On the Philosophy of Discovery, Chapters Historical and Critical

CHAPTER XXIX.
Necessary Truth is progressive. Objections considered

The doctrine that necessary truth is progressive is a doctrine very important in its bearing upon the nature of the human mind; and, as I conceive, in its theological bearing also. But it is a doctrine to which objections are likely to be made from various quarters, and I will consider some of these objections.

1. Necessary truths, it will be said, cannot increase in number. New ones cannot be added to the old ones. For necessary truths are those of which the necessity is plain and evident to all mankind—to the common sense of man; such as the axioms of geometry. But that which is evident to all mankind must be evident from the first: that which is plain to the common sense of man cannot require scientific discovery: that which is necessarily true cannot require accumulated proof.

To this I reply, that necessary truths require for their apprehension a certain growth and development of the human mind. Though it is seen that they are necessarily true, this is seen only by those who think steadily and clearly, and to think steadily and clearly on any kind of subject, requires time and attention;—requires mental culture. This may be seen even in the case of the axioms of geometry. These axioms are self-evident: but to whom are they self-evident? Not to uncultured savages, or young children; or persons of loose vague habits of thought. To see the truth and necessity of geometrical axioms, we need geometrical culture.

Therefore that any axioms are not evident without patient thought and continued study of the subject, does not disprove their necessity. Principles may be axiomatic and necessary, although they require time, and the progress of thought and of knowledge, to bring them to light. And axioms may be thus gradually brought to light by the progress of knowledge.

Nor is it difficult to give examples of such axioms, other than geometrical. There is an axiom which has obtained currency among thoughtful men from the time that man began to speculate about himself and the universe:—E nihilo nil fit: Nothing can be made of nothing. No material substance can be produced or destroyed by natural causes, though its form and consistence may be changed indefinitely. Is not this an axiom? a necessary truth? Yet it is not evident to all men at first, and without mental culture. At first and before habits of steady and consistent thought are formed, men think familiarly of the creation and destruction of matter. Only when the mind has received some philosophical culture does it see the truth and necessity of the axiom of substance, and then it does see it.

And the axioms on which the science of mechanics rests, that the cause is measured by the effects, that reaction is equal and opposite to action, and the like,—are not these evident to a mind cultivated by steady thought on such subjects? and do they not require such culture of the mind in order to see them? Are they not obscure or uncertain to those who are not so cultured, that is to common thinkers: to the general bulk of mankind? Thus then it requires the discipline of the science of mechanics to enable the mind to see the axioms of that science.

And does not this go further, as science and the careful study of the grounds of science go further? To a person well disciplined in mechanical reasoning it has become, not a conclusion, but a principle, that in mechanical action what is gained in power is lost in time: or that in any change, the force gained is equal to the force lost, so that new force cannot be generated, any more than new matter, by natural changes. Is this an axiom? a necessary fundamental truth? It appears so to at least one great thinker and discoverer now alive among us. If it do not appear so to us, or not in the same sense, may not this be because we have not yet reached his point of view? May not the conviction which is now his alone become hereafter the conviction of the philosophical world? And whatever the case may be in this instance, have there not been examples of this progress? Did not Galileo and the disciples of Galileo reduce several mechanical principles to the character of necessary truths, after they had by experiment and reasoning discovered them to be actually true? And have we not in these cases so many proofs that necessary truth is progressive, along with the progress of knowledge?

2. But, it will be said, the necessary character claimed for such truths is an illusion. The propositions so brought into view are really established by observation: by the study of external facts: and it is only the effect of habit and familiarity which makes men of science, when they well know them to be true, think them to be necessarily true. They are really the results of experience, as their history shows; and therefore cannot be necessary and à priori truths.

