The Online Library of Liberty

A project of Liberty Fund, Inc.

• Preface.
• Part I.: Special Analysis.
• Chapter I.: A Datum Wanted.
• Chapter II.: The Universal Postulate.
• Chapter III.: Its Corollaries.
• Chapter IV.: Our Present Position.
• Part II.: Special Analysis.
• Chapter I.: Compound Quantitative Reasoning.
• Chapter II.: Compound Quantitative Reasoning (continued).
• Chapter III.: Imperfect and Simple Quantitative Reasoning.
• Chapter IV.: Quantitative Reasoning In General.
• Chapter V.: Perfect Qualitative Reasoning.
• Chapter VI.: Imperfect Qualitative Reasoning.
• Chapter VII.: Reasoning In General.
• Chapter VIII.: Classification, Naming, and Recognition.
• Chapter IX.: The Perception of Special Objects.
• Chapter X.: The Perception of Body As Presenting Dynamical, Statico-dynamical, and Statical Attributes. ∗
• Chapter XI.: The Perception of Body As Presenting Statico-dynamical and Statical Attributes.
• Chapter XII.: The Perception of Body As Presenting Statical Attributes.
• Chapter XIII.: The Perception of Space.
• Chapter XIV.: The Perception of Time.
• Chapter XV.: The Perception of Motion.
• Chapter XVI.: The Perception of Resistance.
• Chapter XVII.: Perception In General.
• Chapter XVIII.: The Relations of Similarity and Dissimilarity.
• Chapter XIX.: The Relations of Cointension and Non-cointension.
• Chapter XX.: The Relations of Coextension and Non-coextension.
• Chapter XXI.: The Relations of Coexistence and Non-coexistence.
• Chapter XXII.: The Relations of Connature and Non-connature.
• Chapter XXIII.: The Relations of Likeness and Unlikeness.
• Chapter XXIV.: The Relation of Sequence.
• Chapter XXV.: Consciousness In General.
• Chapter XXVI.: Results.
• Part III.: General Synthesis.
• Chapter I.: Method.
• Chapter II.: Connexion of Mind and Life.
• Chapter III.: Proximate Definition of Life.
• Chapter IV.: The Correspondence Between Life and Its Circumstances.
• Chapter V.: The Degree of Life Varies As the Degree of Correspondence.
• Chapter VI.: The Correspondence As Direct and Homogeneous.
• Chapter VII.: The Correspondence As Direct But Heterogeneous.
• Chapter VIII.: The Correspondence As Extending In Space.
• Chapter IX.: The Correspondence As Extending In Time.
• Chapter X.: The Correspondence As Increasing In Speciality.
• Chapter XI.: The Correspondence As Increasing In Generality.
• Chapter XII.: The Correspondence As Increasing In Complexity.
• Chapter XIII.: The Co-ordination of Correspondences.
• Chapter XIV.: The Integration of Correspondences.
• Chapter XV.: The Correspondences In Their Totality.
• Part IV.: Special Synthesis.
• Chapter I.: The Nature of Intelligence.
• Chapter II.: The Law of Intelligence.
• Chapter III.: The Growth of Intelligence.
• Chapter IV.: Reflex Action.
• Chapter V.: Instinct.
• Chapter VI.: Memory.
• Chapter VII.: Reason.
• Chapter VIII.: The Feelings.
• Chapter IX.: The Will.

CHAPTER II.

THE UNIVERSAL POSTULATE.

§ 5. When we try to reduce the genesis of our knowledge to scientific ordination, and when to this end we search for the fundamental fact—the fact on which all knowledge depends—we meet the difficulty that there are several facts apparently answering to this description. Personal existence, the existence of ideas, of consciousness, of beliefs—these look equally primordial. Each seems to presuppose one or more of the others; and yet each in turn may be assigned with some plausibility as the basis of the others. Personal existence may be held the most certain fact of all. Yet it may be argued, that personal existence is merely a belief; and that the existence of beliefs is, therefore, more certain than personal existence. To which again there is the reply that a belief implies something believed; and that this something believed must be antecedent to, and more certain than, the belief. All things are resolvable into ideas, is another position for which much may be said. But this position is liable to the criticism that ideas presuppose something to take cognizance of them—a consciousness; and that, all ideas being states of consciousness, the existence of consciousness must be prior to the existence of ideas. In rejoinder to which it is urged, that we become conscious only by the reception of ideas; and hence that there must be an idea before there can be consciousness. If it be said that ideas and consciousness must be classed amongst beliefs—that we have no other proof of their existence than that we believe them to exist—there comes the answer that beliefs are themselves ideas or states of consciousness; and this again may be met by saying that the conclusion that beliefs are states of consciousness is itself a belief. Thus we are driven from one position to another, only that we may relinquish that for a third; until there appears no alternative but to assume these facts to be equally fundamental—to lie on the same plane, either as mutually dependent facts, or as different aspects of the same fact.

