Now the attitude of the positivist toward this fact is that induced by its relation to the law which is subsequently discovered. It has then fallen into place in a series, and his doctrine is that all laws are but uniformities of such events. He treats the fact when it is an exception to law as an instance of the new law and assumes that the exception to the old law and the instance of the new are identical. And this is a great mistake,—the mistake made also by the neo-realist when he assumes that the object of knowledge is the same within and without the mind, that nothing happens to what is to be known when it by chance strays into the realm of conscious cognition. Any as yet unexplained exception to an old theory can happen only in the experience of an individual, and that which has its existence as an event in some one's biography is a different thing from the future instance which is not beholden to any one for its existence. Yet there are, as I indicated earlier, meanings in this exceptional event which, at least for the time, are unaffected by the exceptional character of the occurrence. For example, certain clinical symptoms by which an infectious disease is identified have remained unchanged in diagnosis since the days of Hippocrates. These characters remain as characters of the instance of the law of germ-origin when this law has been discovered. This may lead us to say that the exception which appears for the time being as a unique incident in a biography is identical with the instance of a germ-induced disease. Indeed, we are likely to go further and, in the assurance of the new doctrine, state that former exceptions can (or with adequate acquaintance with the facts could) be proved to be necessarily an instance of a disease carried by a germ. The positivist is therefore confident that the field of scientific knowledge is made up of events which are instances of uniform series, although under conditions of inadequate information some of them appear as exceptions to the statements of uniformities, in truth the latter being no uniformities at all.
That this is not a true statement of the nature of the exception and of the instance, it is not difficult to show if we are willing to accept the accounts which the scientists themselves give of their own observation, the changing forms which the hypothesis assumes during the effort to reach a solution and the ultimate reconstruction which attends the final tested solution. Wherever we are fortunate enough, as in the biographies of men such as Darwin and Pasteur, to follow a number of the steps by which they recognized problems and worked out tenable hypotheses for their solution, we find that the direction which is given to attention in the early stage of scientific investigation is toward conflicts between current theories and observed phenomena, and that since the form which these observations take is determined by the opposition, it is determined by a statement which itself is later abandoned. We find that the scope and character of the observations change at once when the investigator sets about gathering as much of the material as he can secure, and changes constantly as he formulates tentative hypotheses for the solution of the problem, which, moreover, generally changes its form during the investigation. I am aware that this change in the form of the data will be brushed aside by many as belonging only to the attitude of mind of the investigator, while it is assumed that the "facts" themselves, however selected and organized in his observation and thought, remain identical in their nature throughout. Indeed, the scientist himself carries with him in the whole procedure the confidence that the fact-structure of reality is unchanged, however varied are the forms of the observations which refer to the same entities.[35]
The analysis of the fact-structure of reality shows in the first place that the scientist undertakes to form such an hypothesis that all the data of observation will find their place in the objective world, and in the second place to bring them into such a structure that future experience will lead to anticipated results. He does not undertake to preserve facts in the form in which they existed in experience before the problem arose nor to construct a world independent of experience or that will not be subject itself to future reconstructions in experience. He merely insists that future reconstructions will take into account the old in re-adjusting it to the new. In such a process it is evident that the change of the form in the data is not due to a subjective attitude of the investigator which can be abstracted from the facts. When Darwin, for instance, found that the marl dressings which farmers spread over their soil did not sink through the soil by the force of gravity as was supposed, but that the earthworm castings were thrown up above these dressings at nearly the same rate at which they disappeared, he did not correct a subjective attitude of mind. He created in experience a humus which took the place of a former soil, and justified itself by fitting it into the whole process of disintegration of the earth's surface. It would be impossible to separate in the earlier experiences certain facts and certain attitudes of mind entertained by men with reference to these facts. Certain objects have replaced other objects. It is only after the process of analysis, which arose out of the conflicting observations, has broken up the old object that what was a part of the object, heavier-things-pushing-their way-through-soil-of-lighter-texture, can become a mere idea. Earlier it was an object. Until it could be tested the earthworm as the cause of the disappearance of the dressings was also Darwin's idea. It became fact. For science at least it is quite impossible to distinguish between what in an object must be fact and what may be idea. The distinction when it is made is dependent upon the form of the problem and is functional to its solution, not metaphysical. So little can a consistent line of cleavage between facts and ideas be indicated, that we can never tell where in our world of observation the problem of science will arise, or what will be regarded as structure of reality or what erroneous idea.
There is a strong temptation to lodge these supposititious fact-structures in a world of conceptual objects, molecules, atoms, electrons, and the like. For these at least lie beyond the range of perception by their very definition. They seem to be in a realm of things-in-themselves. Yet they also are found now in the field of fact and now in that of ideas. Furthermore, a study of their structure as they exist in the world of constructive science shows that their infra-sensible character is due simply to the nature of our sense-processes, not to a different metaphysical nature. They occupy space, have measurable dimensions, mass, and are subject to the same laws of motion as are sensible objects. We even bring them indirectly into the field of vision and photograph their paths of motion.