To which I reply: Such principles as I have mentioned,—that material substance cannot be produced or destroyed—that the cause is measured by the effect—that reaction is equal and opposite to action: are not the results of experience, nor can be. No experience can prove them; they are necessarily assumed as the interpretation of experience. They were not proved in the course of scientific investigations, but brought to light as such investigations showed their necessity. They are not the results, but the conditions of experimental sciences. If the Axiom of Substance were not true, and were not assumed, we could not have such a science as Chemistry, that is, we could have no knowledge at all respecting the changes of form of substances. If the Axioms of Mechanics were not true and were not assumed, we could have no science of Mechanics, that is, no knowledge of the laws of force acting on matter. It is not any special results of the science in such cases; but the existence, the possibility, of any science, which establishes the necessity of these axioms. They are not the consequences of knowledge, acquired from without, but the internal condition of our being able to know. And when we are to know concerning any new subject contained in the universe, it is not inconceivable nor strange that there should be new conditions of our knowledge.

It is not inconceivable or strange, therefore, that as new sciences are formed, new axioms, the foundations of such sciences, should come into view. As the light of clear and definite knowledge is kindled in successive chambers of the universe, it may disclose, not only the aspect of those new apartments, but also the form and structure of the lamp which man is thus allowed to carry from point to point, and to transmit from hand to hand. And though the space illumined to man's vision may always be small in comparison with the immeasurable abyss of darkness by which it is surrounded, and though the light may be dim and feeble, as well as partial; this need not make us doubt that, so far as we can by the aid of this lamp, we see truly: so far as we discern the necessary laws of the universe, the laws are true, and their truth is rooted in that in which the being of the universe is rooted.

And, to dwell for a moment longer on this image, we may also conceive that all that this lamp—the intellect of man cultivated by science,—does, by the light which it gives, is this—that it dispels a darkness which is dark for man alone, and discloses to him some things in some measure as all things lie in clear and perfect light before the eye of God. To the Divine Mind all the laws of the universe are plain and clear in all their multiplicity, extent and depth. The human mind is capable of seeing some of these laws, though only a few; to some extent, though but a little way; to some depth, though never to the bottom. But the Human Mind, can, in the course of ages and generations, by the long exercise of thought, successfully employed in augmenting knowledge, improve its powers of vision; and may thus come to see more laws than at first, to trace their extent more largely, to understand them more thoroughly; and thus the inward intellectual light of man may become broader and broader from age to age, though ever narrow when compared with completeness.

3. Is it strange to any one that inward light, as well as outward knowledge, should thus increase in the course of man's earthly career? that as knowledge extends, the foundations of knowledge should expand? that as man goes on discovering new truths, he should also discover something concerning the conditions of truth? Is it wonderful that as science is progressive the philosophy of science also should be progressive? that as we know more of everything else, we should also come to know more of our powers of knowing?

This does not seem to have been supposed by philosophers in general; or rather, they have assumed that they could come to know more about the powers of knowing by thinking about them, even without taking into account the light thrown upon the nature of knowledge by the progress of knowledge. From Plato downwards, through Aristotle, through the Schoolmen, to Descartes, to Locke, to Kant, Schelling and Hegel, philosophers have been perpetually endeavouring to explore the nature, the foundations, the consequences of our knowledge. But since Plato, scarcely one of them has ever proceeded as if new light were thrown upon knowledge by new knowledge. They have, many or all of them, attempted to establish fundamental truths, some of them new fundamental truths, about the human mind and the nature and conditions of its knowledge. These attempts show that they do not deny or doubt that there may be such new fundamental truths. Such new fundamental truths respecting the human mind and respecting knowledge must be, in many cases at least, (as it will be seen that they are, on examining the systems proposed by the philosophers just mentioned,) seen by their own light to be true. They are new axioms in philosophy. These philosophers therefore, or their disciples, cannot consistently blame us for holding the possibility of new axioms being introduced into philosophy from age to age, as there arise philosophers more and more clear-sighted.

