Chapter VII: Conclusion (2)

In the work of M. Mismer will be found some of the great and striking qualities of the observing and thoughtful mind. In connection with a special problem of great importance in public instruction, that of heredity, I shall call to the attention of my readers the following statement, made with reference to the young men of the “Egyptian Mission” in France, directed by M. Mismer for ten years. “The capacity of a pupil,” says he, “was always found to be intimately connected with the cerebral culture of his ancestors and the faculties constituting the superiorities of his race.” “It was the same,” adds he, “from the moral standpoint.” Undoubtedly, if M. Mismer had taken the pains to make a note of the facts summed up in his statement, and to present the full case of the numerous pupil’s that he has had under his care, he would have been able to furnish science with data of the greatest value. Let us at least receive his lessons as he offers them to us. They are the fruit of the experience of a “man of action,” and it speaks well for an observation that it has rendered good service in practice.

LUCIEN ARRÉAT.

FOOTNOTES:

[17] The hypothesis of the division of consciousness explains, consequently, much better than that of the motive force of mental images, the facts of automatic writing (spiritism). [The works of Binet, Roberty, and Lombroso are published by Alcan.]

CRITICISMS AND DISCUSSIONS.

COMTE AND TURGOT.

_To the Editor of The Monist_:

Your “note of inquiry” mentioned on p. 611 of the last _Monist_ is answered in full by Littré in _Auguste Comte et la Philosophie Positive_, where Turgot’s name heads the third chapter. He shows that the latter discovered the law of the three stages, theological, metaphysical, and positive, by the following quotation from his _Histoire des progrès de l’esprit humain_.

“While the connection between physical effects was yet unknown, nothing was more natural than to suppose that they were produced by intelligent beings, invisible and resembling ourselves; for what else could they have resembled? Everything that happened without the intervention of man, had its god, whose worship was soon established by fear or hope, and this worship was conceived in accordance with the deference accorded powerful men; for the gods were only more powerful men and more or less perfect according as they were the product of an age more or less enlightened as to the true perfections of humanity. When philosophers had recognised the absurdity of these fables, without however having obtained true light upon natural history, they imagined an explanation of the causes of phenomena by abstract expressions, such as essences and faculties: expressions that nevertheless explained nothing and that were reasoned about as if they had been beings, new divinities substituted for the old ones. These analogies were followed out, and faculties were multiplied to account for each effect. It was only very late, in observing the mechanical action that bodies have upon one another, that other hypotheses were drawn from this mechanics, (_de cette mécanique_) which mathematics could develop and experience verify.”

Littré calls attention to “the great sureness of judgment” that led Turgot to cite only physical phenomena when he spoke of those that had ceased to be interpreted either theologically or metaphysically. “When he wrote this passage, positivity (I use this word, a necessary creation of M. Comte’s) was only beginning to reach chemical phenomena and had not yet attained those of biology and sociology.”

But, says Littré, “after reserving the rights of priority for this eminent thinker, there is nothing to prevent M. Comte from keeping all the part that he had made himself and that belongs to him. Three principal points mark Comte’s independence of Turgot. The latter saw in the conception nothing more than an idea to meditate upon; Comte saw in it a sociological law; Turgot did not attach to it a sketch of human development; Comte developed with the aid of this law the whole historical series; Turgot did not perceive that he held one of the necessary elements of a philosophy; Comte, in the same flight of thought, went from history become science to philosophy become positive. The sociological law, isolated in Turgot, makes part, in Comte, of a vast whole: there were therefore two independent creations. Either M. Comte had not read Turgot, or, more probably, he had read him at a time when this passage, which to-day awakens attention, had no particular significance.”

The fourth chapter in Littré’s Life of Comte has for heading the names of Kant and Condorcet. The whole of the former’s remarkable sketch of general history is given and reference is made to the letter in chap. viii, where Comte, in 1824, being twenty-six years old, says to M. d’Eichthal, his former pupil, “I have read and reread with infinite pleasure Kant’s little treatise; it is prodigious for the epoch, and if I had known it six or seven years sooner it would have saved me trouble. I am delighted that you have translated it; it can contribute very efficaciously to preparing minds for positive philosophy. Its general conception or at least its method is still metaphysical, but the details show the positive spirit at every instant. I had always regarded Kant not only as a very strong head, but as the metaphysician that approaches the nearest to positive philosophy. But this reading has greatly fortified and especially given precision to my conviction in that regard. If Condorcet had had knowledge of this writing, which I do not believe, very little merit would remain to him, since he can pretend only to that of the conception, which is almost as firm and, in some respects, even clearer in Kant. As for me, after this reading I can find in myself, up to the present time, no other value than that of having systematised and fixed the conception that had been sketched by Kant unknown to me, which I owe chiefly to a scientific education; and even the most positive and distinct step that I have taken after him, seems to me only the discovery of the law of the passage of human ideas through the three stages, theological, metaphysical, and scientific; a law that appears to me to be the foundation of the work whose execution Kant has counselled. I thank my lack of erudition to-day; for if my work, such as it is now, had been preceded by a study of Kant’s treatise, it would have lost much of its value in my eyes. I conceive now, as you said, that, for the German philosophers that are familiar with this treatise, my work will really have a great effect only with the second part.” This work was a short one reprinted in Saint-Simon’s _Catéchisme des industriels_ and called “A System of Positive Politics.” It had been inserted two years before, under the title of “A Plan of the Work Necessary for the Reorganisation of Society,” in a pamphlet of Saint-Simon’s, without Comte’s name, and it was because the latter insisted, this time, upon an acknowledgment of his authorship that Saint-Simon broke with him. The “second part,” which was to produce the great effect upon the German philosophers, never appeared; or rather, it soon grew to be the _Course of Positive Philosophy_, begun on the 2d of April, 1826, before Humboldt, Blainville, and other celebrated listeners.

