Popular Science Monthly/Volume 4/November 1873/The Primary Concepts of Modern Physical Science II

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Popular Science Monthly Volume 4 November 1873  (1873) 
The Primary Concepts of Modern Physical Science II
By John Bernhard Stallo

THE PRIMARY CONCEPTS OF MODERN PHYSICAL SCIENCE.
By J. B. STALLO.

II.-The Atomic Constitution of Matter as a Postulate of Thought.

MY inquiry thus far has touched the assertion according to which the atomic hypothesis is the necessary basis of the theories which constitute the sciences of physics and chemistry. I propose now to consider the claim that this hypothesis is an essential prerequisite of the realization of material existence in thought.

To show how pointedly this claim is made, it will be sufficient to extract a passage from a recent lecture of Prof. John Tyndall, before the British Association at Liverpool, "On the Scientific Use of the Imagination" ("Fragments of Science," American edition, p. 135). The words of Prof. Tyndall, whose opinions, by reason of his eminence among physicists, may be taken instar omnium, are these:

" Many chemists of the present day refuse to speak of atoms and molecules as real things. Their caution leads them to stop short of the clear, sharp, mechanically-intelligible atomic theory enunciated by Dalton, or any form of that theory, and to make the doctrine of multiple proportions their intellectual bourn. I respect the caution, though I think it is here misplaced. The chemists who recoil from these notions of atoms and molecules, accept without hesitation the undulatory theory of light. Like you and me, they one and all believe in an ether and its light-producing waves. Let us consider what this belief involves. Bring your imagination once more into play, and figure a series of sound-waves passing through air. Follow them up to their origin, and what do you there find? A definite, tangible, vibrating body. It may be the vocal chords of a human being, it may be an organ-pipe, or it may be a stretched string. Follow in the same manner a train of ether-waves to their source; remembering at the same time that your ether is matter, dense, elastic, and capable of motions subject to and determined by mechanical laws. What, then, do you expect to find as the source of a series of ether-waves? Ask your imagination if it will accept a vibrating multiple proportion—a numerical ratio in a state of oscillation? I do not think it will. You cannot crown the edifice by this abstraction. The scientific imagination, which is here authoritative, demands as the origin and cause of a series of ether-waves a particle of vibrating matter quite as definite, though it may be excessively minute, as that which gives origin to a musical sound. Such a particle we name an atom, or a molecule. I think the seeking intellect, when focussed so as to give definition without penumbral haze, is sure to realize this image at the last."

The import of these sentences is plain. It is that an ethereal or other atom, or a molecule, is related to its vibratory motion just as any ordinary body is related to its movements of translation—as a stellar or planetary body, for instance, is related to its movements of rotation or revolution; and that, just as the conception of the stellar or planetary body of necessity precedes the conception of its rotary or revolutionary motion, so also the conception of the atom or molecule of necessity precedes the conception of the vibratory motion whereof light, heat, electricity, chemical action, etc., are known or supposed to be modes. In other words: to make the existence of matter, such as we deal with in action and in thought, conceivable, we are constrained, according to Tyndall, to assume ultimate material particles as preexisting to those motions or manifestations of force which are apprehended as light, heat, electricity, chemical action, etc.

In order to preclude all possibility of misunderstanding, it is perhaps well to call attention to the fact that, while Tyndall speaks in terms only of the relation of the ether to its vibratory motion, it is evident from his own language that this is meant as an illustration or exemplification of the relation of all matter to any or all motion whatever.

Now, let us for a moment contemplate an ultimate particle of matter in this state of existence in advance of all its motion. It is without color, and neither light nor dark; for color, lightness, darkness, etc., are luminar affections, and, according to the received mechanical theory of "imponderables," of which Prof. Tyndall is a distinguished champion, simply modes of motion. It is similarly without temperature—neither hot nor cold; for heat also is a mode of motion. For the same reason it is without electrical or chemical properties—in short, it is utterly destitute of all those properties in virtue of which, irrespective of its magnitude, it could be an appreciable object of sense, unless we except the properties of weight and extension. But weight is a mere play of attractive forces; and extension, too, is known to us only as resistance, which in turn is a manifestation of force, and thus a phase of motion. Extension per se, abstract extension, cannot be realized in thought, whatever ground there may be for dissenting from the opinion of Sir W. Hamilton ("Lectures on Metaphysics," Boston edition, p. 385), that "we cannot represent extension to the mind except as colored."

Thus the solid, tangible reality, craved by Prof. Tyndall's "scientific imagination," wholly vanishes from the "seeking intellect" the moment this intellect attempts to grasp it apart from the notion which is said to presuppose it as its necessary substratum. If the deliverances of the scientific imagination are authoritative in science, the notion of the primordial atom must be relegated to the regions beyond the bounds of scientific thought.

