Mill versus Hamilton -- The test of truth

[First published in The Fortnightly Review for July 1865.]

British speculation, to which, the chief initial ideas and established truths of Modern Philosophy are due, is no longer dormant. By his System of Logic, Mr. Mill probably did more than any other writer to re-awaken it. And to the great service he thus rendered some twenty years ago, he now adds by his Examination of Sir William Hamilton’s Philosophy—a work which, taking the views of Sir William Hamilton as texts, reconsiders sundry ultimate questions that still remain unsettled.

Among these questions is one of much importance which has already been the subject of controversy between Mr. Mill and others; and this question I propose to discuss afresh. Before doing so, however, it will be desirable to glance at two cardinal doctrines of the Hamiltonian philosophy from which Mr. Mill shows reasons for dissenting—desirable, because comment on them will elucidate what is to follow.

In his fifth chapter, Mr. Mill points out that “what is rejected as knowledge by Sir William Hamilton,” is “brought back by him under the name of belief.” The quotations justify this description of Sir W. Hamilton’s position, and warrant the assertion that the relativity of knowledge was held by him but nominally. His inconsistency may, I think, be traced to the use of the word “belief” in two quite different senses. We commonly say we “believe” a thing for which we can assign preponderating evidence, or concerning which we have received some indefinable impression. We believe that the next House of Commons will not abolish Church-rates; or we believe that a person on whose face we look is good-natured. That is, when we can give con­fes­sed­ly-in­ad­e­quate proofs or no proofs at all for the things we think, we call them “beliefs.” And it is the peculiarity of these beliefs, as contrasted with cognitions, that their connexions with antecedent states of con­scious­ness may be easily severed, instead of being difficult to sever. But, unhappily, the word “belief” is also applied to each of those temporarily or permanently indissoluble connexions in con­scious­ness, for the acceptance of which the only warrant is that it cannot be got rid of. Saying that I feel a pain, or hear a sound, or see one line to be longer than another, is saying that there has occurred in me a certain change of state; and it is impossible for me to give a stronger evidence of this fact than that it is present to my mind. Every argument, too, is resolvable into successive affections of con­scious­ness which have no warrants beyond themselves. When asked why I assert some mediately known truth, as that the three angles of a triangle are equal to two right angles, I find that the proof may be decomposed into steps, each of which is an immediate con­scious­ness that certain two quantities or two relations are equal or unequal—a con­scious­ness for which no further evidence is assignable than that it exists in me. Nor, on finally getting down to some axiom underlying the whole fabric of demonstration, can I say more than that it is a truth of which I am immediately conscious. But now observe the confusion that has arisen. The immense majority of truths which we accept as beyond doubt, and from which our notion of unquestionable truth is abstracted, have this other trait in common—they are severally established by affiliation on deeper truths. These two characters have become so associated, that one seems to imply the other. For each truth of geometry we are able to assign some wider truth in which it is involved; for that wider truth we are able, if required, to assign some still wider; and so on. This being the general nature of the demonstration by which exact knowledge is established, there has arisen the illusion that knowledge so established is knowledge of higher validity than that immediate knowledge which has nothing deeper to rest on. The habit of asking for proof, and having proof given, in all these multitudinous cases, has produced the implication that proof may be asked for those ultimate dicta of con­scious­ness into which all proof is resolvable. And then, because no proof of these can be given, there arises the vague feeling that they are akin to other things of which no proof can be given—that they are uncertain—that they have unsatisfactory bases. This feeling is strengthened by the accompanying misuse of words. “Belief” having, as above pointed out, become the name of an impression for which we can give only a con­fes­sed­ly-in­ad­e­quate reason, or no reason at all; it happens that when pushed hard respecting the warrant for any ultimate dictum of con­scious­ness, we say, in the absence of all assignable reason, that we believe it. Thus the two opposite poles of knowledge go under the same name; and by the reverse connotations of this name, as used for the most coherent and least coherent relations of thought, profound misconceptions have been generated. Here, it seems to me, is the source of Sir William Hamilton’s error. Classing as “beliefs” those direct, undecomposable dicta of con­scious­ness which transcend proof, he asserts that these are of higher authority than knowledge (meaning by knowledge that for which reasons can be given); and in asserting this he is fully justified. But when he claims equal authority for those affections of con­scious­ness which go under the same name of “beliefs,” but differ in being ex­treme­ly-in­di­rect affections of con­scious­ness, or not definite affections of con­scious­ness at all, the claim cannot be admitted. By his own showing, no positive cognition answering to the word “infinite” exists; while, contrariwise, those cognitions which he rightly holds to be above question, are not only positive, but have the peculiarity that they cannot be suppressed. How, then, can the two be grouped together as of like degrees of validity?

