Studies in Logical Theory Part 7

There are cases, however, where the facts seem clearly to contradict the old theory and thus give rise to a new one. For example, we find in Darwin's introduction to his _Origin of Species_ the following: "In considering the origin of species it is quite conceivable that a naturalist reflecting on the mental affinities of organic beings, on their embryological relations, their geographical distribution, geological succession, and other such facts, might come to the conclusion that species had not been independently created but had descended, like varieties, from other species." It would seem from this statement that certain data were found for which the older theory of independent creation did not offer an adequate explanation. And yet the naturalist would hardly "reflect" on all these topics in a comparative way unless some other mode of interpretation were already dawning upon him, which led him to review the accepted reflections or views.

As a more simple ill.u.s.tration, we may cite the common experience of a person who is uncertain concerning the ident.i.ty of an approaching object, say, another person. At first he may not be sure it is a person at all. He then sees that it is someone, and as the person approaches he is inclined to believe him to be an acquaintance. As the supposed acquaintance continues to approach, the observer may distinguish certain features that cause him to doubt, and then relinquish his supposition that it is an acquaintance. Or, he may conclude at once that the approaching person is another individual he knows, and the transition may be so readily made from one to the other that it would be difficult to determine whether the discordant features are discordant before the new supposition arises, or whether they are not recognized as conflicting till this second person is in mind. Or, again, the identification of the new individual and the discovery of the features that are in conflict with the first supposition may appear to go on together.

Now, marked lines of likeness appear between this relatively simple judgment and the far more involved ones of scientific research. In the more extended scientific process we find data contradicting an old theory and a new hypothesis arising to account for them. The hypothesis is tested, and along with its verification we have the rejection, or rather the modification, of the old theory. Similarly, in case of the approaching stranger all these features are present, though in less p.r.o.nounced degree. In scientific investigation there is an interval of testing by means of more careful consideration of the data and even actual experimentation. Before an explanation is accepted subject to test, a number of others may have been suggested and rejected. They may not have received even explicit recognition. In case of the identification of the stranger this feature is also present. Between two fairly definite attempts to identify the mind does not remain a mere blank or stationary, but other possible identifications may be suggested which do not have sufficient plausibility to command serious attention; they are only comparatively brief suggestions or tendencies.

It is to be noted that in all these instances the first supposition was not _entirely_ abandoned, but was modified and more exactly determined.

(Why it could not be wholly false and the new one wholly new, will be considered later in connection with discussion of the persistence and re-formation of habit.) There was such a modification of the old theory as would meet the requirements of the new data, and the new explanations thus contained both old and new features.

We have seen that the predicate of the scientific judgment is a hypothesis which is consciously applied to certain data. If the similarity between the scientific judgment and the more immediate and simple judgment is to be maintained, it is clear that the predicate of the simple judgment must be of like nature. The structure of the two varieties of judgment differs only in the degree of explicitness which the hypothesis acquires. That is, the predicate of a judgment, as such, is ideal; it is meaning, significant quality. If conditions are such as to make the one judging hesitant or doubtful the mind wavers; the predicate is not applied at once to the determination or qualification of data, and hence comes to more distinct consciousness on its own account. From being "ideal," it becomes _an_ idea. Yet its sole purpose and value remains in its possible use to interpret data. Let the idea remain detached, and let the query whether it be a true predicate (_i. e_., really fit to be employed in determining the present data) become more critical, and the idea becomes clearly a hypothesis.[57] In other words, the hypothesis is just the predicate-function of judgment definitely apprehended and regarded with reference to its nature and adequacy.

_Psychological a.n.a.lysis of judgment._--This hypothetical nature of the predicate will be even more apparent after a further psychological a.n.a.lysis, which, while applying more directly to the simpler and more immediate judgments, may be extended to the more involved ones as well.

In psychological terms, we may say, in explanation of the judging process, that some stimulus to action has failed to function properly as a stimulus, and that the activity which was going on has thus been interrupted. Response in the accustomed way has failed. In such a case there arises a division in experience into sensation content as subject and ideal content as predicate. In other words, an activity has been going on in accordance with established habits, but upon failure of the accustomed stimulus to be longer an adequate stimulus this particular activity ceases, and is resumed in an integral form only when a new habit is set up to which the new or altered stimulus is adequate. It is in this process of reconstruction that subject and predicate appear.

