universities. Dr Schiller has stated that his emphatic assertion of some truths which would seem to be obvious to every common-sense mind, and his criticisms on sundry minor points which I, for one, am in no way disposed to dispute, are necessitated by the methods of teaching the subject. He is in a position to know; and any defence on these matters should come from a professional teacher, and is more suitable for the technical journals than for the pages of this Review. Universities, university teaching and management, are open to criticism in many ways. Logicians are not the only specialists who overestimate the value of their own study; and logic is not the only subject in which we find the element of sham and pretence, and in which the power of vested interests can be discovered. Such are the common vices of all endowment of university teaching, and, it must be admitted, also of scientific research. Such matters, which continually appear throughout Dr Schiller's attack on logic, we cannot deal with here.

The point with which we are immediately concerned is that, in spite of all his diatribes, Dr Schiller admits nearly all that the old-fashioned philosopher, with no axe to grind, needs to assert. Truth will out, even in the most embittered controversy. In his penultimate chapter, with many a jibe and joke, Dr Schiller admits for formal logic a certain sphere, within certain prescribed limits. It is called a game. Perhaps it is. But, if we examine closely enough, much else beside logic can be described in similar terms. Symbolic logic is referred to as another game, played with the same rules, formal logic only more so. By a strange coincidence, it happens that, in the main, the limits that Dr Schiller has laid down for formal logic, as a final jibe against its validity and usefulness, are similar to those which I have myself laid down in all seriousness; and, what is more striking, I have, with a considerable consensus of agreement from mathematicians, shown that the same principles apply also to mathematics. Mathematics is also capable of degenerating into a game; and the mathematicians also are subject to the same vice of mistaking their conceptualism for objective reality. If I may take the liberty of adding myself to Mr Alfred

Sidgwick as a consistently formal logician, I would say that I am quite content that the formal logician should 'confine himself strictly within the formal limits he has marked out for himself and must not pronounce upon those logical topics which involve a knowledge either of material truth or of human psychology.' Dr Schiller's admission, however, grudging as it is, is an answer to the passage I have already quoted, asserting that such an abstraction and limitation is not possible.

Another point that we cannot grant to Dr Schiller and the pragmatists concerns the nature of axioms rather than that of reasoning itself. There has always been, as Dr Coffey, following the schoolmen, points out, a fallacy arising from the unnecessary multiplication of axioms, but it is on the nature of the axioms themselves that the battle with the pragmatist must be fought. The formal logician holds a view which differs fundamentally from the pragmatist concerning the nature of axioms. If once we grant the existence of axioms which are, as we may call it, given, we supply a solid foundation on which formal logic can build. If once we admit psychologic into the sphere of axiomatic truth or within the process of reasoning itself, not only formal logic but reason itself crumbles into nothingness and futility.

The foregoing remarks are a necessary preliminary to a consideration of the development of the study in recent years. In spite of the interest shown in the development of the science of logic, not only by experts but by the amateur philosopher and by the general public, we are bound to note that, in the opinion of at least one expert fully competent to judge, the interest is mistaken and misleading, and that, for the advancement of knowledge, it would be better if the whole fabric were swept away. To those who agree with him there is little left to discuss. And, while it is fully possible to allow that many detailed criticisms on the content of the current logic are sound, we can only reserve any scope for logic by disagreeing with his general standpoint and with his fundamental diagnosis.

In order to retain logic as possible or desirable, we are bound to assume that there are valid forms of reasoning, and that, in so far as we reason in valid form,

we may or may not obtain material truth, but we do obtain conclusions which are undeniably implicit in the premisses we adopt. Let us take a well-known example. Euclidean geometry starts with certain postulates and axioms. Recently, other geometries have arisen, and in these systems the axioms of Euclid are varied in certain particulars. A body of conclusions follows which is wholly at variance with those of ordinary geometry. The angles of a triangle are no longer equal to two right angles; parallel lines meet; and we need only to travel far enough in one direction to return to the point from which we started. It is in considerations of this kind that the concept of formal validity arises. There may be, and indeed is, some dispute whether Euclidean or non-Euclidean geometry is materially true. Such a dispute does not, to anyone but an expert, sound very sensible, but it has, in fact, occurred. But one thing is beyond dispute. Euclidean and non-Euclidean geometries cannot both be materially true, cannot both refer to perceptual space. Yet there is no doubt of the nexus which connects each form of geometry with its premisses. How can this nexus be explained unless we admit an abstraction of form from matter? To discuss this point fully would require the whole of the space at our disposal, and would, moreover, be somewhat uninteresting to the general reader. We must, therefore, without full discussion, assume that Dr Schiller is wrong and state our disagreement with him as to the fundamental axiom of logic. Dr Schiller would call it a postulate, and, as, in his view, there is small distinction between the two, we will take as our fundamental logical postulate that we can abstract form from matter and that formal logic is, at least, a theoretical possibility.

