or appreciation of those facts. Attempts have indeed been made,-which will receive notice in their due place,—to evade the necessity of any such appeal, but as it seems to me without avail. No distinction will really satisfy our requirements which does not involve the admission that the essential attributes are those which are 'universally recognized', or at least so far agreed upon by all reasonable authorities as to be 'implied in the use of the name', or which does not involve in some equivalent way a conventional standard of attainment in respect of the significance of the name. And this holds good throughout our treatment of the whole doctrine of Definition under its various aspects, such for instance as the distinction between Real and Verbal propositions. We are perpetually encountered, in all these discussions, by the necessity of admitting a distinctly subjective element in the way of a conventional or normal estimate of the facts as distinguished from the mere occurrence of the facts themselves.

Where, however, these considerations become most prominent is in the treatment of the syllogistic process. For instance the statement is frequently made, and has found its way into works of merit that no new truth is ever reached by reasoning; and, in more cautious and restricted language, that every syllogism is a petitio principii. In any intelligible sense of the words the former statement seems palpably absurd. De Morgan meets it in his usual happy style by the reply that "persons not spoiled by sophistry will smile when they are told that knowing two straight lines cannot enclose a space, the whole is greater than its part, &c.,-they as good as knew that the three intersections of opposite sides of a hexagon inscribed in a circle must be in the same straight line. Many of my readers will learn this now for the first time: it will comfort them much to be assured, on many high authorities, that they virtually knew it ever since their childhood" (Formal Logic, p. 45). This is conclusive as against those who do not hold that geometrical reasoning is largely a process of intuition; but, if this objection against its applicability be raised, we have only to take a few of the complicated propositions which the Symbolic Logic will readily furnish, set these down side by side with some remote conclusion from them, and ask the ingenuous reader if there is nothing 'new' to him in the latter. The conclusion

may follow as a consequence from a few propositions which in themselves are admitted readily enough, but if we are to allow the objection in question we must either maintain that the conclusion is not new or maintain that it was not reached by reasoning.

What is confusedly intended by those who use such an objection as that in question is probably this. They mean that the conclusion is, so to say, in the facts, equally with the premises; being indeed nothing else than those very premises, or a portion of them, differently worded. Mill himself uses this argument in a narrower application, when contending that simple conversion of a proposition is not inference, because there is no new fact involved. In other words, given better powers of comprehension or intuition, we might directly perceive the conclusion in the premises, just as we perceive the import of the premises separately. This is certainly true; but then, in this sense, all knowledge is lying there before us in the facts. The riddle of the world in general, along with all minor puzzles, is there sure enough, only unfortunately we cannot make the virtual knowledge serve the purpose of knowledge which is real.

The acceptance which this opinion has received is probably largely due to the almost absurdly trite and obvious examples by which the syllogistic process is commonly illustrated. This will occupy our attention hereafter when we come to discuss the Syllogism. All that I am now concerned to establish is that 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 passing from one to the other, from facts which we have 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.

So much then, for the present, as tempting to over-objectify the science. when we underestimate the objective

to the results of at

On the other hand, element the conse

1

quences are quite as mischievous. It has, of course, never escaped notice that some original appeal to the world of phenomena was necessary in order to acquire our data, and to attach any value to our definitions. All logicians have admitted as much as this. But a much closer and more continuous appeal to the external world is demanded in order to carry out our system to any satisfactory results. The substance of the remarks made above might indeed be repeated in great part, with as much justice, in order to show the necessity of such an appeal to phenomena as to show the impossibility of attempting to appeal to nothing but them. The whole Theory of Induction, for instance, and the processes of Rational Classification, demand continual resort to nature at first hand. No mere introspection, and no rules which do not go beyond simple consistency nor attempt to grapple with the true and the false, can avail us here. As to this there is but little need to insist, for nothing can be more conclusive than the frank avowals, in fact the claims, of such a consistent writer as Mansel. A considerable portion of his Prolegomena Logica is occupied with an almost contemptuous refusal to admit one application after another which has commonly found acceptance amongst logicians, and in regard to what he does admit he is certainly free from any charge that he has thrown light on the processes of Induction or of Classification.

