The simple fact is, that the educated men of our time, owing to the prepossessions which they have imbibed from their cradle and to the specimens of philosophy which have fallen across their path, have not as yet realized the fact that Metaphysics is a science, -- with its own terminology and its own first principles, -- most difficult of acquisition, -- requiring long-continued, patient, devoted, laborious, study. They seem to imagine that they can jump into it all at once with as much ease as they can get into a new suit of ready-made clothes.
Know, then, gentle reader, that, if you would be a metaphysician, you must make up your mind for work, -- mental work of no ordinary kind. It is an error to suppose that true philosophy is easy of comprehension, or that it can be mastered in an hour. You are told, (and nothing is more certain), that philosophy must be built upon common sense; and you may, therefore, hazard the eonclusion that the former will present no greater difficulties than the latter to your endeavours after the acquisition of its truths. But it must be remembered that, if common sense is the foundation, the metaphysical science is the lofty temple erected ou it. It may be easy work to traverse the ground-floor; but it requires a steady head and sure foot to walk along the parapet of the roof or to stand upon the pinnacle.
There is another not uncommon impediment. to success in the study of Metaphysics, to which the writer in the Pall Mall Gazette makes allusion in the concluding quotation: -- 'Then we have,' he writes, 'ignorance of the philosophical conditions; in other words, absence of the special training required to deal effectively with philosophical questions as such. In this way it may come about that men of science give the philosophers their revenge.' This impediment consists of a certain peculiar bent which the mind acquires from exclusive devotion for a long period of time to certain particular sciences or disciplines. I refer more especially to the study of Physics and Mathematics. This difficulty has been already hinted at; but the practical importance of the subject justifies me in putting it more directly and explicitly before the reader.
But, before doing so, I would interpose an observation. It is an old proverb, that there is no rule without an exception. I should be the last to deny, that there may have been men, eminent in Mathematics or Physics, who have been likewise eminent in Metaphysics or Theology. Genius and resolution conquer all difficulties. Again: I am not speaking of the simple study of these branches of knowledge, but of the (morally speaking) exclusive study of them for a long period of time. Accordingly, I contemplate for the most part students whose intellectual formation is already complete, and who have lost in mental elasticity that which they have gained in mental nerve and thew. I repeat, then, that the exclusive pursuit of these studies gradually tends to form habits of thought, in the generality of cases, which render after application to metaphysical subjects exceptionally difficult. As this impediment assumes a very different form in Physics to what it does in Mathematics, I propose to consider each in turn.
I must premise that, in the observations which follow, it would be a great mistake to suppose that I have any intention of depreciating the value of physical investigations, or of ignoring the many indisputable advantages which accrue from the brilliant discoveries that have been made in this important, though lower, field of Truth. All truths, physical no less than metaphysical, natural as well as supernatural, spring from one Source, and return to Him again. Wherefore, physical truths cannot safely be disregarded by him, who is a servant at the Court of the Queen of Sciences. Nay, -- to say out what I think, -- while unable to adopt to the letter the somewhat rhetorical assertion of Mr. Huxley, that 'the laboratory is the foreground of the temple of philosophy; and whoso has not offered sacrifices and undergone purification there, has little chance of admission into the sanctuary,'{1} it is my settled belief, that a previous general acquaintance with the progress of physical investigations will prove a valuable aid to the student who proposes entering upon the study of Metaphysics.
All I am contending for, is this; that the exclusive application to Physics or to any particular branch of it, continued for any length of time, has a tendency to unfit the mind for the after study of Metaphysics, and so to make such study more than ordinarily difficult. If I am asked to assign a cause to this effect, I should be inclined to attribute such mental bias, partly, to the necessity of invariably using the inductive method in all physical research. If we would know nature's laws, we must have recourse to nature's facts; in order that, by a progressive synthesis of these latter, -- the phenomena of hodies, -- we may be able to infer that constant order which is what is understood by natural law. But such is the inductive method. Now, physical induction can never be logically perfect. It inevitably includes the assumption, that the quasi-Middle Term (that is to say, the collection of experimental facts) equals the Major Term (that is to say, all the past, present, future, and possible facts that have, or have not, been subjected to experiment). When, therefore, the mind has been long accustomed to these imperfect forms of thought, it is liable to become loose in its logic, from being wholly unaccustomed to the use of stricter and perfect forms.