The ultimate elements referred to above provide a consistent symbolism for the finding and formulating of applied mathematical sciences, within which lies the whole field of physics, including Euclidian geometry as well. However, they have succeeded in providing nothing more than a language and logic pruned of the obstinate contradictions, inaccuracies, and unanalyzed sensuous stuff of earlier mathematical science. Such a rationalistic doctrine can never present in an unchanged form the objects with which natural science deals in any of the stages of its investigation. It can deal only with ultimate elements and forms of propositions. It is compelled to fall back on a theory of analysis which reaches ultimate elements and an assumption of inference as an indefinable. Such an analysis is actually impossible either in the field of the conceptual objects into which physical science reduces physical objects, or in the field of sensuous experience. Atoms can be reduced into positive and negative electrical elements and these may, perhaps do, imply a structure of ether that again invites further analysis and so on ad infinitum. None of the hypothetical constructs carry with themselves the character of being ultimate elements unless they are purely metaphysical. If they are fashioned to meet the actual problems of scientific research they will admit of possible further analysis, because they must be located and defined in the continuity of space and time. They cannot be the points and instants of modern mathematical theory. Nor can we reach ultimate elements in sensuous experience, for this lies also within a continuum. Furthermore, our scientific analyses are dependent upon the form that our objects assume. There is no general analysis which research in science has ever used. The assumption that psychology provides us with an analysis of experience which can be carried to ultimate elements or facts, and which thereby provides the elements out of which the objects of our physical world must be constructed, denies to psychology its rights as a natural science of which it is so jealous, turning it into a Berkeleyan metaphysics.
This most modern form of rationalism being unable to find ultimate elements in the field of actual science is compelled to take what it can find there. Now the results of the analysis of the classical English psychological school give the impression of being what Mr. Russell calls "hard facts," i.e., facts which cannot be broken up into others. They seem to be the data of experience. Moreover, the term hard is not so uncompromising as is the term element. A fact can be more or less hard, while an ultimate element cannot be more or less ultimate. Furthermore, the entirely formal character of the logic enables it to deal with equal facility with any content. One can operate with the more or less hard sense-data, putting them in to satisfy the seeming variables of the propositions, and reach conclusions which are formally correct. There is no necessity for scrutinizing the data under these circumstances, if one can only assume that the data are those which science is actually using. The difficulty is that no scientist ever analyzed his objects into such sense-data. They exist only in philosophical text-books. Even the psychologists recognize that these sensations are abstractions which are not the elements out of which objects of sense are constructed. They are abstractions made from those objects whose ground for isolation is found in the peculiar problems of experimental psychology, such as those of color or tone perception. It would be impossible to make anything in terms of Berkeleyan sense-data and of symbolic logic out of any scientific discovery. Research defines its problem by isolating certain facts which appear for the time being not as the sense-data of a solipsistic mind, but as experiences of an individual in a highly organized society, facts which, because they are in conflict with accepted doctrines, must be described so that they can be experienced by others under like conditions. The ground for the analysis which leads to such facts is found in the conflict between the accepted theory and the experience of the individual scientist. The analysis is strictly ad hoc. As far as possible the exception is stated in terms of accepted meanings. Only where the meaning is in contradiction with the experience does the fact appear as the happening to an individual and become a paragraph out of his biography. But as such an event, whose existence for science depends upon the acceptance of the description of him to whom it has happened, it must have all the setting of circumstantial evidence. Part of this circumstantial evidence is found in so-called scientific control, that is, the evidence that conditions were such that similar experiences could happen to others and could be described as they are described in the account given. Other parts of this evidence which we call corroborative are found in the statements of others which bear out details of this peculiar event, though it is important to note that these details have to be wrenched from their settings to give this corroborative value. To be most conclusive they must have no intentional connection with the experience of the scientist. In other words, those individuals who corroborate the facts are made, in spite of themselves, experiencers of the same facts. The perfection of this evidence is attained when the fact can happen to others and the observer simply details the conditions under which he made the observation, which can be then so perfectly reproduced that others may repeat the exceptional experience.