Nearly allied in nature to this, is another Hamiltonian doctrine, which Mr. Mill effectively combats. I refer to the corollary respecting noumenal existence which Sir William Hamilton draws from the law of the Excluded Middle, or, as it might be more intelligibly called, the law of the Alternative Necessity. A thing must either exist or not exist—must have a certain attribute or not have it: there is no third possibility. This is a postulate of all thought; and in so far as it is alleged of phenomenal existence, no one calls it in question. But Sir William Hamilton, applying the formula beyond the limits of thought, draws from it certain conclusions respecting things as they are, apart from our con­scious­ness. He says, for example, that though we cannot conceive Space as infinite or as finite, yet, “on the principle of the Excluded Middle, one or other must be admitted.” This inference Mr. Mill shows good reason for rejecting. His argument may be supplemented by another, which at once suggests itself if from the words of Sir William Hamilton’s propositions we pass to the thoughts for which they are supposed to stand. When remembering a certain thing as in a certain place, the place and the thing are mentally represented together; while to think of the non-existence of the thing in that place, implies a con­scious­ness in which the place is represented but not the thing. Similarly, if, instead of thinking of an object as colourless, we think of it as having colour, the change consists in the addition to the concept of an element that was before absent from it—the object cannot be thought of first as red and then as not red, without one component of the thought being expelled from the mind by another. The doctrine of the Excluded Middle, then, is simply a generalization of the universal experience that some mental states are directly destructive of other states. It formulates a certain ab­so­lute­ly-con­stant law, that no positive mode of con­scious­ness can occur without excluding a correlative negative mode; and that the negative mode cannot occur without excluding the correlative positive mode: the antithesis of positive and negative, being, indeed, merely an expression of this experience. Hence it follows that if con­scious­ness is not in one of the two modes, it must be in the other. But now, under what conditions only can this law of con­scious­ness hold? It can hold only so long as there are positive states of con­scious­ness which can exclude the negative states, and which the negative states can in their turn exclude. If we are not concerned with positive states of con­scious­ness at all, no such mutual exclusion takes place, and the law of the Alternative Necessity does not apply. Here, then, is the flaw in Sir William Hamilton’s proposition. That Space must be infinite or finite, are alternatives of which we are not obliged to regard one as necessary; seeing that we have no state of con­scious­ness answering to either of these words as applied to the totality of Space, and therefore no exclusion of two antagonist states of con­scious­ness by one another. Both alternatives being unthinkable, the proposition should be put thus: Space is either or is; neither of which can be conceived, but one of which must be true. In this, as in some other cases, Sir William Hamilton continues to work out the forms of thought when they no longer contain any substance; and, of course, reaches nothing more than verbal conclusions.

Ending here these comments on doctrines of Sir William Hamilton, which Mr. Mill rejects on grounds that will be generally recognized as valid, let me now pass to a doctrine, partly held by Sir William Hamilton, and held by others in ways variously qualified and variously extended—a doctrine which, I think, may be successfully defended against Mr. Mill’s attack.

In the fourth and fifth editions of his Logic, Mr. Mill treats, at considerable length, the question—Is in­con­ceiv­abil­ity an evidence of untruth?—replying to criticisms previously made on his reasons for asserting that it is not. The chief answers which he there makes to these criticisms, turn upon the interpretation of the word inconceivable. This word he considers is used as the equivalent of the word unbelievable; and, translating it thus, readily disposes of sundry arguments brought against him. Whether any others who have used these words in philosophical discussion, have made them synonymous, I do not know; but that they are so used in those reasonings of my own which Mr. Mill combats, I was not conscious, and was surprised to find alleged. It is now manifest that I had not adequately guarded myself against the misconstruction which is liable to arise from the double meaning of the word belief—a word which, we have seen, is used for the most coherent and the least coherent connexions in con­scious­ness, because they have the common character that no reason is assignable for them. Throughout the argument to which Mr. Mill replies, the word is used by me only in the first of these senses. The “invariably existent beliefs,” the “indestructible beliefs,” are the indissoluble connexions in con­scious­ness—never the dissoluble ones. But unbelievable implies the dissoluble ones. By association with the other and more general meaning of the word belief, the word unbelievable suggests cases in which the proposition admits of being represented in thought, though it may be with difficulty; and in which, consequently, the coun­ter-pro­po­si­tion admits of being decomposed. To be quite sure of our ground, let us define and illustrate the meanings of inconceivable and unbelievable. An inconceivable proposition is one 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 the predicate offer an insurmountable resistance to union in thought. An unbelievable proposition is one which admits of being framed in thought, but is so much at variance with experience that its terms cannot be put in the alleged relation without effort. Thus, it is unbelievable that a cannon-ball fired from England should reach America; but it is not inconceivable. Conversely, it is inconceivable that one side of a triangle is equal to the sum of the other two sides—not simply unbelievable. The two sides cannot be represented in con­scious­ness as becoming equal in their joint length to the third side, without the rep­re­sen­ta­tion of a triangle being destroyed; and the concept of a triangle cannot be framed without a simultaneous destruction of a concept in which these magnitudes are represented as equal. That is to say, the subject and predicate cannot be united in the same intuition—the proposition is unthinkable. It is in this sense only that I have used the word inconceivable; and only when rigorously restricted to this sense do I regard the test of in­con­ceiv­able­ness as having any value.

I had concluded that when this explanation was made, Mr. Mill’s reasons for dissent would be removed. Passages in his recently-published volume, however, show that, even restricting the use of the word inconceivable to the meaning here specified, he still denies that a proposition is proved to be true by the in­con­ceiv­able­ness of its negation. To meet, within any moderate compass, all the issues which have grown out of the controversy, is difficult. Before passing to the essential question, however, I will endeavour to clear the ground of certain minor questions.

Describing Sir William Hamilton’s doctrine respecting the ultimate facts of con­scious­ness, or those which are above proof, Mr. Mill writes:

“The only condition he requires is that we be not able to ‘reduce it [a fact of this class] to a generalization from experience.’ This condition is realized by its possessing the ‘character of necessity.’ ‘It must be impossible not to think it. In fact, by its necessity alone can we recognize it as an original datum of intelligence, and distinguish it from any mere result of generalization and custom.’ In this Sir William Hamilton is at one with the whole of his own section of the philosophical world; with Reid, with Stewart, with Cousin, with Whewell, we may add, with Kant, and even with Mr. Herbert Spencer. The test by which they all decide a belief to be a part of our primitive con­scious­ness—an original intuition of the mind—is the necessity of thinking it. Their proof that we must always, from the beginning, have had the belief, is the impossibility of getting rid of it now. This argument, applied to any of the disputed questions of philosophy, is doubly illegitimate: neither the major nor the minor premise is admissible. For in the first place, the very fact that the question is disputed, disproves the alleged impossibility. Those against whom it is needful to defend the belief which is affirmed to be necessary, are unmistakable examples that it is not necessary . . . . These philosophers, therefore, and among them Sir William Hamilton, mistake altogether the true conditions of psychological investigation, when, instead of proving a belief to be an original fact of con­scious­ness by showing that it could not have been acquired, they conclude that it was not acquired, for the reason, often false, and never sufficiently substantiated, that our con­scious­ness cannot get rid of it now.”