On carefully reconsidering the matter, however, we may perceive that be the genesis of these facts simultaneous or successive, and if successive whatever be the order, there is still one of them which being unavoidably taken for granted, in every process of thought, must necessarily have priority of the others; namely, belief. Every logical act of the intellect is a predication—is an assertion that something is; and this is what we call belief. Each major premiss is a belief; each minor premiss is a belief; each conclusion is a belief. An argument is a series of dependent beliefs. Hence all connected thought being made up of beliefs, it is clear that be the propositions it embodies what they may—be they even the existence of consciousness, of ideas, of personality—they must be less certain than the existence of beliefs.

Or to state the matter in another form—Belief is the recognition of existence—is a knowing of the existent from the non-existent. All our reasoning is a distinguishing of truth from error—of that which exists from that which does not. Consequently upon the reality of the distinction we make between that which is, and that which is not; or, in other words—on the reality of belief; depends the possibility of reasoning. We may deny all other things, and yet leave our logical forms intact. But deny beliefs, and not only do the things about which we argue disappear; argument itself disappears. Now the thing which being abolished carries everything else with it must be the fundamental thing.

It may seem very clear that in order of genesis, belief is not primary but secondary. It may be plausibly urged that it is a particular state of the ego, and must therefore exist subsequently to the ego; or that it is a complex idea, dependent upon, and arising out of, simple ideas; or that it is not an idea at all, but a peculiarity in certain of our ideas. But cogent as may be the arguments brought in support of these propositions, they cannot touch the conclusion above drawn. For each of these propositions is itself a belief; and each of the reasons given in proof of it is a belief. Dig down as deep as we may, we can never get to anything beyond beliefs; seeing that the deepest thing we reach becomes a belief at the moment of its disclosure, and for logical purposes can never be anything else. Let it be granted, for argument's sake, that all our beliefs are predications concerning pre-existing things—sensations, ideas, consciousness; let it be granted that until these exist there can be no predications about them,—no beliefs; let it be granted, that in reasoning or in forming beliefs, we, as it were, look down upon these sensations and ideas, and observe certain of their properties, which we could not do unless they were previously there—let all this be granted: it nevertheless remains true, that as the reasoning faculty can deal with no facts until they are cognized by it—as until they are cognized by it they are to it non-existent—it follows that in being cognized, that is, in becoming beliefs, they begin to exist relatively to our reason. Whether really pre-existent or not they can have no logical pre-existence; since the being perceived to exist is the being believed.

Hence, belief is the fact which, to our intellects, is antecedent to, and inclusive of, all other facts. It is the form in which every fact must present itself to us, and therefore underlies every fact. It alone of all things cannot be denied without direct self-contradiction. The propositions—there is no consciousness, there are no ideas, there is no personal identity, may be absurd; but they are not immediately self-destructive. To say, however—there is no belief, is to utter a belief which denies itself—is to draw a distinction between that which is, and that which is not, and at the same time to say that we do not distinguish between that which is, and that which is not.

Belief, then, being the ultimate fact which we can never transcend, there next come the questions—How do we class our beliefs? Why do we consider certain of our beliefs more trustworthy than others? What is the peculiarity of those beliefs which we never question, and to which all the rest of our beliefs defer?

To give any psychological answer—to discuss Hume's theory of belief or any other, would be beside the argument. No concrete analysis of belief is possible without taking for granted ideas, or consciousness, or personal identity; and to do this would be to involve in our desired test of credibility some of the cognitions which are to be tested by it. At present our assumptions are limited to three—existence, its correlative non-existence, and a cognition of the difference, that is—belief. The problem is to find a canon of belief without assuming anything further. For if, in classing our beliefs according to their degrees of validity, some fourth thing should be taken for granted, the existence of such degrees of validity could have no greater certainty than the existence of this fourth thing.

Existence, non-existence, and belief, being thus the terms to which we are confined, there is clearly no alternative but to define different kinds of belief by qualities expressible in the other two terms. At first sight this appears hopeless; for whilst there can be existent beliefs, there cannot be non-existent beliefs. But though it seems paradoxical to say so, we may, by the union of the two terms existence and non-existence, obtain a third which describes the nature of some of our beliefs as contrasted with others. Here at least is the only possible classification—that into beliefs of which existence alone can be predicated, and beliefs of which partly existence and partly non-existence can be predicated—beliefs that invariably exist, and beliefs that do not invariably exist. That this division really corresponds with our experience scarcely needs saying. All know that, on the one hand, they have beliefs which are constant and which no mental effort can for a moment rid them of; whilst on the other they have beliefs which are not only changed by evidence, but which can be temporarily suppressed by the imagination.