4. But though they have no ground for rejecting our new axioms merely because they are new, we may have good ground for doubting the value of their new axioms, that is, of the foundations of their systems; because they are new truths about knowledge gathered by merely exploring the old fields of knowledge. We found our hopes of obtaining a larger view of the constitution of the human mind than the early philosophers had, on this:—that we obtain our view by studying the operation of the human mind since their time; its progress in acquiring a large stock of uncontested truths and in obtaining a wide and real knowledge of the universe. Here are new materials which the ancients had not; and which may therefore justify the hope that we may build our philosophy higher than the ancients did. But modern philosophers who use only the same materials as the ancient philosophers used, have not the same grounds for hope which we have. If they borrow all their examples and illustrations of man's knowledge of the universe, from the condition of the universe as existing in Space and Time, that is, from the geometrical condition of the universe, they may fail to obtain the light which might be obtained if they considered that the universe is also subject to conditions of Substance, of Cause and Effect, of Force and Matter: is filled with Kinds of things, in whose structure we assume Design and Ends; and so on; and if they reflected that these conditions or Ideas are not mere vague notions, but the bases of sciences which all thoughtful persons allow to be certain and real.

It is then, as I have said, from taking advantage of the progressive character which physical science, in the history of man, has been found to possess, that I hope to learn more of the nature and prospects of the human mind and soul, than those can learn who still take their stand on the old limited ground of man's knowledge. The knowledge of Geometry by the Greeks was the starting-point of their sound philosophy. It showed that something might be certainly known, and it showed, in some degree, how it was known. It thus refuted the skepticism which was destroying philosophy, and offered specimens of solid truth for the philosopher to analyse. But the Greeks tried to go beyond geometry in their knowledge of the universe. They tried to construct a science of Astronomy—of Harmonics—of Optics—of Mechanics. In the two former subjects, they succeeded to a very considerable extent. The question then arose, What was the philosophical import of these new sciences? What light did they throw on the nature of the universe, on the nature of knowledge, on the nature of the human mind? These questions Plato attempted to answer. He said that the lesson of these new sciences is this:—that the universe is framed upon the Divine Ideas; that man can to a certain extent obtain sight of these Ideas; and that when he does this, he knows concerning the universe. And again, he also put the matter otherwise: there is an Intelligible World, of which the Visible and Sensible world is only a dim image. Science consists in understanding the Intelligible World, which man is to a certain extent able to do, by the nature of his understanding. This was Plato's philosophy, founded upon the progress which human knowledge had made up to his time. Since his time, knowledge, that is science, has made a large additional progress. What is the philosophical lesson to be derived from this progress, and from the new provinces thus added to human knowledge? This is a question which I have tried to answer. I am not aware that any one since Plato has taken this line of speculation;—I mean, has tried to spell out the lesson of philosophy which is taught us, not by one specimen, or a few only, of the knowledge respecting the universe which man has acquired; but by including in his survey all the provinces of human knowledge, and the whole history of each. At any rate, whatever any one else may have done in this way, it seems to me that new inferences remain to be drawn, of the nature of those which Plato drew: and those I here attempt to deduce and to illustrate.

CHAPTER XXX.
The Theological Bearing of the Philosophy of Discovery

That necessary truth is progressive;—that science is the idealization of facts, and that this process goes on from age to age, and advances with the advance of scientific discovery;—these are doctrines which I have endeavoured to establish and to elucidate. If these doctrines are true, they are so important that I may be excused should I return to them again and again, and trace their consequences in various directions. Especially I would examine the bearing of these doctrines upon our religious philosophy. I have hitherto abstained in a great measure from discussing religious doctrines; but such a reserve carried too far must deprive our philosophy of all completeness. No philosophy of science can be complete which is not also a philosophy of the universe; and no philosophy of the universe can satisfy thoughtful men, which does not include a reference to the power by which the universe came to be what it is. Supposing, then, such a reference to be admitted, let us see what aspect our doctrines give to it.

1. (How can there be necessary truths concerning the actual universe?)—In looking at the bearing of our doctrine on the philosophy of the universe, we are met by a difficulty, which is indeed, only a former difficulty under a new aspect. When we are come to the conclusion that science consists of facts idealized, we are led to ask, How this can be? How can facts be idealized? How can that which is a fact of external observation become a result of internal thought? How can that which was known à posteriori become known à priori? How can the world of things be identified with the world of thoughts? How can we discover a necessary connexion among mere phenomena?