This rep­re­sen­ta­tion, in so far as it concerns my own views, has somewhat puzzled me. Considering that I have avowed a general agreement with Mr. Mill in the doctrine that all knowledge is from experience, and have defended the test of in­con­ceiv­able­ness on the very ground that it expresses “the net result of our experiences up to the present time” (Principles of Psychology, § 430)—considering that, so far from asserting the distinction quoted from Sir William Hamilton, I have aimed to abolish such distinction—considering that I have endeavoured to show how all our conceptions, even down to those of Space and Time, are “acquired”—considering that I have sought to interpret forms of thought (and by implication all intuitions) as products of organized and inherited experiences (Principles of Psychology, § 208); I am taken aback at finding myself classed as in the above paragraph. Leaving the personal question, however, let me pass to the assertion that the difference of opinion respecting the test of necessity itself disproves the validity of the test. Two issues are here involved. First, if a particular proposition is by some accepted as a necessary belief, but by one or more denied to be a necessary belief, is the validity of the test of necessity thereby disproved in respect of that particular proposition? Second, if the validity of the test is disproved in respect of that particular proposition, does it therefore follow that the test cannot be depended on in other cases?—does it follow that there are no beliefs universally accepted as necessary, and in respect of which the test of necessity is valid? Each of these questions may, I think, be rightly answered in the negative.

In alleging that if a belief is said by some to be necessary, but by others to be not necessary, the test of necessity is thereby shown to be no test, Mr. Mill tacitly assumes that all men have powers of introspection enabling them in all cases to say what con­scious­ness testifies; whereas a great proportion of men are incapable of correctly interpreting con­scious­ness in any but its simplest modes, and even the remainder are liable to mistake for dicta of con­scious­ness what prove on closer examination not to be its dicta. Take the case of an arithmetical blunder. A boy adds up a column of figures, and brings out a wrong total. Again he does it and again errs. His master asks him to go through the process aloud, and then hears him say “35 and 9 are 46”—an error which he had repeated on each occasion. Now without discussing the mental act through which we know that 35 and 9 are 44, and through which we recognize the necessity of this relation, it is clear that the boy’s mis­in­ter­pre­ta­tion of con­scious­ness, leading him tacitly to deny this necessity by asserting that “35 and 9 are 46,” cannot be held to prove that the relation is not necessary. This, and kindred misjudgments daily made by accountants, merely show that there is a liability to overlook what are necessary connexions in our thoughts, and to assume as necessary others which are not. In these and hosts of cases, men do not distinctly translate into their equivalent states of con­scious­ness the words they use. This negligence is with many so habitual, that they are unaware that they have not clearly represented to themselves the propositions they assert; and are then apt, quite sincerely though erroneously, to assert that they can think things which it is really impossible to think.

But supposing it to be true that whenever a particular belief is alleged to be necessary, the existence of some who profess themselves able to believe otherwise, proves that this belief is not necessary; must it be therefore admitted that the test of necessity is invalid? I think not. Men may mistake for necessary, certain beliefs which are not necessary; and yet it may remain true that there are necessary beliefs, and that the necessity of such beliefs is our warrant for them. Were conclusions thus tested proved to be wrong in a hundred cases, it would not follow that the test is an invalid one; any more than it would follow from a hundred errors in the use of a logical formula, that the logical formula is invalid. If from the premise that all horned animals ruminate, it were inferred that the rhinoceros, being a horned animal, ruminates; the error would furnish no argument against the worth of syllogisms in general—whatever their worth may be. Daily there are thousands of erroneous deductions which, by those who draw them, are supposed to be warranted by the data from which they draw them; but no multiplication of such erroneous deductions is regarded as proving that there are no deductions truly drawn, and that the drawing of deductions is illegitimate. In these cases, as in the case to which they are here paralleled, the only thing shown is the need for verification of data and criticism of the acts of con­scious­ness.

“This argument,” says Mr. Mill, referring to the argument of necessity, “applied to any of the disputed questions of philosophy, is doubly illegitimate; . . . the very fact that the question is disputed, disproves the alleged impossibility.” Besides the foregoing replies to this, there is another. Granting that there have been appeals illegitimately made to this test—granting that there are many questions too complex to be settled by it, which men have nevertheless proposed to settle by it, and have consequently got into controversy; it may yet be truly asserted that in respect of all, or almost all, questions legitimately brought to judgment by this test, there is no dispute about the answer. From the earliest times on record down to our own, men have not changed their beliefs concerning the truths of number. The axiom that if equals be added to unequals the sums are unequal, was held by the Greeks no less than by ourselves, as a direct verdict of con­scious­ness, from which there is no escape and no appeal. Each of the propositions of Euclid appears to us absolutely beyond doubt as it did to them. Each step in each demonstration we accept, as they accepted it, because we immediately see that the alleged relation is as alleged, and that it is impossible to conceive it otherwise.