I need hardly remind the reader that the remarks in the last few pages are not offered as an adequate discussion of the points involved, but are meant to prepare the way for future reference. They are intended to indicate how many and important are the consequences of the general position here maintained, viz. that a system of comprehensive Logic must postulate, must in fact take as its basis, a fundamental duality. This twofold aspect of the science,-objective and subjective,is so important a characteristic that it will be perpetually presenting itself in various applications throughout the course of this work. It seems to me almost peculiar to Logic amongst the sciences. There are some, like Psychology, in which the primary reference is throughout to the mental processes; and there are others, like the ordinary physical sciences, in which the primary reference is throughout to the external phenomena. But a science like Logic, which has to do with the processes

of the human mind when judging about phenomena, and, more particularly, with the process of gradually extending our knowledge of those phenomena, occupies necessarily an intermediate position. The treatment here adopted may indeed by comparison be called Material or Objective,-I have chosen to insist here and elsewhere upon the convenience of this designation of my conception of Logic, but it must be remembered that the epithet is employed to mark the departure from the extreme subjectiveness of the customary treatment. If it were not for this bias of traditional treatment against which we have to press, it would be inappropriate to adopt a designation which implies closer affinity with one side of the duality than with the other, for the neglect of either distorts and damages our view of the whole,

VI. The next postulate we have to discuss follows as a direct consequence of the above duality. It is best described summarily by the double statement that we must not only recognize the distinction between the true and the false, but that we must also have decided in any given case what sort of test we intend to adopt in order to distinguish between them. I desire expressly to call attention to this twofold way of stating our requirement, because there really are two very distinct questions involved whenever we speak of logical truth and falsehood. I cannot but think that it is greatly owing to a lack of appreciation of this distinction that we find such extraordinary diversity of opinion amongst logicians as to whether they have any business to take truth and falsehood into account. Whereas some writers (for instance, Mill) declare that "it is only as a means to material truth that the formal, or to speak more clearly, the conditional validity of an operation of thought is of any value", and that the consideration of the former is “Logic κατ' ἐξοχήν, and anything else called by the name is only ancillary to it" (Exam. of Sir W. Hamilton, pp. 402, 3); we have on the other hand Jevons curtly remarking in reference to an examination question which had touched on this point (by enquiring 'whether predication involves real existence?') that it "must have been asked under some misapprehension. The inferences of formal logic have nothing whatever to do with real existence; that is, occurrence under the conditions of time and space." (Studies in Deductive Logic, p. 55.)

(1) To clear our way through this confusion it is quite essential to divide our enquiry into two parts. The first of these concerns the general necessity of admitting the distinction between the true and the false, between what does exist and what does not. This necessity springs at once from the postulate last considered. Start with a world of phenomena, on the one side and an observant mind contemplating this, on the other, and there arises at once the possibility of agreement or diversity between the two. In the mere phenomena there is nothing which can be termed true or false. Equally so in the mere notions which we entertain of the phenomena. To produce the distinction in question these two elements have to be brought somehow into relation.

In saying this I need hardly remind the reader that we have already, in our first assumption, decided to pass over the fundamental question as to the ultimate criterion of truth. In Logic we take the world substantially as it appears to us, that is, as it is given to us in sense. We leave to Metaphysics the question of the ultimate validity of sense and consciousness what exactly they tell us, and with what certainty. We have to stop short of this primary stage, and we understand by 'truth' the agreement of our notions with the testimony of sense This agreement must be briefly considered in its threefold application, to terms, to propositions, and to reasonings.

First then as regards the term, or rather,-what will be more convenient to treat here,―its corresponding mental element, the notion or concept. Every notion we entertain must either be in harmony with its supposed object, or not. The work of verification may of course be a tedious and delicate one: it may even be one which in our present circumstances we are unable completely to carry out. But we must always presuppose that the process of verification is conceivable, whether or not it be, in any particular case, feasible. A full account of the process must be sought in Psychology, so I only add the few remarks necessary in order to obviate misunderstanding. Remember then that we are in no wise concerned with the question which for ages perplexed philosophers, viz. in what sense our ideas 'resemble' or are 'copies of' actual external objects. All that we compare is the impression at first hand and at second hand, the presentation and the re