There is another and very obtrusive aspect of the atomic theory in which its utter inability to satisfy the demands of the "scientific imagination" has long since been recognized. As I have already shown, the atomic theory, in whatever form it is held, presupposes the separation of the atoms by void, interstitial spaces. The only difference of opinion respecting these spaces is as to their magnitude, the emergencies of the modern theories of heat and light having led to the supposition that even in the case of the purely hypothetical "ether" (which is nothing but a clothes-horse for all the insoluble difficulties presented by the phenomena of sensible material existence—a fagot of occult qualities and principia expressiva whose róle in the material world at large is analogous to the part formerly played by the aura vitalis, and similar phantasms, in the organic world) the interspaces are very great in comparison with the dimensions of the atoms, so that a group of these atoms is not infrequently compared with a stellar or planetary system. Nevertheless, their motions are construed as effects of their mutual attractions and repulsions. But how is the mutual action of atoms existing by themselves in complete insulation and wholly without contact to be realized in thought? We are here in the presence of the old difficulties respecting the possibility of actio in distans which presented themselves to the minds of the physicists in Newton's time, and constituted one of the topics of the famous discussion between Leibnitz and Clarke, in the course of which Clarke made the remarkable admission (Fourth Letter of Clarke, §45, "Leibnitii Opera," ed. Erdmann, p. 762) that, "if one body attracted another without an intervening body, that would be, not a miracle, but a contradiction; for it would be to suppose that a body acts where it is not"—otherwise expressed: inasmuch as action is but a mode of being, the assertion that a body can act where it is not would be tantamount to the assertion that a body can be where it is not. This admission was entirely in consonance with Newton's own opinion; indeed, Clarke's words are but a paraphrase of the celebrated passage in one of Newton's letters to Bentley, cited by John Stuart Mill in his "System of Logic," which runs as follows:

"It is inconceivable that inanimate brute matter should, without the mediation of something else, which is not material, operate upon and affect other matter without mutual contact. . . . That gravity should be innate, inherent, and essential to matter, so that one body may act on another, at a distance, through a vacuum, without the mediation of any thing else by and through which their action and force may be conveyed from one to the other, is to me so great an absurdity that I believe no man, who in philosophical matters has a competent faculty of thinking, can ever fall into it."

The thesis of the impossibility of actio in distans has been a standing dogma among physicists ever since the revival of physical science, three centuries ago. Twenty-five years before the publication of Descartes's "Discours" it found expression in the axiom of Bartholomew Keckermann ("Systema Physicum," Hanau, 1612): "Omnis alteratio fit per contactum;" and Descartes's whole physical system had its root in the proposition that "a body can no more act where it is not than it can act when it has ceased to be, the principle, cessante causa cessat effectus, holding good in either case." It was this "patent absurdity" of material action through empty space which led the greatest mathematicians of Continental Europe (the elder Bernouillis, Huyghens, etc.) to reject the doctrines of Newton's "Principia," and induced Leibnitz to construct his system of "cosmic circulations," in which the old Cartesian vortices reappeared in a new dress, and under another name.

The conflict between the theory of distant attraction and the authority of the "scientific imagination" is one of the instances adduced by John Stuart Mill ("System of Logic," book ii., chap, v., §6) in support of his proposition that conceivability is no test of truth, because it is the simple result of familiarity of thought or experience; and he expresses the opinion that "the majority of scientific men have at last learned to conceive the sun attracting the earth without an intervening fluid, and that "the ancient maxim, that a thing cannot act where it is not, probably is not now believed by any educated person in Europe" ("Logic," book v., chap, iii., §3). But Herbert Spencer ("Principles of Psychology," ii., 409) justly doubts the truth of this opinion, expressing the belief that "the most that can be said is that they" (the scientific men) "have given up attempting to conceive how gravitation results." How formidable the difficulty under discussion still appears to the minds of physicists at the present day, and how completely the mental predicament of the nineteenth century is identical with that of the seventeenth, is evident from the many recent renewals of the attempt to construe the action of gravity as a case of ethereal pressure or impact. I content myself with the citation of a very characteristic paragraph, written long after the sentences quoted from Mill, in a late article of Prof. Challis "On the Fundamental Ideas of Matter and Force in Theoretical Physics" (Philosophical Magazine, 4, vol. xxxi., p. 467). "There is no other kind of force," says Prof. Challis, "than pressure by contact of one body with another. This hypothesis is made on the principle of admitting no fundamental ideas that are not referable to sensation and experience. It is true that we see bodies obeying the influence of an external force, as when a body descends toward the earth by the action of gravity; and, so far as the sense of sight informs us, we do not in such cases perceive either the contact or the pressure of another body. But we have also the sense of touch or of pressure by contact—for instance, of the hand with another body—and we feel in ourselves the power of causing motion by such pressure. The consciousness of this power and the sense of touch give a distinct idea, such as all the world understands and acts upon, as to how a body may be moved; and the rule of philosophy which makes personal sensation and experience the basis of scientific knowledge, as they are the basis of the knowledge that regulates the common transactions of life, forbids recognizing any other mode of moving a body than this. When, therefore, a body is caused to move without apparent contact and pressure of another body, it must still be concluded that the pressing body, although invisible, exists, unless we are prepared to admit that there are physical operations which are and ever will be incomprehensible by us. This admission is incompatible with the principles of the philosophy I am advocating, which assume that the information of the senses is adequate, with the aid of mathematical reasoning, to explain phenomena of all kinds. . . . All physical force being pressure, there must be a medium by which the pressure is exerted."