With this assumption, there is still room for dispute as to whether the theoretical possibility is an actuality. There is still the battle to be fought concerning its degree of utility, actual and potential. The existence of logic, per se, does not necessarily imply that the Aristotelian syllogism is its best representative. But our postulate does at least imply that, if contemporary formal logic is inadequate, the remedy is further advancement and research, not the obsolescence of the whole study.

The potential importance of the study is increased by a view which, though it is not easy to assign it to any particular logician, and though it has not reached some of the current text-books, has become almost a commonplace among logicians. There has been, since the days of Mill, much loose talk concerning inductive logic and inductive reasoning. Such discussions are based on a misapprehension. It is becoming more and more fully recognised that there is only one form of reasoning, deductive reasoning, and only one form of logic, properly so called, deductive logic. In scientific enquiry, experiment and observation there is much else than reasoning properly so called, but, in so far as the scientist reasons, he deduces, and the method of his reasoning comes within the sphere of ordinary formal logic. To this extent the logic of thought and the logic of science are identical. The rightful extension of logic, now called methodology, consists, or should consist, of the study of scientific method, especially those aspects which are additional to reasoning properly so called. But the rise of scientific studies should, in theory, make the significance, though not the scope, of logic greater rather than less.

The most important of the somewhat numerous extant logical forms is the Aristotelian syllogism. Of recent years it has been the occasion of many attacks, much attempt at extension and improvement, endless discussion and criticism, yet, in spite of all, it holds the field. On this point, the two critics of formal logic cancel each other. Dr Mercier's criticism is mainly a spirited attack on the syllogism as a logical form and an attempt to displace it by others. But Dr Mercier, though he does not carry it out in practice, upholds, in the main, the ideal of formal validity. He is by no means consistent in so doing. Here and there throughout his volume occur attempts to use the pragmatic catchwords and to refer to the purpose of the argument. But such reference is not consistent with the main trend of his argument. In so far as he is attempting to found a new logic of deduction he is merely trying to substitute one variety of logical inference for another. This aim is diametrically opposed to Dr Schiller's attack on the ideal of formal validity. It is well indicated by his own illustration. Modern geometry (not metageometry), in so far as it

has displaced the old Euclid (the change is neither so widespread nor so final as Dr Mercier thinks, and the advantages are somewhat dubious), is but the displacement of one mode of formally valid geometrical proof by another. The premisses and the conclusions in both cases are identical; it is only the order and method of exposition that is changed. The illustration enables us to put the syllogism in its place, and to defend it both from those who claim too much for it and from those who publish spirited and not very well-informed attacks. The syllogism is a mode of deductive inference. In addition to having the advantage of tradition, authority and two thousands of years' teaching and discussion, it is a form in which every valid argument can be expressed. Even Dr Schiller regards the syllogism as a great discovery. He may be understood to say that he objects to formal logic on principle; but, if he admitted the principle, he would give a high place to the syllogism.

It is on this account that the old-fashioned exponents of logic, so ably represented by Dr Coffey, who uphold the scholastic tradition, can so easily defend it against modern attacks. They have a well-established logic which works. Their weakness lies in the danger that they are inclined to make extravagant claims and to say that they have the only possible logic. It is correct to say that we can always, if we wish, express valid reasoning syllogistically. It is incorrect to say that we always naturally or necessarily reason in syllogisms. The syllogism is an admirable mode of testing the formal validity of inference, but it does not follow that the mind, in inferring from premiss to conclusion, naturally adopts that form. The modern representa

tives of the schoolmen must abandon such a claim. Mr Bradley expressed the idea clearly and epigrammatically many years ago. He showed, and his argument has never successfully been controverted, that we cannot and do not reason directly from particulars to particulars. All reasoning takes place through a universal, stated or implied, true or false. The syllogism is thus in accordance with modern philosophical theory. But it does not follow that the only possible, or the natural, or the clearest, or the most convenient, or the truest universal is the major premiss of a syllogism.