Sensory quality marks the point of stress, or seeming arrest, while the ideal or imaged aspect defines the continuing activity as projected, and hence that with which start is to be made in coping with the obstacle.

It serves as standpoint of regard and mode of indicated behavior. The sensation stands for the interrupted habit, while the image stands for the new habit, that is, the new way of dealing with the subject-matter.[58]

It appears, then, that the purpose of the judgment is to obtain an adequate stimulus in that, when stimulus and response are adjusted to each other, activity will be resumed. But if this reconstruction and response were to follow at once, would there be any clearly defined act of judging at all? In such a case there would be no judgment, properly speaking, and no occasion for it. There would be simply a ready transition from one line of activity to another; we should have changed our method of reaction easily and readily to meet the new requirements.

On the one hand, our subject-matter would not have become a clearly recognized datum with which we must deal; on the other hand, there would be no ideal method of construing it.[59] Activity would have changed without interruption, and neither subject nor predicate would have arisen.

In order that judgment may take place there must be interruption and suspense. Under what conditions, then, is this suspense and uncertainty possible? Our reply must be that we hesitate because of more or less sharply defined alternatives; we are not sure which predicate, which method of reaction, is the right one. The clearness with which these alternatives come to mind depends upon the degree of explicitness of the judgment, or, more exactly, the explicitness of the judgment depends upon the sharpness of these alternatives. Alternatives may be carefully weighed one against the other, as in deliberative judgments; or they may be scarcely recognized as alternatives, as in the case in the greater portion of our more simple judgments of daily conduct.

_The predicate is essentially hypothetical._--If we review in a brief resume the types of judgment we have considered, we find in the explicit scientific judgment a fairly well-defined subject-matter which we seek further to determine. Different suggestions present themselves with varying degrees of plausibility. Some are pa.s.sed by as soon as they arise. Others gain a temporary recognition. Some are explicitly tested with resulting acceptance or rejection. The acceptance of any one explanation involves the rejection of some other explanation. During the process of verification or test the newly advanced supposition is recognized to be more or less doubtful. Besides the hypothesis which is tentatively applied there is recognized the possibility of others. In the disjunctive judgment these possible reactions are thought to be limited to certain clearly defined alternatives, while in the less explicit judgments they are not so clearly brought out. Throughout the various forms of judgment, from the most complex and deliberate down to the most simple and immediate, we found that a process could be traced which was like in kind and varied only in degree. And, finally, in the most immediate judgments where some of these features seem to disappear, the same account not only appears to be the most reasonable one, but there is the additional consideration, from the psychological side, that were not the judgment of this doubtful, tentative character, it would be difficult to understand how there could be judgment as distinct from a reflex. It appears, then, that throughout, the predicate is essentially of the nature of a hypothesis for dealing with the subject-matter. And, however simple and immediate, or however involved and prolonged, the judgment may be, it is to be regarded as essentially a process of reconstruction which aims at the resumption of an interrupted experience; and when experience has become itself a consciously intellectual affair, at the restoration of a unified objective situation.

II

_Criticism of certain views concerning the hypothesis._--The explanation we have given of the hypothesis will enable us to criticise the treatment it has received from the empirical and the rationalistic schools. We shall endeavor to point out that these schools have, in spite of their opposed views, an a.s.sumption in common--something given in a fixed, or non-instrumental way; and that consequently the hypothesis is either impossible or else futile.

Bacon is commonly recognized as a leader in the reactionary inductive movement, which arose with the decline of scholasticism, and will serve as a good example of the extreme empirical position. In place of authority and the deductive method, Bacon advocated a return to nature and induction from data given through observation. The new method which he advanced has both a positive and a negative side. Before any positive steps can be taken, the mind must be cleared of the various false opinions and prejudices that have been acquired. This preliminary task of freeing the mind from "phantoms," or "eidola," which Bacon likened to the cleansing of the thres.h.i.+ng-floor, having been accomplished, nature should be carefully interrogated. There must be no hasty generalization, for the true method "collects axioms from sense and particulars, ascending continuously and by degrees, so that in the end it arrives at the most general axioms." These axioms of Bacon's are generalizations based on observation, and are to be applied deductively, but the distinguis.h.i.+ng feature of Bacon's induction is its carefully graduated steps. Others, too, had proceeded with caution (for instance Galileo), but Bacon laid more stress than they on the subordination of steps.