It is not my purpose, of course, to question the Newtonian doctrine of gravitation, or to urge the adoption of the views of Prof. Challis and others, who seek to show that what seems to be attraction is in reality a propulsion of solid bodies in immediate contact. That the transfer of motion from one body to another by impact is no less incomprehensible than actio in distans becomes apparent on a moment's reflection; and that the hypothesis of an intervening "ether"—itself composed of atoms, the interspaces between which are larger in proportion to these atoms than the interstellar spaces—is simply a new presentation of the old perplexity in a worse form, and in no wise helps to remove the difficulties involved in the phenomenon of the correspondence between the movements of two bodies without contact, is equally clear, and has been sufficiently pointed out by Herbert Spencer ("First Principles," p. 59). My object is merely to show that, if the validity of every theory of the constitution of matter is to be tested by our ability to realize it in thought—to bring it clearly before the scientific imagination, to represent it mentally as a distinct image, or whatever may be the form of words in which this requirement is expressed—the atomic theory fails as completely as any other theory of the nature of matter which has ever been propounded.

But what ground is there for the assumption that conceivability is a test of reality? This question has been the subject of a famous controversy between Dr. Whewell and John Stuart Mill, and of a more recent discussion between Mill and Herbert Spencer. Mill broadly denies that "our capacity or incapacity of conceiving a thing has any thing to do with the possibility of the thing in itself," while Spencer deems it to be a universal postulate of all thought that an inconceivable proposition, i. e., a proposition "of which the terms cannot, by any effort, be brought before consciousness in that relation which the proposition asserts between them—a proposition of which the subject and predicate offer an insurmountable resistance to union in thought"—must necessarily be held to be untrue. My present purpose does not, in strictness, call for a thorough examination of this question; nevertheless, it is desirable that the confusion into which (as is usual in such cases) it has been thrown by the emergencies of the debate should be partially cleared up.

Here, at the outset, it appears to me to be unfortunate that Mill repudiates, and Spencer does not insist upon, a distinction suggested by Coleridge between the Inconceivable and the Unimaginable, though we may find reason for dissenting from Coleridge's proposition, that "the Unimaginable may possibly be true, but the Inconceivable cannot." It is true, as has been observed by Reid (and after him by Stewart), that "conceiving, imagining, and apprehending, are commonly used as synonyms in our language;" but the distinction above referred to is, nevertheless, both real and important. Mill, indeed, declines to recognize this distinction, not from any deference to the usages of ordinary speech, but by reason of his antagonism to a philosophical system. He is a strict scholastic nominalist, and denies that there are any objects corresponding to concepts in the mind any more than in Nature, for the reason that concepts, being the results of abstraction, are general, while objects can be represented or imaged in thought only as particular. And, having pointed out ("Examination of Sir W. Hamilton's Philosophy," chap, xvii.) that in reasoning we rarely attend to all the attributes of which a concept is said to be the complement, but deal exclusively with more or less of these attributes which we are able to bring separately before the mind by means of names that suggest them, on the principle of the association of ideas, he claims that our reasoning is carried on by means, not of concepts, but of names.

At the first blush, the remark of Sir W. Hamilton, that the war between the conceptualists and nominalists is a mere war of words, would appear to be just. Surely the most inveterate nominalist must admit that the material of our reasoning processes consists, not of the sounds or written symbols composing words, but of the meanings which underlie them. And, roughly stated, concepts are nothing but these meanings. If a concept be, in the language of Sir W. Hamilton, a "bundle of attributes"—as for purposes of discursive reasoning it undoubtedly is—then every increase or diminution of this bundle is in effect the formation of a new concept; and Mill's objection that we cannot think by means of concepts, because in reasoning we bring before the mind a varying number of the attributes composing them, is seen to be founded on the mistaken assumption that for every object there is but one corresponding concept, the truth being that an object may be represented in thought by concepts without number. For every object is the first link in innumerable chains of abstractions varying in kind and diverging in direction with the comparisons instituted between it and other objects; and each of the links beyond the first is a concept under which the object may, in scholastic phrase, be subsumed. A horse, for example, may be considered mechanically as a system of levers and strings, a self-regulating locomotive, a machine, etc., or as a thousand pounds moving at the rate of 2.40 per mile, a heavy body, etc.; or, chemically, as a congeries of calcium and magnesium phosphates, carbonates, and fluorids, with albumine, fibrine, and similar substances, as a compound of oxygen, hydrogen, carbon, nitrogen, sulphur, phosphorus, calcium, magnesium, silicon, etc.; or, zoologically, as a solipede, an ungulate, a mammal, an animal, etc.; or, economically, as a beast of burden, a domestic animal—and so on, indefinitely. The formation of concepts like these is incident to all productive reasoning about individual things, and their fixation by means of language (speaking of language in the comprehensive sense of all symbols by which forms of thought may be represented) an indispensable condition of the progress of scientific knowledge, or, indeed, knowledge of any sort.