But how are legitimate appeals to the test to be distinguished? The answer is not difficult to find. Mr. Mill cites the belief in the antipodes as having been rejected by the Greeks because inconceivable, but as being held by ourselves to be both conceivable and true. He has before given this instance, and I have before objected to it (Principles of Psychology, § 428), for the reason that the states of con­scious­ness involved in the judgment are too complex to admit of any trustworthy verdict being given. An illustration will show the difference between a legitimate appeal to the test and an illegitimate appeal to it. A and B are two lines. How is it decided that they are equal or not equal? No way is open but that of comparing the two impressions they make on con­scious­ness. I know them to be unequal by an immediate act, if the difference is great, or if, though only moderately different, they are close together; and supposing the difference is but slight, I decide the question by putting the lines in apposition when they are movable, or by carrying a movable line from one to the other if they are fixed. But in any case, I obtain in con­scious­ness the testimony that the impression produced by the one line differs from that produced by the other. Of this difference I can give no further evidence than that I am conscious of it, and find it impossible, while contemplating the lines, to get rid of the con­scious­ness. The proposition that the lines are unequal is a proposition of which the negation is inconceivable. But now suppose it is asked whether B and C are equal; or whether C and D are equal. No positive answer is possible. Instead of its being inconceivable that B is longer than C, or equal to it, or shorter, it is conceivable that it is any one of the three. Here an appeal to the direct verdict of con­scious­ness is illegitimate, because on transferring the attention from B to C, or C to D, the changes in the other elements of the impressions so entangle the elements to be compared, as to prevent them from being put in apposition. If the question of relative length is to be determined, it must be by rectification of the bent line; and this is done through a series of steps, each one of which involves an immediate judgment akin to that by which A and B are compared. Now as here, so in other cases, it is only simple percepts or concepts respecting the relations of which immediate con­scious­ness can satisfactorily testify; and as here, so in other cases, it is by resolution into such simple percepts and concepts, that true judgments respecting complex percepts and concepts are reached. That things which are equal to the same thing are equal to one another, is a fact which can be known by direct comparison of actual or ideal relations, and can be known in no other way: the proposition is one of which the negation is inconceivable, and is rightly asserted on that warrant. But that the square of the hypothenuse of a right-angled triangle equals the sum of the squares of the other two sides, cannot be known immediately by comparison of two states of con­scious­ness. Here the truth can be reached only mediately, through a series of simple judgments respecting the likenesses or unlikenesses of certain relations: each of which judgments is essentially of the same kind as that by which the above axiom is known, and has the same warrant. Thus it becomes apparent that the fallacious result of the test of necessity which Mr. Mill instances, is due to a misapplication of the test.

These preliminary explanations have served to make clear the question at issue. Let us now pass to the essence of it.

Metaphysical reasoning is usually vitiated by some covert petitio principii. Either the thing to be proved or the thing to be disproved, is tacitly assumed to be true in the course of the proof or disproof. It is thus with the argument of Idealism. Though the conclusion reached is that Mind and Ideas are the only existences; yet the steps by which this conclusion is reached, take for granted that external objects have just the kind of independent existence which is eventually denied. If that extension which the Idealist contends is merely an affection of con­scious­ness, has nothing out of con­scious­ness answering to it; then, in each of his propositions concerning extension, the word should always mean an affection of con­scious­ness and nothing more. But if wherever he speaks of distances and dimensions we write ideas of distances and dimensions, his propositions are reduced to nonsense. So, too, is it with Scepticism. The resolution of all knowledge into “impressions” and “ideas,” is effected by an analysis which assumes at every step an objective reality producing the impressions and the subjective reality receiving them. The reasoning becomes impossible if the existence of object and subject be not admitted at the outset. Agree with the Sceptic’s doubt, and then propose to revise his argument so that it may harmonize with his doubt. Of the two alternatives between which he halts, assume, first, the reality of object and subject. His argument is practicable; whether valid or not. Now assume that object and subject do not exist. He cannot stir a step toward his conclusion—nay, he cannot even state his conclusion; for the word “impression” cannot be translated into thought without assuming a thing impressing and a thing impressed.

Though Empiricism, as at present understood, is not thus suicidal, it is open to an analogous criticism on its method, similarly telling against the validity of its inference. It proposes to account for our so-called necessary beliefs, as well as all our other beliefs; and to do this without postulating any one belief as necessary. Bringing forward abundant evidence that the connexions among our y our experiences—that two experiences frequently recurring together in con­scious­ness, become so coherent that one strongly suggests the other, and that when their joint recurrence is perpetual and invariable, the connexion between them becomes indissoluble; it argues that the indissolubility, so produced, is all that we mean by necessity. And then it seeks to explain each of our so-called necessary beliefs as thus originated. Now could pure Empiricism reach this analysis and its subsequent synthesis without taking any thing for granted, its arguments would be unobjectionable. But it cannot do this. Examine its phraseology, and there arises the question, Experiences of what? Translate the word into thought, and it clearly involves something more than states of mind and the connexions among them. For if it does not, then the hypothesis is that states of mind are generated by the experiences of states of mind; and if the inquiry be pursued, this ends with initial states of mind which are not accounted for—the hypothesis fails. Evidently, there is tacitly assumed something beyond the mind by which the “experiences” are produced—something in which exist the objective relations to which the subjective relations correspond—an external world. Refuse thus to explain the word “experiences,” and the hypothesis becomes meaningless. But now, having thus postulated an external reality as the indispensable foundation of its reasonings, pure Empiricism can subsequently neither prove nor disprove its postulate. An attempt to disprove it, or to give it any other meaning than that originally involved, is suicidal; and an attempt to establish it by inference is reasoning in a circle. What then are we to say of this proposition on which Empiricism rests? Is it a necessary belief, or is it not? If necessary, the hypothesis in its pure form is abandoned. If not necessary—if not posited à priori as absolutely certain—then the hypothesis rests on an uncertainty; and the whole fabric of its argument is unstable. More than this is true. Besides the insecurity implied by building on a foundation that is confessedly not beyond question, there is the much greater insecurity implied by raising proposition upon proposition of which each is confessedly not beyond question. For to say that there are no necessary truths, is to say that each successive inference is not necessarily involved in its premises—is an empirical judgment—a judgment not certainly true. Hence, applying rigorously its own doctrine, we find that pure Empiricism, starting from an uncertainty and progressing through a series of uncertainties, cannot claim much certainty for its conclusions.