The term _positive philosophy_ had long been used by Saint-Simon and his school, Comte among the rest, not in the special sense that the latter now gave it, but as a “generic name for the whole of science.” The first use of the words as we now understand them is in a letter from Comte to M. d’Eichthal, dated Aug. 5, 1824. “I cannot help recalling your judicious reflection upon the influence that social physics, once formed, will have upon scientific philosophy. I go even further than you, for I think that it will be only then that a veritable philosophy of the sciences can exist. All the philosophical ideas that are there to-day, although very precious up to that time, appear to me to have nothing more than a simply provisory (provisoire) character. I shall speak a little about this relation in the general preface that I announce to you, where I shall explain that the true title of my work would be _positive philosophy_, and that if I preferred _politics_, it is because that is the most urgent philosophical application and the one that is to found the science, but that later I or you or others will complete this system of ideas by the encyclopedic re-coinage of all our positive cognitions (connaissances), which ought really to be conceived as a single mass, although, for good culture, it is indispensable to preserve and to push even, in one sense, further than it is, the division of labor, so that each special savant can always, subsequently, conceive the relation of his branch and even of his twig to the universal trunk.”

In a letter of about this date Comte refers to his habit of never rewriting anything. His memory permitted him to look upon a volume as finished when it had been thought out and before a line had been written. But even in his letters we notice some of the disadvantages of this procedure, which, while conducive to unity, sacrifices literary form.

It is true that Comte studied under Saint-Simon; but, according to Littré, his purely philosophical dependence was very slight, while his influence upon his master was important. “What forms the distinguishing characteristic of Saint-Simon at the epoch when he lived, is the social destination that he assigns without hesitating to the ideas that preoccupy him. He has, as we have seen, only the most confused notion of what this philosophy will be; but, no matter what it is to be, he consecrates it in advance to the reorganisation of society.”

As regards Condorcet, Comte enthusiastically acknowledges his indebtedness to the “Sketch of an Historical Table of the Progress of the Human Mind,” and even goes beyond the facts, as he did in his praise of Kant.

Littré makes a fair division of credit among others as well as those already named, and concludes as follows: “Turgot had discovered that human conceptions, at first theological, afterwards become metaphysical and end by being positive. Kant had known that history is a natural phenomenon, subjected to a determinate course, and Condorcet, pushed harder than his predecessors by advancing time,” (he had been condemned to death) “had attempted to trace a table that should put in evidence the enchainment of the progresses of civilisation. These are great things, but they are still only rudiments; for neither Turgot nor his successors make use of the discovered law to found upon this general fact evolution; Kant, who perceives clearly the necessity of conceiving history as regulated by the conditions inherent to humanity, is unable to base this important notion on anything better than an _à priori_ idea” (the metaphysical principle that nature does nothing in vain, and that as human faculties do not reach their development in the individual, who is ephemeral, they must do so in the species, which is durable) “and thus he leaves it incapable of fixing the attention of a century whose tendencies were more and more positive; lastly Condorcet has no other guide than the negative philosophy of the eighteenth century in a work to which it could bring only contradiction.”

John Stuart Mill says of Comte that “far from pretending to originality when he had really no right to do so, he was eager to attach his most original thoughts to every germ of a similar idea that he met with among his predecessors.”

Speaking for himself, Littré says of the law of the three stages, “I do not reject it, I restrain it. As long as we remain in the scientific order and consider the conception of the world first theological, then metaphysical, finally positive, the law of the three stages has its full efficacy in directing the speculations of history.... But in history all is not comprised in the scientific order. M. Comte, who has said somewhere that it is necessary to suppose, at the beginning of humanity, certain notions that were neither theological nor metaphysical, has indicated the germ, I will not say of my objection, but of my restriction. In fact this law of the three stages comprehends neither industrial, nor moral, nor æsthetic development. It has however, the excellent character of being relative to the speculations in which evolution by filiation is most manifest and consequently of giving a positive notion of the march of history.”