On the other hand, the most obstinate conceptualist will not deny that, before any one of these concepts can stand as the representative of an actual, concrete object, it must be supplemented with all those circumstances of singularity or particularity which were left behind in the progress of abstraction.

On closer examination, however, the war of words between Mill and his antagonists proves to be a real contest of principles. The elaboration of the data of experience into concepts implies an establishment of relations between these data in conformity to laws not immediately derivable from this experience itself—a mental digestion of the crude material of sense; and this is, in Mill's opinion, inadmissible in view of the purely sensational origin of all knowledge. Mill has an instinctive horror of every thing which purports to be something else than a deliverance of sense, and contends that in our thought we are at all times conversant, not with abstractions, but with facts. Whether this be true or not, depends upon the meaning of the word "facts," irrespective of the necessary reservation that all the facts about which we know any thing at all are the facts of consciousness. A satisfactory discussion of this topic (to which very valuable contributions have been made by Mr. Ferrier) is beyond the scope of my inquiry; it is sufficient for my purpose to have it conceded that in thought properly so called, i. e., in those intellectual operations in which the deliverances of sense are digested into that system of ideal forms and relations which we call knowledge, or (what is the same thing) science, we never deal with things as they exist, or are represented as existing, objectively—that we have not, nor can we have, present to our minds the whole complement of phenomena which are the constituents of a material object, but always some one or more of them selected or "abstracted" from the rest; that being so, not only for the reason that all our thought is, in the language of Leibnitz (adopted by Herbert Spencer in the first chapter of his "First Principles"), symbolical, the attributes even of the simplest material object being too numerous to be represented in consciousness at the same time, but for the far weightier reason that our knowledge of the attributes of a material object is never complete. I may say here, incidentally, that, in asserting the abstract nature of thought, I am not taking sides in the interminable controversy between Realism and Idealism, or Presentationism and Representationism; a controversy which would be speedily ended if it came to be thoroughly understood that the phenomena of vision, which, ever since the time of Plato, have furnished nearly all the metaphors for the description of intellectual operations, present but distant analogies of the phenomena of perception, and that the puzzle about mediate and immediate perception is but the common case of the obscuration of a subject by a series of figures meant to illustrate it. In my discussion, I am only generally concerned with the fundamental relation which all our thought about objective reality bears to that reality itself.

There is, of course, no agreement among thinkers as to the nature or even the number of successive steps which lead to the formation of the elements of distinct thought. The terms most commonly employed of late (by those, at least, whose authority commands the most respect, viz., the comparative philologists, who are constrained, by the methods of their own science, to treat psychological questions inductively), to designate those steps, are Sensation, Perception, Representation, and Conception. The first two of these I shall, for the moment, leave wholly out of the account, as not relevant to the present inquiry, it being admitted on all hands that the materials of distinct thought are either representations or concepts. A representation may be generally defined as an exhibition to the mind of the deliverances of sense (if the object be real, or of the phantasy if the object be imaginary), in their empirical order and form—in other words, as a mere mental image of the object; while, in the concept, these deliverances are reduced to unity by the establishment of relations between them other than the relation of their fortuitous concurrence, the concept, at the same time, being made distinct by the establishment of relations between it and the previous concepts of the mind. If I were writing a treatise on logic, or psychology, these definitions would have to be reduced to forms far more precise; but I purposely refrain from an attempt at exact definition, because I wish to remain on ground common to all who have made the matter in hand the subject of their investigation. For my purpose, it is of little consequence whether or not the distinction here indicated between representations and concepts is accurate and clear; nor is it necessary to determine the exact nature of the relations established in conception between the constituents of a concept, or between the various concepts themselves; it is sufficient to know that both in the representation and in the concept we have in some form a complex of attributes which are ultimately, in the case of material objects at least, traceable to sensible experience, and that the elaboration of representations into concepts involves the establishment of some sort of mental relations between their elements, as well as between the several concepts themselves.

