Creative Intelligence Part 3

REFORMATION OF LOGIC

ADDISON W. MOORE

I

In a general survey of the development of logical theory one is struck by the similarity, not to say ident.i.ty, of the indictments which reformers, since the days of Aristotle, have brought against it. The most fundamental of these charges are: first, that the theory of logic has left it formal and with little significance for the advancement of science and the conduct of society; second, that it has great difficulty in avoiding the predicament of logical operations that are merely labored reproductions of non-logical activities and therefore tautologous and trifling, or of logical operations that are so far removed from immediate, non-logical experience that they are irrelevant; third, that logical theory has had trouble in finding room in its own household for both truth and error; each crowds out the other.

The ident.i.ty of these indictments regardless of the general philosophical faith, empiricism, or rationalism, realism, or idealism to which the reformer or the logic to be reformed has belonged, suggests that whatever the differences in the doctrines of these various philosophic traditions, they possess a common ground from which these common difficulties spring.

It is the conviction of a number who are at present attempting to rid logic of these ancient disabilities that their common source is to be found in a lack of continuity between the acts of intelligence (or to avoid the dangers of hypostasis, intelligent acts) and other acts; between logical conduct and other conduct. So wide, indeed, is this breach, that often little remains of the act of knowing but the name. It may still be called an act, but it has no describable instruments nor technique of operation. It is an indefinable and often mystical performance of which only the results can be stated. In recent logical discussion this techniqueless act of knowing has been properly enough transformed into an indefinable "external relation" in which an ent.i.ty called a knower stands to another ent.i.ty called the known.

For many centuries this breach between the operations of intelligence and other operations has been closed by various metaphysical devices with the result that logic has been a hybrid science,--half logic, half metaphysics and epistemology. So great has been the momentum of the metaphysical tradition that long after we have begun to discover the connection between logical and non-logical operations its methods remain to plague us. Efforts to heal the breach without a direct appeal to metaphysical agencies have been made by attempting a complete logicizing of all operations. But besides requiring additional metaphysics to effect it, the procedure is as fatal to continuity as is an impa.s.sable disjunction. Continuity demands distinction as well as connection. It requires the development, the _growth_ of old material and functions into new forms.

Driven by the difficulties of this complete logicization, which are as serious as those of isolation, logical theory was obliged to reinstate some sort of distinction. This it did by resorting to the categories of "explicit" and "implicit." All so-called non-logical operations were regarded as "implicitly" logical. And, paradoxically, logical operations had for their task the transformation of the implicit into the explicit.

An adequate account of the origin and continuance of this isolation of the conduct of intelligence from other conduct is too long a story to be told here. Suffice it to recall that in the society in which the distinction between immediate and reflective experience, between opinion and science, between percepts and universals was first made, intelligence was largely the possession of a special and privileged cla.s.s removed in great measure from hand-to-hand contact with nature and with much of society. Because it did not fully partic.i.p.ate in the operations of nature and society intelligence could not become fully domesticated, i.e., fully naturalized and socialized in its world. It was a charmed spectator of the cosmic and social drama. Doubtless when Greek intelligence discovered the distinction between immediate and reflective experience--possibly the most momentous discovery in history--"the world," as Kant says of the speculations of Thales, "must suddenly have appeared in a new light." But not recognizing the full significance of this discovery, ideas, universals, became but a wondrous spectacle for the eye of reason. They brought, to be sure, blessed relief from the bewildering and baffling flux of perception. But it was the relief of sanctuary, not of victory.

That the brilliant speculations of Greek intelligence were barren because there was no technique for testing and applying them in detail is an old story. But it is merely a restatement, not a solution, of the pertinent question. This is: why did not Greek intelligence develop such a technique? The answer lies in the fact that the technique of intelligence is to be found precisely in the details of the operations of nature and of human conduct from which an aristocratic intelligence is always in large measure shut off. Intelligence cannot operate fruitfully in a vacuum. It must be incarnate. It must, as Hegel said, have "hands and feet." When we turn to the history of modern science the one thing that stands out is that it was not until the point was reached where intelligence was ready (continuing the Hegelian figure) to thrust its hands into the vitals of nature and society that it began to acquire a real control over its operations.

In default of such controlling technique there was nothing to be done with this newly found instrument of intelligence--the universal--but to retain it as an object of contemplation and of worshipful adoration.