To say that as a corollary from this, the invariable existence of a belief is our final test of certainty—to say that where there are conflicting propositions, one of which corresponds to an invariably existent belief, whilst the other does not, we must adopt the one that so corresponds, is needless—is in fact a truism. For an invariably existent belief is, by virtue of its being one, incapable of being replaced by any other. It is not that we ought to adopt that belief, but that we can do nothing else. In saying that it is invariably existent we say that there is no alternative belief.

That its invariable existence is the ultimate guarantee assignable for any belief, is, indeed, a conclusion which may be otherwise arrived at. For when we assign for any belief, a deeper belief on which it rests—when as warrant for some belief A, we cite some fundamental belief B which involves it, and say that we hold the belief A because it is implied in the belief B, it is manifest that the validity of the warrant depends upon the validity of the belief that B does involve A; and for this belief we have no other reason to assign but that it exists. So that supposing we knew the belief B to possess absolute truth, it could never give to the consequent belief A any higher guarantee than this of invariable existence; seeing that we can produce no higher guarantee for our belief that the one involves the other.

Or perhaps the fact may be more clearly shown thus:—If we assign as a reason for any belief the belief on which it rests, and then assign for that belief an anterior one, and so on continuously, it is clear that we must eventually come to the end of the series—must arrive at some primordial belief of which no proof can be given. This remains true, whatever theory we hold respecting the origin of our knowledge. For if we say that all knowledge is organized experience, and that, in assigning one belief in proof of another, we are simply assigning a wider experience in proof of a narrower, it is clear that we cannot continue to assign wider and wider experiences in proof of each other, without arriving finally at the widest. As our experience had a beginning, it follows that, in tracing it backwards, we must ultimately come to our first or deepest experience—an experience which has no other to rest upon. Similarly with the hypothesis of fundamental ideas. An analytical examination of beliefs must eventually bring us down to these; and for these the hypothesis itself implies that no reason is assignable. Hence, whether our lowest beliefs be innate or derived from experience, it is equally clear that, as they do not admit of proof, we can but say that they invariably exist. And whilst this fact of their invariable existence is alone our warrant for them, it at the same time expresses the necessity we are under of holding them.

It results, then, from all that has been said,—first, that the existence of beliefs is the fundamental fact; and second, that beliefs which invariably exist are those which, both rationally and of necessity, we must adopt.

§ 6. For the further development of these conclusions into the specific datum we are in search of, another element is needful; and I cannot more conveniently bring this into view than by some comments upon the controversy that has lately been carried on respecting the nature and origin of necessary truths.

In his “Philosophy of the Inductive Sciences,” Dr. Whewell defines necessary truths as “those in which we not only learn that the proposition is true, but see that it must be true; in which the negation of the truth is not only false, but impossible; in which we cannot, even by an effort of imagination, or in a supposition, conceive the reverse of that which is asserted.” Or, to quote the abridged form to which Mr. Mill, in his criticism, reduces it—“A necessary truth is a proposition the negation of which is not only false but inconceivable.”

The first thing to be said of this definition is, that it includes many other truths than those called “necessary.” His personal existence is a truth which every man can cite this warrant for. To his consciousness it is a truth of which the negation is inconceivable. That he might not exist he can conceive well enough; but that he does not exist he finds it impossible to conceive. The pain felt on plunging the hand into scalding water, is a pain which the sufferer cannot, “by an effort of imagination,” conceive non-existent. Were the existence of the pain a truth of which the negation was conceivable, he would quickly conceive the negation, and thus rid himself of the pain. But so convenient a mode of obtaining relief, the sufferer finds, to his cost, impracticable. Unless, therefore, the propositions—“I exist,” “I feel pain,” and others like them, be classed as necessary truths, the definition will not hold. Doubtless there is a wide difference between the universal truths which Dr. Whewell has in view, and the particular truths here instanced; but the difference is not that implied in his definition.

This fact, that the truths of immediate perception have the same warrant as the so-called necessary truths, is quite in harmony with, and, indeed, serves to confirm, the arguments which Mr. Mill brings forward to disprove the alleged à priori character of these necessary truths. But whilst agreeing with him in the belief that axioms are simply “our earliest inductions from experience,” it is possible to differ from him widely as to the worth of the test of inconceivableness. In attacking the theory I think he has needlessly undervalued the witness. He says:—

“I cannot but wonder that so much stress should be laid on the circumstance of inconceivableness, when there is ample experience to show that our capacity or incapacity of conceiving a thing has very little to do with the possibility of the thing in itself; but is, in truth, very much an affair of accident, and depends on the past history and habits of our own minds…. When we have often seen and thought of two things together, and have never, in any one instance, either seen or thought of them separately, there is, by the primary law of association, an increasing difficulty, which may, in the end, become insuperable, of conceiving the two things apart…. There are remarkable instances of this in the history of science: instances in which the most instructed men rejected as impossible, because inconceivable, things which their posterity, by earlier practice and longer perseverance in the attempt, found it quite easy to conceive, and which everybody now knows to be true.”—“System of Logic,” pp. 265, 266.