Hence arises, or may arise, a mental slovenliness, if I may so express myself, which is wont to manifest itself in a neglect of logical order, -- in the use of an undefined terminology, -- in causeless repetitions, -- in careless and imperfect definitions, when they are given at all, -- in the perpetual confusion of legitimate physical inductions with mere theories, or with deductions which, because they are deductions, belong to some other science. It would be difficult for me to illustrate these defects by illustrations taken from living authors, without rendering myself obnoxious to the charge of personality and possibly wounding the feelings of those respectable writers who would be thus invidiously brought before the public notice. Yet, illustrations from living authors are the only ones that I could furnish, because my reading has been almost entirely directed to them; as they are the ones that best suit my purpose, because they occur in the latest developments of physical science.
But happily it is in my power to adduce an instance of what I mean, -- by no means, however, the most striking, -- where there will be no danger of those evil results which I should so much deprecate. Professor Tait stands so deservedly high in public estimation as one of the most eminent physicists of his time, that he can well afford to endure the ordeal, such as it is. Besides, his style is so lucid, -- there is, for the most part, such attention to unity of plan, -- comparatively so sparing a use of unusual terms, -- that I may be thought, not without reason, to have put myself at a disadvantage by selecting him. I propose, then, to take my illustrations from his most interesting and instructive Lectures on some recent advances in Physical Science.
In his introductory Lecture, the learned Professor calls especial attention to the fact, that the advances of physical science are attributable to the use of the inductive method. By way of emphasis, he italicizes the following canon, as it may be called: 'These advances come or not, according as we remember, or forget, that our science is to be based entirely upon experiment, or mathematical deductions from experiment.'{2} According to this author, then, the advance of physical science depends upon the exclusive use of the inductive method, with one exception. He admits of mathematical deduction, and no other. But those mathematical deductions must be founded on experiment. Now, turn we to another passage in the same Lecture. The Professor is occupied in extolling the praises of the discovery of what is denominated Dissipation of Energy. He calls it a Principle; and anticipates great results in the future from its general application to physical phenomena. Referring in particular to its bearings on Astronomy, he writes as follows: 'Finally, as it alone is able to lead us, by sure steps of deductive reasoning, to the necessary future of the universe -- necessary, that is, if physical laws for ever remained unchanged -- so it enables us distinctly to say that the present order of things has not been evolved through infinite past time by the agency of laws now at work, but must have had a distinct beginning, a state beyond which we are totally unable to penetrate; a state, in fact, which must have been produced by other than the now (visibly) acting causes.'{3} Now, these conclusions are not 'based entirely upon experiment;' for we are told that they are the result of deductive reasoning. Consequently, if the application of this so-called Principle is to give birth to these great advances in Physical Science, the aforesaid conclusions must be 'mathematical deductions from experiment.' But they are attributed to the Principle, (or as some, in its relation at least to Astronomy, might prefer to call it, Theory), of Dissipation of Energy. Are we, then, to understand that mathematical deductions from this Theory can lead us 'by sure steps' to such conclusions? Where are 'the experiments' from which these mathematical deductions must proceed? If we seek for them in the phenomena revealed to astronomical observation, as interpreted by the said Theory, I would respectfully inquire whether the facts are certain; about which one is naturally more anxious, since Mr. Lockyer's spectroscopic investigations have cast a serious doubt upon the supposition that there is any identity between the physical composition of the earth and that of the celestial bodies.{4} Finally: assuming the facts, the Principle, and the applicability of the Principle to Astronomy, to be free from all doubt; I would fain know whether there are any mathematical calculations, starting from these premisses, which could demonstratively elicit the like conclusions?
I will take another instance of a different character from the same Lecture. The learned Professor complains, and justly complains, of the vague, confused, employment of the word, Force. Accordingly, he gives one of his own. 'Force,' he writes, 'is any cause which alters or tends to alter a body's state of rest or of uniform motion in a straight line.'{5} It is right to subjoin, that he limits this definition to Force, as it is understood in physical science; but even so, I question whether the definition would be universally accepted by his brother physicists. This is not the point, however, to which I wish to call attention. Professor Tait finds one serious difficulty in his own definition; and it consists in the use of the word cause. 'For this,' he proceeds to say, 'among material things, usually implies objective existence. Now we have absolutely no proof of the objective existence of force in the sense just explained. In every case in which force is said to act, what is really observed . . . is either a transference, or a tendency to transference, of what is called energy from one portion of matter to another.'
