral Ideas; for there has ever been, in the actual doings of men, a large portion of facts which had no moral character; acts of desire, deeds of violence, transgressions of acknowledged law, and the like. But such events are not a part of the genuine progress of humanity. They do not belong to the history of man as man, but to the history of man as brute. On the other hand, there are events which belong to the history of man as man, events which belong to the genuine progress of humanity; such as the establishment of just laws; their enforcement; their improvement by introducing into them a fuller measure of moral Ideas. By such means there is a constant progress of man as a moral being. By this realization of moral Ideas there is a constant progress of Humanity.

7. I have made this reflection, because it appears to me to bring into view an analogy between the Progress of Science and the Progress of Man, or of Humanity, in the sense in which I have used the term. In both these lines of Progress, Facts are more and more identified with Ideas. In both, there is a fundamental 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 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 where²⁹⁸ Schelling condemns Newton's Opticks as a fabric of fallacies: and where²⁹⁹ 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.

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 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 Unconditioned³⁰⁰. 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 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 infinitesimal 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.

In reality the definition of an Infinite Quantity is not negative merely, but contains a positive part as well. We assume a quantity of a certain kind which may be augmented by carrying onward its limits in one or more directions: this is a finite quantity of a given kind. We then—when we have thus positively determined the kind of the quantity—suppose the limit in one or more directions to be annihilated, and thus we have an infinite quantity. But in this infinite quantity there remain the positive properties from which we began, as well as the negative property, the negation of a limit; and the positive properties joined with the negative property may and do supply grounds of reasoning respecting the infinite quantity.

4. This is lore so elementary to mathematicians that it appears almost puerile to dwell upon it; but this seems to have been overlooked, in the proof that we can have no knowledge concerning infinites. In such proof it is assumed as quite evident, that all infinites are equal. Yet, as we have seen, infinites may differ infinitely among themselves, both in quantity and in kind. A German writer is quoted³⁰¹ for an "ingenious" proof of this kind. In his writings, the opponent is supposed to urge that a line BAC may be made infinite by carrying the extremity C infinitely to the right, and again infinite by carrying the extremity B infinitely to the left; and thus the line infinitely extended both ways would be double of the line infinite on one side only. The supposed reply to this is, that it cannot be so, because one infinite is equal to another: and moreover that what is bounded at one end A, cannot be infinite: both which assumptions are without the smallest ground. That one infinite quantity may be double of another, is just as clear and certain as that one finite quantity may. For instance, if one leaf of the book which the reader has before him were produced infinitely upwards it would be an infinite space, though bounded at the bottom and at both sides. If the other leaf were in like manner produced infinitely upwards it would in like manner be infinite; and the two together, though each infinite, would be double of either of them.

5. As I have said, infinite quantities are conceived by conceiving finite quantities increased by the transfer of a certain limit, and then by negativing this limit altogether. And thus an infinite number is conceived by assuming the series 1, 2, 3, 4, and so on, up to a limit, and then removing this limit altogether. And this shows the baselessness of another argument quoted from Werenfels. The opponent asks, Are there in the infinite line an infinite number of feet? Then in the double line there must be twice as many; and thus the former infinite number did not contain all the (possible) unities; (numerus infinitus non omnes habet unitates, sed præter eum concipi possunt totidem unitates, quibus ille careat, eique possunt addi). To which I reply, that the definition of an infinite number is not that it contains all possible unities: but this—that the progress of numeration being begun according to a certain law, goes on without limit. And accordingly it is easy to conceive how one infinite number may be larger than another infinite number, in any proportion. If, for instance, we take, instead of the progression of the natural numbers 1, 2, 3, 4, &c. and the progression of the square numbers 1, 4, 9, 16, &c. any term of the latter series will be greater than the corresponding term of the other series in a ratio constantly increasing, and the infinite term of the one, infinitely greater than the corresponding infinite term of the other.

6. In the same manner we form a conception of infinite time, by supposing time to begin now, and to go on, after the nature of time, without limit; or by going back in thought from the present to a past time, and by continuing this retrogression without limit. And thus we have time infinite a parte ante and a parte post, as the phrase used to run; and time infinite both ways includes both, and is the most complete notion of eternity.

7. Perhaps those who thus maintain that we cannot conceive anything infinite, mean that we cannot form to ourselves a definite image of anything infinite. And this of course is true. We cannot form to ourselves an image of anything of which one of the characteristics is that it is, in a certain way, unlimited. But this impossibility does not prevent our reasoning about infinite quantities; combining as elements of our reasoning, the absence of a limit with other positive characters.