Is it true, as stated on p. 565 of _The Monist_ for July, that Stuart Mill adopted Hume’s “erroneous conception of causality” to the extent implied in the following passage? “This idea of ‘sequence’ however was exactly Hume’s mistake, adopted by Mr. Mill, and through Mr. Mill popularised among English thinkers. If the nature of cause and effect were really constituted by invariable sequence, then the night might be called the effect of the day because night is invariably consequent upon day.”

The only authority at hand on the island from which I write is Clemenceau’s translation of Mill’s “Auguste Comte and Positivism,” where, on p. 61, I read as follows, “The succession of day and night is just as much an invariable succession as the alternate exposition of the earth’s two opposite sides to the sun. Yet day and night are not the cause of each other; why? Because their succession, although invariable, according to our experience, is not so unconditionally: these phenomena succeed each other only upon the condition that the presence and the absence of the sun succeed each other; and if this alternation were to cease, day and night would not follow each other. There are thus two kinds of uniformities of succession, one without conditions, the other dependent on the former: laws of causation, and other successions which depend on these laws.”

In a note Mill refers to his _System of Deductive and Inductive Logic_.

LOUIS BELROSE, JR.

SOME REMARKS UPON PROFESSOR JAMES’S DISCUSSION OF ATTENTION.

In his recent treatise on psychology Professor James discusses in an interesting and suggestive way the relation of ideation to attention, maintaining that “ideational preparation ... is concerned in all attentive acts.” Attention is “anticipatory imagination” or “preperception” which prepares the mind for what it is to experience. Thus the schoolboy, listening for the clock to strike twelve, anticipates in imagination and is prepared to hear perfectly the very first sound of the striking.

It is undoubtedly true that in the form of attention we term expectant, where we are awaiting _some given impression_, there is a representing, antedating experience, which may be a preparatory preperception. But with a wrong imaging of what is to be experienced there is hindrance, as when in a dark quiet room we are led to expect sensation of light but actually receive sensation of sound. Very often, indeed, our anticipations make us unprepared for experience. Further, the experiments adduced by Professor James from Wundt and Helmholtz are in the single form of expectant attention, and we must remark that in these experiments the reagent is also experimenter, and this introduces a new attention, consciousness of consciousness, and that of a peculiar kind, which complicates an already complex consciousness. In general we may say that experimentally incited consciousness is artificial, at least as far as it feels itself as such, and for certain points like simple attention this tends to vitiate results. Self-experimentation or experiment on those conscious of it as such may mislead in certain cases, and must, so far as this element of consciousness of experiment is not allowed for. In physical science things always act naturally whether with observation or experiment, but in psychology observation, other things being equal, is more trustworthy than experiment.

In all cases of expectant or experimentally expectant attention, the attention does not, however, lie in the expectancy or in the imaging as such, but it is merely the will effort concerned in these operations. Yet as we may expect without effort, and preconceive without volition, attention is necessarily involved in neither. A perception or a preperception is an attention only as accomplished by will with effort, but only an unattention when purely involuntary. Professor James’s use of attention as preperception brings us back to the common idea of attention, as any consciousness which cognises something. This is so inbred in thought and language that it is most difficult to avoid using the term in this sense. Many psychologists like Mr. James and Mr. Sully frequently mention attention as a will phenomenon but they do not treat it under will, and they constantly return to the cognition meaning. Höffding, however, treats attention under psychology of will. Attention as the exercise of will in building up and maintaining cognitive activity, is naturally treated under cognition; but it is on the whole safer and better to discuss attention under will so as to keep it sharply distinguished from the presentation form which it vitalises. I have endeavored to hold the term strictly to this sense, yet it is not unlikely I may sometimes unwittingly countenance the common confusion, but trust the instances will be few.

When we have, then, a case of expectant attention we must distinguish the attention in the imaging from the attention in the actual cognising. It is, indeed, true for us almost invariably that cognitive strain without immediate realisation is incentive to ideating. In listening in the night in vain for a sound we hear in imagination many sounds, and we form preparatory ideas of what we are to hear. Sense-adjustments call up a train of sensations in ideal form. But it is obvious that low intelligences which have no power of expectancy or ideation do yet really attend. The very first cognitions and all early cognitions by their very newness and difficulty were attentions long before ideation was evolved. With low organisms, as cognitive power extends only to the present in time and space, immediacy of reaction is imperatively demanded, and every tension of cognitive apparatus is immediately directive of motor apparatus so that suitable motion is at once accomplished. The cognition, though dim and evanescent factor, is yet powerfully energised, and so a true attention. Always with lowest sentiencies, and often with higher, pain is suddenly realised without anticipation, followed quickly by attention as strong effort to cognise the nature and quality of the pain-giver and so to effectually get rid of pain-giver and pain.

Preliminary idea, then, cannot occur in early attentions and in late attentions it is by no means necessary. It is said that we see only what we look for, but it must be answered that seeing commonly happens without any looking for. The kindergarten child, Professor James to the contrary notwithstanding, is not confined in his seeing to merely those things which he has been told to see and whose names have been given him. A child continually asks, What is that? and is quick to discern the absolutely new and strange. He accomplishes a wide variety of attentions without ideas and gives himself almost entirely to immediate presentations.