And he then proceeds to give sundry illustrations showing this dependence of conceivability upon experience—illustrations, however, which, as will hereafter be shown, are not altogether unobjectionable.

Granting, nevertheless, that the evidence assigned affords sufficient disproof of the doctrine that truths of which the negation is inconceivable are à priori, it does not really warrant Mr. Mill's inference that it is absurd “to reject a proposition as impossible on no other ground than its inconceivableness;” however much it may seem to warrant him. For the facts cited simply go to show that men have mistaken for inconceivable things, some things which were not inconceivable—a species of error which, if it vitiates the test of inconceivableness, must similarly vitiate all tests whatever. We consider an inference logically drawn from established premisses to be true. Yet, in millions of cases, men have been wrong in the inferences they have thought thus drawn. Do we, therefore, argue that it is absurd to consider an inference true “on no other ground” than that it is logically drawn from established premisses? No; we say that though men may have taken for logical inferences, inferences that were not logical, there nevertheless are logical inferences, and that we are justified in assuming the truth of what seem to us such, until better instructed. Similarly, though men may have thought some things inconceivable which were not so, there may still be inconceivable things; and the inability to conceive the negation of a thing, may still be our best warrant for believing it.

Conceding the entire truth of Mr. Mill's position, that, during any phase of human progress, the ability or inability to form a specific conception wholly depends on the experiences men have had; and that, by a widening of their experiences, they may, by and by, be enabled to conceive things before inconceivable to them; it may still be argued that as, at any time, the best warrant men can have for a belief is the perfect agreement of all pre-existing experience in support of it, it follows that, at any time, the inconceivableness of its negation is the deepest test any belief admits of. Though occasionally it may prove an imperfect test, yet, as our most certain beliefs are capable of no better, to doubt any one belief because we have no higher guarantee for it, is really to doubt all beliefs.

Or to state the case in another form—If all our knowledge is derived from experience, then our notions of possible and impossible are derived from experience. Possible means—not at variance with our experience; impossible means—wholly at variance with our experience. Clearly, unless we possess fundamental ideas, or can gain a knowledge of things in themselves, no logical process can give to the notion, impossible, any larger meaning than this. But if, at any time, the inability of men to conceive the negation of a given proposition simply proves that their experience, up to that time, has, without exception, confirmed such proposition; then when they assert that its untruth is impossible, they really assert no more than when they assert that its negation is inconceivable. If, subsequently, it turn out that the proposition is untrue; and if it be therefore argued that men should not have held its untruth impossible because inconceivable, I reply, that to say this, is to condemn the use of the word impossible altogether. If the inconceivability of a thing be considered insufficient warrant for asserting its impossibility, it is implied that there can exist a sufficient warrant; but such warrant, whatever its kind, must be originally derived from experience; and if further experience may invalidate the warrant of inconceivableness, further experience may invalidate any warrant on which we assert impossibility. Therefore, we should call nothing impossible.

It is, indeed, surprising that so acute a critic as Mr. Mill should not have seen that his own analysis supplies the best justification of this test of inconceivableness. What is the object of any such test? To insure a correspondence between subjective beliefs and objective facts. Well, objective facts are ever impressing themselves upon us; our experience is a register of these objective facts; and the inconceivableness of a thing implies that it is wholly at variance with the register. Even were this all, it is not clear how, if every truth is primarily inductive, any better test of truth could exist. But it must be remembered that whilst many of these facts, impressing themselves upon us, are occasional; whilst others again are very general; some are universal and unchanging. These universal and unchanging facts are, by the hypothesis, certain to establish beliefs of which the negations are inconceivable; whilst the others are not certain to do this; and if they do, subsequent facts will reverse their action. Hence if, after an immense accumulation of experiences, there remain beliefs of which the negations are still inconceivable, most, if not all of them, must correspond to universal objective facts. If there be, as Mr. Mill holds, certain absolute uniformities in nature; if these uniformities produce, as they must, absolute uniformities in our experience; and if, as he shows, these absolute uniformities in our experience disable us from conceiving the negations of them; then answering to each absolute uniformity in nature which we can cognize, there must exist in us a belief of which the negation is inconceivable, and which is absolutely true. In this wide range of cases subjective inconceivableness must correspond to objective impossibility. Further experience will produce correspondence where it may not yet exist; and we may expect the correspondence to become ultimately complete. In nearly all cases this test of inconceivableness must be valid now; and where it is not, it still expresses the net result of our experience up to the present time; which is the most that any test can do.∗

But the inconsistency into which Mr. Mill has thus fallen, is most clearly seen in the second of his two chapters on “Demonstration and Necessary Truths.”