This involved, of course, its hypostasis as the metaphysical reality of supreme importance. With this, the only difference between "opinion" and "science" became one of the kind of objects known. That universals were known by reason and particulars by sense was of little more logical significance than that sounds are known by the ear and smells by the nose. Particulars and universals were equally given. If the latter required some abstraction this was regarded as merely auxiliary to the immediate vision, as sniffing is to the perception of odor. That universals should or could be conceived as experimental, as hypotheses, was, when translated into later theology, the sin against the Holy Ghost.

However, the fact that the particulars in the world of opinion were the stimuli to the "recollection" of universals and that the latter in turn were the patterns, the forms, for the particulars, opened the way in actual practice for the exercise of a great deal of the controlling function of the universals. But the failure to recognize this control value of the universal as fundamental, made it necessary for the universal to exercise its function surrept.i.tiously, in the disguise of a pattern and in the clumsy garb of imitation and partic.i.p.ation.

With perceptions, desires, and impulses relegated to the world of opinion and shadows, and with the newly discovered instrument of knowledge turned into an object, the knower was stripped of all his knowing apparatus and was left an empty, scuttled ent.i.ty definable and describable only as "a knower." The knower must know, even if he had nothing to know with. Hence the mystical almost indefinable character of the knowing act or relation. I say "almost indefinable"; for as an act it had, of course, to have some sort of conceptualized form. And this form vision naturally furnished. "Naturally," because intelligence was so largely contemplative, and vision so largely immediate, una.n.a.lyzed, and diaphanous. There was, to be sure, the concept of effluxes. But this was a statement of the fact of vision in terms of its results, not of the process itself. Thus it was that the whole terminology of knowing which we still use was moulded and fixed upon a very crude conception of one of the const.i.tuents of its process. There can be no doubt that this terminology has added much to the inertia against which the advance of logical theory has worked. It would be interesting to see what would be the effect upon logical theory of the subst.i.tution of an auditory or olfactory terminology for visual; or of a visual terminology revised to agree with modern scientific a.n.a.lysis of the _act_ of vision as determined by its connections with other functions.

With the act of knowing stripped of its technique and left a bare, unique, indescribable act or relation, the foundations for epistemological and metaphysical logic were laid. That Greek logic escaped the ravages of epistemology was due to the saving materialism in its metaphysical conception of mind and to the steadfastness of the aristocratic regime. But when medieval theology and Cartesian metaphysics had destroyed the last remnant of metaphysical connection between the knowing mind and nature, and when revolutions had torn the individual from his social moorings, the stage for epistemological logic was fully set. I do not mean to identify the epistemological situation with the Cartesian disjunction. That disjunction was but the metaphysical expression of the one which const.i.tutes the real foundation of epistemology--the disjunction, namely, between the act of knowing and other acts.

From this point logic has followed one of two general courses. It has sought continuity by attempting to reduce non-logical things and operations to terms of logical operations, i.e., to sensations or universals or both; or it has attempted to exclude entirely the act of knowing from logic and to transfer logical distinctions and operations, and even the attributes of truth and error to objects which, significantly enough, are still composed of these same hypostatized logical processes. The first course results in an epistemological logic of some form of the idealistic tradition, rationalism, sensationalism, or transcendentalism, depending upon whether universals, or sensations, or a combination of both, is made fundamental in the const.i.tution of the object. The second course yields an epistemological logic of the realistic type,--again, sensational or rationalistic (mathematical), or a combination of the two--a sort of realistic transcendentalism. Each type has essentially the same difficulties with the processes of inference, with the problem of change, with truth and error, and, on the ethical side, with good and evil.

With the processes of knowing converted into objects, and with the act of knowing reduced to a unique and external relation between the despoiled knower and the objects made from its own hypostatized processes, all knowing becomes in the end immediate. All attempts at an inference that is anything more than an elaborated and often confused restatement of non-logical operations break down. The a.s.sociational inference of empiricism, the subsumptive inference of rationalism, the transcendental inference of objective idealism, the a.n.a.lytical inference of neo-realism--all alike face the dilemma of an inference that is trifling or miraculous, tautologous or false. Where the knower and its object are so const.i.tuted that the only relation in which the latter can stand to the former is that of presence or absence, and if to be present is to be known, how, as Plato asked, can there be any false knowing?