Or to put the matter otherwise: How is it that the deductions of the intellect are verified in the world of sense? How is it that the truths of science obtained à priori are exemplified in the general rules of facts observed à posteriori? How is it that facts, in science, always do correspond to our ideas?

I have propounded this paradox in various forms, because I wish it to be seen that it is, at first sight, a real, not merely a verbal contradiction, or at least a difficulty. If we can discover the solution of this difficulty in any one form, probably we can transpose the answer so as to suit the other forms of the question.

2. Suppose the case to be as I have stated it; that in some sciences at least, laws which were at first facts of observation come to be seen as necessary truths; and let us see to what this amounts in the several sciences.

It amounts to this: the truths of Geometry, such as we discern them by the exercise of our own thoughts, are always verified in the world of observation. The laws of space, derived from our Ideas, are universally true in the external world.

In the same way, as to number: the laws or truths respecting number, which are deduced from our Idea of Number, are universally true in the external world.

In the same way, as to the science which deals with matter and force: the truths of which I have spoken as derived from Ideas:—that action is equal to reaction; and that causes are measured by their effects;—are universally verified in all the laws of phenomena of the external world, which are disclosed by the science of Mechanics.

In the same way with regard to the composition and resolution of bodies into their elements; the truths derived from our Idea of Matter:—that no composition or resolution can increase or diminish the quantity of matter in the world, and that the properties of compounds are determined by their composition;—are truths derived from Ideas of quantity of matter, and of composition and resolution; but these truths are universally verified when we come to the facts of Chemistry.

In the same way it is a truth flowing from the Ideas of the Kinds of things, (as the possible subject of general propositions expressed in language,) that the kinds of things must be definite; and this law is verified whenever we express general propositions in general terms: for instance, when we distinguish species in Mineralogy.

3. This last example may appear to most readers doubtful. I have purposely pursued the enumeration till I came to a doubtful example, because it is, and I conceive always will be, impossible to extend this general view to all the Sciences. On the contrary, this doctrine applies at present to only a very few of the sciences, even in the eyes of those who hold the existence of ideal truths. The doctrine extends at present to a few only of the sciences, even if it extend to one or two besides those which have been mentioned—Geometry, Mechanics, Chemistry, Mineralogy: and though it may hereafter appear that Ideal Truths are possible and attainable for a few other sciences, yet the laws disclosed by sciences which cannot be reduced to ideal elements will, I conceive, always very far outnumber those which can be so reduced. The great body of our scientific knowledge will always be knowledge obtained by mere observation, not knowledge obtained by the use of theories alone.

4. The survey of the history and philosophy of the Sciences which we have attempted in previous works enables us to offer a sort of estimate of the relative portions of science which have and which have not thus been idealized. For the Aphorisms³¹⁷ which we have collected from that survey, contain Axioms which may be regarded as the Ideal portions of the various sciences; and the inspection of that series of aphorisms will show us to how such a portion of science, anything of this axiomatic or ideal character can he applied. These Axioms are the Axioms of Geometry (Aphorism XXVI); of Arithmetic (XXXVI); of Causation (XLVII); of a medium for the sensation of secondary qualities (LVIII), and their measure (LXIX); of Polarity (LXXII); of Chemical Affinity (LXXVI); of Substance (LXXVII); of Atoms (LXXIX).

Have we any axioms in the sciences which succeed these in our survey, as Botany, Zoology, Biology, Palæontology?

There is the Axiom of Symmetry (LXXX); of Kind, (already in some measure spoken of, (LXXXIII)); of Final Cause (CV); of First Cause (CXVI).

5. (Small extent of necessary truth.)—It is easily seen how small a portion of each of these latter sciences is included in these axioms: while, with regard to the sciences first mentioned, the Axioms include, in a manner, the whole of the science. The science is only the consequence of the Axioms. The whole science of Mechanics is only the development of the Axioms concerning action and reaction, and concerning cause and its measures, which I have mentioned as a part of our Ideal knowledge.