Doubtless, it may be replied that any theory of human knowledge must set out with assumptions—either permanent or provisional; and that the validity of these assumptions is to be determined by the results reached through them. But that such assumptions may be made legitimately, two things are required. In the first place they must not be multiplied step after step as occasion requires; otherwise the conclusion reached might as well be assumed at once. And in the second place, the fact that they are assumptions must not be lost sight of: the conclusions drawn must not be put forward as though they have a certainty which the premises have not. Now pure Empiricism, in common with other theories of knowledge, is open to the criticism, that it neglects thus avowedly to recognize the nature of those primary assumptions which it lays down as provisionally valid, if it denies that they can be necessarily valid. And it is open to the further criticism, that it goes on at every step in its argument making assumptions which it neglects to specify as provisional; since they, too, cannot be known as necessary. Until it has assigned some warrant for its original datum and for each of its subsequent inferences, or else has acknowledged them all to be but hypothetical, it may be stopped either at the outset or at any stage in its argument. Against every “because” and every “therefore,” an opponent may enter a caveat, until he is told why it is asserted: contending, as he may, that if this inference is not necessary he is not bound to accept it; and that if it is necessary it must be openly declared to be necessary, and some test must be assigned by which it is distinguished from propositions that are not necessary.

These considerations will, I think, make it obvious that the first step in a metaphysical argument, rightly carried on, must be an examination of propositions for the purpose of ascertaining what character is common to those which we call unquestionably true, and is implied by asserting their unquestionable truth. Further, to carry on this inquiry legitimately, we must restrict our analysis rigorously to states of con­scious­ness considered in their relations to one another: wholly ignoring any thing beyond con­scious­ness to which these states and their relations may be supposed to refer. For if, before we have ascertained by comparing propositions what is the trait that leads us to class some of them as certainly true, we avowedly or tacitly take for granted the existence of something beyond con­scious­ness; then, a particular proposition is assumed to be certainly true before we have ascertained what is the distinctive character of the propositions which we call certainly true, and the analysis is vitiated. If we cannot transcend con­scious­ness—if, therefore, what we know as truth must be some mental state, or some combination of mental states; it must be possible for us to say in what way we distinguish this state or these states. The definition of truth must be expressible in terms of con­scious­ness; and, indeed, cannot otherwise be expressed if con­scious­ness cannot be transcended. Clearly, then, the metaphysician’s first step must be to shut out from his investigation every thing but what is subjective; not taking for granted the existence of any thing objective corresponding to his ideas, until he has ascertained what property of his ideas it is which he predicates by calling them true. Let us note the result if he does this.

The words of a proposition are the signs of certain states of con­scious­ness; and the thing alleged by a proposition is the connexion or disconnexion of the states of con­scious­ness signified. When thinking is carried on with precision—when the mental states which we call words, are translated into the mental states they symbolize (which they very frequently are not)—thinking a proposition consists in the occurrence together in con­scious­ness of the subject and predicate. “The bird was brown,” is a proposition which implies the union in thought of a particular attribute with a group of other attributes. When the inquirer compares various propositions thus rendered into states of con­scious­ness, he finds that they differ very greatly in respect of the facility with which the states of con­scious­ness are connected and disconnected. The mental state known as brown may be united with those mental states which make up the figure known as bird, without appreciable effort, or may be separated from them without appreciable effort: the bird may easily be thought of as black, or green, or yellow. Contrariwise, such an assertion as “The ice was hot,” is one to which he finds much difficulty in making his mind respond. The elements of the proposition cannot be put together in thought without great resistance. Between those other states of con­scious­ness which the word ice connotes, and the state of con­scious­ness named cold, there is an extremely strong cohesion—a cohesion measured by the resistance to be overcome in thinking of the ice as hot. Further, he finds that in many cases the states of con­scious­ness grouped together cannot be separated at all. The idea of pressure cannot be disconnected from the idea of something occupying space. Motion cannot be thought of without an object that moves being at the same time thought of. And then, besides these connexions in con­scious­ness which remain absolute under all circumstances, there are others which remain absolute under special circumstances. Between the elements of those more vivid states of con­scious­ness which the inquirer distinguishes as perceptions, he finds that there is a temp­or­ar­i­ly-in­dis­sol­u­ble cohesion. Though when there arises in him that comparatively faint state of con­scious­ness which he calls the idea of a book, he can easily think of the book as red, or brown, or green; yet when he has that much stronger con­scious­ness which he calls seeing a book, he finds that so long as there continue certain accompanying states of con­scious­ness which he calls the conditions to perception, those several states of con­scious­ness which make up the perception cannot be disunited—he cannot think of the book as red, or green, or brown; but finds that, along with a certain figure, there absolutely coheres a certain colour.