It is evident that Bacon left very little room for hypotheses, and this is in keeping with his aversion to antic.i.p.ation of nature by means of "phantoms" of any sort; he even said explicitly that "our method of discovery in science is of such a nature that there is not much left to acuteness and strength of genius, but all degrees of genius and intellect are brought nearly to the same level."[60] Bacon gave no explanation of the function of the hypothesis; in his opinion it had no lawful place in scientific procedure and must be banished as a disturbing element. Instead of the reciprocal relation between hypothesis and data, in which hypothesis is not only tested in experience, but at the same time controls in a measure the very experience which tests it, Bacon would have a gradual extraction of general laws from nature through direct observation. He is so afraid of the distorting influence of conception that he will have nothing to do with conception upon any terms. So fearful is he of the influence of pre-judgment, of prejudice, that he will have no judging which depends upon ideas, since the idea involves antic.i.p.ation of the fact.

Particulars are somehow to arrange and cla.s.sify themselves, and to record or register, in a mind free from conception, certain generalizations. Ideas are to be registered derivatives of the given particulars. This view is the essence of empiricism as a logical theory.

If the views regarding the logic of thought before set forth are correct, it goes without saying that such empiricism is condemned to self-contradiction. It endeavors to construct judgment in terms of its subject alone; and the subject, as we have seen, is always a co-respondent to a predicate--an idea or mental att.i.tude or tendency of intellectual determination. Thus the subject of judgment can be determined only with reference to a corresponding determination of the predicate. Subject and predicate, fact and idea, are contemporaneous, not serial in their relations (see pp. 110-12).

Less technically the failure of Bacon's denial of the worth of hypothesis--which is in such exact accord with empiricism in logic--shows itself in his att.i.tude toward experimentation and toward observation. Bacon's neglect of experimentation is not an accidental oversight, but is bound up with his view regarding the worthlessness of conception or antic.i.p.ation. To experiment means to set out from an idea as well as from facts, and to try to construe, or even to discover, facts in accordance with the idea. Experimentation not only antic.i.p.ates, but strives to make good an antic.i.p.ation. Of course, this struggle is checked at every point by success or failure, and thus the hypothesis is continuously undergoing in varying ratios both confirmation and transformation. But this is not to make the hypothesis secondary to the fact. It is simply to remain true to the proposition that the distinction and the relations.h.i.+p of the two is a thoroughly contemporaneous one. But it is impossible to draw any fixed line between experimentation and scientific observations. To insist upon the need of systematic observation and collection of particulars is to set up a principle which is as distinct from the casual acc.u.mulation of impressions as it is from nebulous speculation. If there is to be observation of a directed sort, it must be with reference to some problem, some doubt, and this, as we have seen, is a stimulus which throws the mind into a certain att.i.tude of response. Controlled observation is inquiry, it is search; consequently it must be search for something. Nature cannot answer interrogations excepting as such interrogations are put; and the putting of a question involves antic.i.p.ation. The observer does not inquire about anything or look for anything excepting as he is after something. This search implies at once the incompleteness of the particular given facts, and the possibility--that is ideal--of their completion.

It was not long until the development of natural science compelled a better understanding of its actual procedure than Bacon possessed.

Empiricism changed to experimentalism. With experimentalism inevitably came the recognition of hypotheses in observing, collecting, and comparing facts. It is clear, for instance, that Newton's fruitful investigations are not conducted in accordance with the Baconian notion.

It is quite clear that his celebrated four rules for philosophizing[61]

are in truth statements of certain principles which are to be observed in forming hypotheses. They imply that scientific technique had advanced to a point where hypotheses were such regular and indispensable factors that certain uniform conditions might be laid down for their use. The fourth rule in particular is a statement of the relative validity of hypothesis as such until there is ground for entertaining a contrary hypothesis.