He admits in this, the validity of proof by a reductio ad absurdum. Now what is a reductio ad absurdum unless a reduction to inconceivableness? And why, if inconceivableness be in other cases an insufficient ground for rejecting a proposition as impossible, is it a sufficient ground in this case?

Again, calling in question the necessity commonly ascribed to the deductive sciences, he says:—

“The results of these sciences are indeed necessary, in the sense of necessarily following from certain first principles, called axioms and definitions; of being certainly true, if these axioms and definitions are so. But their claim to the character of necessity in any sense beyond this….must depend on the previous establishment of such a claim in favour of the definitions and axioms themselves.”—Chapter vi.

Or, as he previously expresses the same view:—

“The only sense in which necessity can be ascribed to the conclusions of any scientific investigation, is that of necessarily following from some assumption which, by the conditions of the inquiry, is not to be questioned.”—Chapter v.

Here, and throughout the whole of his argument, Mr. Mill assumes that there is something more certain in a demonstration than in anything else—some necessary truth in the steps of our reasoning, which is not possessed by the axioms they start from. How can this assumption be justified? In each successive syllogism the dependence of the conclusion upon its premisses is a truth of which we have no other proof than the inconceivability of the negation. Unless our perception of logical truth is à priori, which Mr. Mill will not contend, it too, like our perceptions of mathematical truth, has been gained from experience. In the one case, as in the other, we have simply an induction, with which no fact has, to our knowledge, ever conflicted. And if this be an insufficient warrant for asserting the necessity of the one order of truth, it is an insufficient warrant for asserting the necessity of the other.

How complete is the parallelism may indeed be best proved from Mr. Mill's own admissions. In an earlier chapter he has endeavoured to show that by analysis of the syllogism we arrive at “a fundamental principle, or rather two principles, strikingly resembling the axioms of mathematics. The first, which is the principle of affirmative syllogisms, is, that things which coexist with the same thing, coexist with one another. The second is the principle of negative syllogisms, and is to this effect: that a thing which coexists with another thing, with which other a third thing does not coexist, is not coexistent with that third thing.” Elsewhere, if I remember rightly, he points out the remarkable analogy between this logical axiom—things which coexist with the same thing, coexist with one another—and the mathematical axiom—things which are equal to the same thing are equal to one another. Analogous, however, as they are, and similarly derived as they must be, Mr. Mill claims for the first a necessity which he denies to the last. When, as above, he asserts that the deductive sciences are not necessary, save “in the sense of necessarily following from certain first principles called axioms and definitions, of being certainly true if those axioms and definitions are so”—he assumes that whilst the mathematical axioms possess only hypothetical truth, this logical axiom involved in every step of the demonstration possesses absolute truth—that whilst the inconceivability of its negation is an imperfect guarantee for the one, it is a perfect guarantee for the other. Evidently this is an untenable position. Unless it can be shown that this truth—things which coexist with the same thing coexist with each other—has some higher warrant than the inconceivability of its negation (which cannot be shown), it must be admitted that axioms and demonstration stand on the same footing; that if necessity be denied to the one, it must be denied to the other, and, indeed, to all things whatever.

Of objections to the test of inconceivability it remains but to notice the one pointed out by Sir William Hamilton in his edition of Reid (p. 377). In proof that inconceivability is not a criterion of impossibility, he cites the fact, that “we can neither conceive, on the one hand, an ultimate minimum of space or time; nor can we, on the other, conceive their infinite divisibility. In like manner, we cannot conceive the absolute commencement of time, nor the utmost limit of space, and are yet equally unable to conceive them without any commencement or limit.” The implication being, that as there must be either minimum or no minimum, limit or no limit, one of the two inconceivable things must in each case be true. Exception might be taken to this argument on several grounds—on the ground that space and time in the abstract, are not strictly conceivable things at all in the sense that other things are: on the ground that the alleged inconceivableness of a minimum or a limit is not really of the same nature as those with which it is classed—is not due to an arrest of the conceptive power, but a baffling of it—is not an inability to put one conception in place of another, but an inability to form any conception. Moreover, it might be urged that there is no true parallelism between these cases in which both alternatives are alike inconceivable, and all other cases, in which one alternative is conceivable and the other not. Passing over these points, however, and granting, as has already been granted, that conceivableness depends on experience, and that hence, in respect to all things beyond the measure of our faculties it must ever remain an inapplicable test—granting all this, we say, Sir William Hamilton's argument may still be met. He says that inconceivability is no criterion of impossibility. Why? Because, of two propositions, one of which must be true, it proves both impossible—it proves that space cannot have a limit, because a limit is inconceivable, and yet that it must have a limit, because unlimited space is inconceivable; it proves, therefore that space has a limit and has no limit, which is absurd. How absurd? Absurd, because “it is impossible for the same thing to be and not to be.” But how do we know that it is impossible for the same thing to be and not to be? What is our criterion of this impossibility? Can Sir William Hamilton assign any other than this same inconceivability? If not, his argument is self-destructive; seeing that he assumes the validity of the test in proving its invalidity.

