CHAPTER XIII.
ON THE CONCEPTION AND TREATMENT OF MODALITY.
§ 1. The reader who knows anything of the scholastic Logic will have perceived before now that we have been touching in a variety of places upon that most thorny and repulsive of districts in the logical territory;—modality. It will be advisable, however, to put together, somewhat more definitely, what has to be said upon the subject. I propose, therefore, to devote this chapter to a brief account of the principal varieties of treatment which the modals have received at the hands of professed logicians.
It must be remarked at the outset that the sense in which modality and modal propositions have been at various times understood, is by no means fixed and invariably the same. This diversity of view has arisen partly from corresponding differences in the view taken of the province and nature of logic, and partly from differences in the philosophical and scientific opinions entertained as to the constitution and order of nature. In later times, moreover, another very powerful agent in bringing about a change in the treatment of the subject must be recognized in the gradual and steady growth of the theory of Probability, as worked out by the mathematicians from their own point of view.
§ 2. In spite, however, of these differences of treatment, there has always been some community of subject-matter in the discussions upon this topic. There has almost always been some reference to quantity of belief; enough perhaps to justify De Morgan's[1] remark, that Probability was “the unknown God whom the schoolmen ignorantly worshipped when they so dealt with this species of enunciation, that it was said to be beyond human determination whether they most tortured the modals, or the modals them.” But this reference to quantity of belief has sometimes been direct and immediate, sometimes indirect and arising out of the nature of the subject-matter of the proposition. The fact is, that that distinction between the purely subjective and purely objective views of logic, which I have endeavoured to bring out into prominence in the eleventh chapter, was not by any means clearly recognized in early times, nor indeed before the time of Kant, and the view to be taken of modality naturally shared in the consequent confusion. This will, I hope, be made clear in the course of the following chapter, which is intended to give a brief sketch of the principal different ways in which the modality of propositions has been treated in logic. As it is not proposed to give anything like a regular history of the subject, there will be no necessity to adhere to any strict sequence of time, or to discuss the opinions of any writers, except those who may be taken as representative of tolerably distinct views. The outcome of such investigation will be, I hope, to convince the reader (if, indeed, he had not come to that conviction before), that the logicians, after having had a long and fair trial, have failed to make anything satisfactory out of this subject of the modals by their methods of enquiry and treatment; and that it ought, therefore, to be banished entirely from that science, and relegated to Probability.
§ 3. From the earliest study of the syllogistic process it was seen that, complete as that process is within its own domain, the domain, at any rate under its simplest treatment, is a very limited one. Propositions of the pure form,—All (or some) A is (or is not) B,—are found in practice to form but a small portion even of our categorical statements. We are perpetually meeting with others which express the relation of B to A with various degrees of necessity or probability; e.g.
A must be B, A may be B; or the effect of such facts upon our judgment, e.g.
I am perfectly certain that A is B, I think that A may be B; with many others of a more or less similar type. The question at once arises, How are such propositions to be treated? It does not seem to have occurred to the old logicians, as to some of their successors in modern times, simply to reject all consideration of this topic. Their faith in the truth and completeness of their system of inference was far too firm for them to suppose it possible that forms of proposition universally recognized as significant in popular speech, and forms of inference universally recognized there as valid, were to be omitted because they were inconvenient or complicated.
§ 4. One very simple plan suggests itself, and has indeed been repeatedly advocated, viz.
just to transfer all that is characteristic of such propositions into that convenient receptacle for what is troublesome elsewhere, the predicate.[2] Has not another so-called modality been thus got rid of?[3] and has it not been attempted by the same device to abolish the distinctive characteristic of negative propositions, viz.
by shifting the negative particle into the predicate? It must be admitted that, up to a certain point, something may be done in this way. Given the reasoning, ‘Those who take arsenic will probably die; A has taken it, therefore he will probably die;’ it is easy to convert this into an ordinary syllogism of the pure type, by simply wording the major, ‘Those who take arsenic are people-who-will-probably-die,’ when the conclusion follows in the same form, ‘A is one who-will-probably-die.’ But this device will only carry us a very little way. Suppose that the minor premise also is of the same modal description, e.g.
‘A has probably taken arsenic,’ and it will be seen that we cannot relegate the modality here also to the predicate without being brought to a stop by finding that there are four terms in the syllogism.
But even if there were not this particular objection, it does not appear that anything is to be gained in the way of intelligibility or method by such a device as the above. For what is meant by a modal predicate, by the predicate ‘probably mortal,’ for instance, in the proposition ‘All poisonings by arsenic are probably mortal’? If the analogy with ordinary pure propositions is to hold good, it must be a predicate referring to the whole of the subject, for the subject is distributed. But then we are at once launched into the difficulties discussed in a former chapter (Ch. VI.
§§ 19–25), when we attempt to justify or verify the application of the predicate. We have to enquire (at least on the view adopted in this work) whether the application of the predicate ‘probably mortal’ to the whole of the subject, really means at bottom anything else than that the predicate ‘mortal’ is to be applied to a portion (more than half) of the members denoted by the subject. When the transference of the modality to the predicate raises such intricate questions as to the sense in which the predicate is to be interpreted, there is surely nothing gained by the step.
§ 5. A second, and more summary way of shelving all difficulties of the subject, so far at least as logic, or the writers upon logic, are concerned, is found by simply denying that modality has any connection whatever with logic. This is the course adopted by many modern writers, for instance, by Hamilton and Mansel, in reference to whom one cannot help remarking that an unduly large portion of their logical writings seems occupied with telling us what does not belong to logic. They justify their rejection on the ground that the mode belongs to the matter, and must be determined by a consideration of the matter, and therefore is extralogical. To a certain extent I agree with their grounds of rejection, for (as explained in Chapter VI.)
it is not easy to see how the degree of modality of any proposition, whether premise or conclusion, can be justified without appeal to the matter. But then questions of justification, in any adequate sense of the term, belong to a range of considerations somewhat alien to Hamilton's and Mansel's way of regarding the science. The complete justification of our inferences is a matter which involves their truth or falsehood, a point with which these writers do not much concern themselves, being only occupied with the consistency of our reasonings, not with their conformity with fact. Were I speaking as a Hamiltonian I should say that modality is formal rather than material, for though we cannot justify the degree of our belief of a proposition without appeal to the matter, we can to a moderate degree of accuracy estimate it without any such appeal; and this would seem to be quite enough to warrant its being regarded as formal.