In fact, beginning from Geometry and Arithmetic, and going through the sciences of Mechanics, of Secondary Qualities, and of Chemistry, onwards to the sciences which deal with Organized Beings, we find that our ideal truths occupy a smaller and smaller share of the sciences in succession, and that the vast variety of facts and phenomena which nature offers to us, is less and less subject to any rules or principles which we can perceive to be necessary.

But still, that there are principles,—necessary principles, which prevail universally even in these higher parts of the natural sciences,—appears on a careful consideration of the axioms which I have mentioned:—that in symmetrical natural bodies the similar parts are similarly affected;—that every event must have a cause;—that there must be a First Cause, and the like.

6. It being established, then, that in the progress of science, facts are idealized—that à posteriori truths become à priori truths;—that the world of things is identified with the world of thoughts to a certain extent;—to an extent which grows larger as we see into the world of things more clearly; the question recurs which I have already asked: How can this be?

How can it be that the world without us is thus in some respects identical with the world within us?—that is our question.

7. (How did things come to be as they are?)—It would seem that we may make a step in the solution of this question, if we can answer this other: How did the world without us and the world within us come to be what they are?

To this question, two very different answers are returned by those who do and those who do not believe in a Supreme Mind or Intelligence, as the cause and foundation of the world.

Those who do not believe that the world has for its cause and foundation a Supreme Intelligence, or who do not connect their philosophy with this belief, would reply to our inquiry, that the reason why man's thoughts and ideas agree with the world is, that they are borrowed from the world; and that the persuasion that these Ideas and truths derived from them have any origin except the world without us, is an illusion.

On this view I shall not now dwell; for I wish to trace out the consequences of the opposite view, that there exists a Supreme Mind, which is the cause and foundation of the universe. Those who hold this, and who also hold that the human mind can become possessed of necessary truths, if they are asked how it is that these necessary truths are universally verified in the material world, will reply, that it is so because the Supreme Creative-Mind has made it so to be:—that the truths which exist or can be generated in man's mind agree with the laws of the universe, because He who has made and sustains man and the universe has caused them to agree:—that our Ideas correspond to the Facts of the world, and the Facts to our Ideas, because our Ideas are given us by the same power which made the world, and given so that these can and must agree with the world so made.

8. (View of the Theist).—This, in its general form, would be the answer of the theist, (so we may call him who believes in a Supreme Intelligent Cause of the world and of man,) to the questions which we have propounded—the perplexity or paradox which we have tried to bring into view. But we must endeavour to trace this view—this answer—more into detail.

If a Supreme Intelligence be the cause of the world and of the Laws which prevail among its phenomena, these Laws must exist as Acts of that Intelligence—as Laws caused by the thoughts of the Supreme Mind—as Ideas in the Mind of God. And then the question would be, How we are to conceive these thoughts, these Ideas, to be at the same time Divine and human:—to be at the same time Ideas in the Divine Mind, and necessary truths in the human mind; and this is the question which I would now inquire into.

9. (Is this Platonism?)—To the terms in which the inquiry is now propounded it may be objected that I am taking for granted the Platonic doctrine, that the world is constituted according to the Ideas of the Divine Mind. It may be said that this doctrine is connected with gross extravagancies of speculation and fiction, and has long been obsolete among sound philosophers.

To which I reply, that if such doctrines have been pushed into extravagancies, with them I have nothing to do, nor have I any disposition or wish to revive them. But I do not conceive the doctrine, to the extent to which I have stated it, to be at all obsolete:—that the Cause and Foundation of the Universe is a Divine Mind: and from that doctrine it necessarily follows, that the laws of the Universe are in the Ideas of the Divine Mind.