§ 7. Fully to comprehend this matter, and at the same time to advance a stage nearer the desired datum, it now only needs to recall the propositions awhile since established; namely, that the existence of beliefs is the fundamental fact, and that beliefs which invariably exist are those which both rationally and of necessity we must adopt. For when, to the fact that the invariable existence of a belief is the deepest warrant we can have for it, we add the further fact that we consider those beliefs true of which the negations are inconceivable, it becomes at once obvious that the inconceivability of its negation is the test by which we ascertain whether a given belief invariably exists or not.

Instinctively we recognize the truth above demonstrated, that its invariable existence is the ultimate authority for any belief; or rather, we yield to the rigorous necessity of holding any belief that does invariably exist: the fact that it invariably exists being the obverse of the fact that there is no alternative belief. But how do we ascertain that a given belief is invariably existent—that we have no alternative belief? Evidently we can do this only by trying to make such belief non-existent—by trying to put some other belief in its place; or, in other words, by trying to conceive the negation of it. When, failing by any mental effort to make it disappear, even for a moment, we say that nothing else is conceivable, and that it is therefore unquestionably true, we practically say that it is true because it is a belief which invariably exists.

What we mean by this word, true—whether we express by it an assumed correspondence between some objective fact and our subjective state, or whether it really implies nothing more than the continued existence of the belief to which it is applied, it would be out of place here to inquire. At present we have to consider the contents of the intellect solely as a system of beliefs, with a view to determine their relative validity. We have seen that beliefs must be their own sureties—that an indestructible belief can have no other warrant than its indestructibility; and what we have just found is, that the inconceivableness of its negation is simply an experimental proof of its indestructibility.

It results then, that for our primary beliefs, the fact of invariable existence tested by an abortive effort to cause non-existence, is the only reason assignable. If, in justifying those of our beliefs which rest upon other beliefs, we must ultimately come down to this as the foundation of the series, it follows that all beliefs not based upon other beliefs must rest directly on this foundation. Such we find to be the case. The truths of immediate consciousness have no other warrant. For the proposition “I am,” no one who utters it can find any proof but the invariable existence of his belief in it. And that he cannot for an instant displace this belief by any other—cannot conceive otherwise—is the only proof he can give of its invariable existence. So, too, is it with sensations. When cold, we cannot get rid of our belief in the feeling of coldness so long as that feeling continues—cannot, while cold, conceive that we are warm. Such belief, though not invariably existent in an absolute sense, is so in a relative one: it exists as long as the sensation exists. Whilst the proposition remains true, the negation of it remains inconceivable. Hence, properly understood, the belief in a sensation has the same warrant as belief in personal existence. In each case the belief invariably exists whilst its subject-matter exists—in the sensation whilst the sensation continues; in personal existence whilst personal existence continues.

And here we may recognize the real distinction between those universal truths which Dr. Whewell has supposed to stand alone in the inconceivableness of their negations, and those particular truths which we find to have the same guarantee. It is in the prevalence of the subject-matter that the difference consists. Whilst looking at the sun a man can no more conceive that he is then looking into darkness, than he can conceive the part greater than the whole. How then does the belief—this is sunlight, differ in nature from the belief—the whole is greater than its part? Simply thus; that in the one instance the antecedents of the conviction are present only on special occasions, whilst in the other they are present on all occasions. In either case subject the mind to the required antecedents, and no belief save the appropriate one is conceivable. But whilst in the first case only a single object serves for antecedent, in the other any object, real or imagined, serves for antecedent.

Not only, however, is the invariable existence of a belief our sole warrant for every truth of immediate consciousness, and for every primary generalization of the truths of immediate consciousness—every axiom; but it is our sole warrant for every demonstration. Logic is simply a systematization of the process by which we indirectly obtain this warrant for beliefs that do not directly possess it. To gain the strongest conviction possible respecting any complex fact, we either analytically descend from it by successive steps, each of which we unconsciously test by the inconceivableness of its negation, until we reach some axiom or truth which we have similarly tested; or we synthetically ascend from such axiom or truth by such steps. In either case we connect some isolated belief, with a belief which invariably exists, by a series of intermediate beliefs which invariably exist.

To prevent misapprehension on the part of those who have not much considered the matter, it may be well, as I have yet spoken only of beliefs which invariably exist, to contrast them with a belief which, though strong, does not invariably exist; especially as in doing this there will be an opportunity of clearing up the seeming confusion which some may have perceived in the last few pages between beliefs and conceptions—a seeming confusion which the abstract nature of the argument has hitherto forbidden me to notice.