To be sure, every one sees only what he is prepared to see, only what is made possible for him by his mental constitution as determined by his own pre-experience and the experience of his ancestors, but this does not signify ideation. Every cognising is conditioned by the past, but this does not call for a reawakening and projecting in ideal form at every instance of cognitive effort, before any real cognition is reached.

In fact, many, if not the most of our attentions, are merely intensifyings of some present cognition, of some cognitive psychosis which has simply come or happened. Take the instance of attention to marginal retinal images, this certainly does not always imply preperception, the forming of an idea of what we are to see, though in the cases mentioned by Professor James it may. For example, I was writing the above seated with my profile to the window when I became suddenly aware, through the physiological agency of a marginal image, of a moving object to my right. This perception of bare undefined object was spontaneous, a pure given; I exercised no will in attaining it, and so the state of cognition was not an attention. However, by attending, by intensifying the cognition by will effort, I perceive that the indefinite object is a man walking on the sidewalk, who is of a certain height, clothed in a certain way, etc. I do not trace the least ideation in the whole process, the slight attending as act of will did not imply any anterior or posterior idea or representation. The reason for the will act was the intrinsic interest of movement, and this intrinsic interest arises in the fact that moving objects have had for all life a special pleasure-pain significance, the moving object is the most dangerous, and so motion perceived has become ingrained in mind as a special stimulant of attention. This habit of attentiveness to things in motion survives and continues for cases where it is of no use and even of harm; thus, in the present instance, it diverts me from my work. It is obvious that attention often occurs in the same way for other senses without preliminary idea.

On the whole we must conclude that attention is a much abused term, and it is to be hoped that psychologists will for the future keep to the definite and best use of the term; namely, to denote cognitive effort in all its degrees and modes.

HIRAM M. STANLEY.

IS MONISM ARBITRARY?

In Vol. II, No. 3, of _The Monist_, a very kind criticism appeared from the pen of Mr. Francis C. Russell of the doctrine of a double-faced unity of mind and matter. It was said that this doctrine is very far from inducing that final satisfaction which we rightly expect of a competent theory, and the critic propounded as a possible explanation of mental phenomena the postulate of a conservation of spirit. He calls spirit the elementary basis of consciousness considered as a quality. Spirit would be the subjectivity of nature, the elements of feeling, or as Professor Morgan calls it metakinesis; and consciousness would originate in the same way as electricity, i. e., by rending spirit asunder into positive and negative spirit so as to produce a tension. This would account for the appearance and disappearance of consciousness in that spiritual “dynamo” which is called the nervous system.

This proposition seems to be highly acceptable because it stands upon the principle of a conservation of substance and attempts to represent the phenomenon of consciousness as due to a transformation. But does it for that reason remove the difficulties of the doctrine of a double-faced unity of nature, which, as Mr. Russell says, “is open to the charge of being arbitrary and brings no access of insight”? Is not perhaps the term double-faced unity (which is none of my invention, and which I have been careful to avoid) a misleading and unsatisfactory term? Why should nature be double-faced? Why are feeling and motion the only two attributes of natural phenomena? Is this not arbitrary? Could nature not be just as well a treble or quadruple-faced unity. Nature might possess, as Spinoza actually declares, infinite attributes of which these two only, viz. extension and thought, i. e. motion and feeling, happen to be known to us.

It is this apparent arbitrariness which bars our insight and deprives us of the satisfaction that ought to attend the real solution of a problem. But let us avoid the term double-faced unity; let us speak of the subjectivity and the objectivity of nature, and the clouds will disappear.

The doctrine of a double-faced unity has been criticised as dualism, and the proposition that nature consists of two radically different attributes—exactly of two, not more and not less—must most decidedly appear as dualism. But is it dualistic to say that every subject appears to its objects not as a subject but as an object among other objects? Certainly not.

The relativity of the terms subject and object affords us the key to a comprehension of the situation. This world of ours is a world of relations. The phenomena of nature exhibit an unceasing activity; they consist of constant changes, and every change, every motion, has a whence and a whither. Every transformation is a series of events among which any prior one is called cause and any subsequent one effect.

If we regard feeling and motion as two attributes of nature, we are actually on the brink of dualism, and we shall understand how Spinoza, in order to escape from dualism and arrive at a monistic view, assumed without any plausible argument the existence of an infinite number of attributes. This assumption however is of no avail, for the problem would arise: How is it that we know only two of all these infinite attributes? Why do we not know any other? and why are we unable to form even a dim notion of any other? If they exist why do they exhibit no effects upon us? Perhaps because we ourselves and this world of ours consist only of two! And if they exhibit no effects upon us and upon our world, can they be said to exist at all? Might we not, in that case, consider them as non-existent and count the two known attributes alone as actual realities? Thus the dualism would remain; and Spinoza’s monism is only apparent.