The subsequent history of logical theory in England is conditioned upon its attempt to combine into one system the theories of empiristic logic with recognition of the procedure of experimental science. This attempt finds its culmination in the logic of John Stuart Mill. Of his interest in and fidelity to the actual procedure of experimental science, as he saw it, there can be no doubt. Of his good faith in concluding his _Introduction_ with the words following there can be no doubt: "I can conscientiously affirm that no one proposition laid down in this work has been adopted for the sake of establis.h.i.+ng, or with any reference for its fitness in being employed in establis.h.i.+ng, preconceived opinions in any department of knowledge or of inquiry on which the speculative world is still undecided." Yet Mill was equally attached to the belief that ultimate reality, as it is for the human mind, is given in sensations, independent of ideas; and that all valid ideas are combinations and convenient ways of using such given material. Mill's very sincerity made it impossible that this belief should not determine, at every point, his treatment of the thinking process and of its various instrumentalities.

In Book III, chap. 14, Mill discusses the logic of explanation, and in discussing this topic naturally finds it necessary to consider the matter of the proper use of scientific hypotheses. This is conducted from the standpoint of their use as that is reflected in the technique of scientific discovery. In Book IV, chap. 2, he discusses "Abstraction or the Formation of Conceptions"--a topic which obviously involves the forming of hypotheses. In this chapter, his consideration is conducted in terms, not of scientific procedure, but of general philosophical theory, and this point of view is emphasized by the fact that he is opposing a certain view of Dr. Whewell.

The contradiction between the statements in the two chapters will serve to bring out the two points already made, viz., the correspondent character of datum and hypothesis, and the origin of the latter in a problematic situation and its consequent use as an instrument of unification and solution. Mill first points out that hypotheses are invented to enable the deductive method to be applied earlier to phenomena; that it does this by suppressing the first of the three steps, induction, ratiocination, and verification. He states that:

The process of tracing regularity in any complicated, and at first sight confused, set of appearances is necessarily tentative; we begin by making any supposition, even a false one, to see what consequences will follow from it; and by observing how these differ from the real phenomena, we learn what corrections to make in our a.s.sumption.... _Neither induction nor deduction would enable us to understand even the simplest phenomena_, if we did not often commence by antic.i.p.ating the results; by making a provisional supposition, at first essentially conjectural, as to some of the very notions which const.i.tute the final object of the inquiry.[62]

If in addition we recognize that, according to Mill, our direct experience of nature always presents us with a complicated and confused set of appearances, we shall be in no doubt as to the importance of ideas as antic.i.p.ations of a possible experience not yet had. Thus he says:

The order of nature, as perceived at a first glance, presents at every instant a chaos followed by another chaos. We must decompose each chaos into single facts. We must learn to see in the chaotic antecedent a mult.i.tude of distinct antecedents, in the chaotic consequent a mult.i.tude of distinct consequents.[63]

In the next section of the same chapter he goes on to state that, having discriminated the various antecedents and consequents, we then "are to inquire which is connected with which." This requires a still further resolution of the complex and of the confused. To effect this we must vary the circ.u.mstances; we must modify the experience as given with reference to accomplis.h.i.+ng our purpose. To accomplish this purpose we have recourse either to observation or to experiment: "We may either _find_ an instance in nature _suited to our purposes_, or, by an artificial arrangement of circ.u.mstances, _make_ one" (the italics in "suited to our purpose" are mine; the others are Mill's). He then goes on to say that there is no real logical distinction between observation and experimentation. The four methods of experimental inquiry are expressly discussed by Mill in terms of their worth in singling out and connecting the antecedents and consequents which actually belong together, from the chaos and confusion of direct experience.

We have only to take these statements in their logical connection with each other (and this connection runs through the entire treatment by Mill of scientific inquiry), to recognize the absolute necessity of hypothesis to undertaking any directed inquiry or scientific operation.

Consequently we are not surprised at finding him saying that "the function of hypotheses is one which must be reckoned absolutely indispensable in science;" and again that "the hypothesis by suggesting observations and experiments puts us on the road to independent evidence."[64]

Since Mill's virtual retraction, from the theoretical point of view, of what is here said from the standpoint of scientific procedure, regarding the necessity of ideas is an accompaniment of his criticism of Whewell, it will put the discussion in better perspective if we turn first to Whewell's views.[65] The latter began by stating a distinction which easily might have been developed into a theory of the relation of fact and idea which is in line with that advanced in this chapter, and indeed in this volume as a whole. He questions (chap. 2) the fixity of the distinction between theory and practice. He points out that what we term facts are in effect simply accepted inferences; and that what we call theories are describable as facts, in proportion as they become thoroughly established. A true theory is a fact. "All the great theories which have successively been established in the world are now thought of as facts." "The most recondite theories when firmly established are accepted as facts; the simplest facts seem to involve something of the nature of theory."