We commonly regard the belief that the sun will rise to-morrow as a constant one. It may, however, for an interval be destroyed. We find that by an effort of imagination, as we call it, the sun may be supposed to explode, burn out, or in some way be prevented from appearing to-morrow; and during the time in which we are figuring to ourselves the non-appearance of the sun to-morrow, the belief that he will appear is non-existent. It is very true that this belief is quickly reproduced; but it is none the less true that it is temporarily annihilated. Possibly, indeed, it may be alleged that the belief is never really absent, but that it remains even whilst we are conceiving the event to be otherwise. This, however, is an illusion consequent upon our habit of using words without fully realizing their meanings, and so mistaking verbal propositions for real ones. On taking care that our thoughts duly respond to the expressions, we shall find that the belief in the sun's rising to-morrow consists in a mental representation of the occurrence of certain phenomena at a certain time. And if so, it is clear that we cannot conceive the event otherwise—cannot represent to ourselves the non-occurrence of the phenomena, without abolishing the representation of their occurrence; that is,—without abolishing the belief. Though in common language we speak of a belief as something separate from the conception to which it relates, yet on analysis we find that we simply express by it a certain property of such conception—its persistence. When after given antecedents there arises a state of consciousness which we can change with very little effort, we have a weak belief; when the state of consciousness is one which we can change with difficulty, we call the belief a strong one; when it is one which we find ourselves utterly unable to change, we consider it a belief of the highest order. As then in each of these cases the belief is not a something more than the state of consciousness, but merely expresses its persistence, it follows that in no case can the state of consciousness be changed, even temporarily, without the belief becoming non-existent for a corresponding period. The belief being the persistence, the persistence cannot be destroyed without the belief being destroyed. And hence the rationale of testing the invariable existence of a belief in a given proposition by the inconceivableness of its negation; seeing that the effort to conceive the negation of the proposition is the effort to change the state of consciousness which arises after certain antecedents; and if this can be done—if the persistence of the state of consciousness can be broken—the belief is thereby proved to be not invariably existent.∗

Dismissing, however, all psychological explanations, which are allowable here only as being needed to meet a psychological objection, and returning to the purely abstract view of the matter, we see—first, that belief is fundamental, and that the invariable existence of a belief is our highest warrant for it; second, that we can ascertain the invariable existence of a belief only as we ascertain the invariable existence of anything else, by observing whether under any circumstances it is absent from the place in which it occurs; third, that the effort to conceive the negation of a belief is the looking in the place in which it occurs (viz., after its antecedents), and observing whether there are any occasions on which it is absent, or can be made absent; and fourth, that when we fail to find such occasions—when we perceive that the negation of the belief is inconceivable, we have all possible warrant for asserting the invariability of its existence; and, in asserting this, we express alike our logical justification of it, and the inexorable necessity we are under of holding it. Mean what we may by the word truth, we have no choice but to hold that a belief which is proved by the inconceivableness of its negation to invariably exist, is true. We have seen that this is the assumption on which every conclusion whatever ultimately rests. We have no other guarantee for the reality of consciousness, of sensations, of personal existence; we have no other guarantee for any axiom; we have no other guarantee for any step in a demonstration. Hence, as being taken for granted in every act of the understanding, it must be regarded as the Universal Postulate.

§ 8. An appeal to this Universal Postulate as an absolute warrant for any conviction may still, however, be objected to, on the ground that, as it has on past occasions proved an insufficient warrant, it may prove so again. Beliefs that once were shown by the inconceivableness of their negations to invariably exist, have since been found untrue. And as beliefs that now possess this character may some day share the same fate, the test is clearly not an infallible one.

There is, doubtless, force in this argument, though not so much as at first appears. As we hinted when commenting on his position, the evidence cited by Mr. Mill, to show that inconceivable things may yet be true, is not strictly applicable evidence. There is a wide difference in nature between the cases in which the test has been found fallacious, and those in which we may regard it as trustworthy—a difference arising from the relative complexities of the conceptions involved. When, on receiving a sensation, the subject of it, finding himself unable to conceive that he is not receiving it, asserts that he is receiving it, it is clear that he deals only with one state of consciousness of which he simply recognizes the continued existence. On the other hand, those Greek philosophers referred to by Mr. Mill, who “could not credit the existence of antipodes”—who “were unable to conceive, in opposition to old association, the force of gravity acting upwards instead of downwards,” and who, therefore, denied that there could be men on the other side of the earth—were dealing with many states of consciousness and with the connections between them. There entered into their proposition the concepts Earth, man, distance, position, force, and the various relations of these to each other. Evidently, then, these cases differ so widely, that what may be a legitimate test in the first, may be an illegitimate one in the second. We must distinguish between those appeals to the Universal Postulate in which the act of thought is decomposable, and those in which it is undecomposable. In proportion as the number of concepts which a proposition involves is great, and the mental transitions from concept to concept are numerous, the fallibility of the test will increase; and will do this because the formation of the belief is separable into many steps, each of which involves the postulate.