The same objection cannot be made if we remain conscious of the fact that feelings are as much abstracts as motions. Subjectivity and objectivity are correlative terms. There is as little a duality in the idea, that subjects presuppose objects as that effects presuppose causes. There are not causes in the world which are nothing but causes, nor are there effects which are nothing but effects. Take for instance an historical event. Was Cæsar’s death a cause or an effect? Plainly, this depends upon the view we take. As the sequence of the wounds which Cæsar received from his assassins it was an effect; as the beginning of the civil war consequent thereupon it was a cause. If I look at you, you are the object and I am the subject. If you look at me, it is the reverse. Thus the relation of a certain thing to its surroundings makes of it a subject, while the surroundings are its objects.

Subject and object being correlatives, we can very well understand why there are no “subjects in themselves”; every subject is at the same time an object in the objective world. We can further understand, why every subjectivity except our own withdraws itself from direct observation. We can observe the movements of organisms like ourselves and judge by way of analogy that they feel pain or enjoy pleasure. We see their motions which betray certain feelings, but we can never see the feelings themselves; and even supposing that we could enter into the brain of a man and that the whole mechanism of brain-action were laid open to our inspection in its minutest details, we should see motions, combinations and separations, integrations and disintegrations, we should see the oxydation of the gray substance, which would appear as a great turmoil and excitement, but we should see (as Leibnitz says) no thoughts, no perceptions, no feelings. That it cannot be otherwise is obvious when we consider that our objects will always present to us the character of objectivity.

But suppose We were an atom of oxygen and entered into the process of brain-action as an active factor, our subjectivity would soon become absorbed and welded into a higher unity with the subjectivity of the other atoms. We should then, as a part of that brain’s consciousness, feel these feelings, perceptions, and thoughts; we should, then, _be_ the subject which we could not see and which we were searching for in vain in the world of objectivity.

This conception of the correlation of subjectivity and objectivity does not only convincingly explain the unity of feeling and motion, it does not only establish a satisfactory monism, it throws light also on some other of the questions that puzzle us. How is it that we do not feel our brain-motions to be brain-motions? We feel our feelings only; and when feeling our feelings we do not so much feel _that_ we feel as _what_ we feel. In other words, we feel the contents of our feelings; we feel their import, their meaning; we are aware of their significance; our consciousness is conscious of the object, the presence of which is indicated by this special feeling. Our attention is concentrated upon the messages conveyed by and contained in the different feelings.

These messages of certain feelings are the interpretations given either to certain sense-impressions or they are the thought-symbols representing some abstracts, representing certain features of sense-impressions.

How little we feel our brain-motions when we think, can be learned from the fact that some nations place the seat of thinking in the heart, others in the stomach or even the bowels, while even so great a naturalist as Aristotle regarded the brain as cold and insensible; he made the observation that man is in possession of the relatively largest brain, but he understood its function so little that he thought it served to cool the warmth rising from the heart.

It is strange that every subjective feeling so long as it remains within itself can neither be localised nor determined. We know nothing whatever of the brain-motion that thinks a certain idea. We can fairly assume that every idea is in its objective existence a peculiar kind of brain motion taking place in a particular part of the brain, but we are not conscious of the brain-motion as a special and localised motion. We are quite unable to tell the difference that we must suppose to exist between the forms of the brain-structures or combinations of brain-structures and their motions when we think say for instances of virtue and of vice. We are conscious only of the idea and not of their objective correlates.

Whatever we know of our body, we know only through sensation; i. e., by the same means by which we know of other things. Our body is to us, and is represented with the assistance of the senses, as an object in the objective world. As such it is localised and all its relations and activities are determined. Whatever subjective feeling we have concerning any state of ourselves, remains indistinct until with the help of the senses it is made an object to our observation. Who has not as yet made the experience that he was unable to localise a toothache. The pain itself gives no information either as to its nature and cause or as to the seat of the suffering. The pain itself is purely subjective. All the objective facts have to be localised with the assistance of the senses. The suspected regions must be made the object of experiments and if any irritation of a certain spot increases the ache, it will be assumed to be the seat of the pain. And even then how often is a patient mistaken not only almost always as to the nature but often also as to the seat of the pain.

These facts appear strange, but they cease to be strange, when we consider that the nature of subjectivity is feeling. Subjectivity can as little become directly conscious of its own objectivity as an eye can look at itself. However, an eye can look at its image in the mirror. So the complex of subjective existence, which is through the interaction of an organism united in what we call a soul, can and does turn the channels of its own senses back upon itself and thus forms an opinion concerning its own objectivity. Man’s knowledge of his own objective existence is not due to any internal and direct perception of self, but solely to the same experience through which he receives information concerning the rest of the world.

P. C.

A REPLY TO A CRITIC.

WITH A DISCUSSION OF NECESSARY TRUTHS.

_To the Editor of The Monist_:

I hope it is not a breach of etiquette to ask you to forward to your reviewer the following remarks in reply to his criticism of my work (_The Foundations of Geometry_, reviewed in Vol. II, No. 1, of _The Monist_). If he is good enough to review my second book also, I think they will clear up some misunderstandings.

