Mill on Hamilton [From The Nation 1.9 (31 August 1865): pp. 278-281.] ¹⁸, “An Examination of Sir William Hamilton’s Philosophy, and of the principal Philosophical Questions discussed in his writings. By John Stuart Mill.” Boston: William V. Spencer. 1865. 2 vols., pp. 330 and 354. ¹⁹.
4. — A Treatise on Logic, or the Laws of Pure Thought; comprising both the Aristotelic and Hamiltonian Analyses of Logical Forms, and some Chapters of Applied Logic. By Francis Bowen, Alford Professor of Moral Philosophy in Harvard College. Cambridge: Sever and Francis. 1864. pp. xv., 450.

The subject of this work “is not Sir William Hamilton, but the questions which Sir William Hamilton discussed.” Many of these, though originating in the school of philosophy of which Sir William Hamilton is the most eminent representative of the present generation, and though often ignored under the general designation of metaphysics by the school to which Mr. Mill belongs, are questions which he regards as important enough to justify his elaborate work. “A true psychology,” he says, “is the indispensable scientific basis of morals, of politics, of the science and art of education, and “the difficulties of metaphysics lie at the root of all science.” In his work on logic, and in many of his shorter essays, there is manifested the same appreciation of metaphysical studies, with which, however, he always deals warily, and he has reserved as the work of his maturest powers the complete definition and defence of his metaphysical opinions. Questions which often engage the attention and tempt the powers of immature thought Mr. Mill has reserved for his latest work, and he has thereby contributed to philosophy most important additions.

Much more space is given, it is true, to dissecting and estimating Sir William Hamilton’s special opinions and characteristics than the proposed design of the work seems to warrant, but this does not diminish in the least its interest, nor in fact its positive value as an exposition of the opinions it. advocates. A master in the tactics of philosophical polemics, Mr. Mill

strikes very effective blows for his own opinions, and builds on the ruin he makes of the best accredited rival philosophy. Disciples of this philosophy may justly object, however, that the opinions they hold are not responsible for the defects of a teacher, even of so unquestionable a master as Sir William Hamilton; and his very excellences seem to us to furnish the vantage ground from which his critic makes so effective an assault on the opinions of his school. Few writers of this school present so clearly and distinctly the fundamental questions of metaphysics as Hamilton. His statements have such precision and scientific distinctness that his critic is able to exhibit even in his own words the contradictions and inconsistencies which abound in his writings.

Many of these, however, are, we think, apparent rather than real, and are explicable from the metaphysician’s point of view, which Mr. Mill does not appear to us to have clearly comprehended. We willingly concede that so far as perfect candor, most patient study, and an earnest desire to ascertain Sir William Hamilton’s opinions could avail, Mr. Mill’s examination is all that could be desired. But something more than justice is required of a critic in matters so difficult and profound. Sympathy—a certain degree of sympathy—is essential to supply the links and concordances of thoughts, which were never reduced to a coherent system, but were scattered through the writings of many years, and stand much in need of a commentary—not by an opponent, but by an admiring and competent disciple. It is not less true of a philosophical system than of a religious creed, that to judge it competently one must first believe in it, and then, perhaps, cease to believe in it—at least lose the ardor of the disciple.

Although Mr. Mill is by no means so far removed in opinion from the school of philosophy which Hamilton represents as many of his own school are, he is none the less separated from it by that fundamental division which has maintained two great schools throughout the whole history of speculative thought; a division which is at bottom one of feeling and mental character, and one in which no love is lost. No philosopher has had the genius to arbitrate between them. Not even Mr. Mill, sagacious and just as he is, is generous enough to catch the spirit and point of view of his opponents in speculative matters.

We cannot give an adequate illustration of this defect from the topics of Mr. Mill’s book without exceeding the limits of this article. It may suffice to point out one misinterpretation of Hamilton’s doctrines, as we conceive them, which is fundamental, and plays an important part in the “Examination.” Mr. Mill attempts to prove that the doctrine of “the relativity of human knowledge as held by Sir William Hamilton” is in direct conflict with Hamilton’s doctrine of the perception of the primary qualities of matter, two doctrines on which his fame as a philosopher chiefly rests. Nothing could be more damaging to Hamilton’s reputation than this criticism, if it be true. Minor defects and inconsistencies in his writings might be accounted for on grounds not dishonorable to his character as a philosopher; but if the two principal doctrines, on which he has expended so much learning and labor, are incompatible with each other, then indeed his sagacity was much at fault.