At this point, it is important to guard against a confusion which naturally arises from the fact that logicians and psychologists habitually illustrate the evolution of concepts by examples taken from the abstract sciences. There is a very wide distinction between the relation of a concept to the object of thought in mathematics, for instance, and the corresponding relation between a representation, or concept of a material object, to that object itself. In mathematics, as in all the sciences which are conversant with single relations or groups of relations established (and, within the limits of the constitutive laws of the mind, arbitrarily established) by the mind itself, all concepts are exhaustive in the sense that they imply, if they do not explicitly state, all the properties belonging to the object of thought. Not only the constituents of such an object, but also the laws of their interdependence, being determined by the intellect, they may be strictly deduced, each from the other.[1] Thus, a parabola is a line, every point in which is equidistant from a fixed point and a given straight line: that is one of its concepts. And in this all the properties of the parabola—that it is a conic section formed by cutting a cone parallel to its sides, that the area of any of its segments is equal to two-thirds of its circumscribed rectangle, etc.—are implied, and from it they may be deduced. Each one of its attributes is an implication of all the others. Our concepts of material objects, on the contrary, are never exhaustive, for their complement of attributes varies with our experience concerning them. These attributes are expressive of the relations between the object and other objects; and, the number of objects being unlimited, the synthesis of attributes is, of necessity, incomplete. And the interdependence of these attributes, as well as the connection between the objects themselves, or their representative images and concepts, has its origin in laws, of which the laws of the intellect are but a partial reflex. It is true that the concept of a material object contains elements whose interdependence is subjective (every intellectual operation, or rather its result, being in some form a synthesis of subjective and objective data); but even these are liable to determination by undigested empirical elements which are present along with them. Moreover, our knowledge of the attributes of a material body is not only imperfect, but these attributes are variable. This is obvious enough in the case of those properties which are usually designated as secondary qualities; every one knows that the thermic, optic, electric, or magnetic conditions of a body change at every moment. But, in fact, there is no property whatever, of a material body, which is strictly invariable, or the law of whose variation is fully known. For this reason, also, the concept of a material object can never expressly, or by implication, be a full complement of its attributes.[2]

Bearing this in mind, we shall experience little difficulty in determining the conditions under which the representation and conception of a material object as real are possible. A representation of such an object being an exhibition of the deliverances of sense respecting it, it is plain that nothing can be represented as objectively real, except in terms of experience. And, since our experience is only of the singular and particular, it is also evident that a concept cannot be represented in the mind as objectively real. Thus, matter as such is not a real thing, but a concept; it cannot be "realized" in thought. We can realize, or imagine, or represent as actual, only some one particular thing, with all its accidents of particularity—as of particular dimensions, of a particular color, of a particular temperature, and as being either at rest (i. e., in a state of tension) or in motion. All attempts mentally to represent the reality, in and by itself, of any of the elements into which an individual object is analyzed by the process of abstraction are necessarily futile. The history of speculation is full of attempts of this sort—of attempts to grasp the "thing" as distinct from its properties, the substance apart from its attributes, or, conversely, the attributes apart from their unity, the substance. It is this old error which lies hid in the reasoning of Prof. Tyndall in the passage quoted at the beginning of this article. And the same error lurks in Faraday's endeavor to represent matter as a mere complex of forces. In the one case the properties are imagined to be added to the thing, or the attributes are supposed to be implanted in the substance, as the plums are stuck into the pudding, so that the substance will remain after the attributes are removed; in the other case the substance is looked upon as a mere sum of the attributes—the pudding is thought to be all plums, which not only have a reality by themselves, but which are alone real. That this apparently trivial illustration is entirely apposite, is readily shown by a reference to the grounds upon which Faraday rejects the hypothesis of corpuscular atoms. While the advocates of this hypothesis seek to remove the plums and to retain the pudding, Faraday, on the contrary, takes the plums, and then asks, "Where is the pudding?" "What do we know," he says (Tyndall, "Faraday as a Discoverer," p. 123, American ed.)" of the atom apart from its force? You imagine a nucleus which may be called a, and surround it by forces which may be called m; to my mind, the a or nucleus vanishes, and the substance consists in the powers of m. And, indeed, what notion can we form of the nucleus independent of its powers? What thought remains on which to hang the imagination of an a independent of the acknowledged forces?"

The true root of all those errors is a total misconception of the nature of reality. All the reality we know is not only spatially finite, but limited in all its aspects; its whole existence lies in relation and contrast, as I shall show more at length in the next article. We know nothing of force, except by its contrast with mass, or (what is the same thing) inertia; and conversely, as I have already pointed out in my first article, we know nothing of mass, except by its relation to force. Mass, inertia (or, as it is sometimes, though inaccurately, called, matter per se), is indistinguishable from absolute nothingness; for matter reveals its presence, or evinces its reality, only by its action, its force, its tension or motion. But, on the other hand, mere force is equally nothing; for, if we reduce the mass upon which a given force, however small, acts until it vanishes—or, mathematically expressed, until it becomes infinitely small—the consequence is that the velocity of the resulting motion is infinitely great, and that the "thing" (if under these circumstances a thing can still be spoken of) is at any given moment neither here nor there, but everywhere—that there is no real presence. It is impossible, therefore, to construct matter by a mere synthesis of forces. And it is incorrect to say, with Bain ("Logic," ii., 225), that "matter, force, and inertia, are three names for substantially the same fact," or that "force and matter are not two things, but one thing," or (ib., p. 389) that "force, inertia, momentum, matter, are all one fact"—the truth being that force and inertia are conceptual constituents of matter, and neither is in any proper sense a fact. Nor is the ordinary analysis of physical reality into matter + force correct, inasmuch as force is already implied in the term matter. It is an analysis of a thing into two elements, one of which is the thing itself. The true formula of matter is mass × force, or inertia × force.