It must be admitted that Hamilton's account of the matter when he is recommending the rejection of the modals, is not by any means clear and consistent. He not only fails, as already remarked, to distinguish between the formal and the material (in other words, the true and the false) modality; but when treating of the former he fails to distinguish between the extremely diverse aspects of modality when viewed from the Aristotelian and the Kantian stand-points. Of the amount and significance of this difference we shall speak presently, but it may be just pointed out here that Hamilton begins (Vol. I.
p. 257) by rejecting the modals on the ground that the distinctions between the necessary, the contingent, the possible, and the impossible, must be wholly rested on an appeal to the matter of the propositions, in which he is, I think, quite correct. But then a little further on (p. 260), in explaining ‘the meaning of three terms which are used in relation to pure and modal propositions,’ he gives the widely different Kantian, or three-fold division into the apodeictic, the assertory, and the problematic. He does not take the precaution of pointing out to his hearers the very different general views of logic from which these two accounts of modality spring.[4]
§ 6. There is one kind of modal syllogism which it would seem unreasonable to reject on the ground of its not being formal, and which we may notice in passing. The premise ‘Any A is probably B,’ is equivalent to ‘Most A are B.’ Now it is obvious that from two such premises as ‘Most A are B,’ ‘Most A are C,’ we can deduce the consequence, ‘Some C are B.’ Since this holds good whatever may be the nature of A, B, and C, it is, according to ordinary usage of the term, a formal syllogism. Mansel, however, refuses to admit that any such syllogisms belong to formal logic. His reasons are given in a rather elaborate review[5] and criticism of some of the logical works of De Morgan, to whom the introduction of ‘numerically definite syllogisms’ is mainly due. Mansel does not take the particular example given above, as he is discussing a somewhat more comprehensive algebraic form. He examines it in a special numerical example:[6]—18 out of 21 Ys are X; 15 out of 21 Ys are Z; the conclusion that 12 Zs are X is rejected from formal logic on the ground that the arithmetical judgment involved is synthetical, not analytical, and rests upon an intuition of quantity. We cannot enter upon any examination of these reasons here; but it may merely be remarked that his criticism demands the acceptance of the Kantian doctrines as to the nature of arithmetical judgments, and that it would be better to base the rejection not on the ground that the syllogism is not formal, but on the ground that it is not analytical.
§ 7. There is another and practical way of getting rid of the perplexities of modal reasoning which must be noticed here. It is the resource of ordinary reasoners rather than the decision of professed logicians,[7] and, like the first method of evasion already pointed out in this chapter, is of very partial application. It consists in treating the premises, during the process of reasoning, as if they were pure, and then reintroducing the modality into the conclusion, as a sort of qualification of its full certainty. When each of the premises is nearly certain, or when from any cause we are not concerned with the extent of their departure from full certainty, this rough expedient will answer well enough. It is, I apprehend, the process which passes through the minds of most persons in such cases, in so far as they reason consciously. They would, presumably, in such an example as that previously given (§ 4), proceed as if the premises that ‘those who take arsenic will die,’ and that ‘the man in question has taken it,’ were quite true, instead of being only probably true, and they would consequently draw the conclusion that ‘he would die.’ But bearing in mind that the premises are not certain, they would remember that the conclusion was only to be held with a qualified assent. This they would express quite correctly, if the mere nature and not the degree of that assent is taken into account, by saying that ‘he is likely to die.’ In this case the modality is rejected temporarily from the premises to be reintroduced into the conclusion.
It is obvious that such a process as this is of a very rough and imperfect kind. It does, in fact, omit from accurate consideration just the one point now under discussion. It takes no account of the varying shades of expression by which the degree of departure from perfect conviction is indicated, which is of course the very thing with which modality is intended to occupy itself. At best, therefore, it could only claim to be an extremely rude way of deciding questions, the accurate and scientific methods of treating which are demanded of us.
§ 8. In any employment of applied logic we have of course to go through such a process as that just mentioned. Outside of pure mathematics it can hardly ever be the case that the premises from which we reason are held with absolute conviction. Hence there must be a lapse from absolute conviction in the conclusion. But we reason on the hypothesis that the premises are true, and any trifling defection from certainty, of which we may be conscious, is mentally reserved as a qualification to the conclusion. But such considerations as these belong rather to ordinary applied logic; they amount to nothing more than a caution or hint to be borne in mind when the rules of the syllogism, or of induction, are applied in practice. When, however, we are treating of modality, the extent of the defection from full certainty is supposed to be sufficiently great for our language to indicate and appreciate it. What we then want is of course a scientific discussion of the principles in accordance with which this departure is to be measured and expressed, both in our premises and in our conclusion. Such a plan therefore for treating modality, as the one under discussion, is just as much a banishment of it from the field of real logical enquiry, as if we had determined avowedly to reject it from consideration.
§ 9. Before proceeding to a discussion of the various ways in which modality may be treated by those who admit it into logic, something must be said to clear up a possible source of confusion in this part of the subject. In the cases with which we have hitherto been mostly concerned, in the earlier chapters of this work, the characteristic of modality (for in this chapter we may with propriety use this logical term) has generally been found in singular and particular propositions. It presented itself when we had to judge of individual cases from a knowledge of the average, and was an expression of the fact that the proposition relating to these individuals referred to a portion only of the whole class from which the average was taken. Given that of men of fifty-five, three out of five will die in the course of twenty years, we have had to do with propositions of the vague form, ‘It is probable that AB (of that age) will die,’ or of the more precise form, ‘It is three to two that AB will die,’ within the specified time. Here the modal proposition naturally presents itself in the form of a singular or particular proposition.
§ 10. But when we turn to ordinary logic we may find universal propositions spoken of as modal. This must mostly be the case with those which are termed necessary or impossible, but it may also be the case with the probable. We may meet with the form ‘All X is probably Y.’ Adopting the same explanation here as has been throughout adopted in analogous cases, we must say that what is meant by the modality of such a proposition is the proportional number of times in which the universal proposition would be correctly made. And in this there is, so far, no difficulty. The only difference is that whereas the justification of the former, viz.
the particular or individual kind of modal, was obtainable within the limits of the universal proposition which included it, the justification of the modality of a universal proposition has to be sought in a group or succession of other propositions. The proposition has to be referred to some group of similar ones and we have to consider the proportion of cases in which it will be true. But this distinction is not at all fundamental.
It is quite true that universal propositions from their nature are much less likely than individual ones to be justified, in practice, by such appeal. But, as has been already frequently pointed out, we are not concerned with the way in which our propositions are practically obtained, nor with the way in which men might find it most natural to test them; but with that ultimate justification to which we appeal in the last resort, and which has been abundantly shown to be of a statistical character. When, therefore, we say that ‘it is probable that all X is Y,’ what we mean is, that in more than half the cases we come across we should be right in so judging, and in less than half the cases we should be wrong.