For those who accept the foregoing general diagnosis the prescription is obvious. The present task of logical theory is the restoration of the continuity of the act and agent of knowing with other acts and agents.

But this is not to be done by merely furnishing the act of knowing with a body and a nervous system. If the nervous system be regarded as only an onlooking, beholding nervous system, if no connection be made between the logical operations of a nervous system and its other operations a nervous system has no logical advantage over a purely psychical mind.

It was to be expected that this movement toward restoration of continuity made in the name of "instrumental" or "experimental" logic would be regarded, alike, by the logics of rationalism and empiricism, of idealism and of realism, as an attempt to rob intelligence of its own unique and proper character; to reduce it to a merely "psychological"

and "existential" affair; to leave no place for genuine intellectual interest and activity; and to make science a series of more or less respectable adventures. The counter thesis is, that this restoration is truly a restoration--not a despoliation of the character and rights of intelligence; that only such a restoration can preserve the unique function of intelligence, can prevent it from becoming merely "existential," and can provide a distinct place for intellectual and scientific interest and activity. It does not, however, promise to remove the stigma of "adventure" from science. Every experiment is an adventure; and it is precisely the experimental character of scientific logic that distinguishes it from scholasticism, medieval or modern.

II

First it is clear that a reform of logic based upon the restoration of knowing to its connections with other acts will begin with a chapter containing an account of these other operations and the general character of this connection.[13] Logical theory has been truncated. It has tried to begin and end in the middle, with the result that it has ended in the air. Logic presents the curious anachronism of a science which attempts to deal with its subject-matter apart from what it comes from and what comes from it.

The objection that such a chapter on the conditions and genesis of the operations of knowing belongs to psychology, only shows how firmly fixed is the discontinuity we are trying to escape. As we have seen, the original motive for leaving this account of genesis to psychology was that the act of knowing was supposed to originate in a purely psychical mind. Such an origin was of course embarra.s.sing to logic, which aimed to be scientific. The old opposition between origin and validity was due to the kind of origin a.s.sumed and the kind of validity necessitated by the origin. One may well be excused for evading the question of how ideas, originated in a purely psychical mind, can, in Kant's phrase, "have objective validity," by throwing out the question of origin altogether. Whatever difficulties remain for validity after this expulsion could not be greater than those of the task of combining the objective validity of ideas with their subjective origin.

The whole of this chapter on the connection between logical and non-logical operations cannot be written here. But its central point would be that these other acts with which the act of knowing must have continuity are just the operations of our unreflective conduct. Note that it is "unreflective," not "unconscious," nor yet merely "instinctive" conduct. It is our perceptive, remembering, imagining, desiring, loving, hating conduct. Note also that we do not say "psychical" or "physical," nor "psycho-physical" conduct. These terms stand for certain distinctions in logical conduct,[14] and we are here concerned with the character of non-logical conduct which is to be distinguished from, and yet kept in closest continuity with, logical conduct.

If, here, the metaphysical logician should ask: "Are you not in this a.s.sumption of a world of reflective and unreflective conduct and affection, and of a world of beings in interaction, begging a whole system of metaphysics?" the reply is that if it is a metaphysics bad for logic, it will keep turning up in the course of logical theory as a constant source of trouble. On the other hand, if logic encounters grave difficulties when it attempts to get on without it, its a.s.sumption, for the purposes of logic, has all the justification possible.

Again it will be urged that this alleged non-logical conduct, in so far as it involves perception, memory, and antic.i.p.ation, is already cognitive and logical; or if the act of knowing is to be entirely excluded from logic, then, in so far as what is left involves objective "terms and relations," it, also, is already logical. And it may be thought strange that a logic based upon the restoration of continuity between the act of knowing and other acts should here be insisting on distinction and separation. The point is fundamental; and must be disposed of before we go on. First, we must observe that the unity secured by making all conscious conduct logical turns out, on examination, to be more nominal than real. As we have already seen, this attempt at a complete logicizing of all conduct is forced at once to introduce the distinction of "explicit" and "implicit," of "conscious and unconscious" or "subconscious" logic. Some cynics have found that this suggests dividing triangles into explicit and implicit triangles, or into triangles and sub-triangles.