Still shutting himself up within these limits, let us suppose the inquirer to ask himself what he thinks about these various degrees of cohesion among his states of con­scious­ness—how he names them, and how he behaves toward them. If there comes, no matter whence, the proposition—“The bird was brown,” subject and predicate answering to these words spring up together in con­scious­ness; and if there is no opposing proposition, he unites the specified and implied attributes without effort, and believes the proposition. If, however, the proposition is—“The bird was necessarily brown,” he makes an experiment like those above described, and finding that he can separate the attribute of brownness, and can think of the bird as green or yellow, he does not admit that the bird was necessarily brown. When such a proposition as “The ice was cold” arises in him, the elements of the thought behave as before; and so long as no test is applied, the union of the con­scious­ness of cold with the accompanying states of con­scious­ness, seems to be of the same nature as the union between those answering to the words brown and bird. But should the proposition be changed into—“The ice was necessarily cold,” quite a different result happens from that which happened in the previous case. The ideas answering to subject and predicate are here so coherent, that in the absence of careful examination they might pass as inseparable, and the proposition be accepted. But suppose the proposition is deliberately tested by trying whether ice can be thought of as not cold. Great resistance is offered in con­scious­ness to this. Still, by an effort, he can imagine water to have its temperature of congelation higher than blood heat; and can so think of congealed water as hot instead of cold. Now the extremely strong cohesion of states of con­scious­ness, thus experimentally proved by the difficulty of separating them, he finds to be what he calls a strong belief. Once more, in response to the words—“Along with motion there is something that moves,” he represents to himself a moving body; and, until he tries an experiment upon it, he may suppose the elements of the rep­re­sen­ta­tion to be united in the same way as those of the representations instanced above. But supposing the proposition is modified into—“Along with motion there is necessarily something that moves,” the response made in thought to these words, discloses the fact that the states of con­scious­ness called up in this case are indissolubly connected in the way alleged. He discovers this by trying to conceive the negation of the proposition—by trying to think of motion as not having along with it something that moves; and his inability to conceive this negation is the obverse of his inability to tear asunder the states of con­scious­ness which constitute the affirmation. Those propositions which survive this strain, are the propositions he distinguishes as necessary. Whether or not he means any thing else by this word, he evidently means that in his con­scious­ness the connexions they predicate are, so far as he can ascertain, unalterable. The bare fact is that he submits to them because he has no choice. They rule his thoughts whether he will or not. Leaving out all questions concerning the origin of these connexions—all theories concerning their significations, there remains in the inquirer the con­scious­ness that certain of his states of con­scious­ness are so welded together that all other links in the chain of con­scious­ness yield before these give way.

Continuing rigorously to exclude everything beyond con­scious­ness, let him now ask himself what he means by reasoning? what is the essential nature of an argument? what is the peculiarity of a conclusion? Analysis soon shows him that reasoning is the formation of a coherent series of states of con­scious­ness. He has found that the thoughts expressed by propositions, vary in the cohesions of their subjects and predicates; and he finds that at every step in an argument, carefully carried on, he tests the strengths of all the connexions asserted and implied. He considers whether the object named really does belong to the class in which it is included—tries whether he can think of it as not like the things it is said to be like. He considers whether the attribute alleged is really possessed by all members of the class—tries to think of some member of the class that has not the attribute—And he admits the proposition only on finding, by this criticism, that there is a greater degree of cohesion in thought between its elements, than between the elements of the coun­ter-pro­po­si­tion. Thus testing the strength of each link in the argument, he at length reaches the conclusion, which he tests in the same way. If he accepts it, he does so because the argument has established in him an indirect cohesion between states of con­scious­ness that were not directly coherent, or not so coherent directly as the argument makes them indirectly. But he accepts it only supposing that the connexion between the two states of con­scious­ness composing it, is not resisted by some stronger counter-connexion. If there happens to be an opposing argument, of which the component thoughts are felt, when tested, to be more coherent; or if, in the absence of an opposing argument, there exists an apposing conclusion, of which the elements have some direct cohesion greater than that which the proffered argument indirectly gives; then the conclusion reached by this argument is not admitted. Thus, a discussion in con­scious­ness proves to be simply a trial of strength between different connexions in con­scious­ness—a systematized struggle serving to determine which are the least coherent states of con­scious­ness. And the result of the struggle is, that the least coherent states of con­scious­ness separate, while the most coherent remain together—form a proposition of which the predicate persists in rising up in the mind along with its subject—constitute one of the connexions in thought which is distinguished as something known, or as something believed, according to its strength.

What corollary may the inquirer draw, or rather what corollary must he draw, on pushing the analysis to its limit? If there are any indissoluble connexions, he is compelled to accept them. If certain states of con­scious­ness absolutely cohere in certain ways, he is obliged to think them in those ways. The proposition is an identical one. To say that they are necessities of thought is merely another way of saying that their elements cannot be torn asunder. No reasoning can give to these absolute cohesions in thought any better warrant; since all reasoning, being a process of testing cohesions, is itself carried on by accepting the absolute cohesions; and can, in the last resort, do nothing more than present some absolute cohesions in justification of others—an act which unwarrantably assumes in the absolute cohesions it offers, a greater value than is allowed to the absolute cohesions it would justify. Here, then, the inquirer comes down to an ultimate mental uniformity—a universal law of his thinking. How completely his thought is subordinated to this law, is shown by the fact that he cannot even represent to himself the possibility of any other law. To suppose the connexions among his states of con­scious­ness to be otherwise determined, is to suppose a smaller force overcoming a greater—a proposition which may be expressed in words but cannot be rendered into ideas. No matter what he calls these indestructible relations, no matter what he supposes to be their meanings, he is completely fettered by them. Their in­de­struc­ti­bil­i­ty is the proof to him that his con­scious­ness is imprisoned within them; and supposing any of them to be in some way destroyed, he perceives that in­de­struc­ti­bil­ity would still be the distinctive character of the bounds that remained—the test of those which he must continue to think.