The conclusion is that the distinction is a historic one, depending upon the state of knowledge at the time, and upon the att.i.tude of the individual. What is theory for one epoch, or for one inquirer in a given epoch, is fact for some other epoch, or even for some other more advanced inquirer in the same epoch. It is theory when the element of inference involved in judging any fact is consciously brought out; it is fact when the conditions are such that we have never been led to question the inference involved, or else, having questioned it, have so thoroughly examined into the inferential process that there is no need of holding it further before the mind, and it relapses into unconsciousness again. "If this greater or less consciousness of our own internal act be all that distinguishes fact from theory, we must allow that the distinction is still untenable" (untenable, that is to say, as a fixed separation). Again, "fact and theory have no essential difference except in the degree of their _certainty and familiarity_.

Theory, when it becomes firmly established and steadily lodged in the mind becomes fact." (P. 45; italics mine.) And, of course, it is equally true that as fast as facts are suspected or doubted, certain aspects of them are transferred into the cla.s.s of theories and even of mere opinions.

I say this conception might have been developed in a way entirely congruous with the position of this chapter. This would have happened if the final distinction between fact and idea had been formulated upon the basis simply of the points, "relative certainty and familiarity." From this point of view the distinction between fact and idea is one purely relative to the doubt-inquiry function. It has to do with the evolution of an experience as regards its conscious surety. It has its origin in problematic situations. Whatever appears to us as a problem appears as contrasted with a possible solution. Whatever objects of thought refer particularly to the problematic side are theories, ideas, hypotheses; whatever relates to the solution side is surety, unquestioned familiarity, fact. This point of view makes the distinctions entirely relative to the exigencies of the process of reflective transformation of experience.

Whewell, however, had no sooner started in this train of thought than he turns his back upon it. In chap. 3 he transforms what he had proclaimed to be a relative, historic, and working distinction into a fixed and absolute one. He distinguishes between sensations and ideas, not upon a genetic basis with reference to establis.h.i.+ng the conditions of further operation; but with reference to a fundamentally fixed line of demarkation between what is pa.s.sively _given_ to the mind and the _activity_ put forth by the mind. Thus he reinstates in its most generalized and fixed, and therefore most vicious, form the separation which he has just rejected. Sensations are a brute unchangeable element of fact which exists and persists independent of ideas; an idea is a mode of mental operation which occurs and recurs in an independent individuality of its own. If he had carried out the line of thought with which he began, sensation as fact would have been that residuum of familiarity and certainty which cannot be eliminated, however much else of an experience is dissolved in the inner conflict. Idea as hypothesis or theory would have been the corresponding element in experience which is necessary to redintegrate this residuum into a coherent and significant experience.

But since Whewell did not follow out his own line of thought, choosing rather to fall back on the Kantian ant.i.thesis of sense and thought, he had no sooner separated his fact and idea, his given datum and his mental relation, than he is compelled to get them together again. The idea becomes "a general relation which is imposed upon perception by an act of the mind, and which is different from anything which our senses directly offer to us" (p. 26). Such conceptions are necessary to connect the facts which we learn from our senses into truths. "The ideal conception which the mind itself supplies is superinduced upon the facts as they are originally presented to observation. Before the inductive truth is detected, the facts are there, but they are many and unconnected. The conception which the discoverer applies to them gives them connection and unity." (P. 42.) All induction, according to Whewell, thus depends upon superinduction--imposition upon sensory data of certain ideas or general relations existing independently in the mind.[66]

We do not need to present again the objections already offered to this view: the impossibility of any orderly stimulation of ideas by facts, and the impossibility of any check in the imposition of idea upon fact.

"Facts" and conception are so thoroughly separate and independent that any sensory datum is indifferently and equally related to any conceivable idea. There is no basis for "superinducing" one idea or hypothesis, rather than any other, upon any particular set of data.