§ 11. It is at this step that the possible ambiguity is encountered. When we talk of the chance that All X is Y, we contemplate or imply the complementary chance that it is not so. Now this latter alternative is not free from ambiguity. It might happen, for instance, in the cases of failure, that no X is Y, or it might happen that some X, only, is not Y; for both of these suppositions contradict the original proposition, and are therefore instances of its failure. In practice, no doubt, we should have various recognized rules and inductions to fall back upon in order to decide between these alternatives, though, of course, the appeal to them would be in strictness extralogical. But the mere existence of such an ambiguity, and the fact that it can only be cleared up by appeal to the subject-matter, are in themselves no real difficulty in the application of the conception of modality to universal propositions as well as to individual ones.
§ 12. Having noticed some of the ways in which the introduction of modality into logic has been evaded or rejected, we must now enter into a brief account of its treatment by those who have more or less deliberately admitted its claims to acceptance.
The first enquiry will be, What opinions have been held as to the nature of modality?
that is, Is it primarily an affection of the matter of the proposition, and, if not, what is it exactly? In reference to this enquiry it appears to me, as already remarked, that amongst the earlier logicians no such clear and consistent distinction between the subjective and objective views of logic as is now commonly maintained, can be detected.[8] The result of this appears in their treatment of modality. This always had some reference to the subjective side of the proposition, viz.
in this case to the nature or quantity of the belief with which it was entertained; but it is equally clear that this characteristic was not estimated at first hand, so to say, and in itself, but rather from a consideration of the matter determining what it should be. The commonly accepted scholastic or Aristotelian division, for instance, is into the necessary, the contingent, the possible, and the impossible. This is clearly a division according to the matter almost entirely, for on the purely mental side the necessary and the impossible would be just the same; one implying full conviction of the truth of a proposition, and the other of that of its contradictory. So too, on the same side, it would not be easy to distinguish between the contingent and the possible. On the view in question, therefore, the modality of a proposition was determined by a reference to the nature of the subject-matter. In some propositions the nature of the subject-matter decided that the predicate was necessarily joined to the subject; in others that it was impossible that they should be joined; and so on.
§ 13. The artificial character of such a four-fold division will be too obvious to modern minds for it to be necessary to criticize it. A very slight study of nature and consequent appreciation of inductive evidence suffice to convince us that those uniformities upon which all connections of phenomena, whether called necessary or contingent, depend, demand extremely profound and extensive enquiry; that they admit of no such simple division into clearly marked groups; and that, therefore, the pure logician had better not meddle with them.[9]
The following extract from Grote's Aristotle (Vol. I. p. 192) will serve to show the origin of this four-fold division, its conformity with the science of the day, and consequently its utter want of conformity with that of our own time:—“The distinction of Problematical and Necessary Propositions corresponds, in the mind of Aristotle, to that capital and characteristic doctrine of his Ontology and Physics, already touched on in this chapter. He thought, as we have seen, that in the vast circumferential region of the Kosmos, from the outer sidereal sphere down to the lunar sphere, celestial substance was a necessary existence and energy, sempiternal and uniform in its rotations and influence; and that through its beneficent influence, pervading the concavity between the lunar sphere and the terrestrial centre (which included the four elements with their compounds) there prevailed a regularizing tendency called Nature; modified, however, and partly counteracted by independent and irregular forces called Spontaneity and Chance, essentially unknowable and unpredictable. The irregular sequences thus named by Aristotle were the objective correlate of the Problematical Proposition in Logic. In these sublunary sequences, as to future time, may or may not, was all that could be attained, even by the highest knowledge; certainty, either of affirmation or negation, was out of the question. On the other hand, the necessary and uniform energies of the celestial substance, formed the objective correlate of the Necessary Proposition in Logic; this substance was not merely an existence, but an existence necessary and unchangeable… he considers the Problematical Proposition in Logic to be not purely subjective, as an expression of the speaker's ignorance, but something more, namely, to correlate with an objective essentially unknowable to all.”
§ 14. Even after this philosophy began to pass away, the divisions of modality originally founded upon it might have proved, as De Morgan has remarked,[10] of considerable service in mediæval times. As he says, people were much more frequently required to decide in one way or the other upon a single testimony, without there being a sufficiency of specific knowledge to test the statements made. The old logician “did not know but that any day of the week might bring from Cathay or Tartary an account of men who ran on four wheels of flesh and blood, or grew planted in the ground, like Polydorus in the Æneid, as well evidenced as a great many nearly as marvellous stories.” Hence, in default of better inductions, it might have been convenient to make rough classifications of the facts which were and which were not to be accepted on testimony (the necessary, the impossible, &c.), and to employ these provisional inductions (which is all we should now regard them) as testing the stories which reached him. Propositions belonging to the class of the impossible might be regarded as having an antecedent presumption against them so great as to prevail over almost any testimony worth taking account of, and so on.
§ 15. But this old four-fold division of modals continued to be accepted and perpetuated by the logicians long after all philosophical justification for it had passed away. So far as I have been able to ascertain, scarcely any logician of repute or popularity before Kant, was bold enough to make any important change in the way of regarding them.[11] Even the Port-Royal Logic, founded as it is on Cartesianism, repeats the traditional statements, though with extreme brevity. This adherence to the old forms led, it need not be remarked, to considerable inconsistency and confusion in many cases. These forms were founded, as we have seen, on an objective view of the province of logic, and this view was by no means rigidly carried out in many cases. In fact it was beginning to be abandoned, to an extent and in directions which we have not opportunity here to discuss, before the influence of Kant was felt. Many, for instance, added to the list of the four, by including the true and the false; occasionally also the probable, the supposed, and the certain were added. This seems to show some tendency towards abandoning the objective for the subjective view, or at least indicates a hesitation between them.
§ 16. With Kant's view of modality almost every one is familiar. He divides judgments, under this head, into the apodeictic, the assertory, and the problematic. We shall have to say something about the number and mutual relations of these divisions presently; we are now only concerned with the general view which they carry out. In this respect it will be obvious at once what a complete change of position has been reached. The ‘necessary’ and the ‘impossible’ demanded an appeal to the matter of a proposition in order to recognize them; the ‘apodeictic’ and the ‘assertory’, on the other hand, may be true of almost any matter, for they demand nothing but an appeal to our consciousness in order to distinguish between them. Moreover, the distinction between the assertory and the problematic is so entirely subjective and personal, that it may vary not only between one person and another, but in the case of the same person at different times. What one man knows to be true, another may happen to be in doubt about. The apodeictic judgment is one which we not only accept, but which we find ourselves unable to reverse in thought; the assertory is simply accepted; the problematic is one about which we feel in doubt.
This way of looking at the matter is the necessary outcome of the conceptualist or Kantian view of logic. It has been followed by many logicians, not only by those who may be called followers of Kant, but by almost all who have felt his influence. Ueberweg, for instance, who is altogether at issue with Kant on some fundamental points, adopts it.