These results the inquirer arrives at without assuming any other existence than that of his own con­scious­ness. They postulate nothing about mind or matter, subject or object. They leave wholly untouched the questions—what does con­scious­ness imply? and how is thought generated? There is not involved in the analysis any hypothesis respecting the origin of these relations between thoughts—how there come to be feeble cohesions, strong cohesions, and absolute cohesions. Whatever some of the terms used may have seemed to connote, it will be found, on examining each step, that nothing is essentially involved beyond states of mind and the connexions among them, which are themselves other states of mind. Thus far, the argument is not vitiated by any petitio principii.

Should the inquirer enter upon the question, How are these facts to be explained? he must consider how any further investigation is to be conducted, and what is the possible degree of validity of its conclusions. Remembering that he cannot transcend con­scious­ness, he sees that anything in the shape of an interpretation must be subordinate to the laws of con­scious­ness. Every hypothesis he entertains in trying to explain himself to himself, being an hypothesis which can be dealt with by him only in terms of his mental states, it follows that any process of explanation must itself be carried on by testing the cohesions among mental states, and accepting the absolute cohesions. His conclusions, therefore, reached only by repeated recognitions of this test of absolute cohesion, can never have any higher validity than this test. It matters not what name he gives to a conclusion—whether he calls it a belief, a theory, a fact, or a truth. These words can be themselves only names for certain relations among his states of con­scious­ness. Any secondary meanings which he ascribes to them must also be meanings expressed in terms of con­scious­ness, and therefore subordinate to the laws of con­scious­ness. Hence he has no appeal from this ultimate dictum; and seeing this, he sees that the only possible further achievement is the reconciliation of the dicta of con­scious­ness with one another—the bringing all other dicta of con­scious­ness into harmony with this ultimate dictum.

Here, then, the inquirer discovers a warrant higher than that which any argument can give, for asserting an objective existence. Mysterious as seems the con­scious­ness of something which is yet out of con­scious­ness, he finds that he alleges the reality of this something in virtue of the ultimate law—he is obliged to think it. There is an indissoluble cohesion between each of those vivid and definite states of con­scious­ness which he calls a sensation, and an indefinable con­scious­ness which stands for a mode of being beyond sensation, and separate from himself. When grasping his fork and putting food into his mouth, he is wholly unable to expel from his mind the notion of something which resists the force he is conscious of using; and he cannot suppress the nascent thought of an independent existence keeping apart his tongue and palate, and giving him that sensation of taste which he is unable to generate in con­scious­ness by his own activity. Though self-criticism shows him that he cannot know what this is which lies outside of him; and though he may infer that not being able to say what it is, it is a fiction; he discovers that such self-criticism utterly fails to extinguish the con­scious­ness of it as a reality. Any conclusion into which he argues himself, that there is no objective existence connected with these subjective states, proves to be a mere verbal conclusion to which his thoughts will not respond. The relation survives every effort to destroy it—is proved by experiment, repeated no matter how often, to be one of which the negation is inconceivable; and therefore one having supreme authority. In vain he endeavours to give it any greater authority by reasoning; for whichever of the two alternatives he sets out with, leaves him at the end just where he started. If, knowing nothing more than his own states of con­scious­ness, he declines to acknowledge any thing beyond con­scious­ness until it is proved, he may go on reasoning for ever without getting any further; since the perpetual elaboration of states of con­scious­ness out of states of con­scious­ness, can never produce anything more than states of con­scious­ness. If, contrariwise, he postulates external existence, and considers it as merely postulated, then the whole fabric of his argument, standing upon this postulate, has no greater validity than the postulate gives it, minus the possible invalidity of the argument itself. The case must not be confounded with those cases in which an hypothesis, or provisional assumption, is eventually proved true by its agreement with facts; for in these cases the facts with which it is found to agree, are facts known in some other way than through the hypothesis: a calculated eclipse of the moon serves as a verification of the hypothesis of gravitation, because its occurrence is observable without taking for granted the hypothesis of gravitation. But when the external world is postulated, and it is supposed that the validity of the postulate may be shown by the explanation of mental phenomena which it furnishes, the vice is, that the process of verification is itself possible only by assuming the thing to be proved.

But now, recognizing the indissoluble cohesion between the con­scious­ness of self and an unknown not-self, as constituting a dictum of con­scious­ness which he is both compelled to accept and is justified by analysis in accepting, it is competent for the inquirer to consider whether, setting out with this dictum, he can base on it a satisfactory explanation of what he calls knowledge. He finds such an explanation possible. The hypothesis that the more or less coherent relations among his states of con­scious­ness, are generated by experience of the more or less constant relations in something beyond his con­scious­ness, furnishes him with solutions of numerous facts of con­scious­ness: not, however, of all, if he assumes that this adjustment of inner to outer relations has resulted from his own experiences alone. Nevertheless, if he allows himself to suppose that this moulding of thoughts into correspondence with things, has been going on through countless preceding generations; and that the effects of experiences have been inherited in the shape of modified organic structures; then he is able to interpret all the phenomena. It becomes possible to understand how these persistent cohesions among states of con­scious­ness, are themselves the products of often-repeated experiences; and that even what are known as “forms of thought,” are but the absolute internal uniformities generated by infinite repetitions of absolute external uniformities. It becomes possible also to understand how, in the course of organizing of these multiplying and widening experiences, there may arise partially-wrong connexions in thought, answering to limited converse with things; and that these connexions in thought, temporarily taken for indissoluble ones, may afterwards be made dissoluble by presentation of external relations at variance with them. But even when this occurs, it can afford no ground for questioning the test of indissolubility; since the process by which some connexion previously accepted as indissoluble, is broken, is simply the establishment of some antagonistic connexion, which proves, on a trial of strength, to be the stronger—which remains indissoluble when pitted against the other, while the other gives way. And this leaves the test just where it was; showing only that there is a liability to error as to what are indissoluble connexions. From the very beginning, therefore, to the very end of the explanation, even down to the criticism of its conclusions and the discovery of its errors, the validity of this test must be postulated. Whence it is manifest, as before said, that the whole business of explanation can be nothing more than that of bringing all other dicta of con­scious­ness into harmony with this ultimate dictum.

