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Reasoning is necessarily always deductive. This was implicitly admitted by all the attempts to justify ampliative induction by demonstrating or proving its logical legitimacy, i.e., by providing a deductive interpretation of induction. The plight of empiricism consists precisely in its failure to explain satisfactorily how it is possible to infer from observed facts something concerning facts yet unobserved.
All human knowledge concerning the universe presupposes and rests upon the cognition of the regularity in the succession and concatenation of observable events. It would be vain to search for a rule if there were no regularity. Inductive inference is conclusion from premises that invariably include the fundamental proposition of regularity.
The practical problem of ampliative induction must be clearly distinguished from its logical problem. For the men who embark upon inductive inference are faced with the problem of correct sampling. Did we or did we not, out of the innumerable characteristics of the individual case or cases observed, choose those which are relevant for the production of the effect in question? Serious shortcomings of endeavors to learn something about the state of reality, whether in the mundane search for truth in everyday life or in systematic scientific research, are due to mistakes in this choice. No scientist doubts that what is correctly observed in one case must also be observed in all other cases offering the same conditions. The aim of laboratory experiments is to observe the effects of a change in one factor only, all the other factors remaining unchanged. Success or failure of such experiments presupposes, of course, the control of all the conditions that enter into their arrangement. The conclusions derived from experimentation are not based upon the repetition of the same arrangement, but upon the assumption that what happened in one case must necessarily also happen in all other cases of the same type. It would be impossible to infer anything from one case or from an innumerable series of cases without this assumption, which implies the a priori category of regularity. Experience is always the experience of past events and could not teach us anything about future events if the category of regularity were merely a vain assumption.
The panphysicalists' probability approach to the problem of induction is an abortive attempt to deal with induction without reference to the category of regularity. If we do not take account of regularity, there is no reason whatever to infer from anything that happened in the past what will happen in the future. As soon as we try to dispense with the category of regularity, all scientific effort appears useless, and the search for knowledge about what is popularly called the laws of nature becomes meaningless and futile. What is natural science about if not about the regularity in the flux of events?
Yet the category of regularity is rejected by the champions of logical positivism. They pretend that modern physics has led to results incompatible with the doctrine of a universally prevailing regularity and has shown that what has been considered by the "school philosophy" as the manifestation of a necessary and inexorable regularity is merely the product of a great number of atomic occurrences. In the microscopic sphere there is, they say, no regularity whatever. What macroscopic physics used to consider as the outcome of the operation of a strict regularity is merely the result of a great number of purely accidental elementary processes. The laws of macroscopic physics are not strict laws, but actually statistical laws. It could happen that the events in the microscopic sphere produce in the macroscopic sphere events that are different from those described by the merely statistical laws of macroscopic physics, although, they admit, the probability of such an occurrence is very small. But, they contend, the cognition of this possibility demolishes the idea that there prevails in the universe a strict regularity in the succession and concatenation of all events. The categories of regularity and causality must be abandoned and replaced by the laws of probability.8
It is true that the physicists of our age are faced with behavior on the part of some entities that they cannot describe as the outcome of a discernible regularity. However, this is not the first time that science has been faced with such a problem. The human search for knowledge must always encounter something that it cannot trace back to something else of which it would appear as the necessary effect. There is always in science some ultimate given. For contemporary physics the behavior of the atoms appears as such an ultimate given. The physicists are today at a loss to reduce certain atomic processes to their causes. One does not detract from the marvelous achievements of physics by establishing the fact that this state of affairs is what is commonly called ignorance.
What makes it possible for the human mind to orient itself in the bewildering multiplicity of external stimuli that affect our senses, to acquire what is called knowledge, and to develop the natural sciences is the cognition of an inevitable regularity and uniformity prevailing in the succession and concatenation of such events. The criterion that induces us to distinguish various classes of things is the behavior of these things. If a thing in only one regard behaves (reacts to a definite stimulus) in a way different from the behavior of other things to which it is equal in all other respects, it must be assigned to a different class.
We may look upon the molecules and the atoms the behavior of which is at the bottom of the probabilistic doctrines either as original elements or as derivatives of the original elements of reality. It does not matter which of these alternatives we choose. For in any case their behavior is the outcome of their very nature. (To say it more correctly: It is their behavior that constitutes what we call their nature) As we see it, there are different classes of these molecules and atoms. They are not uniform; what we call molecules and atoms are groups composed of various subgroups the members of each of which in some regards differ in their behavior from the members of the other subgroups. If the behavior of the members of the various subgroups were different from what it is or if the numerical distribution of subgroup membership were different, the joint effect produced by the behavior of all the members of the groups would be different too. This effect is determined by two factors: the specific behavior of the members of each subgroup and the size of subgroup membership.