§ 17. The next question to be discussed is, How many subdivisions of modality are to be recognized? The Aristotelian or scholastic logicians, as we have seen, adopted a four-fold division. The exact relations of some of these to each other, especially the possible and the contingent, is an extremely obscure point, and one about which the commentators are by no means agreed. As, however, it seems tolerably clear that it was not consciously intended by the use of these four terms to exhibit a graduated scale of intensity of conviction, their correspondence with the province of modern probability is but slight, and the discussion of them, therefore, becomes rather a matter of special or antiquarian interest. De Morgan, indeed (Formal Logic, p. 232), says that the schoolmen understood by contingent more likely than not, and by possible less likely than not. I do not know on what authority this statement rests, but it credits them with a much nearer approach to the modern views of probability than one would have expected, and decidedly nearer than that of most of their successors.[12] The general conclusion at which I have arrived, after a reasonable amount of investigation, is that there were two prevalent views on the subject. Some (e.g.
Burgersdyck, Bk. I.
ch. 32) admitted that there were at bottom only two kinds of modality; the contingent and the possible being equipollent, as also the necessary and the impossible, provided the one asserts and the other denies. This is the view to which those would naturally be led who looked mainly to the nature of the subject-matter. On the other hand, those who looked mainly at the form of expression, would be led by the analogy of the four forms of proposition, and the necessity that each of them should stand in definite opposition to each other, to insist upon a distinction between the four modals.[13] They, therefore, endeavoured to introduce a distinction by maintaining (e.g.
Crackanthorpe, Bk. III.
ch. 11) that the contingent is that which now is but may not be, and the possible that which now is not but may be. A few appear to have made the distinction correspondent to that between the physically and the logically possible.
§ 18. When we get to the Kantian division we have reached much clearer ground. The meaning of each of these terms is quite explicit, and it is also beyond doubt that they have a more definite tendency in the direction of assigning a graduated scale of conviction. So long as they are regarded from a metaphysical rather than a logical standing point, there is much to be said in their favour. If we use introspection merely, confining ourselves to a study of the judgments themselves, to the exclusion of the grounds on which they rest, there certainly does seem a clear and well-marked distinction between judgments which we cannot even conceive to be reversed in thought; those which we could reverse, but which we accept as true; and those which we merely entertain as possible.
Regarded, however, as a logical division, Kant's arrangement seems to me of very little service. For such logical purposes indeed, as we are now concerned with, it really seems to resolve itself into a two-fold division. The distinction between the apodeictic and the assertory will be admitted, I presume, even by those who accept the metaphysical or psychological theory upon which it rests, to be a difference which concerns, not the quantity of belief with which the judgments are entertained, but rather the violence which would have to be done to the mind by the attempt to upset them. Each is fully believed, but the one can, and the other cannot, be controverted. The belief with which an assertory judgment is entertained is full belief, else it would not differ from the problematic; and therefore in regard to the quantity of belief, as distinguished from the quality or character of it, there is no difference between it and the apodeictic. It is as though, to offer an illustration, the index had been already moved to the top of the scale in the assertory judgment, and all that was done to convert this into an apodeictic one, was to clamp it there. The only logical difference which then remains is that between problematic and assertory, the former comprehending all the judgments as to the truth of which we have any degree of doubt, and the latter those of which we have no doubt. The whole range of the former, therefore, with which Probability is appropriately occupied, is thrown undivided into a single compartment. We can hardly speak of a ‘division’ where one class includes everything up to the boundary line, and the other is confined to that boundary line. Practically, therefore, on this view, modality, as the mathematical student of Probability would expect to find it, as completely disappears as if it were intended to reject it.
§ 19. By less consistent and systematic thinkers, and by those in whom ingenuity was an over prominent feature, a variety of other arrangements have been accepted or proposed. There is, of course, some justification for such attempts in the laudable desire to bring our logical forms into better harmony with ordinary thought and language. In practice, as was pointed out in an earlier chapter, every one recognizes a great variety of modal forms, such as ‘likely,’ ‘very likely,’ ‘almost certainly,’ and so on almost without limit in each direction. It was doubtless supposed that, by neglecting to make use of technical equivalents for some of these forms, we should lose our logical control over certain possible kinds of inference, and so far fall short even of the precision of ordinary thought.
With regard to such additional forms, it appears to me that all those which have been introduced by writers who were uninfluenced by the Theory of Probability, have done little else than create additional confusion, as such writers do not attempt to marshal their terms in order, or to ascertain their mutual relations. Omitting, of course, forms obviously of material modality, we have already mentioned the true and the false; the probable, the supposed, and the certain. These subdivisions seem to have reached their climax at a very early stage in Occam (Prantl, III. 380), who held that a proposition might be modally affected by being ‘vera, scita, falsa, ignota, scripta, prolata, concepta, credita, opinata, dubitata.’
§ 20. Since the growth of the science of Probability, logicians have had better opportunities of knowing what they had to aim at; and, though it cannot be said that their attempts have been really successful, these are at any rate a decided improvement upon those of their predecessors. Dr Thomson,[14] for instance, gives a nine-fold division. He says that, arranging the degrees of modality in an ascending scale, we find that a judgment may be either possible, doubtful, probable, morally certain for the thinker himself, morally certain for a class or school, morally certain for all, physically certain with a limit, physically certain without limitation, and mathematically certain. Many other divisions might doubtless be mentioned, but, as every mathematician will recognize, the attempt to secure any general agreement in such a matter of arrangement is quite hopeless. It is here that the beneficial influence of the mathematical theory of Probability is to be gratefully acknowledged. As soon as this came to be studied it must have been perceived that in attempting to mark off clearly from one another certain gradations of belief, we should be seeking for breaches in a continuous magnitude. In the advance from a slight presumption to a strong presumption, and from that to moral certainty, we are making a gradual ascent, in the course of which there are no natural halting-places. The proof of this continuity need not be entered upon here, for the materials for it will have been gathered from almost every chapter of this work. The reader need merely be reminded that the grounds of our belief, in all cases which admit of number and measurement, are clearly seen to be of this description; and that therefore unless the belief itself is to be divorced from the grounds on which it rests, what thus holds as to their characteristics must hold also as to its own.
It follows, therefore, that modality in the old sense of the word, wherein an attempt was made to obtain certain natural divisions in the scale of conviction, must be finally abandoned. All that it endeavoured to do can now be done incomparably better by the theory of Probability, with its numerical scale which admits of indefinite subdivision. None of the old systems of division can be regarded as a really natural one; those which admit but few divisions being found to leave the whole range of the probable in one unbroken class, and those which adopt many divisions lapsing into unavoidable vagueness and uncertainty.
§ 21. Corresponding to the distinction between pure and modal propositions, but even more complicated and unsatisfactory in its treatment, was that between pure and modal syllogisms. The thing discussed in the case of the latter was, of course, the effect produced upon the conclusion in respect of modality, by the modal affection of one or both premises. It is only when we reach such considerations as these that we are at all getting on to the ground appropriate to Probability; but it is obvious that very little could be done with such rude materials, and the inherent clumsiness and complication of the whole modal system come out very clearly here. It was in reference probably to this complication that some of the bitter sayings[15] of the schoolmen and others which have been recorded, were uttered.