8. One of the consequences which is drawn by the assertors of the doctrine that we cannot know anything about Infinity, is that we cannot obtain from science any knowledge concerning God: And I have been the more desirous to show the absence of proof of this doctrine, because I conceive that science does give us some knowledge, though it be very little, of the nature of God: as I shall endeavour to show hereafter.

For instance, I conceive that when we say that God is an eternal Being, this phraseology is not empty and unmeaning. It has been used by the wisest and most thoughtful men in all ages, and, as I conceive, may be used with undiminished, or with increased propriety, after all the light which science and philosophy have thrown upon such declarations. The reader of Newton will recollect how emphatically he uses this expression along with others of a cognate character³⁰²: "God is eternal and infinite, … that is, He endures from eternity to eternity, and is present from infinity to infinity.... He is not eternity and infinity, but eternal and infinite. He is not duration and space, but He endures and is present. He endures always, and is present everywhere, and by existing always and everywhere He constitutes duration and space." We shall see shortly that the view to which we are led may be very fitly expressed by this language.

But I will first notice some other aspects of this philosophy.

CHAPTER XXVII.
Sir William Hamilton on Inertia and Weight

In a preceding chapter I have spoken of Sir William Hamilton as the expositor, to English readers, of modern German systems, and especially of the so-called "Philosophy of the Unconditioned." But the same writer is also noticeable as a continuator of the speculations of English and Scottish philosophers concerning primary and secondary qualities; and these speculations bear so far upon the philosophy of science that it is proper to notice them here.

1. In our survey of the sciences, we have spoken of a class which we have termed the Secondary Mechanical Sciences; these being the sciences which explain certain sensible phenomena, as sound, light, and heat, by means of a medium interposed between external bodies and our organs of sense. In these cases, we ascribe to bodies certain qualities: we call them resonant, bright, red or green, hot or cold. But in the sciences which relate to these subjects, we explain these qualities by the figure, size and motions of the parts of the medium which intervenes between the object and the ear, eye, or other sensible organ. And those former qualities, sound, warmth and colour, are called secondary qualities of the bodies; while the latter, figure, size and motion, are called the primary qualities of body.

2. This distinction, in its substance, is of great antiquity. The atomic theory which was set up at an early period of Greek philosophy was an attempt to account for the secondary qualities of bodies by means of their primary qualities. And this is really the scientific ground of the distinction. Those are primary qualities or attributes of body by means of which we, in a scientific view, explain and derive their other qualities. But the explanation of the sensible qualities of bodies by means of their operation through a medium has till now been very defective, and is so still. We have to a certain extent theories of Sound, Light and Heat, which reduce these qualities to scales and standards, and in some measure account mechanically for their differences and gradations. But we have as yet no similar theory of Smells and Tastes. Still, we do not doubt that fragrance and flavour are perceived by means of an aerial medium in which odours float, and a fluid medium in which sapid matters are dissolved. And the special odour and flavour which are thus perceived must depend upon the size, figure, motion, number, &c. of the particles thus conveyed to the organs of taste and smell: that is, those secondary qualities, as well as the others, must depend upon the primary qualities of the parts of the medium.

3. In this way the distinction of primary and secondary qualities is definite and precise. But when men attempt to draw the distinction by guess, without any scientific principle, the separation of the two classes is vague and various. I have, in the History of Scientific Ideas³⁰³, pointed out some of the variations which are to be found on this subject in the writings of philosophers. Sir William Hamilton³⁰⁴ has given an account of many more which he has compared and analysed with great acuteness. He has shown how this distinction is treated, among others, by the ancient atomists, Leucippus and Democritus, by Aristotle, Galen, Galileo, Descartes, Boyle, Malebranche, Locke, Reid, Stewart, Royer-Collard. He then proceeds to give his own view; which is, that we may most properly divide the qualities of bodies into three classes, which he calls Primary, Secundo-primary, and Secondary. The former he enumerates as 1, Extension; 2, Divisibility; 3, Size; 4, Density or Rarity; 5, Figure; 6, Incompressibility absolute; 7, Mobility; 8, Situation. The Secundo-primary are Gravity, Cohesion, Inertia, Repulsion. The Secondary are those commonly so called, Colour, Sound, Flavour, Savour, and Tactical Sensation; to which he says may be added the muscular and cutaneous sensation which accompany the perception of the Secundo-primary qualities. "Such, though less directly the result of foreign causes, are Titillation, Sneezing, Horripilation, Shuddering, the feeling of what is called Setting-the-teeth-on-edge, &c."