In the chapter already referred to upon abstraction, or the formation of conceptions, Mill seizes upon this difficulty. Yet he and Whewell have one point in common: they both agree in the existence of a certain subject-matter which is given for logical purposes quite outside of the logical process itself. Mill agrees with Whewell in postulating a raw material of pure sensational data. In criticising Whewell's theory of superinduction of idea upon fact, he is therefore led to the opposite a.s.sertion of the complete dependence of ideas as such upon the given facts as such--in other words, he is led to a reiteration of the fundamental Baconian empiricism; and thus to a virtual retraction of what he had a.s.serted regarding the necessity of ideas to fruitful scientific inquiry, whether in the way of observation or experimentation. The following quotation gives a fair notion of the extent of Mill's retraction:

The conceptions then which we employ for the colligation and methodization of facts, do not develop themselves from within, _but are impressed upon the mind from without_; they are never obtained otherwise than by way of comparison and abstraction, and, in the most important and most numerous cases, are evolved by abstraction _from the very phenomena which it is their office to colligate_.[67]

Even here Mill's sense for the positive side of scientific inquiry suffices to reveal to him that the "facts" are somehow inadequate and defective, and are in need of a.s.sistance from ideas--and yet the ideas which are to help out the facts are to be the impress of the unsure facts! The contradiction comes out very clearly when Mill says: "The really difficult cases are those in which the conception destined to create light and order out of darkness and confusion has to be sought for among the very phenomena which it afterward serves to arrange."[68]

Of course, there is a sense in which Mill's view is very much nearer the truth than is Whewell's. Mill at least sees that "idea" must be relevant to the facts or data which it is to arrange, which are to have "light and order" introduced into them by means of the idea. He sees clearly enough that this is impossible save as the idea develops _within_ the same experience in which the "dark and confused" facts are presented. He goes on to show correctly enough how conflicting data lead the mind to a "confused feeling of an a.n.a.logy" between the data of the confused experience and of some other experience which is orderly (or already colligated and methodized); and how this vague feeling, through processes of further exploration and comparison of experiences, gets a clearer and more adequate form until we finally accept it. He shows how in this process we continually judge of the worth of the idea which is in process of formation, by reference to its appropriateness to _our purpose_. He goes so far as to say: "The question of appropriateness is relative to the _particular object we have in view_."[69] He sums up his discussion by stating: "We cannot frame good general conceptions beforehand. That the conception we have obtained is the one we want can only be known when we have _done the work for the sake of which we wanted it_."[70]

This all describes the actual state of the case, but it is consistent only with a logical theory which makes the distinction between fact and hypothesis instrumental in the transformation of experience from a confused into an organized form; not with Mill's notion that sensations are somehow finally and completely given as ultimate facts, and that ideas are mere re-registrations of such facts. It is perfectly just to say that the hypothesis is impressed upon the mind (in the sense that any notion which occurs to the mind is impressed) _in the course_ of an experience. It is well enough, if one define what he means, to say that the hypothesis is impressed (that is to say, occurs or is suggested) through the medium of given facts, or even of sensations. But it is equally true that the _facts_ are presented and that _sensations_ occur within the course of an experience which is larger than the bare facts, because involving the conflicts among them and the corresponding intention to treat them in some fas.h.i.+on which will secure a unified experience. Facts get power to suggest ideas to the mind--to "impress"--only through their position in an entire experience which is in process of disintegration and of reconstruction--their "fringe" or feeling of tendency is quite as factual as they are. The fact that "the conception we have obtained is the one we want can be known only when we have done the work for the sake of which we wanted it," is enough to show that it is not bare facts, but facts in relation to want and purpose and purpose in relation to facts, which originate the hypothesis.

It would be interesting to follow the history of discussion of the hypothesis since the time of Whewell and of Mill, particularly in the writings of Jevons, Venn, and Bosanquet. This history would refine the terms of our discussion by introducing more complex distinctions and relations. But it would be found, I think, only to refine, not to introduce any fundamentally new principles. In each case, we find the writer struggling with the necessity of distinguis.h.i.+ng between fact and idea; of giving the fact a certain primacy with respect to testing of idea and of giving the idea a primacy with respect to the significance and orderliness of the fact; and of holding throughout to a relations.h.i.+p of idea with fact so intimate that the idea develops only by being "compared" with facts (that is, used in construing them), and facts get to be known only as they are "connected" through the idea--and we find that what is a maze of paradoxes and inconsistencies from an absolute, from a non-historic standpoint, is a matter of course the moment it is looked at from the standpoint of experience engaged in self-transformation of meaning through conflict and reconst.i.tution.

