§ 3. It must be admitted that there is some warrant for this omission of all reference to the subjective side of inference so long as we are dealing with Inductive Logic. The inductive discoverer is of course in a very different position. If he is worthy of the name his mind at every moment will be teeming with notions which he would be as far as any one from calling facts: he is busy making them such to the best of his power. But the logician who follows in his steps, and whose business it is to explain and justify what his leader has discovered, is rather apt to overlook this mental or uncertain stage. What he mostly deals in are the ‘complete inductions’ and ‘well-grounded generalizations’ and so forth, or the exploded errors which contradict them: the prisoners and the corpses respectively, which the real discoverer leaves on the field behind him whilst he presses on to complete his victory. The whole method of science,—expository as contrasted with militant,—is to emphasize the distinction between fact and non-fact, and to treat of little else but these two. In other words a treatise on Inductive Logic can be written without any occasion being found to define what is meant by a notion or concept, or even to employ such terms.
§ 4. And yet, when we come to look more closely, signs may be detected even within the field of Inductive Logic, of an occasional breaking down of the sharp distinction in question; we may meet now and then with entities (to use the widest term attainable) in reference to which it would be hard to say that they are either facts or conceptions. For instance, Inductive Logic has often occasion to make use of Hypotheses: to which of the above two classes are these to be referred? They do not seem in strictness to belong to either; nor are they, as will presently be pointed out, by any means a solitary instance of the kind.
It is true that within the province of Inductive Logic these hypotheses do not give much trouble on this score. However vague may be the form in which they first present themselves to the philosopher's mind, they have not much business to come before us in our capacity of logicians until they are well on their way, so to say, towards becoming facts: until they are beginning to harden into that firm tangible shape in which they will eventually appear. We generally have some such recommendations given to us as that our hypotheses shall be well-grounded and reasonable. This seems only another way of telling us that however freely the philosopher may make his guesses in the privacy of his own study, he had better not bring them out into public until they can with fair propriety be termed facts, even though the name be given with some qualification, as by terming them ‘probable facts.’ The reason, therefore, why we do not take much account of this intermediate state in the hypothesis, when we are dealing with the inductive processes, is that here at any rate it plays only a temporary part; its appearance in that guise is but very fugitive. If the hypothesis be a sound one, it will soon take its place as an admitted fact; if not, it will soon be rejected altogether. Its state as a hypothesis is not a normal one, and therefore we have not much occasion to scrutinize its characteristics. In so saying, it must of course be understood that we are speaking as inductive logicians; the philosopher in his workshop ought, as already remarked, to be familiar enough with the hypothesis in every stage of its existence from its origin; but the logician's duty is different, dealing as he does with proof rather than with the processes of original investigation and discovery.
We might indeed even go further, and say that in many cases the hypothesis does not present itself to the reader, that is to the recipient of the knowledge, until it has ceased to deserve that name at all. It may be first suggested to him along with the proof which establishes it, he not having had occasion to think of it before. It thus comes at a single step out of the obscurity of the unknown into the full possession of its rights as a fact, skipping practically the intermediate or hypothetical stage altogether. The original investigator himself may have long pondered over it, and kept it present to his mind, in this its dubious stage, but finally have given it to the world with that amount of evidence which raises it at once in the minds of others to the level of commonly accepted facts.
Still this doubtful stage exists in every hypothesis, though for logical purposes, and to most minds, it exists in a very fugitive way only. When attention has been directed to it, it may be also detected elsewhere in Logic. Take the case, for instance, of the reference of names. Mill gives the examples of the sun, and a battle, as distinguished from the ideas of them which we, or children, may entertain. Here the distinction is plain and obvious enough. But if, on the other hand, we take the case of things whose existence is doubtful or disputed, the difficulty above mentioned begins to show itself. The case of merely extinct things, or such as have not yet come into existence, offers indeed no trouble, since of course actually present existence is not necessary to constitute a fact. The usual distinction may even be retained also in the case of mythical existences. Centaur and Griffin have as universally recognised a significance amongst the poets, painters, and heralds as lion and leopard have. Hence we may claim, even here, that our conceptions shall be ‘truthful,’ ‘consistent with fact,’ and so on, by which we mean that they are to be in accordance with universal convention upon such subjects. Necessary and universal accordance is sometimes claimed to be all that is meant by ‘objective,’ and since universal accordance is attainable in the case of the notoriously fictitious, our fundamental distinction between fact and conception, and our determination that our terms shall refer to what is objective rather than to what is subjective, may with some degree of strain be still conceived to be tenable even here.