Doubtless the attempt to make all perceptions, memories, and antic.i.p.ations, and even instincts and habits, into implicit or subconscious inference is an awkward effort to restore the continuity of logical and non-logical conduct. Its awkwardness consists in attempting to secure this continuity by the method of subsumptive ident.i.ty, instead of finding it in a transitive continuity of function;--instead of seeing that perception, memory, and antic.i.p.ation _become_ logical processes when they are employed in a process of inquiry, whose purpose is to relieve the difficulties into which these operations in their function as direct stimuli have fallen. Logical conduct is const.i.tuted by the cooperation of these processes for the improvement of their further operation. To regard perception, memory, and imagination as implicit forms or as sub-species of logical operation is much like conceiving the movements of our fingers and arms as implicit or imperfect species of painting, or swimming.

Moreover, this doctrine of universal logicism teaches that when that which is perfect is come, imperfection shall be done away. This should mean that when painting becomes completely "explicit" and perfect, fingers and hands shall disappear. Perfect painting will be the pure essence of painting. And this interpretation is not strained; for this logic expressly teaches that in the perfected real system all temporal elements are unessential to logical operations. They are, of course, _psychologically_ necessary for finite beings, who can never have perfectly logical experiences. But, from the standpoint of a completely logicized experience, all finite, temporal processes are accidents, not essentials, of logical operations.

The fact that the processes of perception, memory, and antic.i.p.ation are transformed in their logical operation into sensations and universals, terms, and relations, and, as such, become the subject-matter of logical theory, does not mean that they have lost their mediating character, and have become merely objects of logical contemplation at large. Sensations or sense-data, and ideas, terms and relations, are the subject-matter of logical theory for the reason that they sometimes succeed and sometimes fail in their logical operations. And it is the business of logical theory to diagnose the conditions of this success and failure. If, in writing, my pen becomes defective and is made an object of inquiry, it does not therefore lose all its character as a pen and become merely an object at large. It is _as_ an instrument of writing that it is investigated. So, sense-data, universals, terms, and relations as subject-matter of logic are investigated in their character _as_ mediators of the ambiguities and conflicts, of non-logical experience.

If the operations of habit, instinct, perceptions, memory, and antic.i.p.ation _become_ logical, when, instead of operating as direct stimuli, they are employed in a process of inquiry, we must next ask: (1) under what conditions do they pa.s.s over into this process of inquiry? (2) what modifications of operation do they undergo, what new forms do they take, and what new results do they produce in their logical operations?

If the act of inquiry be not superimposed, it must arise out of some specific condition in the course of non-logical conduct. Once more, if the alarm be sounded at this proposal to find the origin of logical in non-logical operations it must be summarily answered by asking if the one who raises the cry finds it impossible to imagine that one who is not hungry, or angry, or patriotic, or wise may become so. Non-logical conduct is not the abstract formal contradictory of logical conduct any more than present satiety or foolishness is the contradictory of later hunger or wisdom, or than anger at one person contradicts cordiality to another, or to the same person, later. The old bogie of the logical irrelevance of origin was due to the inability to conceive continuity except in the form of ident.i.ty in which there was no place for the notion of _growth_.

The conditions under which non-logical conduct _becomes_ logical are familiar to those who have followed the doctrines of experimental logic as expounded in the discussions of the past few years. The transformation begins at the point where non-logical processes instead of operating as direct unambiguous stimuli and response become ambiguous with consequent inhibition of conduct. But again this does not mean that at this juncture the non-logical processes quit the field and give place to a totally new faculty and process called reason. They stay on the job. But there is a change in the job, which now is to get rid of this ambiguity. This modification of the task requires, of course, corresponding modification and adaptation of these operations. They take on the form of sensations and universals, terms and relations, data and hypotheses. This modification of function and form const.i.tutes "reason"

or, better, reasoning.

Here some one will ask, "Whence comes this ambiguity? How can a mere perception or memory as such be ambiguous? Must it not be ambiguous to, or for, something, or some one?" The point is well taken. But it should not be taken to imply that the ambiguity is for a merely onlooking, beholding psychical mind--especially when the perception is itself regarded as an act of beholding. Nor are we any better off if we suppose the beholding mind to be equipped with a faculty of reason in the form of the principle of "contradiction." For this throws no light on the origin and meaning of ambiguity. And if we seek to make all perceptions as such ambiguous and contradictory, in order to make room for, and justify, the operations of reason, other difficulties at once beset us.