We now have before us, in full view, one of the fundamental fallacies of the atomic theory. This fallacy consists in the delusion that the conceptual constituents of matter can be grasped as separate and real entities. The corpuscular atomists take the element of inertia and treat it as real by itself, while Boscovich, Faraday, and all those who define atoms as "centres of force," seek to realize the corresponding element, force, as an entity by itself. In both cases elements of reality are mistaken for kinds of reality. It is, therefore, sheer nonsense to speak, with Papillon (see the article on the Constitution of Matter in the September number of this journal, p. 553), of a "bare energy, stripped of its material dress;" of a "force in its purest essence, upon which we look as on the marble of the antique, in splendid nakedness, which is radiant beauty too."[3]

This disposes, in my judgment, of the authority of the "scientific imagination," in all cases where an attempt is made to determine the constitution of matter. In respect to the general question, however, whether our ability to imagine a thing is decisive of its possible reality, it is necessary to add, that this question must be answered in the negative. Whether or not we can imagine, or mentally represent, a thing as real, depends upon the question whether our past experience has furnished us the data for such a representation; and our experience is constantly furnishing us new data.

That the impossibility or difficulty of imagining a thing (which, however, must be carefully distinguished from the absolute impossibility of forming certain concepts, of which I shall presently speak) is no evidence for or against its reality, is a truth of the greatest moment to the student of natural science. Liebig expressed it long ago (Ann. Pharm., x., 179), in the words: "The secret of all those who make discoveries is, that they regard nothing as impossible."

I come now to the conditions of conceivability, strictly and properly so called. These conditions are readily deduced from the incidents in the act of conception to which I have referred. These incidents are: The reduction of the elements of a representation to consistent unity by bringing them into relation, and the establishment of relations between the unit thus evolved and the previous concepts of the mind. A concept can, therefore, be formed, if a, its elements, can be united in thought by the establishment of relations between them by which they are reduced to a unit—in other words, if the constituent attributes are consistent with each other—and if b, the resulting concept, can be brought into relation, so as to be consistent with the previously-formed concepts of the mind.

Consistency of the constituent attributes with each other, therefore, is the first, and consistency of the concept with other concepts the second, condition of its successful formation. The first of these is what is known in logic as the law of non-contradiction, or the law of consistency, and is the fundamental condition of all thought. It requires that what is expressly or by implication asserted in the subject shall not expressly or by implication be denied in the predicate of any proposition into which the concept may be resolved, or, in plain words, that what is asserted in one form of words shall not be denied in another.

Now, it is evident that, whenever the formation of a concept involves a violation of the first condition, we have before us a case of absolute inconceivability, and therefore of impossibility. For this condition, as I have said, is the first constitutive law of all intelligence, without which the whole system of relations, in which both subjective and objective realities have their only warrant and support, instantly collapses into the nothingness in which alone all things are identical, and disappears in the night of absolute confusion. No one, not even John Stuart Mill, ever seriously doubted the absolute impossibility of the conception or existence of a round square, or of a straight line which is not the shortest distance between two points. Whenever such a doubt has been expressed, it has arisen from a mental confusion as to the import of the terms employed in the propositions, as we shall see presently in the case of Mill.

But it is otherwise with the second condition of conceivability: that the concept, when framed, shall be consistent with other concepts previously formed. For these latter concepts may be spurious or invalid. Inconceivability arising from non-compliance with the second condition is therefore purely relative, depending on the validity of the concepts with which the concept in question appears to be incompatible. For example, until the discovery of the composition of water, of the true theory of combustion, and of the relative affinities of potassium and hydrogen for oxygen, it was impossible to conceive a substance which would ignite on contact with water, it being one of the recognized attributes of water––in other words, a part of the concept water—that it antagonized fire. This previous concept was spurious, and, when it had been destroyed, the inconceivability of a substance like potassium disappeared. Similarly, we are now unable to conceive a warm-blooded animal without a respiratory system, because we conceive the idiothermic condition of an animal organism to depend mainly on the chemical changes taking place within it, chief among which is the oxidation of the blood, which requires some form of contact between the blood and the air, and therefore some form of respiration. If, however, future researches should destroy this latter concept—if it should be shown that the heat of a living body may be produced in sufficient quantity by mechanical agencies, such as friction—a non-respiring warm-blooded animal would at once become conceivable.

Mill not only refuses to recognize the distinction between what may be conceived and what may be represented in imagination, but he also ignores the distinction between the cases of inconceivability from the one or the other of the two causes just mentioned; and he maintains that all conceivability whatever is relative. The examples which he discusses at length are all cases of inconceivability, and not of unimaginability, and I propose to notice the more important of them in passing. The most noteworthy of these examples is the inconceivability of a round square. In order not to do Mill injustice, it will be best to quote his own language ("Examination of the Philosophy of Sir W. Hamilton," vol. i., p. 88, et seq., American edition):

"We cannot conceive a round square," says Mill, "not merely because no such object has ever presented itself in our experience, for that would not be enough. Neither, for any thing we know, are the two ideas in themselves incompatible. To conceive a round square, or to conceive a body all black and yet all white, would only be to conceive two different sensations as produced in us simultaneously by the same object—a conception familiar to our experience—and we should probably be as well able to conceive a round square as a hard square, or a heavy square, if it were not that in our uniform experience, at the instant when a thing begins to be round, it ceases to be square, so that the beginning of the one impression is inseparably associated with the departure or cessation of the other. Thus our inability to form a conception always arises from our being compelled to form another contradictory to it."