So let it be; but what is a transference? A transference, if I mistake not, is the passage, or communication, of something from one entity to another. But this connotes three things, -- something which is transferred, that which makes the transfer, and that which is Subject of the transfer. Now, if the entity which makes the transfer is hypothetically, (i. e. under the circumstances and according to natural law) necessary and of itself sufficient for the existence of the energy in the Subject of the transfer, that entity is univocally and truly a cause. But let us now see whether the Professor gains anything in this respect by the substitution of the term Energy for that of Force. Energy, we are told, is the power of doing work, or, if we like to put it so, of doing mischief.'{6} Now, with submission, I must venture on the expression of an opinion, that this declaration does not satisfy the laws of definition. For it is, first of all, essential to a true and proper definition, that it should be more intelligible -- clearer -- than the word or idea defined. But the power of doing work or of doing mischief confuses, rather than illustrates, the simple idea of energy, in the case of those at least who are not versed in the new theory. I am not at all sure that the proposed definition is adequate, -- another essential requisite, nevertheless, of a true definition; since there are energies, such as life itself, which are purely immanent activities. Certainly, it offends against the third canon, which excludes a redundancy of words. For the second clause, of doing mischief, is implicitly contained in the first, the power of doing work; for that which does work harmful to another, does mischief. If the or is to be taken in a substitutive sense, the student should not be left unaided to make the selection. Finally, I object to the definition, because the phrase is not univocal.
But that which I specially wish to call attention to is, that the idea of Energy is preferred to that of Force, because Energy 'claims recognition on account of its objective existence.'{7} If, however, we analyze the definition given, we shall find that it essentially connotes the idea of Force; more particularly, if we interpret the definition by the light of the illustrations that follow. For, to do work, and more notably, to do mischief, imply some other in which the work is done, -- the mischief effected. But such energy is causal. The mass of snow on the mountain top has a power of doing mischief on the traveller in the gorge; because, if it falls by the force of gravitation, it may cause his death. The food of animals is not a mere transfer. There is a multiform causal action by which the material substance is decomposed, -- the nutritive constituents, absorbed and assimilated, -- the useless, rejected .'{8} Briefly, in these and the other instances, there is an agent, the Subject, and some thing caused by means of the former in the latter. Therefore, there is causality; and, because the agent cannot do the work or mischief unless it has the force, or power, to do it, it must have a force.
My last illustration shall be taken, again, from a different order. Professor Tait observes, as follows: 'A revelation of anything which we can discover for ourselves, by studying the ordinary course of nature, would be an absurdity.'{9} This assertion directly impugns the truth alike of Judaism and of Christianity; however innocent its author may have been of such an intention. For, in the Old Testament, the existence and unity of God, -- the free-will and accountability of man, -- the fundamental principles of the -- natural law, -- are all subjects of Revelation. In the New Testament, the beauty of the lily, -- the unfitness of building on sand, -- the growth of corn, of the fig-tree, in Palestine, -- are all subjects of Revelation. But it may be, that the learned Professor would not agree with me in either of these statements. Wherefore, I will change the venue, and consider the question independently of the facts of Revelation. Why is it an absurdity to suppose that God should reveal a truth, already discovered by a study of the ordinary course of nature, in order to seal it with the sanction of His own Infallibility? Anyhow, the subject is fully considered and discussed in the Science of supernatural Theology; but I deprecate, as wanton, its parenthetical introduction into a Work devoted to the consideration of material phenomena.