After an introduction, in which Mr. Mill sets forth the scope of his work, he discusses in the second chapter the authentic meanings of the phrase “relativity of knowledge,” and the varieties of the doctrine as held by different philosophers. In its simplest form the doctrine is this, that we know only our sensations, and know not any other things save as existences which, in themselves unknown, produce sensations in us. Other things are only supposed, not known; and are only supposed as powers to produce sensations, not as reasons or inmost natures, which might explain the phenomena of sensation. They are as inmost natures inexplicable, and cannot be described in known terms, but only as the unknowable. This doctrine is fundamental in one of the two great systems of metaphysics, but can be understood in a less definite sense. If a philosopher should hold that some properties of things are not powers to produce sensations in us, but existences, which like our sensations are immediately known, he would not hold, our author thinks, to the relativity of knowledge in a perfectly definite sense. He might mean that all knowledge is a mixture of the relative and absolute kinds, but he ought not to affirm that all knowledge is relative.

The author then comes to the discussion of the meaning in which Hamilton taught the relativity of knowledge. Hamilton affirms the complete relativity of human knowledge, but in his doctrine of natural realism he appears to deny it. He affirms it of the secondary qualities of matter, such as colors, odors, tastes, etc., but denies it of the primary qualities, such as extension, figure, resistance, etc. The existence of matter as the cause of sensations can only be affirmed, Hamilton thinks, by being known immediately and in itself as extended. An extended something is immediately known, the property of extension not being a power to produce a sensation or a group of sensations, but an existence known as immediately as our sensations are. By “immediate” Hamilton does not mean non-relative to us, but without the intervention of a representative object or sensation. The knowledge is immediate, though the thing is related to us in the act of knowledge. But Mr. Mill enquires whether this knowledge is supposed to involve more than exists in this relation; that is, whether this immediate knowledge is of anything non-relative to us. Hamilton appears to think that it is, and he therefore appears to hold that the knowledge is not wholly relative to us. Hamilton asserts in the plainest terms, says Mr. Mill, that this immediate knowledge of things “is a knowledge of somewhat in the thing ulterior to any effect on us;” but in his doctrine of the relativity of knowledge he asserts that neither matter nor mind are known in themselves as substances or subjects of the phenomena. Matter is known “only in its effects.” “The existence of an unknown substance is only an inference we are compelled to make from the existence of known phenomena.” In such words Hamilton lays down the doctrine of the relativity of human knowledge in an exposition which, Mr. Mills says, “would have satisfied Hartley, Brown, and even Comte.” The doctrine that we know matter “only in its effects,” and that “its existence is only an inference we are compelled to make” from phenomena, is the doctrine, however, says Mr. Mill, “which, under the name of cosmothetic idealism, is elsewhere the object of some of Hamilton’s most cutting attacks.”

We have dwelt somewhat at length on this topic, since it illustrates very completely how much a philosopher’s comprehension may be limited by his creed. Even with the words before his eyes, Mr. Mill appears to have overlooked, or else rejected as trivial, a distinction of great consequence in Hamilton’s philosophy—the distinction between “effects on us” and effects in general, or those relative phenomenal existences of which unknown substances, matter or mind, are the causes. In this is all the difference between Hamilton’s doctrine of the relativity of knowledge, and that doctrine of cosmothetic idealism which he attacks. That a knowledge should be of effects, and yet not of effects on us, does not appear to have occurred to Mr. Mill; but this is briefly Hamilton’s doctrine. Mr. Mill and Sir William Hamilton (in his metaphysics) use the words “cause and effect,” however, in different senses; but Mr. Mill does, not appear to be aware of this, else his chapter on Hamilton’s “Theory of Causation” would, we think, have been made less severe.