Aristotle has given an intricate investigation of this subject, and his followers naturally were led along a similar track. It would be quite foreign to my purpose in the slight sketch in this chapter to attempt to give any account of these enquiries, even were I competent to do so; for, as has been pointed out, the connection between the Aristotelian modals and the modern view of the nature of Probability, though real, is exceedingly slight. It need only be remarked that what was complicated enough with four modals to be taken account of, grows intricate beyond all endurance when such as the ‘probable’ and the ‘true’ and the ‘false’ have also to be assigned a place in the list. The following examples[16] will show the kind of discussions with which the logicians exercised themselves. ‘Whether, with one premise certain, and the other probable, a certain conclusion may be inferred’: ‘Whether, from the impossible, the necessary can be inferred’; ‘Whether, with one premise necessary and the other de inesse, the conclusion is necessary’, and so on, endlessly.
§ 22. On the Kantian view of modality the discussion of such kinds of syllogisms becomes at once decidedly more simple (for here but three modes are recognized), and also somewhat more closely connected with strict Probability, (for the modes are more nearly of the nature of gradations of conviction). But, on the other hand, there is less justification for their introduction, as logicians might really be expected to know that what they are aiming to effect by their clumsy contrivances is the very thing which Probability can carry out to the highest desired degree of accuracy. The former methods are as coarse and inaccurate, compared with the latter, as were the roughest measurements of Babylonian night-watchers compared with the refined calculations of the modern astronomer. It is indeed only some of the general adherents of the Kantian Logic who enter upon any such considerations as these; some, such as Hamilton and Mansel, entirely reject them, as we have seen. By those who do treat of the subject, such conclusions as the following are laid down; that when both premises are apodeictic the conclusion will be the same; so when both are assertory or problematic. If one is apodeictic and the other assertory, the latter, or ‘weaker,’ is all that is to be admitted for the conclusion; and so on. The English reader will find some account of these rules in Ueberweg's Logic.[17]
§ 23. But although those modals, regarded as instruments of accurate thought, have been thus superseded by the precise arithmetical expressions of Probability, the question still remains whether what may be termed our popular modal expressions could not be improved and adapted to more accurate use. It is true that the attempt to separate them from one another by any fundamental distinctions is futile, for the magnitude of which they take cognizance is, as we have remarked, continuous; but considering the enormous importance of accurate terminology, and of recognizing numerical distinctions wherever possible, it would be a real advance if any agreement could be arrived at with regard to the use of modal expressions. We have already noticed (Ch. II.
§ 16) some suggestions by Mr Galton as to the possibility of a natural system of classification, resting upon the regularity with which most kinds of magnitudes tend to group themselves about a mean. It might be proposed, for instance, that we should agree to apply the term ‘good’ to the first quarter, measuring from the best downwards; ‘indifferent’ to the middle half, and ‘bad’ to the last quarter. There seems no reason why a similarly improved terminology should not some day be introduced into the ordinary modal language of common life. It might be agreed, for instance, that ‘very improbable’ should as far as possible be confined to those events which had odds of (say) more than 99 to 1 against them; and so on, with other similar expressions. There would, no doubt, be difficulties in the way, for in all applications of classification we have to surmount the two-fold obstacles which lie in the way, firstly (to use Kant's expression) of the faculty of making rules, and secondly of that of subsumption under rules. That is to say, even if we had agreed upon our classes, there would still be much doubt and dispute, in the case of things which did not readily lend themselves to be counted or measured, as to whether the odds were more or less than the assigned quantity.
It is true that when we know the odds for or against an event, we can always state them explicitly without the necessity of first agreeing as to the usage of terms which shall imply them. But there would often be circumlocution and pedantry in so doing, and as long as modal terms are in practical use it would seem that there could be no harm, and might be great good, in arriving at some agreement as to the degree of probability which they should be generally understood to indicate. Bentham, as is well known, in despair of ever obtaining anything accurate out of the language of common life on this subject, was in favour of a direct appeal to the numerical standard. He proposed the employment, in judicial trials, of an instrument, graduated from 0 to 10, on which scale the witness was to be asked to indicate the degree of his belief of the facts to which he testified: similarly the judge might express the force with which he held his conclusion. The use of such a numerical scale, however, was to be optional only, not compulsory, as Bentham admitted that many persons might feel at a loss thus to measure the degree of their belief. (Rationale of Judicial Evidence, Bk. I., Ch. VI.)
§ 24. Throughout this chapter we have regarded the modals as the nearest counterpart to modern Probability which was afforded by the old systems of logic. The reason for so regarding them is, that they represented some slight attempt, rude as it was, to recognize and measure certain gradations in the degree of our conviction, and to examine the bearing of such considerations upon our logical inferences.
But although it is amongst the modals that the germs of the methods of Probability are thus to be sought; the true subject-matter of our science, that is, the classes of objects with which it is most appropriately concerned, are rather represented by another part of the scholastic logic. This was the branch commonly called Dialectic, in the old sense of that term. Dialectic, according to Aristotle, seems to have been a sort of sister art to Rhetoric. It was concerned with syllogisms differing in no way from demonstrative syllogisms, except that their premises were probable instead of certain. Premises of this kind he termed topics, and the syllogisms which dealt with them enthymemes. They were said to start from ‘signs and likelihoods’ rather than from axioms.[18]
§ 25. The terms in which such reasonings are commonly described sound very much like those applicable to Probability, as we now understand it. When we hear of likelihood, and of probable syllogisms, our first impression might be that the inferences involved would be of a similar character.[19] This, however, would be erroneous. In the first place the province of this Dialectic was much too wide, for it covered in addition the whole field of what we should now term Scientific or Material Induction. The distinctive characteristic of the dialectic premises was their want of certainty, and of such uncertain premises Probability (as I have frequently insisted) takes account of one class only, Induction concerning itself with another class. Again, not the slightest attempt was made to enter upon the enquiry, How uncertain are the premises? It is only when this is attempted that we can be considered to enter upon the field of Probability, and it is because, after a rude fashion, the modals attempted to grapple with this problem, that we have regarded them as in any way occupied with our special subject-matter.
§ 26. Amongst the older logics with which I have made any acquaintance, that of Crackanthorpe gives the fullest discussion upon this subject. He divides his treatment of the syllogism into two parts, occupied respectively with the ‘demonstrative’ and the ‘probable’ syllogism. To the latter a whole book is devoted. In this the nature and consequences of thirteen different ‘loci’[20] are investigated, though it is not very clear in what sense they can every one of them be regarded as being ‘probable.’