§ 5. But when we come to the case of disputed phenomena the difficulty re-emerges. A supposed planet or new mineral, a doubtful fact in history, a disputed theological doctrine, are but a few examples out of many that might be offered. What some persons strenuously assert, others as strenuously deny, and whatever hope there may be of speedy agreement in the case of physical phenomena, experience shows that there is not much prospect of this in the case of those which are moral and historical, to say nothing of theological. So long as those who are in agreement confine their intercourse to themselves, their ‘facts’ are accepted as such, but as soon as they come to communicate with others all distinction between fact and conception is lost at once, the ‘facts’ of one party being mere groundless ‘conceptions’ to their opponents. There is therefore, I think, in these cases a real difficulty in carrying out distinctly and consistently the account which the Materialist logician offers as to the reference of names. It need hardly be pointed out that what thus applies to names or terms applies equally to propositions in which particular or general statements are made involving names.
§ 6. But when we step into Probability, and treat this from the same material or Phenomenal point of view, we can no longer neglect the question which is thus presented to us. The difficulty cannot here be rejected, as referring to what is merely temporary or occasional. The intermediate condition between conjecture and fact, so far from being temporary or occasional only, is here normal. It is just the condition which is specially characteristic of Probability. Hence it follows that however decidedly we may reject the Conceptualist theory we cannot altogether reject the use of Conceptualist language. If we can prove that a given man will die next year, or attain sufficiently near to proof to leave us practically certain on the point, we may speak of his death as a (future) fact. But if we merely contemplate his death as probable? This is the sort of inference, or substitute for inference, with which Probability is specially concerned. We may, if we so please, speak of ‘probable facts,’ but if we examine the meaning of the words we may find them not merely obscure, but self-contradictory. Doubtless there are facts here, in the fullest sense of the term, namely the statistics upon which our opinion is ultimately based, for these are known and admitted by all who have looked into the matter. The same language may also be applied to that extension of these statistics by induction which is involved in the assertion that similar statistics will be found to prevail elsewhere, for these also may rightfully claim universal acceptance. But these statements, as was abundantly shown in the earlier chapters, stand on a very different footing from a statement concerning the individual event; the establishment and discussion of the former belong by rights to Induction, and only the latter to Probability.
§ 7. It is true that for want of appropriate terms to express such things we are often induced, indeed compelled, to apply the same name of ‘facts’ to such individual contingencies. We should not, for instance, hesitate to speak of the fact of the man dying being probable, possible, unlikely, or whatever it might be. But I cannot help regarding such expressions as a strictly incorrect usage arising out of a deficiency of appropriate technical terms. It is doubtless certain that one or other of the two alternatives must happen, but this alternative certainty is not the subject of our contemplation; what we have before us is the single alternative, which is notoriously uncertain. It is this, and this only, which is at present under notice, and whose occurrence has to be estimated. We have surely no right to dignify this with the name of a fact, under any qualifications, when the opposite alternative has claims, not perhaps actually equal to, but at any rate not much inferior to its own. Such language, as already remarked, may be quite right in Inductive logic, where we are only concerned with conjectures of such a high degree of likelihood that their non-occurrence need not be taken into practical account, and which are moreover regarded as merely temporary. But in Probability the conjecture may have any degree of likelihood about it; it may be just as likely as the other alternative, nay it may be much less likely. In these latter cases, for instance, if the chances are very much against the man's death, it is surely an abuse of language to speak of the ‘fact’ of his dying, even though we qualify it by declaring it to be highly improbable. The subject-matter essential to Probability being the uncertain, we can never with propriety employ upon it language which in its original and correct application is only appropriate to what is actually or approximately certain.
§ 8. It should be remembered also that this state of things, thus characteristic of Probability, is permanent there. So long as they remain under the treatment of that science our conjectures, or whatever we like to call them, never develop into facts. I calculate, for instance, the chance that a die will give ace, or that a man will live beyond a certain age. Such an approximation to knowledge as is thus acquired is as much as we can ever afterwards hope to get, unless we resort to other methods of enquiry. We do not, as in Induction, feel ourselves on the brink of some experimental or other proof which at any moment may raise it into certainty. It is nothing but a conjecture of a certain degree of strength, and such it will ever remain, so long as Probability is left to deal with it. If anything more is ever to be made out of it we must appeal to direct experience, or to some kind of inductive proof. As we have so often said, individual facts can never be determined here, but merely ultimate tendencies and averages of many events. I may, indeed, by a second appeal to Probability improve the character of my conjecture, through being able to refer it to a narrower and better class of statistics; but its essential nature remains throughout what it was.
It appears to me therefore that the account of the Materialist view of logic indicated at the commencement of this chapter, though substantially sound, needs some slight reconsideration and re-statement. It answers admirably so far as ordinary Induction is concerned, but needs some revision if it is to be equally applicable to that wider view of the nature and processes of acquiring knowledge wherein the science of logic is considered to involve Probability also as well as Induction.