When we attempt to remove this specific ambiguity of perceptive conduct we shall be forced, before we are through, to appeal back to perception, which we have condemned as inherently contradictory, both for data and for verification.

However, the insistence that perception must be ambiguous to, or for, something beyond itself is well grounded. And this was recognized in the statement that it is equivocal as a stimulus in conduct. There need be no mystery as to how such equivocation arises. That there is such a thing as a conduct at all means that there are certain beings who have acquired definite ways of responding to one another. It is important to observe that these forms of interaction--instinct and habit, perception, memory, etc.--are not to be located in either of the interacting beings but are functions of both. The conception of these operations as the private functions of an organism is the forerunner of the epistemological predicament. It results in a conception of knowing as wholly the act of a knower apart from the known. This is the beginning of epistemology.

But to whatever extent interacting beings have acquired definite and specific ways of behavior toward one another it is equally plain--the theory of external relations notwithstanding--that in this process of interaction these ways of behavior, of stimulus and response, undergo modification. If the world consisted of two interacting beings, it is conceivable that the modifications of behavior might occur in such close continuity of relation to each of the interacting beings that the adjustment would be very continuous, and there might be little or no ambiguity and conflict. But in a world where any two interacting beings have innumerable interactions with innumerable other beings and in all these interactions modifications are effected, it is to be expected that changes in the behavior of each or both will occur, so marked that they are bound to result in breaks in the continuity of stimulus and response--even to the point of tragedy. However, the tragedy is seldom so great that the ambiguity extends to the whole field of conduct.

Except in extreme pathological cases (and in epistemology), complete skepticism and aboulia do not occur. Ambiguity always falls within a field or direction of conduct, and though it may extend much further, and must extend some further than the point at which equivocation occurs, yet it is never ubiquitous. An ambiguity concerning the action of gravitation is no less specific than one regarding color or sound; indeed, the one may be found to involve the other.

Logical conduct is, then, conduct which aims to remove ambiguity and inhibition in unreflective conduct. The instruments of its operation are forged from the processes of unreflective conduct by such modification and adaptation as is required to enable them to accomplish this end.

Since these logical operations sometimes fail and sometimes succeed they become the subject-matter of logical theory. But the technique of this second involution of reflection is not supplied by some new and unique ent.i.ty. It also is derived from modifications of previous operations of both reflective and non-reflective conduct.

While emphasizing the continuity between non-logical and logical operations, we must keep in mind that their distinction is of equal importance. Confusion at this point is fatal. A case in point is the confusion between non-logical and logical observation. The results of non-logical observation, e.g., looking and listening, are direct stimuli to further conduct. But the purpose and result of _logical_ observation are to secure data, not as direct stimuli to immediate conduct but as stimuli to the construction or verification of hypotheses which are the responses of the _logical_ operation of imagination to the data.

Hypotheses are antic.i.p.atory. But they differ from non-logical antic.i.p.ation in that they are tentatively, experimentally, i.e., logically antic.i.p.atory. The non-logical operations of memory and antic.i.p.ation lack just this tentative, experimental character. When we confuse the logical and non-logical operations of these processes the result is either that logical processes will merely repeat non-logical operations in which case we have inference that is tautologous and trifling; or the non-logical will attempt to perform logical operations, and our inference is miraculous. If we seek to escape by an appeal to habit, as in empiricism, or to an objective universal, as in idealism and neo-realism, we are merely disguising, not removing the miracle.

It may be thought that this confusion would be most likely to occur in a theory which teaches that non-logical processes are carried over into logical operations. But this overlooks the fact that the theory recognizes at the same time that these non-logical operations undergo modification and adaptation to the demands of the logical enterprise. On the other hand, those who make all perceptions, memory, and antic.i.p.ation, not to speak of habit and instinct, logical, have no basis for the distinction between logical and non-logical results; while those who refuse to give the operations of perception, memory, etc., any place in logic can make no connections between logical and non-logical conduct. Nor are they able to distinguish in a specific case truth from error.

In all logics that fail to make this connection and distinction between logical and non-logical operations there is no criterion for data. If ultimate simplicity is demanded of the data, there is no standard for simplicity except the _minimum sensibile_ or the _minimum intelligibile_ which have recently been resurrected. On the other hand, where simplicity is waived, as in the logic of objective idealism, there is still no criterion of logical adequacy. But if we understand by _logical_ data not anything that happens to be given, but something _sought_ as material for an hypothesis, i.e., a proposed solution (proposition) of an ambiguous object of conduct and affection, then whatever results of observation meet this requirement are logical data.