Your reviewer commences with some general remarks, against which I have nothing to say. He then proceeds to consider my “requirements for a logical definition.” Here he seems to find a difficulty—which may be due to my not having expressed myself clearly. If so I hope he will read what I say on the same subject in my _Essay on Reasoning_, which I cannot believe he will find “indefinite” or not well “issuable.” But indeed I cannot see where his difficulty comes in with my old statement of the case. I state perfectly clearly that requirements (3) and (4) are not _logically_ necessary for a definition, but are only required if that definition is intended to give a _particular meaning_ to the word. He tries to reduce my argument _ad absurdum_ by giving a definition of “troft.” But so far from being absurd his definition is perfectly good. According to it “troft” would include in its denotation all our percepts and concepts. When however he goes on to say “... These significant names must be so used that the intellectual sensibility shall be excited to perceive that which is intended to be defined,” I differ from him entirely. This is only required for a _description_, not for a _definition_ (see _Essay on Reasoning_, p. 53).

Your reviewer’s only solid objection to my “requirements” seems to be that the fourth includes all the rest. This is only true if the term proposed for definition has an import which has already been determined; but even in such a case it is better to consider the requirements separately, as I have given them. For the force of objections under the different headings varies enormously. An objection under heading (1), if established, would be fatal to any definition whatever. One under heading (2) so far from being fatal would only be a suggestion for the improvement of the definition. Objections under either of the headings (3) and (4) would only be to the effect that the term as defined meant something different from what it was desired that it should mean. It is however convenient to consider (3) and (4) separately as it would generally be possible to decide (3) at once, whereas if a doubt were raised under heading (4) it might lead to a prolonged discussion before it could be laid. I do not however pretend that the “requirements” are laid down in my _Foundations of Geometry_ in the best possible form. Indeed I have altered the form in my second essay. There is moreover one requirement for a logical definition which is not included in my heading (1) in the _Foundations of Geometry_, though it is included in (4). This defect is remedied in the _Essay on Reasoning_ (p. 55). It is curious that your reviewer should have missed this point, as it is the very one on which he attacks my definition of “direction.” It is that the assertions in a definition must not be _independent_ of the meaning of the term defined. If they were, the assertion would be equally true (or false) whatever meaning the term might have. The _import_ of the term would therefore be unlimited. In the case of explicit definitions a similar error is called _circulus in definiendo_.

When your reviewer goes on to attack my definition of “direction” why does he change his front all at once, and disregard all the considerations he has just been discussing? Why does he not apply my, or his own, requirements for a definition to the case in point? The criticism he actually does put forward will not bear a moment’s investigation. If my definition is “circular,” the assertion must be equally true whatever meaning is ascribed to the term. Well, then, let us try the effect of giving to it the meaning we ordinarily ascribe to “cheese.” Is it equally true that “a cheese may be conceived to be indicated by naming two points, as the cheese from one to the other”? Clearly not. But not only does this one assertion out of my definition exclude the import of “cheese” from the meaning of “direction,” but, more particularly, it distinguishes between the “three distinct but closely associated notions” which your reviewer quite rightly says “become confused in thought and expression unless the most solicitous care is taken to distinguish them.” This is exactly the care which I _have_ taken, by framing my definition.

I need not say much about the rest of the criticism. Your reviewer’s remarks on my definition of “angle” are simply due to the fact that he has not read the definition carefully, and probably has not read the note on the top of page 36 at all. It may make it clearer to him if I point out that if “we imagine a northeast-southwest line cutting an east-west line,” we imagine _four_ different directions and therefore (4⋅3)/(1⋅2) = 6 angles. Two of these are the straight angles between the opposite directions of each of the two lines. The other four are what Euclid calls “the angles between the lines.” As an angle, according to my definition, has no local habitation in space, it is, _prima facie_, meaningless to talk of the “right hand upper angle.” But if this is only an abbreviation for “the angle between the directions upwards and to the right,” then “the right hand upper angle” means the same as it would in Euclid.

With the remarks about the nature of the challenge I have thrown down I heartily agree. May I however suggest that I have a right to expect that criticism should be, not only “competent and candid,” but careful? It is a difficult subject, and _I_ at least am not always able to express myself in such a way that my meaning cannot be misunderstood by any one. I think if your reviewer looks at what I have said again, with the aid of what I say further in my _Essay on Reasoning_, he will see that his criticisms have really originated in misunderstandings, and perhaps he will alter his judgment that I have “come short of the high result to which I aspired.”[18]

But my chief object in writing to you to-day is to bring specially to your notice my ideas on the nature of so-called “necessary truths.” I am not quite clear how far you will find my views harmonise with your own. To a great extent I am inclined to think they are simply a further analysis of the views you express in _The Monist_ and in your _Fundamental Problems_. I will briefly sketch my own ideas and you can then judge whether they are yours also or not.