The division of existences into phenomenal and real (the always becoming, the never being, and permanent real existences) is made in the school to which Hamilton belongs, irrespective of any theory of perception. This Platonic distinction is as fundamental in the older metaphysics as the simpler doctrine of relative knowledge is in Mr. Mill’s, but has no reference to the distinction of subject and object in knowledge. Draw the line where we will between the ego and the non-ego; include all cognizable being in the ego, or exclude a part—whether all cognizable modes of existences are sensations and groups of sensation in us, or whether other modes of existence form a part of the phenomena of knowledge—it is in either case true that particular and passing modes of existence, not their substances, are the objects of knowledge. All that Hamilton in his “Theory of Perception” contends for is, that we have a knowledge of modes of the non-ego as immediate as our knowledge of our own sensations; that our consciousness in presentative knowledge is composed of phenomena or modes, which are referable immediately some to a substance ego and some to a non-ego; but that it is only through these phenomena that either ego or non-ego is known, and the knowledge of both is therefore relative. The subjects of phenomena are still unknown in themselves, though the primary qualities of matter be as immediately known as sensations are. The relations involved in the phenomena of. knowledge are, according to Hamilton, sui generis, and cannot be explained, he thinks, as relations of attributes to a single subject, but they are explained to the common sense of mankind by the doctrine which Hamilton calls natural dualism. According to this, a real or immediate knowledge is no more a mode of the ego than of the non-ego, but is a phenomenon, a mode of being, by which two substances manifest themselves equally and in contrast as two substances. When Hamilton speaks of our “knowing nothing absolute, nothing existing absolutely, that is, in and for itself, and without relation to us and to our faculties,” he does not contradict his doctrine of real presentationism. Though things do produce effects on us—namely, sensations—it is not these which constitute knowledge of things. Real knowledge, as a phenomenon, is the joint result of two real causes, neither of which is known in itself, but both are equally known as the necessary substrata of the phenomenal elements of knowledge. Those elements which are immediately referred to the non-ego are not “a knowledge of somewhat in the thing ulterior to any effect on us,” as Mr. Mill interprets them, but at the same time they are no mere modes of the self. They are

the modes of a self and a not-self in union and equipoise. When Hamilton contends that we know the primary qualities of matter as they exist in things, he does not assert that we know things in themselves—that is, the noumena or things independently of us. We only know them as independent of any affections of us. We know them by affections of themselves on the occasions of their mysterious union with us in our intuitions of them.

That this doctrine is a genuine product of the old metaphysical mode of philosophizing, and is exposed to the gravest objections, we willingly admit. It is really an attempt to explain a phenomenon by describing it in terms which imply that it is ultimate and inexplicable. Like much beside in metaphysical philosophy, this doctrine attempts to justify the common opinions and natural prejudices of the undisciplined mind, instead of attempting to account for them. Very profound in appearance, it rests on the most superficial evidence, and does not bear examination. But while we admit all this, we are unwilling that the really strong points of Hamilton’s metaphysical genius should be underestimated. His theories really fit each other much better than they do the more recondite facts of experience. Between this doctrine and the psychological explanations which Mr. Mill gives in Chapter XI. and the two following ones, there is a difference as important as that between the astronomical theories of Plato and those of Newton. We regard Mr. Mill’s definition of substances as “the permanent possibilities of sensation,” and the interpretations of the facts of consciousness which he makes in accordance with it, as among the most important contributions to psychology which have been made in modern times. The chapters devoted to his psychological theory of the belief in an external world, in matter and mind as substances, and the psychological theory of the primary qualities of matter, are the most valuable in the book, and comprise the maturest and most defensible views on these difficult subjects which have been reached.