And here, indeed, we get hold of the clue which leads us out of this logical maze. Let it be granted, that a belief which invariably exists, though the most certain possible to us, is yet not necessarily true. Let it be granted, that either from insufficient experience, or from non-agreement between the subjective and the objective, the inconceivable and the impossible may not correspond even within our mental range. Let it be granted, that for the validity even of a single undecomposable act of thought, the Universal Postulate is an imperfect warrant. Let all this, I say, be granted. Still, be the test fallible or not, the probability of error in any inference will increase in proportion to the number of times the truth of the test has been assumed in arriving at it. If the postulate be uniformly valid, it must yet happen that, as we are liable to mental lapsus, we shall occasionally think we have its warrant when we have not; and in each case the chances of our having done this will vary directly as the number of times we have claimed its warrant. If the postulate be not uniformly valid, then a further source of error is introduced, the effects of which vary in the same ratio. Hence, on either supposition, it follows that that must be the most certain conclusion, at which, starting from the postulate itself, we arrive by the fewest assumptions of the postulate.

We instinctively recognize this fact in our ordinary modes of proof. We hold it more certain that 2 and 2 make 4, than that 5 + 7 + 6 + 9 + 8 make 35. We find that every fresh assumption of the postulate involves some risk of error; and, indeed, where the calculation is extremely intricate, and the assumptions therefore extremely numerous, our experience teaches us that the probability that there has been a wrong assumption, is greater than the probability that there has not. So too in argument. We lose faith in a long series of steps, however logical they may seem, unless we can test the inference by appeal to fact—that is, unless we can get at the inference by a single use of the postulate.

Do we not here then discern a rigorous test of the relative validity of conflicting conclusions? Not only as judged instinctively, but as judged by a fundamental logic, that must be the most certain conclusion which involves the postulate the fewest times. We find that under any circumstances—whether the postulate be uniformly true or not, this must hold good. Here, therefore, we have a method of ascertaining the respective values of all cognitions.

§ 9. Having both reached a specific datum and found a specific method of employing that datum, the purpose of our General Analysis would seem to be fulfilled. Practically to complete that purpose, however, it will be needful to exhibit the chief corollaries which the Universal Postulate involves. Sundry fundamental questions have to be disposed of before any Special Analysis of mental phenomena can be entered upon. No rational Psychology can be constructed save on the basis of some acknowledged relation between thought and the subject-matter of thought—between mind and nature. No explanation whatever can be given of any act of intelligence, but what implicitly affirms or denies certain ontological propositions. Hence, unless some such propositions can be established, no superstructure of science is possible. This must remain true, whatever be the special character of the Psychology to be developed. Is it realistic? Its argument may be taken in flank by a denial of the externality of things. If it be any elaboration of Idealism, it takes for granted mind and personality, and is liable to sceptical criticism on these assumptions. And the sceptic's Psychology, having for foundation its “impressions and ideas,” may be brought to a stand by the assertion that these are not things but relations.

Thus then, besides the abstract datum which our canon of belief supplies, we need, before proceeding further, certain of the concrete data which that canon of belief directly guarantees. Forthwith acting on the conclusion above reached, that those are the most unquestionable propositions at which, starting from the postulate itself, we arrive by the fewest assumptions of the postulate, our first step must be to ascertain the chief truths which do immediately follow from the fundamental truth. The requisite materials having been so obtained, we may proceed safely to make use of them.

Perhaps the most convenient mode of exhibiting these primary deductions, will be by a criticism on the chief metaphysical theories, as tested by the Universal Postulate. An examination of these in their relations to this criterion—a comparison between them and the conviction to which they are opposed, as severally measured by this standard of credibility, will bring out with special distinctness the valid conclusions, by giving them the invalid ones for a foil. And we shall at the same time definitely get rid of the various vicious systems and empty speculations at present encumbering the field of investigation.

[∗]To prevent misconception it may be well to remark that, though here apparently committing myself to the experience-hypothesis in its entirety, I do not hold it in its current acceptation, any more than I so hold the antagonist hypothesis of forms of thought, which, nevertheless, contains a truth. In a future stage of the inquiry I hope to show that both these hypotheses are right in a limited sense, and both wrong in a limited sense; that they admit of reconciliation; and that the truth is expressed by their union.

[∗]The reader must be warned against the confusion that may arise from the double sense in which the word belief is commonly employed, and in which it has been unavoidably employed here also. Men habitually express a belief in a thing, and at other times they call the thing believed, a belief. I have given the word two parallel meanings; using it in the one case to describe the persistence of a state of consciousness, and in the other a persistent state of consciousness. The context will, in each case, show in which sense it is to be understood.