assumes that consciousness as such has energy, in assuming the action of final causes as something per se notum. Where it is something per se notum, and indeed an indisputable fact, is in the domain of common sense; it cannot be said to be so in science. This remark alone would suffice, in my opinion, to show the necessity of some such method as the present, in which subjective analysis should have its distinct place and its due weight secured to it.

I cannot here do more than indicate a few of the more important problems, or rather directions in which problems lie, the proper treatment of which demands a clear distinction of subjective analysis and scientific investigation, followed by its necessary corollary, their combination in what I call a Constructive Branch of Philosophy. What is very often understood by Philosophy is little more than this single branch, isolated from its necessary preliminaries, and based on some supposed self-evident intuitions or necessary axioms. The really fundamental work of philosophy lies in my first and second Rubrics, which it will be remembered are marked off from the third by the guiding principle of the method, namely, the subordination, in philosophy, of questions of genesis to questions of essence.

One more class of questions, however, it is impossible to omit mentioning, both on account of its intrinsic interest, and because it in a manner gathers up and comprises under it all those which have hitherto been mentioned in the present Rubric. I mean the class of questions relating to Religion. When we put together the questions of Ethic, that is, those which relate to man's practice as distinguished from his knowledge, with those which relate to the world in which he finds himself, and consider what we know or can make out of the universe so composed, the universe with man as its highest positively known constituent, we are standing, as it were, at a higher level or plane of construction than in taking the two former classes of questions separately. It is a kind of Teleology of the universe, man included, that we are then considering the possibility of attempting. The questions of contingency and necessity, of possibility and impossibility, of infinity or absoluteness, are therein comprised as subsidiaries; and the teleology is considered as traceable, if at all, in the purpose or system of purposes for which man as representative of the whole is designed.

Here it is plain that we are on ethical ground; it is predominantly a practical problem that we have before us. But at the same time it is Ethic carried to a higher level, Ethic

in presence of the whole imaginable or surmisable universe, not merely in presence of mundane and social relationships. The attitude and frame of mind naturally inspired by considerations of this kind, quite irrespective of demonstrable knowledge, is the religious attitude and frame of mind. The possibility, and indeed the necessity of it, seems to me to be founded in the function of all distinct consciousness, that of reflective perception, which, as we have seen, is the cardinal fact of experience and the basis of philosophy. Experiencing is always looking back upon consciousness while moving forward into the unexperienced future. But the mental attitude of expecting the future does not depend upon what or how much we are entitled to anticipate of its nature from our knowledge of the past. Supposing our grounds for a speculative knowledge of the universe, beyond a certain limit, to fail us, we have still a knowledge of what it is ethically desirable for ourselves to do and to be, whether within that limit or beyond it.

I say if our speculative knowledge fails us beyond a certain limit, because it would be out of place here to argue the question, whether it does so or not. If it does not, and we can consequently frame a positive conception of the nature of that Power which sustains and governs the universe in its totality, our philosophy will belong to what Prof. Fraser, in his excellent little work Berkeley (pt. iii. ch. 4) has well called Gnosticism. If, on the contrary, it fails to enable us to frame such a conception, then we shall have what the same writer calls a Faith-philosophy. Only that here, before adopting so convenient a catchword, it will be necessary to distinguish two very different modes of thought to which at first sight it seems applicable. One is where faith is made to supply the deficiency of evidence in support of some definite conception. The other is where it means practical trust in the universal and unseen power, beyond the reach of any definite conception at all. Prof. Fraser, in speaking of our ideas as requiring to be "cemented" by faith (ibid., p. 232), would seem to be contemplating the former kind only. But faith can never legitimately be among the premisses of philosophy, though it may be among its conclusions.

The ideas in which a faith, which is the conclusion of philosophy, may be embodied would then appear as purely anthropomorphic symbols, enabling us practically to think of it and realise it. They would be objective thoughts incapable of positively representing the object thought of, because incapable (by the supposition) of being completely determined as

objective thoughts. Not that this incommensurability with their object thought of would imply a non-phenomenal nature in the latter. This is forbidden by the nature of reflective perception, which is the central fact on which all philosophy and experience are built. The positive content of the object thought of, not its existence relatively to ourselves, is what is beyond the grasp of speculation. It must be characterised as unknown, but not unknowable a parte rei, provided adequate powers of knowing were supposed. The distinction between a noumenal world of real reality and a phenomenal world of apparent reality, the former being the hidden ground of the latter, and existing (as it is sometimes expressed) "out of time altogether," is a distinction impossible to sustain as true, seeing that the mere thinking of such an existence, so as to draw the distinction, is eo ipso bringing it within the panorama of consciousness, and rendering it phenomenal to reflection. The same thing cannot, in respect of its existence, at once belong and not belong to the panorama.