In the chapter on Sir William Hamilton’s theory of causation, Mr. Mill retorts with great effect the criticism of Hamilton on Brown, but, as we have intimated, this severity could have been spared, if instead of aiming at a polemical success our author had attempted to realize what the metaphysical idea of cause is, and what precisely Hamilton meant in his charge against Brown that “he professes to explain the phenomena of causality, but previously to explanation, evacuates the phenomenon of all that desiderates explanation.” Misled, we suppose, by what must be allowed to be a very faulty account of the principle of causality, in which Hamilton gives a precise scientific explanation of the metaphysical idea of cause, while in fact the idea has only a vague unprecise import, Mr. Mill thinks that Hamilton has confounded the notion of efficient cause with that of substance, the causa efficiens with the materia, and that when Hamilton speaks of the complement of existence always remaining unchanged, and of the impossibility of conceiving any change in it, he has in mind the permanence of material substances, which, as Mr. Mill justly says, is not a necessary conception, such as the principle of causality is supposed to be. Doubtless this conception furnished Hamilton the faulty metaphor under which he describes the principle of causality, but it should have been interpreted like Plato’s archetypal world—that permanent existence which is supposed necessary to account for the changes as well as the apparent permanences in the world of phenomena. Mr. Mill, following Brown, is quite as far from defining, in his law of causation, the metaphysical efficiens as he supposes Hamilton to be. His idea of cause is the scientific one, which is more properly named physical cause. It is the most general law of the successions of phenomena, and is derived from the total results of experience, whereas the principle of causality is supposed to be implied in the very beginnings and elements of experience. The law affirms that all successions are made up of invariable and unconditional sequences, but the metaphysical cause is the supposed real substratum of the unconditionality of a sequence. This principle is a genuine product of the metaphysical mode of philosophizing, and on close examination does not yield much meaning, but such as it is was Hamilton’s meaning. Phenomena change. What makes them change? Not themselves. Not their regularity, which is expressed by the law of causation. “That which can produce changes must itself be permanent” is the metaphysical postulate called the principle of causality. For if it also changes, then something else must make it change, and this something else must either be permanent or the effect of some still more remote unchangeable existence. Such we conceive to be the notion of causality as held by Sir William Hamilton. Doubtless, if Mr. Mill had so comprehended it, and applied to its explanation his psychological method, he would have resolved it into a mere crudity of undisciplined thought—into anything but a necessary principle. This, however, would have been better than misunderstanding it, to the apparent detriment of his author’s reputation.

In respect to one of the principal topics of Mr. Mill’s book, the position of Sir William Hamilton is quite anomalous. Though belonging to the school to which Mr. Mill is opposed, Hamilton, it is well known, agrees in one of his most important opinions with his opponents. This has caused a great quarrel in the family. The absolutists and the quasi absolutists among religious thinkers have found in him a formidable antagonist; but this wins for him no sympathy from his critic of the opposite school, but rather subjects him to a severer condemnation. He is discovered in his lion’s skin. He is not genuinely unorthodox, but, by what appears to his critic to be a subterfuge, retreats from his position on the incognizable and inconceivable character of the infinite and the absolute, by affirming that, though these cannot be known or conceived, they may yet be believed in. “What is rejected as knowledge by Sir William Hamilton, brought back under the name of belief,” is the topic of Chapter V., in which Mr. Mill disposes somewhat summarily of a distinction of great consequence with theological writers, and one which also plays so important a part in Hamilton’s philosophy, that a more careful and sympathetic study of it would have saved Mr. Mill, we think, much perplexity in his interpretations of Hamilton’s opinions, especially in a later chapter on the doctrine of Judgment.

“Belief without knowledge” seems to our author an absurdity, and though the antithesis and the frequent antagonism of faith and science have rendered the distinction a familiar one, it must be confessed that there are few psychological matters more difficult than the discrimination of a faculty of faith from our general faculties of knowledge. But that there is more than a simple difference of degree between knowledge and belief, even in the common acceptation of the terms, seems to us obvious. Hamilton uses the word “belief” in a somewhat technical sense, to express a simple and elementary form of consciousness, which he supposes to underlie every cognitive act, and to take part in the formation of notions as well as of judgments and reasonings. That Mr. Mill is not fully apprized of this use of the word appears when he says that, “according to Sir William Hamilton, we believe premises, but know the conclusions from them,” and adds, “but if we know the theorems of Euclid, and do not know the definitions and axioms on which they rest, the word knowledge, thus singularly applied, must be taken in a merely technical sense.” But really, according to Sir William Hamilton, we not only know these theorems by means of the axioms and definitions, but we also know the axioms, though in a different manner. Though proposed in the form of cognitions, they rest, he thinks, on an instinctive apprehension of certain universal facts, which may govern our actions and even our judgments without passing themselves into the distinct consciousness of knowledge. Expressed in language they may be known, but independently of this they are believed and acted on. They exist and are originally given in the form of “simple feelings or beliefs.” Mr. Mill, of course, gives a different and, we think, a better account of the origin of universal truths, but this is no reason why he should not comprehend and correctly state the real opinions of his author, though it may serve to explain why he does not do so. His own opinions are so different from Hamilton’s that he is very likely to mistake him.