Of the defects in the literature of Physics, which I have already enumerated, by far the most serious is the confused intermixture of legitimate physical inductions with arbitrary hypotheses or theories, and a consequent shaping of facts in order to dovetail them with the theory. I call it a most serious defect; because, even though a clear-headed student of Physics may be able to separate the wheat from the chaff, and thus to pursue his physical researches with success, his mind will be more or less affected by the practical identification of things certain with things dubious. He may, and probably will, become disaffected towards that logical precision which the study of Metaphysics absolutely demands. The metaphysician must accurately distinguish between truths of intuition and truths of demonstration, -- between demonstration and mere opinion, -- and opinions must themselves be graduated with great care, according to the weight of intrinsic, or (in defect of intrinsic) of extrinsic, evidence producible in favour of each. But this presupposes great accuracy of thought, which the student of Physics is tempted to condemn as mere hair-splitting.
Another reason why the continuous and exclusive study of the physical sciences has a tendency to unfit the mind for ascending the heights of Metaphysics, is to be found in the nature of the subject-matter peculiar to each. The intellectual eye of the physicist is continually fixed on the material and concrete, -- that is to say, on those objects which are the least intelligible and are lowest among the orders of truths, while easiest to sensile perception. Metaphysics, on the other hand, contemplates the abstract and immaterial. The physicist deals with the contingent, the temporary; the Metaphysical Science invites him to a contemplation of the necessary, the eternal. Unaccustomed, then, to anything save sensile phenomena, if he accepts the invitation, he is liable to become dazzled and giddy; like men who work day and night in coal-mines when first they revisit the upper earth and encounter the sun's rays. Or the mental twist may take another form. The long concentration of his mental faculties on material matter may have helped to form a cherished prejudice, that there is nothing real but material being, that there is nothing knowable save that which is subject to sensile perception; that, consequently, the immaterial and spiritual are mere creations of the intellect, and destitute of all objective value. Of the two indispositions this latter is, evidently enough, the more difficult of cure; while it would necessarily cause, for so long as it lasts, an invincible aversion for metaphysical study. There are other subsidiary reasons that I could mention; but the limits of a Preface will not admit of my treating this important and interesting question at greater length.
Again: I must be permitted to express my settled conviction, that a long-continued and too exclusive study of Mathematics is liable to unfit the mind for the pursuit of metaphysical truth. I should do an injustice to myself, if I were to afford any ground for the suspicion that I placed Mathematics on a par with Physics in this respect. If we had not the express authority of Aristotle to assure us, a merely superficial acquaintance with Mathematics of would of itself be enough to satisfy us, that it is, in the strictest sense of the word, a science. It is supreme among the subordinate sciences, (with the exception, perhaps, of Logic), in its aptitude for generating in the mind habits of clearness and precision. Moreover, it deals, as all true sciences do, with the abstract and universal; and its conclusions, in their evidence and cogency of demonstration, surpass those of all the other sciences, save the Architectonic. Nay, in one respect, it excels even this latter; for, owing to the nature of their respective subject-matters, the purely mathematical science excludes, while Metaphysics admits, mere opinion, and the sufficiency of the motive of probability, in default of clearer evidence. In all these respects Mathematics markedly contrasts with the physical discip1ines, whose conclusions are all extra-logical. Moreover, though it agrees with those disciplines in dealing exclusively with material entities; nevertheless, it does not treat them as material entities. It fixes upon their Quantity alone, -- the primal Accident of bodies; and not even upon Quantity in the concrete, but upon the universal and immutable her laws or abstract forms of Quantity. It cannot, then, be doubted, that this science occupies the most eminent place, after Logic, in the propaedeutics of Philosophy.
Nevertheless, a too exclusive application to Mathematics has a tendency to indispose the mind for the study of Metaphysics, after and a manner of its own; first of all, because it trains the mind to be too exacting. This is a fault, (if fault it may be called, apart from its indiscriminate application), which is not likely to become epidemic in an age like our own, wherein men are too busy to think and, a fortiori, to acquire true cognition by rigid demonstration. Yet this demand for scientific proof, reasonable and even laudable as it is in itself absolutely, may become excessive; if it is made, irrespective of whatsoever diversity in the nature of the subject-matter. By all means let us have scientific proof, if scientific proof is to be had; but it does not follow that we should quarrel with probable opinions, or conclusions drawn from analogy, in defect of higher evidence. In Mathematics the exaction is just; because the subject-matter of this science is as purely formal in its way, as is that of Logic in its way; the only difference being, that the latter deals with subjective, while the former deals with objective, forms. But, when we ascend to the contemplation of immaterial and spiritual Being, -- of Transcendentals, -- of truths most abstract and difficult to sense, -- and of Him Who is the all-containing Truth; it is not in every case easy to find, and therefore it is not just to postulate, a strictness of demonstration which is only natural to, and is absolutely necessary for, a science that exclusively deals with the abstract forms of material quantity.