II. ON THE NATURE AND FUNCTIONS OF A COMPLETE SYMBOLIC LANGUAGE.

By SOPHIE BRYANT, D.Sc.

SYMBOLIC Logic has, of late years, been issuing slowly from the obscurity in which it had remained so long; and Boole's great work on the subject now receives a fair share of attention from the logicians at least, though the mathematicians are still somewhat behindhand in offers of assistance for its further development, and the general public of educated persons has hardly begun to find out its fascinations. Boole has successors, and these we may consider as of four kinds: (1) critics tending to become opponents, like the late Professor Jevons, (2) semi-disciples, as for instance Mr. C. S. Peirce, who partially accept his methods, but reject or ignore his principles, by an arbitrary use of non-mathematical, in preference to mathematical, symbols, (3) independent successors, like Mr. McColl, who differ from him partly, but more by accident than otherwise, and (4) genuine followers, such as Dr. Venn, whose work mainly consists in developing and supplementing Boole's own work, on the lines which he himself laid down.

In a sense this is satisfactory: it is well that there should be diversity of thinking. It is not well, however, that there should be heterogeneity of result. Even a slight study of the literature of the subject shows that we are threatened by an increasing variety of symbolic procedure, some of it more or less arbitrary; and this is not satisfactory at all. It becomes, therefore, a matter of practical, as well as theoretical, importance that such definite inquiry into the nature of symbolic language should be made as, besides other results, may lead to the establishment of tests for the legitimacy of any proposed symbolic method. Symbolic language, like any common language, has natural laws of growth, in conformity with which it extends its application from one department of thought to another. A consciousness of these natural laws is more necessary in this case than in others, because the growth proceeds with a more deliberate invention on the part of a few individual thinkers, and individual thinkers are liable to eccentricity when they invent what can be invented arbitrarily, without consciousness of a rule of reason that ought to be their guide.

The argument of the following pages is in the direction of such inquiry; and the result will, I believe, be found to be a further realisation of Boole's fundamental idea, that the language of mathematics is naturally the universal language of thought, and that general logic, therefore, is mathematics with all conceptions of quantity struck out. That this is Boole's idea becomes perfectly evident once we are clear as to the sense in which he uses the term mathematics; but he has not expressed himself so as to make misunderstanding impossible on this point, and has, in consequence, been understood by Prof. Jevons and others, to make general logic a branch of the particular logic of quantity, with which the name mathematics is specially associated. In Boole's sense, however, and he does not stand alone in this respect among mathematicians - mathematics includes ordinary quantitative mathematics, but its field is far from being wholly covered thereby. Hence, it is open to the mathematician, as such, to investigate other developments of formal truth, and to bring these within the domain of general mathematics, if he can. This is just what the author of The Laws of Thought set himself to do it was his aim to show that qualitative logic and quantitative mathematics could be treated as departments of the same formal science, and he called that general formal science by the name of mathematics. We may call it general logic, if we please, without in the least affecting Boole's position; for that position consists simply in the assertion that mathematical form is the true type of logical form in general.

Boole's method of establishing this position was by comparison of ordinary logic with ordinary mathematics, and the development of the former on the lines of the latter. Our present inquiry into the fundamental nature of symbolic language, as such, should lead, if it lead us anywhere, to the source of that remarkable analogy which Boole discovered and developed, but did not explain.

An inquiry into the nature of symbolic language is an inquiry into the nature of Language as distinguished from languages. These partake of racial, and even individual, peculiarities; whereas Language with a capital L should be conceived as the medium, more or less perfect, for thought as such, namely as universal thought. We must first decide then on some principle, or principles, universally agreed to, by which we can all pledge ourselves to stand or fall in our choice of symbols and symbolic procedure. If afterwards we offend against this principle, our symbolic language will be self-judged as peculiar to ourselves, sub