§5. Fallibilism, Continuity, and Evolution ¹⁾

141. All positive reasoning is of the nature of judging the proportion of something in a whole collection by the proportion found in a sample. Accordingly, there are three things to which we can never hope to attain by reasoning, namely, absolute certainty, absolute exactitude, absolute universality. We cannot be absolutely certain that our conclusions are even approximately true; for the sample may be utterly unlike the unsampled part of the collection. We cannot pretend to be even probably exact; because the sample consists of but a finite number of instances and only admits special values of the proportion sought. Finally, even if we could ascertain with absolute certainty and exactness that the ratio of sinful men to all men was as 1 to 1; still among the infinite generations of men there would be room for any finite number of sinless men without violating the proportion. The case is the same with a seven legged calf.

142. Now if exactitude, certitude, and universality are not to be attained by reasoning, there is certainly no other means by which they can be reached.

143. Somebody will suggest revelation. There are scientists and people influenced by science who laugh at revelation; and certainly science has taught us to look at testimony in such a light that the whole theological doctrine of the »Evidences« seems pretty weak. However, I do not think it is philosophical to reject the possibility of a revelation. Still, granting that, I declare as a logician that revealed truths — that is, truths which have nothing in their favor but revelations made to a few individuals — constitute by far the most uncertain class of truths there are. There is here no question of universality; for revelation is itself sporadic and miraculous. There is no question of mathematical exactitude; for no revelation makes any pretension to that character. But it does pretend to be certain; and against that there are three conclusive objections. First, we never can be absolutely certain that any given deliverance really is inspired; for that can only be established by reasoning. We cannot even prove it with any very high degree of probability. Second, even if it is inspired, we cannot be sure, or nearly sure, that the statement is true. We know that one of the commandments was in one of the Bibles printed with[out] a not in it.¹⁾ All inspired matter has been subject to human distortion or coloring. Besides we cannot penetrate the counsels of the most High, or lay down anything as a principle that would govern his conduct. We do not know his inscrutable purposes, nor can we comprehend his plans. We cannot tell but he might see fit to inspire his servants with errors. In the third place, a truth which rests on the authority of inspiration only is of a somewhat incomprehensible nature; and we never can be sure that we rightly comprehend it. As there is no way of evading these difficulties, I say that revelation, far from affording us any certainty, gives results less certain than other sources of information. This would be so even if revelation were much plainer than it is.

144. But, it will be said, you forget the laws which are known to us a priori, the axioms of geometry, the principles of logic, the maxims of causality, and the like. Those are absolutely certain, without exception and exact. To this I reply that it seems to me there is the most positive historic proof that innate truths are particularly uncertain and mixed up with error, and therefore a fortiori not without exception. This historical proof is, of course, not infallible; but it is very strong. Therefore, I ask how do you know that a priori truth is certain, exceptionless, and exact? You cannot know it by reasoning. For that would be subject to uncertainty and inexactitude. Then, it must amount to this that you know it a priori; that is, you take a priori judgments at their own valuation, without criticism or credentials. That is barring the gate of inquiry.

145. Ah! but it will be said, you forget direct experience. Direct experience is neither certain nor uncertain, because it affirms nothing — it just is. There are delusions, hallucinations, dreams. But there is no mistake that such things really do appear, and direct experience means simply the appearance. It involves no error, because it testifies to nothing but its own appearance. For the same reason, it affords no certainty. It is not exact, because it leaves much vague; though it is not inexact either; that is, it has no false exactitude.

146. All this is true of direct experience at its first presentation. But when it comes up to be criticized it is past, itself, and is represented by memory. Now the deceptions and inexactitude of memory are proverbial.

147. . . . On the whole, then, we cannot in any way reach perfect certitude nor exactitude. We never can be absolutely sure of anything, nor can we with any probability ascertain the exact value of any measure or general ratio.

This is my conclusion, after many years study of the logic of science; and it is the conclusion which others, of very different cast of mind, have come to, likewise. I believe I may say there is no tenable opinion regarding human knowledge which does not legitimately lead to this corollary. Certainly there is nothing new in it; and many of the greatest minds of all time have held it for true.