It is doubtless true, that if the old logicians had been in possession of such premises as modern Probability is concerned with, and had adhered to their own way of treating them, they would have had to place them amongst such loci, and thus to make the consideration of them a part of their Dialectic. But inasmuch as there does not seem to have been the slightest attempt on their part to do more here than recognize the fact of the premises being probable; that is, since it was not attempted to measure their probability and that of the conclusion, I cannot but regard this part of Logic as having only the very slightest relation to Probability as now conceived. It seems to me little more than one of the ways (described at the commencement of this chapter) by which the problem of Modality is not indeed rejected, but practically evaded.
§ 27. As Logic is not the only science which is directly and prominently occupied with questions about belief and evidence, so the difficulties which have arisen there have been by no means unknown elsewhere. In respect of the modals, this seems to have been manifestly the case in Jurisprudence. Some remarks, therefore, may be conveniently made here upon this application of the subject, though of course with the brevity suitable on the part of a layman who has to touch upon professional topics.
Recall for a moment what are the essentials of modality. These I understand to be the attempt to mark off from one another, without any resort to numerical notation, varying degrees of conviction or belief, and to determine the consequent effect of premises, thus affected, upon our conclusions. Moreover, as we cannot construct or retain a scale of any kind without employing a standard from and by which to measure it, the attainment and recognition of a standard of certainty, or of one of the other degrees of conviction, is almost inseparably involved in the same enquiry. In this sense of the term, modal difficulties have certainly shown themselves in the department of Law. There have been similar attempts here, encountered by similar difficulties, to come to some definite agreement as to a scale of arrangement of the degrees of our assent. It is of course much more practicable to secure such agreement in the case of a special science, confined more or less to the experts, than in subjects into which all classes of outsiders have almost equal right of entry. The range of application under the former circumstances is narrower, and the professional experts have acquired habits and traditions by which the standards may be retained in considerable integrity. It does not appear, however, according to all accounts, as if any very striking success had been attained in this direction by the lawyers.
§ 28. The difficulty in its scientific, or strictly jurisprudential shape, seems to have shown itself principally in the attempt to arrange legal evidence into classes in respect of the degree of its cogency. This, I understand, was the case in the Roman law, and in some of the continental systems of jurisprudence which took their rise from the Roman law. “The direct evidence of so many witnesses was plena probatio. Then came minus plena probatio, then semiplenâ major and semiplenâ minor; and by adding together a certain number of half-proofs—for instance, by the production of a tradesman's account-books, plus his supplementary oath—full proof might be made out. It was on this principle that torture was employed to obtain a confession. The confession was evidence suppletory to the circumstances which were held to justify its employment.”[21]
According to Bentham,[22] the corresponding scale in the English school was:—Positive proof, Violent presumption. Probable presumption, Light or Rash presumption. Though admitted by Blackstone and others, I understand that these divisions are not at all generally accepted at the present day.
§ 29. In the above we are reminded rather of modal syllogisms. The principal practical form in which the difficulty underlying the simple modal propositions presents itself, is in the attempt to obtain some criterion of judicial certainty. By ‘certainty’ here we mean, of course, not what the metaphysicians term apodeictic,[23] for that can seldom or never be secured in practical affairs, but such a degree of conviction, short of this, as every reasonable person will feel to be sufficient for all his wants. Here again, one would think, the quest must appear, to accurate thinkers, an utterly hopeless one; an effort to discover natural breaks in a continuous magnitude. There cannot indeed be the least doubt that, amongst limited classes of keen and practised intellects, a standard of certainty, as of everything else, might be retained and handed down with considerable accuracy: this is possible in matters of taste and opinion where personal peculiarities of judgment are far more liable to cause disagreement and confusion. But then such a consensus is almost entirely an affair of tact and custom; whereas what is wanted in the case in question is some criterion to which the comparatively uninitiated may be able to appeal. The standard, therefore, must not merely be retained by recollection, but be generally recognizable by its characteristics. If such a criterion could be secured, its importance could hardly be overrated. But so far as one may judge from the speeches of counsel, the charges of judges, and the verdicts of juries, nothing really deserving the name is ever attained.
§ 30. The nearest approach, perhaps, to a recognized standard is to be found in the frequent assurance that juries are not bound to convict only in case they have no doubt of the guilt of the accused; for the absolute exclusion of all doubt, the utter impossibility of suggesting any counter hypothesis which this assumes, is unattainable in human affairs. But, it is frequently said, they are to convict if they have no ‘reasonable doubt,’ no such doubt, that is, as would be ‘a hindrance to acting in the important affairs of life.’ As a caution against seeking after unattainable certainty, such advice may be very useful; but it need hardly be remarked that the certainty upon which we act in the important affairs of life is no fixed standard, but varies exceedingly according to the nature of those affairs. The greater the reward at stake, the greater the risk we are prepared to run, and conversely. Hardly any degree of certainty can exist, upon the security of which we should not be prepared to act under appropriate circumstances.[24]
Some writers indeed altogether deny that any standard, in the common sense of the word, either is, or ought to be, aimed at in legal proceedings. For instance, Sir J. F. Stephen, in his work on English Criminal Law,[25] after noticing and rejecting such standards as that last indicated, comes to the conclusion that the only standard recognized by our law is that which induces juries to convict:—“What is judicial proof? That which being permitted by law to be given in evidence, induces twelve men, chosen according to the Jury Act, to say that, having heard it, their minds are satisfied of the truth of the proposition which it affirms. They may be prejudiced, they may be timid, they may be rash, they may be ignorant; but the oath, the number, and the property qualification, are intended, as far as possible, to neutralize these disadvantages, and answer precisely to the conditions imposed upon standards of value or length.” (p. 263.)
To admit this is much about the same thing as to abandon such a standard as unattainable. Evidence which induces a jury to convict may doubtless be a standard to me and others of what we ought to consider ‘reasonably certain,’ provided of course that the various juries are tolerably uniform in their conclusions. But it clearly cannot be proposed as a standard to the juries themselves; if their decisions are to be consistent and uniform, they want some external indication to guide them. When a man is asking, How certain ought I to feel?
to give such an answer as the above is, surely, merely telling him that he is to be as certain as he is. If, indeed, juries composed a close profession, they might, as was said above, retain a traditional standard. But being, as they are, a selection from the ordinary lay public, their own decisions in the past can hardly be held up to them as a direction what they are to do in future.
§ 31. It would appear therefore that we may fairly say that the English law, at any rate, definitely rejects the main assumption upon which the logical doctrine of modality and its legal counterpart are based: the assumption, namely, that different grades of conviction can be marked off from one another with sufficient accuracy for us to be able to refer individual cases to their corresponding classes. And that with regard to the collateral question of fixing a standard of certainty, it will go no further than pronouncing, or implying, that we are to be content with nothing short of, but need not go beyond, ‘reasonable certainty.’