In my _Essay on Reasoning_ I classify assertions as Truisms (assertions whose truth depends solely on the definitions of their terms) and Real Assertions, which convey some real subjective or objective information. I show that the validity of all purely formal knowledge depends on the fact that it is deduced from definitions alone, which are laid down _arbitrarily_ and that the supposed peculiar certainty of the theorems of pure mathematics is merely due to the fact that they are all truisms. Thus, I think it a misnomer to call such theorems “necessary” truths. It would be nearer the mark to call them “arbitrary” truths.

There is no _necessity_ whatever about the theorem “twice two is four.” “Two” is defined as 1 + 1; “twice,” as the operation of adding a thing to itself. It follows from this that “twice two” is 1 + 1 + 1 + 1; and this, by _definition_, is “four.” If “four” were defined as 1 + 1 + 1, (and there is no “necessary” reason why it should not be,) then “twice two” would _not_ be “four.” The assertion “twice two is four” conveys no real information whatever—at best it could only tell us what one of its terms meant if they had not all been previously defined.

I cannot insist too strongly on the importance of a proper understanding and use of logical definition. If you desire to know whether a given assertion is true or false, _a priori_ or _a posteriori_, the first step in the investigation MUST be to find out how its terms were defined. If it turns out that the truth (or falsehood) of the assertion can be formally deduced from these definitions, then the assertion is a truism (or contradiction in terms): in either case it can give no real information, and even if true cannot be a “necessary” truth. Only if the definitions of the terms are both independent and consistent is it open to discussion how we might come to a knowledge of the fact it expresses.

I may briefly indicate here how I think the problem ought to be attacked. “Objective facts” can only be established by induction. I do not mean by that term necessarily the process described by Mill, but some similar process, based ultimately on _inductio per enumerationem simplicem_. Now no such process can ever lead to a necessary truth. The most fundamental and certain induction which can be made, that which induces us to believe in the objectivity of our environment, does not lead to a “necessary truth”; and much less can any other induction based upon this one do so. “Objective facts” then may be established with greater or less probability, but can never be _necessarily_ true. But all inductions are based on our perceptions, that is ultimately on our subjective sensations. And a man can, nay, must be, absolutely certain of the reality of his own sensations though he cannot be certain of the interpretations he puts upon them. If I have a toothache I cannot be absolutely certain that I have a tooth, but, at least while the pain lasts, I am _absolutely_ certain that I have an ache. And so of any subjective sensation.

I can similarly be absolutely certain that I entertain a given concept, while that concept is before my mind; though of course it is possible that if I assert the possession of that concept I may do so in language which may be misunderstood by the person I am addressing. If then a man has certain concepts which he can call up at will, the reality of those concepts, _qua_ concepts, is to him a _necessary truth_. He may lay down such necessary truths as axioms, and by their aid he may give real subjective import to a symbolic argument, and so obtain new and complicated assertions which are also to him necessary truths. This is what I do in my subjective theory of geometry. That theory might be regarded as purely symbolic—the axioms might have been left out, and all its conclusions looked upon as mere truisms. The conclusions of geometry of four or more independent directions can perhaps _only_ be regarded as truisms. But by the aid of the axioms, geometry of two and three independent directions can be given real subjective import, and its conclusions therefore regarded as necessary truths, as long as they are only taken subjectively. They may further be applied objectively by the aid of objective facts established by induction, but in this case their validity is no greater than that of the primary facts, the counterparts of the subjective axioms, which are employed to give the theory objective import.

I confess I have not studied Kant sufficiently to say that his views differ, materially from mine, though I always thought they did until I read your interpretations of them. Perhaps I misunderstood the sense in which Kant used the term _a priori_. The term has been used in so many different senses that I prefer myself to drop it altogether. If it merely refers to priority in time there can be no practical doubt that, whether in the case of the human race or of an individual thinker, a large amount of sense-experience must have preceded even so simple an _a priori_ judgment as “twice two is four.” If the term merely refers to priority in logical validity it seems to me better to say that “such and such assertions are not dependent upon experience.” But Kant says of the assertion “7 + 5 = 12” that it is not only “_a priori_” but “synthetic”. By the latter term he means that its truth was _not_ deduced from definitions alone, and that the assertion therefore conveys real information. In this I believe he was wrong, and though he afterwards declares that “all knowledge _a priori_ is empty and cannot give information about things,” unless the true nature of _a priori_ knowledge is made more clear, people will inevitably continue to believe the contrary—and to believe moreover that Kant taught so.

Any language which seems to imply that there is some dread necessity about mathematical truths—that they could not be otherwise if they would—is very misleading. Of course it is necessarily true that _if_ you have seven objects and add five more to them you will have in all twelve objects. But the whole objective difficulty is begged by the supposition. “Much virtue in if!”

As I understand it the essence of the “laws” of pure mathematics is that they are verbal, that is they are only abbreviated expressions of the results of certain verbal processes. If the processes are repeated and the results similarly expressed, the results must always be the same. Our reason cannot “inform us about the form of existence” unless it is first given, as the _data_ or facts which correspond to the definitions of our symbolic arguments. It is only because our reasoning faculties are limited that symbolic arguments are necessary at all—that it is not evident to us at once that the conclusions of the most intricate mathematical calculations are given to us along with the _data_. Given the data, then in all possible worlds the conclusions must indeed follow, but only because they really are already _in_ the data which were given.