Among the many confusions, real and apparent, which Mr. Mill finds in Hamilton’s writings, the most perplexing belong to this subject. Hamilton appears to our author to propose, at a distance of exactly three pages, two different theories of judgment “without the smallest suspicion on his part that they are not one and the same.” But, in reality, though Mr. Mill does not appear to be aware of it, the first of these theories is a definition of the act of judging in its simplest form the element, which, according to Hamilton, is common to all the products of the understanding or the elaborative faculty, while the second theory defines the special product called specifically a judgment, in which, in addition to the common principle of comparison, there is apprehended and expressed the relation of subject and predicate. It is this relation which, according to Hamilton, distinguishes the logical judgment from a complex concept, and not the element of belief, which, according to Mr. Mill and others, belongs only to the judgment. This difference of opinion and nomenclature occasions Mr. Mill much perplexity. His author seems to him to reach in this matter “the very crown of the self-contradictions which we have found to be sown so thickly in Sir William Hamilton’s speculations. Coming from a writer of such ability, it almost makes one despair,” he adds, “of one’s own intellect and that of mankind, and feel as if the attainment of truth on any of the more complicated subjects of thought were impossible.”

Mr. Mill makes small account, as we have said, of the distinction of knowledge and belief. They differ, he thinks, only in the degree of the conviction with which they are held, or else in the degree of simplicity and directness in the evidence on which they rest. But if we examine them through their correlative ignorance and doubt, an important difference in kind becomes apparent, at least in their psychological relations. Knowledge and

ignorance are wholly beyond the immediate influence of the will. They depend only indirectly on feelings and motives. Belief and doubt, on the other hand, involve volition and depend on feelings and motives. That which Hamilton calls belief, the simple elementary sense we have—from whatever source—of a congruence or conflict among objects and ideas, is that which governs our attention and determines our cognitive acts. Such beliefs control one another like other motives to action, so long as any conflict can arise among them, and it is only when such conflict ceases or is supposed to cease that we attain to knowledge, or suppose ourselves to have attained to it; for much which is called knowledge is only supposed, not real—is a contingent knowledge, held without any actual doubt, but not without a recognized possibility of doubt. Knowledge, then, according to this theory, is not a single simple act of our cognitive faculties, but a harmonious action of all concerned, in which no opposing motive to action exists or is operative; so that what we know, we know without consciousness of choice. In the same way we are ignorant without choice. Conflicting beliefs are not only absent, but all beliefs are absent. Conflict among our elementary beliefs or judgments of agreement and disagreement ceases in two ways, by the discipline of our cognitive objective experiences, and by the discipline of our wills in the formation of character—by submitting our thoughts to the influence of scientific studies, and by submitting them to the control of a restraining culture. Hence the antithesis of the results, science and faith.

This account of the distinction between knowledge and belief is independent of the doctrine, which Hamilton holds in common with his school, that some of our universal beliefs are original and independent of experience; and it is perfectly consistent with what we regard as the truer doctrine of the other school, namely, that there are no postulates in real science—nothing requiring to be admitted beforehand. It is a doctrine, however, associated so strongly with the à priori theory, that it appears to have prejudiced Mr. Mill against it.

