Essays: Scientific, Political, and Speculative, Volume II

In additional justification of the hypothesis, I will only point out that voltaic electricity seems to admit of a kindred interpretation. For any molecular re-arrangement, such as occurs in a chemical decomposition and recombination, implies that the movements of the molecules concerned are mutually perturbed; and their perturbations must conform to the general law already described: the molecules must derange one another’s motions in equal and opposite ways, and so must generate plus and minus derangements that cancel when brought into relation.

Of course I suggest this view simply as one occurring to an outsider. Unquestionably it presents difficulties; as, for instance, that no manifest explanation is yielded by it of electric attractions and repulsions. And there are doubtless objections not obvious to me that will at once strike those to whom the facts are more familiar. The hypothesis must be regarded as speculative; and as set down on the chance that it may be worth consideration.

Since the foregoing postscript was put in type, I have received criticisms upon it, oral and written, from several leading electricians and physicists; and I have profited by them to amend parts of the exposition. While I have remained without endorsements of the hypothesis, the objections raised have not been such as to make clear its untenability.

On one point an addition seems needful to exclude a misconstruction apt to arise. The description of the mutually-produced molecular perturbations, opposite in their kinds, as resulting in waves that are propagated away from the place of disturbance, and that cancel when brought into relation, is met by the criticism that waves, proceeding in opposite directions and meeting, do not mutually cancel, but, passing one another, proceed onwards. There are, however, two respects in which the parallelism does not hold, between the waves referred to and the waves I have described, which perhaps cannot rightly be called waves. The waves referred to, as those on the surface of a liquid, are such that each consists of two opposite deviations from a mean state. Each shows excess and defect. A series of them is a series of plus and minus divergences; and if two such series meet one another, they do not cancel. But there is no analogy between this case and a case in which the whole effect propagated in one direction is a plus motion, and the whole effect propagated in the opposite direction is a minus motion – that is, plus and minus changes in other motions. These, if equal in amount, will cancel when they meet. If one is a continual addition to motion in a certain direction, and the other a corresponding subtraction from motion in that direction, the two, when added together, must produce zero. From another point of view the absence of parallelism between the two cases may be equally well seen. Waves of the kinds instanced as not cancelling one another, are waves produced by some force foreign to the medium exhibiting them – an extrinsic force. Hence, proceeding from the place of initiation, they are necessarily, considered in their totalities, positive in whatever directions they travel; and hence, too, when conducted round so as to meet, an exaggerated perturbation will result. But in the simplest of the cases here dealt with (that of contact-electricity) the perturbation is not of extrinsic origin, but of intrinsic origin. There is no external activity at the expense of which the quantity of motion in the disturbed matter is positively increased. The activity, being such only as is internally possessed, can generate no more motion than already exists; and therefore whatever gain of motion arises anywhere in the molecules must be at the cost of an equal loss elsewhere. Here perturbation cannot be a plus motion in all directions from the place of initiation; but any plus motion continually generated can result only from an equal and opposite minus motion continually generated; and the mutual cancelling becomes a corollary from the mutual genesis.

In the course of the discussions which I have had, the following way of presenting the argument has occurred to me.

1. Two homogeneous bodies are rubbed together and there results heat: the interpretation being that the molar motion is transformed into molecular motion. Here motion produces motion – the form only being changed.

2. Now of the two bodies one is replaced by a body unlike in nature to the other, and they are again rubbed. Again a certain amount of heat is produced: some of the molar motion is, as before, transformed into molecular motion. But, at the same time, another part of the molar motion is changed into – what? Surely not a fluid, a substance, a thing. It cannot be that what in the first case produces a change of state , in the second case produces an entity. And in the second case itself, it cannot be that while part of the original motion becomes changed into another species of motion, part of it becomes changed into a species of matter.

3. Must we not say, then, that if, when the two bodies rubbed are homogeneous, sensible motion is transformed into insensible motion, when they are heterogeneous, sensible motion must still be transformed into insensible motion: such difference of nature as this insensible motion has, being consequent on the difference of nature between the two kinds of molecules acting on one another?

4. If, when the two masses are homogeneous, those molecules which compose the two rubbed surfaces disturb one another, and increase one another’s oscillations; then, when the two masses are heterogeneous, those molecules forming the two rubbed surfaces must also disturb one another in some way – increase one another’s agitations.

5. If, when the two sets of molecules are alike in kind, the mutual disturbance is such that they simply increase the amplitudes of one another’s oscillations, and do this because their times correspond; then, must it not be that when they are unlike in kind, the mutual disturbance will involve a differential action consequent on the unlikeness of their motions? Must not the discord of the oscillations produce a result which cannot be produced when the oscillations are concordant – a compound form of molecular motion?

6. If masses of relatively-simple molecules, placed in apposition and made to act on one another, cause such effects; then must we not say that effects of the same class, but of a different order, will be caused by the mutual actions, not of the molecules as wholes, but of their constituents? If the rubbed surfaces severally consist of highly-compounded molecules – each containing, it may be, several hundreds of minor molecules, united into a definitely-arranged cluster; then, while the molecules as wholes affect one another’s motions, must we not infer that the constituents of the one class will affect the constituents of the other class in their motions? While the molecules as wholes increase one another’s oscillations, or derange one another’s oscillations, or both, the components of them cannot be so stably arranged that members of the one group are wholly inoperative on members of the other group. And if they are operative, then there must be a compound form of molecular motion which arises when masses of highly-compounded molecules of unlike kinds, are made to act on one another.

With this series of propositions and questions, I leave the suggestion to its fate; merely remarking that, setting out with the principles of molecular physics now accepted, it seems difficult to avoid the implication that some actions of the kinds described take place, and that there result from them some classes of phenomena – phenomena which, if not those we call electrical, remain to be identified.

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.