And whenever data are found from which an hypothesis is constructed that succeeds in abolishing the ambiguity, they are simple, adequate, and true data.

No scientist, not even the mathematician, in the specific investigations of his field, seeks for ultimate and irreducible data at large. And if he found them he could not use them. It is only in his metaphysical personality that he longs for such data. The data which the scientist in any specific inquiry seeks are the data which suggest a solution of the question in which the investigation starts. When these data are found they are the "irreducibles" of that problem. But they are relative to the question and answer of the investigation. Their simplicity consists in the fact that they are the data from which a conclusion can be made.

The term "simple data" is tautologous. That one is in need of data more "simple" means that one is in need of new data from which an hypothesis can be formed.

It is true that the actual working elements with which the scientist operates are always complex in the sense that they are always something more than elements in any specific investigation. They have other connections and alliances. And this complexity is at once the despair and the hope of the scientist; his despair, because he cannot be sure when these other connections will interfere with the allegiance of his elements to his particular undertaking; his hope, because when these alliances are revealed they often make the elements more efficient or exhibit capacities which will make them elements in some other undertaking for which elements have not been found. A general resolves his army into so many marching, eating, shooting units; but these elements are something more than marching, shooting units. They are husbands and fathers, brothers and lovers, protestants and catholics, artists and artisans, etc. And the militarist can never be sure at what point these other activities--I do not say merely external relationships--may upset his calculations. If he could find units whose whole and sole nature is to march and shoot, his problem would be, in some respects, simpler, though in others more complex. As it is, he is constantly required to ask how far these other functions will support and at what point they will rebel at the marching and shooting.

Such, in principle, is the situation in every scientific inquiry. When the failure of the old elements occurs it is common to say that "simpler" elements are needed. And doubtless in his perplexity the scientist may long for elements which have no entangling alliances, whose sole nature and character is to be elements. But what in fact he actually seeks in every specific investigation are elements whose nature and functions _will not interfere_ with their serving as units in the enterprise in hand. But from some other standpoint these new elements may be vastly more complex than the old, as is the case with the modern as compared with the ancient atom. When the elements are secured which operate successfully, the non-interfering connections can be ignored and the elements can be treated as if they did not have them,--as if they were metaphysically simple. But there is no criterion for metaphysical simplicity except operative simplicity. To be simple is to serve as an element, and to serve as an element is to be simple.

It is scarcely necessary in view of the foregoing to add that the data of science are not "sense-data," if by sense-data be meant data which are the result of the operations of sense organs alone. Data are as much or more the result of operations, first, of the motor system of the scientist's own organism, and second, of all of the machinery of his laboratory which he calls to his aid. Whether named after the way they are obtained, or after the way they are used, data are quite as much "motor" as "sense." Nor, on the other hand, are there any purely intellectual data--not even for the mathematician. Some mathematicians may insist that their symbols and diagrams are merely stimuli to the platonic operation of pure and given universals. But until mathematics can get on without these symbols or any subst.i.tutes the intuitionist in mathematics will continue to have his say.

Wherever the discontinuity between logical operations and their acts persists, all the difficulties with data have their correlative difficulties with hypotheses. In Mill's logic the account of the origin of hypotheses oscillates between the view that they are happy guesses of a mind composed of states of consciousness, and the view that they are "found in the facts" or are "impressed on the mind by the facts."

The miracle of relevancy required in the first position drives the theory to the second. And the tautologous, useless nature of the hypothesis in the second forces the theory back to the first view. In this predicament, little wonder Mill finds that the easiest way out is to make hypotheses "auxiliary" and not indigenous to inference. But this exclusion of hypotheses as essential leaves his account of inference to oscillate between the a.s.sociation of particulars of nominalism and scholastic formalism, from both of which Mill, with the dignified zeal of a prophet, set out to rescue logic.

Mill's rejection of hypotheses formed by a mind whose operations have no discoverable continuity with the operations of things, or by things whose actions are independent of the operations of ideas, is forever sound. But his acceptance of the discontinuity between the acts of knowing and the operation of things, and the conclusion that these two conceptions of the origin and nature of hypotheses are the only alternatives, were the source of most of his difficulties.