But we can only note one or two points. Jevons's "infinite ballot-box"

of nature which is absolutely neutral as to any particular conception or idea, and which accordingly requires as its correlate the formation of every possible hypothesis (all standing in themselves upon the same level of probability) is an interesting example of the logical consequences of feeling the need of both fact and hypothesis for scientific procedure and yet regarding them as somehow arising independently of each other. It is an attempt to combine extreme empiricism and extreme rationalism. The process of forming hypotheses and of deducing their rational consequences goes on at random, because the disconnectedness of facts as given is so ultimate that the facts suggest one hypothesis no more readily than another. Mathematics, in its two forms of measurements as applied to the facts, and of calculation as applied in deduction, furnishes Jevons the bridge by which he finally covers the gulf which he has first himself created. Venn's theory requires little or no restatement to bring it into line with the position taken in the text. He holds to the origin of hypothesis in the original practical needs of mankind, and to its gradual development into present scientific form.[71] He states expressly:

The _distinction between what is known and what is not known is essential to Logic_, and peculiarly characteristic of it in a degree not to be found in any other science. Inference is the process of pa.s.sing from one to the other; from facts which we had accepted as premises, to those which we have not yet accepted, _but are in the act of doing so by the very process in question_.

No scrutiny of the facts themselves, regarded as objective, can ever detect these characteristics of their greater or less familiarity to our minds. We must introduce also the subjective element if we wish to give any adequate explanation of them.[72]

Venn, however, does not attempt a thoroughgoing statement of logical distinctions, relations, and operations, as parts "of the act of pa.s.sing from the unknown to the known." He recognizes the relation of reflection to a historic process, which we have here termed "reconstruction," and the origin and worth of hypothesis as a tool in the movement, but does not carry his a.n.a.lysis to a systematic form.

III

_Origin of the hypothesis._--In our a.n.a.lysis of the process of judgment, we attempted to show that the predicate arises in case of failure of some line of activity going on in terms of an established habit. When the old habit is checked through failure to deal with new conditions (_i. e._, when the situation is such as to stimulate two habits with distinct aims) the problem is to find a new method of response--that is, to co-ordinate the conflicting tendencies by building up a single aim which will function the existing situation. As we saw that, in case of judgment, habit when checked became ideal, an idea, so the new habit is first formalized as an ideal type of reaction and is the hypothesis by which we attempt to construe new data. In our inquiry as to how this formulation is effected, _i. e._, how the hypothesis is developed, it will be convenient to take some of the currently accepted statements as to their origin, and show how these statements stand in reference to the a.n.a.lysis proposed.

_Enumerative induction and allied processes._--It is pointed out by Welton[73] that the various ways in which hypotheses are suggested may be reduced to three cla.s.ses, viz., enumerative induction, conversion of propositions, and a.n.a.logy. Under the head of "enumeration" he reminds us that "every observed regularity of connection between phenomena suggests a question as to whether it is universal." There are numerous instances of this in mathematics. For example, it is noticed that 1+3=2^2, 1+3+5=3^2, 1+3+5+7=4^2, etc.; and one is led to ask whether there is any general principle involved, so that the sum of the first _n_ odd numbers will be _n_^2, where _n_ is any number, however great. In this early form of inductive inference there are two divergent tendencies. One is the tendency to complete enumeration. This _tendency_ is clearly ideal--it transcends the facts as given. To look for all the cases is thus itself an experimental inquiry, based upon a hypothesis which it endeavors to test. But in most cases enumeration can be only incomplete, and we are able to reach nothing better than probability. Hence the other tendency in the direction of an a.n.a.lysis of content in search for a principle of connection in the elements in any _one_ case. For if a characteristic belonging to a number of individuals suggests a cla.s.s where it belongs to all individuals, it must be that it is found in every individual as such. The hypothesis of complete cla.s.s involves a hypothesis as to the character of each individual in the cla.s.s. Thus a hypothesis as to extension transforms itself into one as to intension.