148. Indeed, most everybody will admit it until he begins to see what is involved in the admission — and then most people will draw back. It will not be admitted by persons utterly incapable of philosophical reflection. It will not be fully admitted by masterful minds developed exclusively in the direction of action and accustomed to claim practical infallibility in matters of business. These men will admit the incurable fallibility of all opinions readily enough; only, they will always make exception of their own. The doctrine of fallibilism will also be denied by those who fear its consequences for science, for religion, and for morality. But I will take leave to say to these highly conservative gentlemen that however competent they may be to direct the affairs of a church or other corporation, they had better not try to manage science in that way. Conservatism — in the sense of a dread of consequences — is altogether out of place in science — which has on the contrary always been forwarded by radicals and radicalism, in the sense of the eagerness to carry consequences to their extremes. Not the radicalism that is cocksure, however, but the radicalism that tries experiments. Indeed, it is precisely among men animated by the spirit of science that the doctrine of fallibilism will find supporters.

149. Still, even such a man as that may well ask whether I propose to say that it is not quite certain that twice two are four — and that it is even not probably quite exact! But it would be quite misunderstanding the doctrine of fallibilism to suppose that it means that twice two is probably not exactly four. As I have already remarked, it is not my purpose to doubt that people can usually count with accuracy. Nor does fallibilism say that men cannot attain a sure knowledge of the creations of their own minds. It neither affirms nor denies that. It only says that people cannot attain absolute certainty concerning questions of fact. Numbers are merely a system of names devised by men for the purpose of counting.¹⁾ It is a matter of real fact to say that in a certain room there are two persons. It is a matter of fact to say that each person has two eyes. It is a matter of fact to say that there are four eyes in the room. But to say that if there are two persons and each person has two eyes there will be four eyes is not a statement of fact, but a statement about the system of numbers which is our own creation.

150. Still, if the matter is pressed, let me ask whether any individual here present thinks there is no room for possible doubt that twice two is four?

What do you think? You have heard of hypnotism. You know how common it is. You know that about one man in twenty is capable of being put into a condition in which he holds the most ridiculous nonsense for unquestionable truth. How does any individual here know but that I am a hypnotist and that when he comes out of my influence he may see that twice two is four is merely his distorted idea; that in fact everybody knows it isn't so? Suppose the individual I am addressing to be enormously wealthy. Then I ask: »Would you, in view of this possibility — or with the possibility that you are seized with a temporary insanity, risk your entire fortune this minute against one cent, on the truth of twice two being four?« You certainly ought not to do so; for you could not go on making very many millions of such bets before you would lose! Why, according to my estimate of probabilities there is not a single truth of science upon which we ought to bet more than about a million of millions to one — and that truth will be a general one and not a special fact. People say »Such a thing is as certain as that the sun will rise tomorrow!« I like that phrase for its great moderation because it is infinitely far from certain that the sun will rise tomorrow.

151. To return to our friends the Conservatives; these ladies and gentlemen will tell me this doctrine of fallibilism can never be admitted because the consequences from it would undermine Religion. I can only say I am very sorry. The doctrine is true; — without claiming absolute certainty for it, it is substantially unassailable. And if its consequences are antagonistic to religion, so much the worse for religion. At the same time, I do not believe they are so antagonistic. The dogmas of a church may be infallible — infallible in the sense in which it is infallibly true that it is wrong to murder and steal — practically and substantially infallible. But what use a church could make of a mathematical infallibility, I fail to see. Messieurs et mesdames les conservateurs have generally taken the lead in determining what the church should say to the novelties of science; and I don't think they have managed the business with very distinguished success so far. They have begun by recoiling with horror from the alleged heresies — about the rotundity of the earth, about its rotation, about geology, about Egyptian history, and so forth — and they have ended by declaring that the church never breathed a single word against any of these truths of science. Perhaps, it be just so with fallibility. For the present those knowing in divine things insist that infallibility is the prerogative of the church, but maybe bye and bye we shall be told that this infallibility had always been taken in an ecclesiastical sense. And that will be true, too. I should not wonder if the churches were to be quite agile in reformed teachings during the coming thirty years. Even one that mainly gathers in the very ignorant and the very rich may feel young blood in its veins.

152. But doubtless many of you will say, as many most intelligent people have said, Oh, we grant your fallibilism to the extent you insist upon it. It is nothing new. Franklin said a century ago that nothing was certain. We will grant it would be foolish to bet ten years' expenditure of the United States Government against one cent upon any fact whatever. But practically speaking many things are substantially certain. So, after all, of what importance is your fallibilism?

We come then to this question: of what importance is it? Let us see.