This process is not an analysis of a known world into ultimate elements and their relations. Such an analysis never isolates this particular exception which constitutes the scientific problems as an individual experience. The extent to which the analysis is carried depends upon the exigencies of the problem. It is the indefinite variety of the problems which accounts for the indefinite variety of the facts. What constitutes them facts in the sense in which we are using the term is their exceptional nature; formally they appear as particular judgments, being denials of universal judgments, whether positive or negative. This exceptional nature robs the events of a reality which would have belonged to them as instances of a universal law. It leaves them, however, with the rest of their meaning. But the value which they have lost is just that which was essential to give them their place in the world as it has existed for thought. Banished from that universally valid structure, their ground for existence is found in the experience of the puzzled observer. Such an observation was that of the moons of Jupiter made possible by the primitive telescope of Galileo. For those who lived in a Ptolemaic cosmos, these could have existence only as observations of individuals. As moons they had distinct meaning, circling Jupiter as our moon circles the earth, but being in contradiction with the Ptolemaic order they could depend for their existence only on the evidence of the senses, until a Copernican order could give them a local habitation and a name. Then they were observed not as the experiences of individuals but as instances of planetary order in a heliocentric system. It would be palpably absurd to refer to them as mere sense-data, mere sensations. They are for the time being inexplicable experiences of certain individuals. They are inexplicable because they have a meaning which is at variance with the structure of the whole world to which they belong. They are the phenomena termed accidental by Aristotle and rejected as full realities by him, but which have become, in the habitat of individual experience, the headstone of the structure of modern research of science.
A rationalism which relegates implication to the indefinables cannot present the process of modern science. Implication is exactly that process by which these events pass from their individual existence into that of universal reality, and the scientist is at pains to define it as the experimental method. It is true that a proposition implies implication. But the proposition is the statement of the result of the process by which an object has arisen for knowledge and merely indicates the structure of the object. In discovery, invention, and research the escape from the exceptional, from the data of early stages of observation, is by way of an hypothesis; and every hypothesis so far as it is tenable and workable in its form is universal. No one would waste his time with a hypothesis which confessedly was not applicable to all instances of the problem. An hypothesis may be again and again abandoned, it may prove to be faulty and contradictory, but in so far as it is an instrument of research it is assumed to be universal and to perfect a system which has broken down at the point indicated by the problem. Implication and more elaborated instances flow from the structure of this hypothesis. The classical illustration which stands at the door of modern experimental science is the hypothesis which Galileo formed of the rate of the velocity of a falling body. He conceived that this was in proportion to the time elapsed during the fall and then elaborated the consequences of this hypothesis by working it into the accepted mathematical doctrines of the physical world, until it led to an anticipated result which would be actually secured and which would be so characteristic an instance of a falling body that it would answer to every other instance as he had defined them. In this fashion he defined his inference as the anticipation of a result because this result was a part of the world as he presented it amended by his hypothesis. It is true that back of the specific implication of this result lay a mass of other implications, many not even presented specifically in thought and many others presented by symbols which generalized innumerable instances. These implications are for the scientist more or less implicit meanings, but they are meanings each of which may be brought into question and tested in the same fashion if it should become an actual problem. Many of them which would not have occurred to Galileo as possible problems have been questioned since his day. What has remained after this period of determined questioning of the foundations of mathematics and the structure of the world of physical science is a method of agreement with oneself and others, in (a) the identification of the object of thought, in (b) the accepted values of assent and denial called truth and falsehood, and in (c) referring to meaning, in its relation to what is meant. In any case the achievement of symbolic logic, with its indefinables and axioms has been to reduce this logic to a statement of the most generalized form of possible consistent thought intercourse, with entire abstraction from the content of the object to which it refers. If, however, we abstract from its value in giving a consistent theory of number, continuity, and infinity, this complete abstraction from the content has carried the conditions of thinking in agreement with self and others so far away from the actual problem of science that symbolic logic has never been used as a research method. It has indeed emphasized the fact that thinking deals with problems which have reference to uses to which it can be put, not to a metaphysical world lying beyond experience. Symbolic logic has to do with the world of discourse, not with the world of things.
What Russell pushes to one side as a happy guess is the actual process of implication by which, for example, the minute form in the diseased human system is identified with unicellular life and the history of the disease with the life history of this form. This identification implies reclassification of these forms and a treatment of the disease that answers to their life history. Having made this identification we anticipate the result of this treatment, calling it an inference.
Implication belongs to the reconstruction of the object. As long as no question has arisen, the object is what it means or means what it is. It does not imply any feature of itself. When through conflict with the experience of the individual some feature of the object is divorced from some meaning the relationship between these becomes a false implication. When a hypothetically reconstructed object finds us anticipating a result which accords with the nature of such objects we assert an implication of this meaning. To carry this relation of implication back into objects which are subject to no criticism or question would of course resolve the world into elements connected by external relations, with the added consequence that these elements can have no content, since every content in the face of such an analysis must be subject to further analysis. We reach inevitably symbols such as X, Y, and Z, which can symbolize nothing. Theoretically we can assume an implication between any elements of an object, but in this abstract assumption the symbolic logician overlooks the fact that he is also assuming some content which is not analyzed and which is the ground of the implication. In other words this logician confuses the scientific attitude of being ready to question anything with an attitude of being willing to question everything at once. It is only in an unquestioned objective world that the exceptional instance appears and it is only in such a world that an experimental science tests the implications of the hypothetically reconstructed object.