CHAPTER II

THE A PRIORI IDEA AND DOUBT IN EXPERIMENTAL REASONING

EVERYONE first works out his own ideas about what he sees and is inclined to interpret natural phenomena by anticipation before knowing them through experience. This tendency is spontaneous; a preconceived idea always has been and always will be the first flight of an investigating mind. But the object of the experimental method is to transform this a priori conception, based on an intuition or a vague feeling about the nature of things, into an a posteriori interpretation founded on the experimental study of phenomena. This is why the experimental method is also called the a posteriori method.

Man is by nature metaphysical and proud. He has gone so far as to think that the idealistic creations of his mind, which correspond to his feelings, also represent reality. Hence it follows that the experimental method is by no means primitive or natural to man, and that only after lengthy wanderings in theological and scholastic discussion has he recognized at last the sterility of his efforts in this direction. At this point man becomes aware that he cannot dictate laws to nature, because he does not contain within himself the knowledge and criterion of external things, and he understands that to find truth he must, on the contrary, study natural laws and submit his ideas, if not his reason, to experience, that is, to the criterion of facts. Yet for all that, the method of work of the human mind is not changed at bottom. The metaphysician, the scholastic, and the experimenter all work with an a priori idea. The difference is that the scholastic imposes his idea as an absolute truth which he has found, and from which he then deduces consequences by logic alone. The more modest experimenter, on the other hand, states an idea as a question, as an interpretative, more or less probable anticipation of nature, from which he logically deduces consequences which, moment by moment, he confronts with reality by means of experiment. He advances, thus, from partial to more general truths, but without ever daring to assert that he has grasped the absolute truth.

Indeed if we held it at any point whatever, we should have it everywhere; for the absolute leaves nothing outside itself.

An experimental idea, then, is also an a priori idea, but it is an idea that presents itself in the form of an hypothesis the consequences of which must be submitted to the criterion of experiment, so that its value may be tested. The experimenter's mind differs from the metaphysician's or the scholastic's in its modesty, because experiment makes him, moment by moment, conscious of both his relative and his absolute ignorance. In teaching man, experimental science results in lessening his pride more and more by proving to him every day that primary causes, like the objective reality of things, will be hidden from him forever and that he can know only relations. Here is, indeed, the one goal of all the sciences, as we shall see further on.

The human mind has at different periods of its evolution passed successively through feeling, reason and experiment. First, feeling alone, imposing itself on reason, created the truths of faith or theology. Reason or philosophy, the mind's next mistress, brought to birth scholasticism. At last, experiment, or the study of natural phenomena, taught man that the truths of the outer world are to be found ready formulated neither in feeling nor in reason. These are indispensable merely as guides; but to attain external truths we must of necessity go down into the objective reality of things where they lie hidden in their phenomenal form.

Thus, in the natural progress of things, appeared the experimental method which includes everything and which, as we shall soon see, leans successively on the three divisions of that unchangeable tripod: sentiment, reason and experiment. In the search for truth by means of this method, feeling always takes the lead, it begets the a priori idea or intuition; reason or reasoning develops the idea and deduces its logical consequences. But if feeling must be clarified by the light of reason, reason in turn must be guided by experiment.

I. EXPERIMENTAL TRUTHS ARE OBJECTIVE OR EXTERNAL

The experimental method is concerned only with the search for objective truths, not with any search for subjective truths.

As there are two kinds of functions in man's body, the first, conscious functions, the rest not, so in his mind there are two kinds of

truths or notions, some conscious, inner or subjective, the others unconscious, outer or objective. Subjective truths are those flowing from principles of which the mind is conscious, and which bring it the sensation of absolute and necessary evidence. The greatest truths, indeed, are at bottom simply a feeling in our mind; that is what Descartes meant by his famous aphorism.

We said, on the other hand, that man would never know either the primary cause, nor the essence of things. Hence truth never shows itself to his mind except in the form of a connection or of a necessary and absolute relation. But this connection may be absolute only in so far as its conditions are simple and subjective, that is, when the mind is aware of knowing them all. Mathematics embodies the relations of things in conditions of ideal simplicity. It follows that these principles or relations, once found, are accepted by the mind as absolute truths, i.e., truths independent of reality. We see now that all logical deductions in a piece of mathematical reasoning are just as certain as their principle, and that they do not require verification by experiment. That would be trying to place the senses above reason; and it would be absurd to seek to prove what is absolutely true for the mind and what it could not conceive otherwise.