If the proponents of the probabilistic doctrine of induction had acknowledged the fact that there are various subgroups of microscopic entities, they would have realized that the joint effect of the operation of these entities results in what the macroscopic doctrine calls a law admitting of no exception. They would have had to confess that we do not know today why the subgroups differ from one another in some regards and how, out of the interaction of the members of the various subgroups, the definite joint effect emerges in the macroscopic sphere. Instead of this procedure they arbitrarily ascribe to the individual molecules and atoms the faculty of choosing among various alternatives of behavior. Their doctrine does not essentially differ from primitive animism. Just as the primitives ascribed to the "soul" of the river the power to choose between quietly flowing in its customary bed or inundating the adjacent fields, so they believe that these microscopic entities are free to determine some characteristics of their behavior, e.g., the speed and the path of their movements. In their philosophy it is implied that these microscopic entities are acting beings just like men.
But even if we were to accept this interpretation, we must not forget that human action is entirely determined by the individuals' physiological equipment and by all the ideas that were working in their minds. As we do not have any reason to assume that these microscopic entities are endowed with a mind generating ideas, we must assume that what are called their choices necessarily correspond to their physical and chemical structure. The individual atom or molecule behaves in a definite environment and under definite conditions precisely as its structure enjoins it. The speed and the path of its movements and its reaction to any encounters with factors external to its own nature or structure are strictly determined by this nature or structure. If one does not accept this interpretation, one indulges in the absurd metaphysical assumption that these molecules and atoms are equipped with free will in the sense which the most radical and naive indeterminist doctrines ascribed to man.
Bertrand Russell tries to illustrate the problem by comparing the position of quantum mechanics with regard to the behavior of the atoms to that of a railroad with regard to the behavior of the people making use of its facilities. The booking-office clerk at Paddington can discover, if he chooses, what proportion of travelers from that station go to Birmingham, what proportion to Exeter, and so on, but he knows nothing of the individual reasons that lead to one choice in one case and another in another. But Russell has to admit that the cases are not "wholly analogous" because the clerk can in his nonprofessional moments find out things about human beings that they do not mention when they are taking tickets, while the physicist in observing atoms has no such advantage.9
It is characteristic of the reasoning of Russell that he exemplifies his case by referring to the mind of a subaltern clerk to whom the unvarying performance of a strictly limited number of simple operations is assigned. What such a man (whose work could be performed as well by a vending automaton) thinks about things that transcend the narrow sphere of his duties is without avail. To the promoters who took the initiative in advancing the project of the railroad, to the capitalists who invested in the company, and to the managers who administer its operations, the problems involved appear in a quite different light. They built and operate the road because they anticipate the fact that there are certain reasons that will induce a number of people to travel from one point of their route to another. They know the conditions that determine these people's behavior, they know also that these conditions are changing, and they are intent upon influencing the size and the direction of these changes in order to preserve and to increase their patronage and the enterprise's proceeds. Their conduct of business has nothing to do with a reliance upon the existence of a mythical "statistical law." It is guided by the insight that there is a latent demand for travel facilities on the part of such a number of people that it pays to satisfy it by the operation of a railroad. And they are fully aware of the fact that the quantity of service they are able to sell could be drastically reduced one day to such an extent that they would be forced to go out of business.
Bertrand Russell and all other positivists referring to what they call "statistical laws" are committing a serious blunder in commenting upon human statistics, i.e., statistics dealing with facts of human action as distinguished from the facts of human physiology. They do not take into account the fact that all these statistical figures are continually changing, sometimes more, sometimes less rapidly. There is in human valuations and consequently in human actions no such regularity as in the field investigated by the natural sciences. Human behavior is guided by motives, and the historian dealing with the past as well as the businessman intent upon anticipating the future must try to "understand" this behavior.10
If the historians and the acting individuals were not able to apply this specific understanding of their fellow men's behavior, and if the natural sciences and the acting individuals were not in a position to grasp something about the regularity in the concatenation and succession of natural events, the universe would appear to them as an unintelligible chaos and they could not contrive any means for the attainment of any ends. There would not be any reasoning, any knowledge, or any science, and there would not be any purposive influencing of environmental conditions on the part of man.
The natural sciences are possible only because there prevails regularity in the succession of external events. Of course, there are limits to what man can learn about the structure of the universe. There are unobservables and there are relations about which science up to now has not provided an interpretation. But the awareness of these facts does not falsify the categories of regularity and causality.