The practical experience of the mathematician would, one might suppose, suffice to teach him, that, -- to use a homely but expressive proverb, -- he must cut his coat according to his cloth. For, as in Logic the forms of thought are subject to modification, when applied to different orders of truths; so, the mathematical science loses somewhat of its rigidity, when applied to the complex facts of nature. If there be no other change in the character of its proofs, so much at all events is undeniable; that these exchange their metaphysical, for purely physical, evidence. A conclusion cannot be stronger than the premisses which give it birth; consequently, syllogisms which, under their pure algebraic form, are strict demonstrations and metaphysically evident, become, when the symbols are interpreted by physical facts, as firm or infirm as the facts which have been substituted. Even within the proper sphere of Mathematics, there is a graduated scale of demonstration. Many of the demonstrations in Euclid, for example, assume the form of a dilemma; others, of a reductio ad absurdum. But neither of these demonstrative forms can pretend to an equality with categorical and ostensive demonstration. Nevertheless, it not unfrequently happens that mathematicians, long habituated to their abstract symbols and the formal rigidity of their subject-matter, are disappointed and repelled at the outset of metaphysical or Theological study, and make less way in either than one might have anticipated; because they desiderate a clearness of demonstration throughout, which the nature of the subject-matter in its relation to human thought will not always admit. I cannot help thinking, that to this mathematical infirmity we are indebted for the philosophical doubt of Descartes, which has had such pernicious influence over modern thought; and, as legitimate parent of the subsequent Schools of Idealism and Scepticism, has contributed more than aught besides towards uprooting the fundamental principles of objective truth out of the minds of men.
Another danger, incident to the exclusive study of Mathematics, -- and a much more serious one it is, serious in itself, more serious in its consequences, -- arises from a proneness to elevate Mathematics above its rightful place and practically to claim for it the throne of supremacy among the sciences. It is an excusable weakness which leads men to exaggerate the importance of their own particular subject of study, and to make it the universal measure. As the physicist, then, would fain make his sensile phenomena the criterion of truth; so the mathematician is often too inclined to intrude the special forms, laws, principles, and ideas of his own science into higher regions of thought. But it can never be permitted to any science, that it should transgress its natural limits; for this would result in revolutionizing the established order. Besides, it is absonous to suppose, that a science, which cannot ascend beyond the sphere of material Being,- should ever become oecumenical. Consequently, it behoves us summarily to reject all those ingenious attempts to transform Logic into a chapter of Mathematics. Logical Mathematics I can understand; but a mathematical Logic is a monstrosity. For the laws, or forms, of Quantity cannot be made, in reason, to regulate the processes of human thought. You might as well try to take the measure of an angel with a theodolite.
So, again, it is not reasonable that Mathematics should be allowed to determine for us the nature of the ultimate constituents of bodies, or material substances; for (as I have more than once remarked) it has nothing to do with bodies themselves, but only with one of their Accidents, -- to wit, Quantity. Let the physical Disciplines, -- more particularly Chemistry, -- supply the necessary facts. Let the common sense of mankind be consulted on a question which, up to a certain point, is evidently subject to its judgment. But it is the metaphysical Science, and the metaphysical Science alone as Queen of the Sciences, that has either the iight to determine the question or the capacity for arriving at such a determination. If this comely order of the sciences had been observed in modern as it was observed in the olden times, we should never have heard of that dynamic theory of Boscovich, which Professor Tait very justly pronounces to be 'a mathematical fiction.'{10}
{1} English Men of Letters. -- Hume, p. 52.
{2} p. 6. I have ventured to punctuate the sentence, in order that it may be more readily understood.
{3} p. 22.
{4} See a Paper read before the Royal Society, March 20, 879, on Young's List of Chromospheric Lines.
{5} p. 16.
{6} p. 18.
{7} p. 17.
{8} p. 18.
{9} p. 25.
{10} Recent Advances in Physical Science, Lecture XII, p. 288.