In Mr. Mill’s examination of Hamilton’s review of Cousin, in spite of certain important agreements in opinion with his author, he is not disposed, as we have said, to grant him any favor. He even seems inclined to charge him with the absurdities involved in “the senseless abstractions,” “the infinite,” and “the absolute,” and to make out as good a case as possible for those who think they attach significance to them. He goes so far as to say that though “the infinite” (what is infinite in all respects) is not merely, a “fasciculus of negations,” but, what is worse, a “fasciculus of contradictions,” yet if in place of “the infinite” we put the idea of something infinite, Hamilton’s idea collapses at once. “Something infinite is a conception, which, like most of our complex ideas, contains a negative element, but which contains positive elements also. Infinite space, for instance; is there nothing positive in that? The negative part of this conception is the absence of bounds. The positive are, the idea of space, and of space greater than any finite space. So of infinite duration; so far as it signifies ‘without end’ it is only known or conceived negatively; but in so far as it means time, and time longer than any given time, the conception is positive. The existence of a negative element in a conception does not make the conception itself negative, and a nonentity.” True, if “infinite space” be a conception, and not a mere juxtaposition of words or incompatible ideas, then space is a positive part of it. But the question is whether the judgment, “Space is infinite,” can be made, so as to bring the ideas together. Mr. Mill simply assumes that it can, and this too by a mistake of the meaning of the term “infinite,” which Hamilton took much pains to guard against. He confounds the “infinite” of the metaphysician with the improper use of the word by mathematicians. In itself and with the metaphysician, this word is simply the negative of the finite; and as such is entirely incomparable with the finite in respect to magnitude or in any other respect. How does Mr. Mill know that the infinite is greater than any finite? Only by substituting for it a false representation of it. “True,” he says, “we cannot have an adequate conception of space or duration as infinite, but between a conception which, though inadequate, is real, and correct as far as it goes, and the impossibility of any conception, there is a wide difference.” But the conception which Mr. Mill puts forward as the “infinite” is not only inadequate, it is a false conception; arising very naturally, it is true, from an association in our minds between the indefinite and the incognizable. Very large magnitudes are the least definitely or adequately conceived, and we therefore attempt, but wrongly and confusedly, to represent infinite space by putting for it an indefinitely great extension. But this indefinitely great does not contradict or exclude the finite. “Greater than any finite” does exclude the finite, it is true, but so does “less than any finite” exclude it, and both are equally entitled to be called the infinite, yet neither of them is conceivable—neither can be judged to exist.

Mr. Mill appeals for the reality of the conception of the infinite to the results of mathematical calculations. “Considering,” he says, “how many recondite laws of physical nature, afterwards verified by experience, have been arrived at by trains of mathematical reasoning, grounded on what, if Sir William Hamilton’s doctrine be correct, is a non-existent conception, one would be obliged to suppose that conjuring is a highly successful mode of the investigation of nature.” When we consider the reproaches which our author heaps upon Hamilton in a later chapter on the “Study of Mathematics” for his presuming to write about a subject of which he knew so little, we are tempted to respond in the same kind. Hamilton was at least fortunate in not knowing just enough of mathematics to be misled by a loose technical term, or else in knowing enough to be aware that mathematicians can afford to be careless about the etymologies and the strict connotations of the terms they employ. Mr. Mill is not given to superstitions, but if he supposes that mathematicians ever drew any conclusions in regard to physical nature involving in the premises a negation of the finite, he should look again to the works of his philosophical mathematician, Mr. De Morgan, for a correction of his error. The conclusions of the calculus are founded, not on a consideration of quantities really infinite, but of those which by the conditions of its problems may be regarded as indefinitely great—or, more correctly, incalculably great and incalculably small; and the conclusions drawn with their aid are proved to differ from the truth by incalculably small amounts—that is, by as little as we please. This is all that mathematicians have to do with the infinite, and this is just nothing at all.

Of the metaphysical infinite and absolute, and the simple feeling or belief, and the religious sentiment through which Sir William Hamilton and Mr. Mansel think these can be regarded as existing, Mr. Mill washes his hands. Rather than worship a being such as Mr. Mansel presents, of which no real conception, however inadequate, can be formed, he is ready to suffer the worst possible fate. Perhaps those among Mr. Mill’s opponents who are more familiar than he with religious æsthetics, would deny the name of worship to the sentiment he is capable of feeling toward a being whose government of the world receives his unqualified support and approbation, with the sanction of “the highest human morality which we are capable of conceiving.”

In spite, however, of Mr. Mill’s incapacity to enter into a requisite degree of sympathy with his opponent’s point of view, his eminent justness of thought and feeling give his criticisms great weight and value. There is much of interest in his book which we cannot even mention in this brief notice, but we earnestly recommend the whole to our philosophical readers.