This is a statement of the standard, with which the logician and scientific man can easily quarrel; and they may with much reason maintain that it has not the slightest claim to accuracy, even if it had one to strict intelligibility. If a man wishes to know whether his present degree of certainty is reasonable, whither is he to appeal? He can scarcely compare his mental state with that which is experienced in ‘the important affairs of life,’ for these, as already remarked, would indicate no fixed value. At the same time, one cannot suppose that such an expression is destitute of all signification. People would not continue to use language, especially in matters of paramount importance and interest, without meaning something by it. We are driven therefore to conclude that ‘reasonable certainty’ does in a rude sort of way represent a traditional standard to which it is attempted to adhere. As already remarked, this is perfectly practicable in the case of any class of professional men, and therefore not altogether impossible in the case of those who are often and closely brought into connection with such a class. Though it is hard to believe that any such expressions, when used for purposes of ordinary life, attain at all near enough to any conventional standard to be worth discussion; yet in the special case of a jury, acting under the direct influence of a judge, it seems quite possible that their deliberate assertion that they are ‘fully convinced’ may reach somewhat more nearly to a tolerably fixed standard than ordinary outsiders would at first think likely.
§ 32. Are there then any means by which we could ascertain what this standard is; in other words, by which we could determine what is the real worth, in respect of accuracy, of this ‘reasonable certainty’ which the juries are supposed to secure? In the absence of authoritative declarations upon the subject, the student of Logic and Probability would naturally resort to two means, with a momentary notice of which we will conclude this enquiry.
The first of these would aim at determining the standard of judicial certainty indirectly, by simply determining the statistical frequency with which the decisions (say) of a jury were found to be correct. This may seem to be a hopeless task; and so indeed it is, but not so much on any theoretic insufficiency of the determining elements as on account of the numerous arbitrary assumptions which attach to most of the problems which deal with the probability of testimony and judgments. It is not necessary for this purpose that we should have an infallible superior court which revised the decisions of the one under consideration;[26] it is sufficient if a large number of ordinary representative cases are submitted to a court consisting even of exactly similar materials to the one whose decisions we wish to test. Provided always that we make the monstrous assumption that the judgments of men about matters which deeply affect them are ‘independent’ in the sense in which the tosses of pence are independent, then the statistics of mere agreement and disagreement will serve our purpose. We might be able to say, for instance, that a jury of a given number, deciding by a given majority, were right nine times out of ten in their verdict. Conclusions of this kind, in reference to the French courts, are what Poisson has attempted at the end of his great work on the Probability of Judgments; though I do not suppose that he attached much numerical accuracy to his results.
A scarcely more hopeful means would be found by a reference to certain cases of legal ‘presumptions.’ A ‘conclusive presumption’ is defined as follows:—“Conclusive, or as they are elsewhere termed imperative or absolute presumptions of law, are rules determining the quantity of evidence requisite for the support of any particular averment which is not permitted to be overcome by any proof that the fact is otherwise.”[27] A large number of such presumptions will be found described in the text-books, but they seem to refer to matters far too vague, for the most part, to admit of any reduction to statistical frequency of occurrence. It is indeed maintained by some authorities that any assignment of degree of Probability is not their present object, but that they are simply meant to exclude the troublesome delays that would ensue if everything were considered open to doubt and question. Moreover, even if they did assign a degree of certainty this would rather be an indication of what legislators or judges thought reasonable than of what was so considered by the juries themselves.
There are indeed presumptions as to the time after which a man, if not heard of, is supposed to be dead (capable of disproof, of course, by his reappearance). If this time varied with the age of the man in question, we should at once have some such standard as we desire, for a reference to the Life tables would fix his probable duration of life, and so determine indirectly the measure of probability which satisfied the law. But this is not the case; the period chosen is entirely irrespective of age. The nearest case in point (and that does not amount to much) which I have been able to ascertain is that of the age after which it has been presumed that a woman was incapable of bearing children. This was the age of 53. A certain approach to a statistical assignment of the chances in this case is to be found in Quetelet's Physique Sociale (Vol. I.
p. 184, note). According to the authorities which he there quotes it would seem that in about one birth in 5500 the mother was of the age of 50 or upwards. This does not quite assign the degree of what may be called the à priori chance against the occurrence of a birth at that age, because the fact of having commenced a family at an early age represents some diminution of the probability of continuing it into later life. But it serves to give some indication of what may be called the odds against such an event.
It need not be remarked that any such clues as these to the measure of judicial certainty are far too slight to be of any real value. They only deserve passing notice as a possible logical solution of the problem in question, or rather as an indication of the mode in which, in theory, such a solution would have to be sought, were the English law, on those subjects, a perfectly consistent scheme of scientific evidence. This is the mode in which one would, under those circumstances, attempt to extract from its proceedings an admission of the exact measure of that standard of certainty which it adopted, but which it declined openly to enunciate.
[1] Formal Logic, p. 232.
[2] This appears to be the purport of some statements in a very confused passage in Whately's Logic (Bk. II., ch. IV.
§ 1). “A modal proposition may be stated as a pure one by attaching the mode to one of the terms, and the proposition will in all respects fall under the foregoing rules;… ‘It is probable that all knowledge is useful;’ ‘probably useful’ is here the predicate.” He draws apparently no such distinction as that between the true and false modality referred to in the next note. What is really surprising is that even Hamilton puts the two (the true and the false modality) upon the same footing. “In regard to these [the former] the case is precisely the same; the mode is merely a part of the predicate.” Logic, I. 257.
[3] I allude of course to such examples as ‘A killed B unjustly,’ in which the killing of B by A was sometimes said to be asserted not simply but with a modification. (Hamilton's Logic, I. 256.) It is obvious that the modification in such cases is by rights merely a part of the predicate, there being no formal distinction between ‘A is the killer of B’ and ‘A is the unjust killer of B.’ Indeed some logicians who were too conservative to reject the generic name of modality in this application adopted the common expedient of introducing a specific distinction which did away with its meaning, terming the spurious kind ‘material modality’ and the genuine kind ‘formal modality’. The former included all the cases in which the modification belonged by right either to the predicate or to the subject; the latter was reserved for the cases in which the modification affected the real conjunction of the predicate with the subject. (Keckermann, Systema Logicæ, Lib. II.
ch. 3.) It was, I believe, a common scholastic distinction.
For some account of the dispute as to whether the negative particle was to be considered to belong to the copula or to the predicate, see Hamilton's Logic, I. 253.
[4] He has also given a short discussion of the subject elsewhere (Discussions, Ed. II.
p. 702), in which a somewhat different view is taken. The modes are indeed here admitted into logic, but only in so far as they fall by subdivision under the relation of genus and species, which is of course tantamount to their entire rejection; for they then differ in no essential way from any other examples of that relation.