But when man stops working with subjective relations, the conditions of which his mind has created, and tries to learn about the objective relations of nature which he has not created, then at once the inner and conscious criterion fails him. He is, of course, still aware that in the objective or outer world truth consists, in the same way, of necessary relations; but he lacks knowledge of the conditions of these relations. Only if he had created these conditions, indeed, could he possess absolute knowledge of them and absolute understanding.

Still man must believe that the objective relations between phenomena of the outer world might attain the certainty of subjective truths if they were reduced to a state of simplicity that his mind could completely grasp. Thus, in the study of the simplest of natural phenomena, experimental science has laid hold on certain relations which appear absolute. Such are the propositions which serve as principles in theoretical mechanics and in some branches of mathematical physics. In these sciences, indeed, we reason by logical deduction which we do not submit to experiment, because we admit, as in mathematics, that the principle being true the deductions are

true also. Still, there is a wide difference to note in this respect, that the starting point here is no longer a subjective and conscious truth, but an objective and unconscious truth, borrowed from observation or experiment. Now this truth is never more than relative to the number of experiments and observations that have been made. Even if no observation has so far disproved the truth in question, still the mind does not therefore imagine that things cannot happen otherwise; so that it is only by hypothesis that we admit the principle as absolute. That is why the application of mathematical analysis to natural phenomena, even very simple ones, may have its dangers if experimental verification is, entirely rejected. In this case, mathematical analysis becomes a blind instrument, if we do not from time to time retemper it in the furnace of experiment. I here express a thought uttered by many great mathematicians and great physicists; and in order to recall one of the most authoritative opinions in this field, I will cite what my learned associate and friend, J. Bertrand, wrote on this subject in his fine tribute to Sénarmont: "For the physicist, geometry should be only a powerful ally: when it has pushed its principles to their last consequences, it can do no more, and the uncertainty of the starting point can only be increased by the blind logic of analysis, if experiment at each step does not serve as compass and ruler."

" 1

Theoretical mechanics and mathematical physics make the connection then between mathematics proper and the experimental sciences. They include the simplest cases. But as soon as we go into physics and chemistry, and especially biology, the phenomena are complicated by so many relations that the principles, embodied in theories to which we have been able to rise, are only provisional and are so hypothetical that our deductions, even though very logical, are absolutely uncertain and can in no case dispense with experimental verification.

In short, man may relate all his reasonings to two criteria: the one, inner and conscious, is sure and absolute; the other, outer and unconscious, is experimental and relative.

When we reason about outer objects, but consider them in their relation to ourselves according to the pleasure or displeasure which they occasion us in proportion to their utility or their disadvantages,

'J. Bertrand, Eloge de M. Sénarmont, address given at the sixth annual public meeting of the Société de secours des amis des sciences.

we still possess an inner criterion in our sensations. So, when we reason about our own actions, we again have a sure guide, because we are conscious of what we are thinking and of what we are feeling. But if we wish to judge the actions of another man and to know the motives which make him act, then it is quite different. Doubtless we see before our eyes the man's movements and the acts which, we are sure, are expressions of his feeling and his will. What is more, we also admit that there is a necessary relation between actions and their cause; but what is this cause? We do not feel it ourselves, we are not aware of it as in our own case; we are therefore forced to interpret and imagine it from the movements that we see and the words that we hear. So we must verify the man's acts, one by another; we consider how he behaves in such and such circumstances, and in short, we turn to the experimental method. In like manner, when a man of science considers the natural phenomena which surround him and which he wishes to know in themselves and in their complex mutual relations of causation, every inner criterion fails him, and he is forced to invoke experiment to verify the suppositions and the reasonings that he is making about them. Experiment, then, according to Goethe's expression, becomes the one mediator between the objective and the subjective, that is to say, between the man of science and the phenomena which surround him.

2

Experimental reasoning is the only reasoning that naturalists and physicians can use in seeking the truth and approaching it as nearly as possible. Indeed, in its very character as an outer and unconscious criterion, experiment gives only relative truth, without being able to prove to the mind that it knows truth absolutely.

An experimenter facing natural phenomena is like a spectator watching a dumb show. He is in some sort the examining magistrate for nature; only instead of grappling with men who seek to deceive him by lying confessions or false witness, he is dealing with natural phenomena which for him are persons whose language and customs he does not know, persons living in the midst of circumstances unknown to him, yet persons whose designs he wishes to learn. For this purpose he uses all the means within his power. He observes their actions, their gait, their behavior, and he seeks to disengage their cause by means of various attempts, called experiments. He

1 Goethe, Œuvres d'histoire naturelle, translation by M. Ch. Martins, Introduction, p. 1.