Our inability to conceive a round square due to the fact "that in our uniform experience, at the instant when a thing begins to be round, it ceases to be square," and to the inseparable association between incipient roundness and departing squareness! Whether any one has ever had such experience as is here described, I do not know; but, if he has, I am confident that, even after being reënforced by a large inheritance of ancestral experience in the light of the modern theory of evolution, it will prove insufficient to account for the inseparable association which Mill brings into play. The simple truth is, that a round square is an absurdity, a contradiction in terms. A square is a figure bounded by four equal straight lines intersecting at right angles; a round figure is a figure bounded by a curve; and the oldest definition of a curve is that of "a line which is neither a straight line, nor made up of straight lines."

It ought to be said that there are expressions in the same chapter of Mill's book, from which I have just quoted, which show that the author was very ill at ease in the presence of his own theory. For instance, he says (ib., p. 88): "These things are literally inconceivable to us, our minds and our experience being what they are. Whether they would be inconceivable if our minds were the same, but our experience different, is open to discussion. A distinction may be made which, I think, will be found pertinent to the question. That the same thing should at once be and not be—that identically the same statement should be both true and false—is not only inconceivable to us, but we cannot conceive that it could be made conceivable."

That so clear and vigorous a thinker as Mill should have been capable (especially when he was grappling with the thoughts of a man like Sir W. Hamilton) of writing these sentences, is indeed wonderful. First, he denies that inconceivability is, in any sense or in any case, a test of truth or reality; but then he says it may be otherwise, if the inconceivability itself is inconceivable! That is to say: a witness is utterly untrustworthy; but, when he makes a declaration respecting his own trustworthiness, he ought to be believed!

That the whole theory of inseparable association, as here advanced and applied by Mill, is without foundation, it being impossible, under his theory, to know what the experience of his numerous readers has been, except again by experience which he cannot have had, since most of these readers were utterly unknown to him—that all attempts to argue questions with any one on such a basis are supremely foolish, Mill being bound, by his own doctrine, to accept the answer, "My experience has been otherwise," as conclusive—that this theory is suicidal and subversive of itself, and that every earnest sentence Mill has ever written is its practical refutation—is too obvious, almost, to require pointing out.

While the example just discussed was a case of absolute inconceivability, the other instances given by Mill are cases of true relative inconceivability. The first is that of antipodes which were long held to be impossible, and are now not only readily conceived as possible, but known to be real. This is true enough, but it finds its explanation, not in the law of inseparable association to which it is referred by Mill, but in the fact that our ancestors held an erroneous concept of the action of gravity. They supposed that the direction in which gravity acted was an absolute direction in space; they did not realize that it was a direction toward the earth's centre of gravity; downward to them meant something very different from the sense we attach to that word. With this erroneous concept they could not reconcile the fact that the force of gravity held our antipodes in position as well as ourselves; nor can we. But we have a juster concept of gravity, and the mode and direction of its action; the spurious notion with which the notion of antipodes was inconsistent, has been removed, and the inconceivability of antipodes is at an end.

Similar observations apply to Mill's remaining example (which is to us the most interesting, and that for the sake of which I have carried the discussion of this dry subject to this length) of the inconceivability of actio in distans, to which I have already alluded. The true source of our inability to conceive actio in distans is, I trust, now apparent. This inability results from the inconsistency of this concept with the prevailing concepts respecting material presence. If we reverse the proposition, that a body acts where it is, and say that a body is where it acts, the inconceivability disappears at once. One of the wisest utterances ever made on this subject is the saying of Thomas Carlyle (quoted by Mill himself in his "System of Logic," in another connection): "You say a body cannot act where it is not? With all my heart; but, pray, where is it?" Of course, a reconstitution of our concepts of material presence, in the sense here indicated, would be in utter conflict with the theory of the mechanical construction of matter from elements which are absolutely limited, hard, unchangeable, and separated from each other by absolutely void spaces. It is significant that nearly all the efficient laborers in the quarries of physical science vaguely feel, if they do not distinctly see, that such a reconstitution is necessary. Such a feeling was at the bottom of Faraday's attempt to construct matter out of the convergence and intersection of mere lines of force, so as to secure to each point of intersection (or, in the language of Faraday, to each centre of force) a virtual omnipresence, the extent of the lines of force being infinite.