[5] Letters, Lectures and Reviews, p. 61. Elsewhere in the review (p. 45) he gives what appears to me a somewhat different decision.
[6] It must be remembered that this is not one of the proportional propositions with which we have been concerned in previous chapters: it is meant that there are exactly 21 Ys, of which just 18 are X, not that on the average 18 out of 21 may be so regarded.
[7] I consider however, as I have said further on ([p. 320]), that the treatment in the older logics of Probable syllogisms, and Dialectic syllogisms, came to somewhat the same thing as this, though they looked at the matter from a different point of view, and expressed it in very different language.
[8] The distinction is however by no means entirely neglected. Thus Smiglecius, when discussing the modal affections of certainty and necessity, says, “certitudo ad cognitionem spectat: necessitas vero est in re” (Disputationes; Disp. XIII., Quæst. XII.).
[9] It may be remarked that Whately (Logic, Bk. II.
ch. II.
§ 2) speaks of necessary, impossible and contingent matter, without any apparent suspicion that they belong entirely to an obsolete point of view.
[10] Formal Logic, p. 233.
[11] The subject was sometimes altogether omitted, as by Wolf. He says a good deal however about probable propositions and syllogisms, and, like Leibnitz before him, looked forward to a “logica probabilium” as something new and desirable. I imagine that he had been influenced by the writers on Chances, as of the few who had already treated that subject nearly all the most important are referred to in one passage (Philosophia Rationalis sive Logica, § 593).
Lambert stands quite apart. In this respect, as in most others where mathematical conceptions and symbols are involved, his logical attitude is thoroughly unconventional. See, for instance, his chapter ‘Von dem Wahrscheinlichen’, in his Neues Organon.
[12] I cannot find the slightest authority for the statement in the elaborate history of Logic by Prantl.
[13] “Hi quatuor modi magnam censeri solent analogiam habere cum quadruplici propositionum in quantitate et qualitate varietate” (Wallis's Instit.
Logic.
Bk. II.
ch. 8).
[14] Laws of Thought, § 118.
[15] “Haud scio magis ne doctrinam modalium scholastici exercuerint, quam ea illos vexarit. Certe usque adeo sudatum hic fuit, ut dicterio locus sit datus; De modalibus non gustabit asinus.” Keckermann, Syst.
Log.
Bk. II.
ch. 3.
[16] Smiglecii Disputationes, Ingolstadt, 1618.
See also Prantl's Geschichte der Logik (under Occam and Buridan) for accounts of the excessive complication which the subtlety of those learned schoolmen evolved out of such suitable materials.
[17] Translation by T. M. Lindsay, p. 439.
[18] “The εἰκòς
and σημεῖον
themselves are propositions; the former stating a general probability, the latter a fact, which is known to be an indication, more or less certain, of the truth of some further statement, whether of a single fact, or of a general belief. The former is a general proposition, nearly, though not quite, universal; as ‘most men who envy hate’; the latter is a singular proposition, which however is not regarded as a sign, except relatively to some other proposition, which it is supposed may by inferred from it.” (Mansel's Aldrich; Appendix F, where an account will be found of the Aristotelian enthymeme, and dialectic syllogism. Also, of course, Grote's Aristotle, Topics and elsewhere.)
[19] “Nam in hoc etiam differt demonstratio, sen demonstrativa argumentatio, à probabili, quia in illâ tam conclusio quam præmissæ necessariæ sunt; in probabili autem argumentatione sicut conclusio ut probabilis infertur ita præmissæ ut probabiles afferuntur” (Crackanthorpe, Bk. V., Ch. 1); almost the words with which De Morgan distinguishes between logic and probability in a passage already cited (see Ch. VI. § 3).
Perhaps it was a development of some such view as this that Leibnitz looked forward to. “J'ai dit plus d'une fois qu'il faudrait une nouvelle espèce de Logique, qui traiteroit des degrés de Probabilité, puisqu'Aristote dans ses Topiques n'a rien moins fait que cela” (Nouveaux essais, Lib. IV.
ch. XVI). It is possible, indeed, that he had in his mind more what we now understand by the mathematical theory of Probability, but in the infancy of a science it is of course hard to say whether any particular subject is definitely contemplated or not. Leibnitz (as Todhunter has shown in his history) took the greatest interest in such chance problems as had yet been discussed.
[20] By loci were understood certain general classes of premises. They stood, in fact, to the major premise in somewhat the same relation that the Category or Predicament did to the term. Crackanthorpe says of them, “sed duci a loco probabiliter arguendi, hoc vere proprium est Argumentationis probabilis; et in hoc a Demonstratione differt, quia Demonstrator utitur solummodo quatuor Locis eisque necessariis…. Præter hos autem, ex quibus quoque probabiliter arguere licet, sunt multo plures Loci arguendi probabiliter; ut a Genere, a Specie, ab Adjuncto, ab Oppositis, et similia” (Logica, Lib. V., ch. II.).
[21] Stephen's General View of the Criminal Law of England, p. 241.
[22] Rationale of Judicial Evidence; Bk. I. ch. VI.
[23] Though this is claimed by some Kantian logicians;—Nie darf an einem angeblichen Verbrecher die gesetzliche Strafe vollzogen werden, bevor er nicht selbst das Verbrechen eingestanden. Denn wenn auch alle Zeugnisse und die übrigen Anzeigen wider ihn wären, so bleibt doch das Gegentheil immer möglich” (Krug, Denklehre, § 131).
[24] As Mr C. J. Monro puts it: “Suppose that a man is suspected of murdering his daughter. Evidence which would not convict him before an ordinary jury might make a grand jury find a true bill; evidence which would not do this might make a coroner's jury bring in a verdict against him; evidence which would not do this would very often prevent a Chancery judge from appointing the man guardian to a ward of the court; evidence which would not affect the judge's mind might make a father think twice on his death-bed before he appointed the man guardian to his daughter.”
[25] The portions of this work which treat of the nature of proof in general, and of judicial proof in particular, are well worth reading by every logical student. It appears to me, however, that the author goes much too far in the direction of regarding proof as subjective, that is as what does satisfy people, rather than as what should satisfy them. He compares the legislative standard of certainty with that of value; this latter is declared to be a certain weight of gold, irrespective of the rarity or commonness of that metal. So with certainty; if people grow more credulous the intrinsic value of the standard will vary.
[26] The question will be more fully discussed in a future chapter, but a few words may be inserted here by way of indication. Reduce the case to the simplest possible elements by supposing only two judges or courts, of the same average correctness of decision. Let this be indicated by x. Then the chance of their agreeing is x2 + (1 − x)2, for they agree if both are right or both wrong. If the statistical frequency of this agreement is known, that is, the frequency with which the first judgment is confirmed by the second, we have the means of determining x.
[27] Taylor on Evidence: the latter part of the extract does not seem very clear.