It may be that you will not only agree with all I have said, but have already said much of it yourself. But there are some passages in your _Fundamental Problems_ which seem to imply otherwise. I think the great objection I have to urge against Kant, and also perhaps against you, is that you do not distinguish as clearly as I could wish between symbolic argument and real, though subjective, knowledge. And the only way to distinguish between them is by inquiring into the definitions of the terms.

For example, on p. 165 of _Fundamental Problems_ you say that to four-dimensional beings Kepler’s third law “would most probably appear as ‘the cubes of their times of revolution being proportional to their mean distances to the fourth power.’”

Now what sort of assertion do you take Kepler’s law to be? Originally it was a purely empirical law obtained by pure induction. If the four-dimensional people obtained their law the same way why should the result appear different to them? Or do you conceive the law to be deduced from Newton’s theory of gravitation? But even so the law of the inverse square was obtained empirically. If you think that law can be explained (as the analogous law for the distribution of light can) by the supposition that the integral of the force over all points at a given distance from the origin is constant, still this supposition is purely gratuitous unless established by induction from experience. If you grant any one of these suppositions you can by symbolic argument obtain the law corresponding to Kepler’s for a four-dimensional space. But I may mention that in no case does the result you anticipate come out. On the first two suppositions the law would be unaltered. On the last supposition the law of gravity would be changed to the inverse cube; but after that the solution of the problem has nothing to do with four dimensions—it is a two-dimensional problem only. The result is that in general planets could not move in closed orbits at all. They might conceivably revolve in circles, but such a condition would be unstable, and if it obtained their periodic times would vary as the squares of their distances.

Again you say (p. 74) “the doctrine of the ‘conservation of matter and energy,’ although it has been discovered with the assistance of experience, can be proved in its full scope by pure reason alone.” I should very much like to see your proof (which I cannot find in _Fundamental Problems_). How do you define the terms of the doctrine? Do you deduce the proof from these definitions—that is do you make it a truism? Or do you base it upon subjective axioms as I do my geometry? Or if you base it on objective facts, how do you prove those facts by pure reason alone? And if it is purely a subjective proof, how, can you say the doctrine is proved “in its full scope”? Surely objective applications come within its scope?

It would not be fair in me to ask you to publish my reply to your reviewer’s criticisms, though if that reply is justified the criticism must have done the prospects of my book some injury, seeing from what a quarter it comes. But I hope you will see your way to publishing the latter part of this letter in _The Monist_, together with your reply to it, if you think it worthy of such a distinction.

I have just come across, in this month’s _Nineteenth Century_, another remarkable instance of reasoning which seems to be rendered entirely nugatory by the want of proper definitions. It is asserted that conceptual thought is impossible without language. At first sight this would certainly appear to be a real assertion. It follows from it that since dogs have no language they have no “conceptual thought.” But it may be plainly shown that dogs do entertain “general notions,” which in ordinary English would be included under the head of “conceptual thought.” The apparent contradiction is however explained when it appears that the author distinguishes general notions as “concepts” or “recepts,” according as they _are_ or _are not named_. This being his definition of “conceptual thought” as opposed to other thought, it appears that the assertion is only a truism after all, and conveys no real information whatever. To discuss it further is then mere waste of time. The author of the assertion doubtless _wished_ it to convey some information, but he did not attend to his definitions and so failed to attain his object.

EDWARD T. DIXON.

FOOTNOTES:

[18] The reviewer of Mr. Dixon’s book has read these remarks on his criticism (_The Monist_, Vol. II, No. 1, p. 126) and has given them what seems to him full consideration. He confesses that he misunderstood what Mr. Dixon meant by “a direction.” (See the article “Logic as Relation-Lore” to be published in a subsequent number.) In regard to the requirements for a logical definition he must still abide by his former opinion. The need of a definition arises either from the inaccuracy in the application of a term or from a supposed lack of knowledge as to its signification. Hence to use the term itself in its own definition is to import into the definition the same vagueness or ignorance which it is the very office of a definition to correct. When Mr. Dixon says that it is requisite for a logical definition that the defining assertions “must not be _independent_ of the meaning of the term defined,” what is that but to say that the same must be _dependent_ upon that meaning? which, unless the reviewer again misunderstands the author, is to say that we must understand the meaning of the term before we can understand the definition.

ρσλ.

MATHEMATICS A DESCRIPTION OF OPERATIONS WITH PURE FORMS.

IN REPLY TO MR. EDWARD DIXON.

It is true, as Mr. Dixon says, that “Any language which seems to imply that there is some dread necessity about mathematical truths is very misleading.” But to say, as Mr. Dixon does in another passage, that the truisms of mathematics are arbitrary truths, is more misleading still. The theorems of the formal sciences are not “assertions whose truth depends solely on the definition of their terms.” They are “real assertions which convey some real subjective or objective information.”