The Secundo-primary qualities Sir William Hamilton traces in further detail. He explains that with reference to Gravity, bodies are heavy or light. With reference to Cohesion, there are many coordinate pairs, of which he enumerates these:—hard and soft; firm and fluid,—the fluid being subdivided into thick and thin; viscid and friable; tough and brittle; rigid and flexible; fissile and infissile; ductile and inductile; retractile and irretractile; rough and smooth; slippery and tenacious. With reference to Repulsion he gives these qualities:—compressible and incompressible; elastic and inelastic. And with reference to Inertia he mentions only moveable and immoveable.

I do not see what advantage is gained to philosophy by such an enumeration of qualities as this, which, after all, does not pretend to completeness; nor do I see anything either precise or fundamental in such distinctions as that of elasticity, a mode of cohesion, and elasticity, a mode of repulsion. But a question in which our philosophy is really concerned is how far any of these qualities are universal qualities of matter. Sir W. Hamilton holds that they are none of them necessary qualities of matter, and therefore of course not universal, and argues this point at some length. With regard to one of his Secundo-primary qualities, I will make some remarks.

4. Inertia.—In discussing the Ideas which enter into the Mechanical Sciences³⁰⁵, I have stated that the Idea of Force and Resistance to Force, that is, of Force and Matter, are the necessary foundations of those sciences. Force cannot act without matter to act on; Matter cannot exist without Force to keep its parts together and to keep it in its place. But Force acting upon matter may either be Force producing rest, or Force producing motion. If we consider Force producing motion, the motion produced, that is, the velocity produced, must depend upon the quantity of matter moved. It cannot be that the same power, acting in the same way, shall produce the same velocity by pushing a small pebble and a large rock. If this were so, we could have no science on such matters. It must needs be that the same force produces a smaller velocity in the larger body; and this according to some measure of its largeness. The measure of the degree in which the body thus resists this communication of motion is inertia. And the inertia is necessarily supposed to be proportional to the quantity of matter, because it is by this inertia that this existence and quantity of the matter is measured. If therefore any Science concerning Force and Matter is to exist, matter must have inertia, and the inertia must be proportional to the quantity of matter.

5. Sir W. Hamilton, in opposition to this, says, that we can conceive a body occupying space, and yet without attraction or repulsion for another body, and wholly indifferent to this or that position, in space, to motion and to rest. He infers thence that inertia is not a necessary quality of bodies.

To this I reply, that even if we can conceive such bodies, (which in fact man, living in a world of matter cannot conceive,) at any rate we cannot conceive any science about such bodies. If bodies were indifferent to motion and rest, Forces could not be measured by their effects; nor could be measured or known in any way. Such bodies might float about like clouds, visible to the eye, but intangible, and governed by no laws of motion. But if we have any science about bodies, they must be tangible, and governed by laws of motion. Not, then, from any observed properties of bodies, but from the possibility of any science about bodies, does it follow that all bodies have inertia.

6. Gravity.—Reasoning of the same kind may be employed about weight. We can conceive, it is urged, matter without weight. But I reply, we cannot conceive a science which deals with matter that has no weight:—a science, I mean, which deals with the quantity of matter of bodies, as arising from the sum of their elements. For the quantity of matter of bodies is and must be measured by those sensible properties of matter which undergo quantitative addition, subtraction and division, as the matter is added, subtracted, and divided. The quantity of matter cannot be known in any other way. But this mode of measuring the quantity of matter, in order to be true at all, must be universally true. If it were only partially true—if some kinds of matter had weight and others had not—the limits of the mode of measuring matter by weight would be arbitrary: and therefore the whole procedure would be arbitrary, and as a mode of obtaining philosophical truth, altogether futile. But we suppose truth respecting the composition of bodies to be attainable; therefore we must suppose the rule, which is the necessary basis of such truth, to be itself true.

Sir W. Hamilton has replied to these arguments, but, as I conceive, without affecting the force of them. I will repeat here the answer which I have already given³⁰⁶, and will reprint in the Appendix the Memoir by which his objections were occasioned.

He says, (1), that our reasoning assumes that we must necessarily have it in our power to ascertain the Quantity of Matter; whereas this may be a problem out of the reach of human determination.

To this I reply, that my reasoning does assume that there is a science, or sciences, which make assertions concerning the Quantity of Matter: Mechanics and Chemistry are such sciences. My assertion is, that to make such sciences possible, Quantity of Matter must be proportional to Weight. If my opponent deny that Mechanics and Chemistry can exist as science, he may invalidate my proof; but not otherwise.

(2) He says that there are two conceivable ways of estimating the Quantity of Matter: by the Space occupied, and by the Weight or Inertia; and that I assume the second measure gratuitously.

To which I reply, that the most elementary steps in Mechanics and in Chemistry contradict the notion that the Quantity of Matter is proportionate to the Space. They proceed necessarily on a distinction between Space and Matter:—between mere Extension and material Substance.