I may be permitted to say, at the end of this long but unavoidable excursion into the regions of logic and psychology, that the doctrine, according: to which there is no warrant for the deliverances of our consciousness except the cumulation of purely sensational experience, which not only may but must vary with the position of the intellects interpreting it—that truth, therefore, is nothing but the inveteracy of error—is the dreariest creed ever promulgated; and its association with the many noble truths of which John Stuart Mill has been the discoverer or the champion, is the most unfortunate "inseparable association" established in recent times. And it is deplorable that Herbert Spencer, who has the merit of being one of the most energetic fumigators of the intellectual atmosphere of our time, should evince a disposition to make concessions to such a creed, and endeavor to eke out its shortcomings by the doctrine (in itself, no doubt, both sound and fertile) of the inheritance of ancestral tendencies of the mind. His own theory leads to conclusions utterly subversive of Mill's doctrine; for, if organic life (including the life of the mind) has been continuously evolved from inorganic matter, then the lines of our ancestry run into all the phenomena of the material world, and the order of these phenomena must be ingrained, not only in the structure of our bodies, but also in the constitution of our minds. Or, to express it in the language of modern comparative psychology: the ancestral inheritance of our intellects must embrace, not only the associations established by experience between the phenomena of consciousness in the minds of our progenitors, but also the regularity in the evolution of the natural events which gave rise to these phenomena—the laws of Nature. These laws must, therefore, in a certain sense, be prefigurations of the forms of our intellect, so that, after all, there is truth in the sentence of Protagoras, that man is the measure of all things, and sense in the words of Goethe (almost identical with a passage in Plotinus), that the eye sees the light, because it is of solar nature. I do not, of course, mean to stand committed to this argument in the form in which it is here presented, not entertaining the notions respecting the relations between organic and inorganic forms which underlie it, and doubting that the continuity of the evolution of these forms is truly represented by current beliefs. But, with the proper modification of its premisses (which, however, cannot be affected by a few verbal definitions), I believe the argument in favor of the a priori sanity of the human intellect to be valid, in spite of certain structural fallacies resulting from the laws of its growth, which I shall have occasion to discuss in my next article; and I further believe the primordial correspondence between the intellect and its objects to be entirely consistent with the theory of evolution, Max Müller to the contrary notwithstanding.

  1. The truth of the proposition that the system of forms and relations, whose discussion constitutes the science of mathematics, is of purely subjective determination, does not involve the assumption (erroneously attributed to Kant, who, on the very first page of his "Critique of Pure Reason," expressly draws the distinction between the "beginning of all knowledge with experience," and "the derivation of all knowledge from experience"), that the mind is furnished a priori with ready-made ideas or concepts; nor is it affected by the circumstance that these forms and relations are ultimately referable to the facts of sensible experience. Mill's refusal to recognize this has betrayed him into writing the extraordinary fifth chapter of the second book of his "System of Logic," in which he questions—albeit falteringly—the necessary truth of the propositions of geometry. The inevitable outcome of this is seen in the writings of Mr. Buckle, who not only boldly asserts that there are no lines without breadth (he strangely forgets the thickness), but also that the neglect of this breadth by the geometrician vitiates his conclusions. His comfort is that the error, after all, is not very considerable. "Since, however," is his language ("History of Civilization in England," ii., 342, Appletons' edition), "the breadth of the faintest line is so slight as to be incapable of measurement, except by an instrument used under the microscope, it follows that the assumption, that there can be lines without breadth, is so nearly true, that our senses, when unassisted by art, cannot detect the error. Formerly, and until the invention of the micrometer, in the seventeenth century, it was impossible to detect it at all. Hence, the conclusions of the geometrician approximate so closely to truth, that we are justified in accepting them as true. The flaw is too minute to be perceived. But that there is a flaw, appears to roe certain. It appears certain that, whenever something is kept back in the premises, something must be wanting in the conclusion. In all such cases, the field of inquiry has not been entirely covered; and, part of the preliminary facts being suppressed, it must, I think, be admitted that complete truth is unattainable, and that no problem in geometry has yet been exhaustively solved." Whether Buckle was able to think of a line as the limit between two surfaces, and whether, in his opinion, such a limit has breadth (i. e., is itself a surface, so that we are driven from limit to limit ad infinitum), he does not tell us. Nor does he say whether or not, in view of the fact that the breadth of a line depends upon the material out of which it is constructed, or upon which it is drawn, there ought to be a pasteboard geometry, a wooden geometry, a stone geometry, and so on, as distinct sciences.
  2. I do not enter into the question whether or not the use of the word "concept," in reference to material objects, can in all cases be justified, and whether the distinction between representations and concepts is not, in many cases, including the case of "singular concepts," so called, very shadowy. In this connection, it is significant that the Germans use the expression "empirical concept" (Erfahrungsbegriff), as equivalent to "representation" (Vorstellung).
  3. The translation of the passage from which the above is taken, though on the whole admirable, fails to do justice to the magniloquence of the original, which reads thus: "Toutes ces energies n'apparaissent à nous à de rares exceptions près que revêtues de cet uniforme qu'on appelle la matière. Une seule de ces energies se montre dépouillée de ce vêtement et nue. . . . Comment la définir autrement que la force en sa plus pure essence, puisque nous la contemplons comme un marbre antique dans une superbe nudité qui est aussi une beauté radieuse."