I would then, as I have said, examine the consequences of this doctrine, in reference to the question of which I have spoken. And in order to do this, it may help us, if we consider separately the bearing of this doctrine upon separate portions of our knowledge of the universe;—separately its bearing upon the laws which form the subject-matter of different sciences:—if we take particular human Ideas, and consider what the Divine Ideas must be with regard to each of them.

10. (Idea of Space.)—Let us take, in the first place, the Idea of Space. Concerning this Idea we possess necessary truths; namely, the Axioms of Geometry; and, as necessarily resulting from them, the whole body of Geometry. And our former inquiry, as narrowed within the limits of this Idea, will be, How is it that the truths of Geometry—à priori truths—are universally verified in the observed phenomena of the universe? And the theist's answer which we have given will now assume this form:—This is so because the Supreme Mind has constituted and constitutes the universe according to the Idea of Space. The universe conforms to the Idea of Space, and the Idea of Space exists in the human mind;—is necessarily evoked and awakened in the human mind existing in the universe. And since the Idea of Space, which is a constituent of the universe, is also a constituent of the human mind, the consequences of this Idea in the universe and in the human mind necessarily coincide; that is, the spacial Laws of the universe necessarily coincide with the spacial Science which man elaborates out of his mind.

11. To this it may be objected, that we suppose the Idea of Space in the Divine Mind (according to which Idea, among others, the universe is constituted,) to be identical with the Idea of Space in the human mind; and this, it may be urged, is too limited and material a notion of the Divine Mind to be accepted by a reverent philosophy.

I reply, that I suppose the Divine Idea of Space and the human Idea of Space to coincide, only so far as the human Idea goes; and that the Divine Idea may easily have so much more luminousness and comprehensiveness as Divine Ideas may be supposed to have compared with human. Further, that this Idea of Space, the first of the Ideas on which human science is founded, is the most luminous and comprehensive of such Ideas; and there are innumerable other Ideas, the foundations of sciences more or less complete, which are extremely obscure and limited in the human mind, but which must be conceived to be perfectly clear and unlimitedly comprehensive in the Divine Mind. And thus, the distance between the human and the Divine Mind, even as to the views which constitute the most complete of the human sciences, is as great in our view as in any other.

12. That the Idea of Space in the human mind, though sufficiently clear and comprehensive to be the source of necessary truths, is far too obscure and limited to be regarded as identical with the Divine Idea, will be plain to us, if we call to mind the perplexities which the human mind falls into when it speculates concerning space infinite. An Intelligence in which all these perplexities should vanish by the light of the Idea itself, would be infinitely elevated in clearness and comprehensiveness of intellectual vision above human intelligence, even though its Idea of Space should coincide with the human Idea as far as the human Idea goes.

I do not shrink from saying, therefore, that the Idea of Space which is a constituent of the human mind existing in the universe is, as far as it goes, identical with the Idea of Space which is a constituent of the universe. And this I give as the answer to the question, How it is that the necessary truths of Geometry universally coincide with the relations of the phenomena of the universe? And this doctrine, it is to be remembered, carries us to the further doctrine, that the Idea of Space in the human mind is, so far as it goes, coincident with the Idea of Space in the Divine Mind.

13. (Idea of Time.)—What I have said of the Idea of Space, may be repeated, for the most part, with regard to the Idea of Time; except that the Idea of Time, as such, does not give rise to a large collection of necessary truths, such as the propositions of Geometry. Some philosophers regard Number as a modification or derivative of the Idea of Time. If we accept this view, we have, in the Science of Arithmetic, a body of necessary truths which flow from the Idea of Time. But this doctrine, whichever way held, does not bear much on the question with which we are now concerned. That which we do hold is, that the Idea of Time in the human mind is, so far as it goes, coincident with the Idea of Time in the Divine Mind: and that this is the reason why the events of the universe, as contemplated by us, conform to necessary laws of succession: while at the same time we must suppose that all the perplexities in the Idea of Time which embarrass the human mind—the perplexities, for instance, which arise from contemplating a past and a future eternity, are, in the Divine Mind, extinguished in the Light of the Idea itself.