To the positive justification of a proposition, may be added that negative justification which is derived from the untenability of the coun­ter-pro­po­si­tion. When describing the attitude of pure Empiricism, some indications that its coun­ter-pro­po­si­tion is untenable were given; but it will be well here to state, more specifically, the fundamental objections to which it is open.

If the ultimate test of truth is not that here alleged, then what is the ultimate test of truth? And if there is no ultimate test of truth, then what is the warrant for accepting certain propositions and rejecting others? An opponent who denies the validity of this test, may legitimately decline to furnish any test himself, so long as he does not affirm any thing to be true; but if he affirms some things to be true and others to be not true, his warrant for doing so may fairly be demanded. Let us glance at the possible response to the demand. If asked why he holds it to be unquestionably true that two quantities which differ in unequal degrees from a third quantity are themselves unequal, two replies seem open to him: he may say that this is an ultimate fact of con­scious­ness, or that it is an induction from personal experiences. The reply that it is an ultimate fact of con­scious­ness, raises the question, How is an ultimate fact of con­scious­ness distinguished? All beliefs, all conclusions, all imaginations even, are facts of con­scious­ness; and if some are to be accepted as beyond question because ultimate, while others are not to be accepted as beyond question because not ultimate, there comes the inevitable inquiry respecting the test of ultimacy. On the other hand, the reply that this truth is known only by induction from personal experiences, suggests the query—On what warrant are personal experiences asserted? The testimony of experience is given only through memory; and its worth depends wholly on the trustworthiness of memory. Is it, then, that the trustworthiness of memory is less open to doubt than the immediate con­scious­ness that two quantities must be unequal if they differ from a third quantity in unequal degrees? This can scarcely be alleged. Memory is notoriously uncertain. We sometimes suppose ourselves to have said things which it turns out we did not say; and we often forget seeing things which it is proved we did see. We speak of many passages of our lives as seeming like dreams; and can vaguely imagine the whole past to be an illusion. We can go much further toward conceiving that our recollections do not answer to any actualities, than we can go toward conceiving the non-existence of Space. But even supposing the deliverances of memory to be above criticism, the most that can be said for the experiences to which memory testifies, is that we are obliged to think we have had them—cannot conceive the negation of the proposition that we have had them; and to say this is to assign the warrant which is repudiated.

A further counter-criticism may be made. Throughout the argument of pure Empiricism, it is tacitly assumed that there may be a Philosophy in which nothing is asserted but what is proved. It proposes to admit into the coherent fabric of its conclusions, no conclusion that is incapable of being established by evidence; and it thus takes for granted that not only may all derivative truths be proved, but also that proof may be given of the truths from which they are derived, down to the very deepest. The result of thus refusing to recognize some fundamental unproved truth, is simply to leave its fabric of conclusions without a base. The giving proof of any special proposition, is the assimilation of it to some class of propositions known to be true. If any doubt arises respecting the general proposition which is cited in justification of this special proposition, the course is to show that this general proposition is deducible from a proposition or propositions of still greater generality; and if pressed for proof of each such still more general proposition, the only resource is to repeat the process. Is this process endless? If so, nothing can be proved—the whole series of propositions depends on some unassignable proposition. Has the process an end? If so, there must eventually be reached a widest proposition—one which cannot be justified by showing that it is included by any wider—one which cannot be proved. Or to put the argument otherwise: Every inference depends on premises; every premise, if it admits of proof, depends on other premises; and if the proof of the proof be continually demanded, it must either end in an unproved premise, or in the acknowledgment that there cannot be reached any premise on which the entire series of proofs depends. Hence Philosophy, if it does not avowedly stand on some datum underlying reason, must acknowledge that it has nothing on which to stand.

The expression of divergence from Mr. Mill on this fundamental question, I have undertaken with reluctance, only on finding it needful, both on personal and on general grounds, that his statements and arguments should be met. For two reasons, especially, I regret having thus to contend against the doctrine of one whose agreement I should value more than that of any other thinker. In the first place, the difference is, I believe, superficial rather than substantial; for it is in the interests of the Ex­per­i­ence-Hy­poth­e­sis that Mr. Mill opposes the alleged criterion of truth; while it is as harmonizing with the Ex­per­i­ence-Hy­poth­e­sis, and reconciling it with all the facts, that I defend this criterion. In the second place, this lengthened exposition of a single point of difference, unaccompanied by an exposition of the numerous points of concurrence, unavoidably produces an appearance of dissent very far greater than that which exists. Mr. Mill, however, whose unswerving allegiance to truth is on all occasions so conspicuously displayed, will fully recognize the justification for this utterance of disagreement on a matter of such profound importance, philosophically considered; and will not require any apology for the entire freedom with which I have criticised his views while seeking to substantiate my own.