essaying to find the foundations of a new political code and of a new rational faith which is above current sophisms and prejudices. He has set himself the task of showing the contractual character of social life, and of so justifying, as contrasted with revolutionary anarchy, the notions of duty and legal sanction, and as opposed to conservative routine the necessity of a constant amelioration of human affairs. But he is perhaps mistaken when he talks to us of a "doctrine" of solidarity. Solidarity is simply a fact, a condition of existence, and that condition is the analogue in social life of what we call interdependence of phenomena in the world of physics, chemistry, and astronomy. But this condition is not the only one and cannot accordingly be used in constructing a perfected political doctrine. Nevertheless, I do not deny that it is opportune to place it in relief, to show its effects in human affairs, and to seek, in fine, motives of action in the sentiment which corresponds to the theoretical knowledge of solidarity. And this sentiment is capable of acquiring such a power that every study which aims at illuminating and strengthening it is largely justified by the end which is set.

M. Bourgeois does not attack practical questions in this work, that is to say, does not attempt to carry solidarity over into the real facts, nor to harmonise it with the conditions which proceed from history, race, environment, etc. He does not overlook the latter, however. He recognises, for example, the natural inequality of men, which has always had and always will have grave consequences for the organisation of societies. We should, in fine, encourage him to devote more of his attention to these problems, and especially to disengage them from the errors which the ignorance or violence of parties so easily introduces into them.

*

M. J. Novicow publishes under the title of Conscience et volonté sociales1 a very interesting study, in which he analyses the higher manifestations of collective life, showing how they grow, are propagated, and rendered efficacious. This study supposes and confirms

1 Giard et Brière, publishers.

the "organic" theory of society so fiercely combated in recent years. I have already touched upon this controversy, inclining to the doctrine to which M. Novicow to-day brings valuable support. The doctrine which views society as an organism, does not prevent him from resolving social acts into psychical acts. "Social movements," he writes, "are a totalisation of cerebral and muscular movements and nothing more. Every social act is resolvable into a certain number of psychical acts." And while it is true that "the action of men upon one another does produce a peculiar resultant product," it is also true that social volitions always result from the ideas and internal sentiments of individuals, "and not all from the mere fact that they are associated together."

On the question of determinism M. Novicow is perhaps less precise. He accepts psychical determinism and rejects social determinism. "Social liberty," he says, "remains intact. The actions of men always conform to what appears to them their interest." Which is correct, provided we recognise that individual determinations necessarily find their echo in the collective life. No doubt it is useless to talk of an outward constraint upon society, of a sort of obscure destiny inhering in things; but we should certainly take account of the constraint exercised by accumulated facts-ideas, habits, institutions, etc.-for their succession, which is not at all fortuitous, constitutes precisely what we call the laws of history.

One lesson among many others may be drawn from these studies. It is the necessity even in democracies of an aristocracy, that is to say, of an élite of men sharply differentiated and adapted for the directing and governing function. M. Novicow deduces this lesson from the organic theory, and he supports it upon facts in the solidest way. He proceeds in the same manner and is not less decisive with regard to the current sophisms of "socialism."

I should like to speak at greater length of this work. It is to be recommended for the clearness of view which its author displays, for the sureness of his criticisms, his wealth of information, and for the lofty confidence which he has in the future, while not veiling. any of the evils of the present.

A curious little work by M. RoISEL, L'idée spiritualiste,1 sketches with rapid strokes the religions of the world and shows us their inevitable ultimate resolution in a monistic philosophy capable of satisfying at once the needs of reason and the heart. M. Roisel has the merit of being clear and succinct; his erudition is tactfully used. Perhaps he does not cite sufficient proof for his not improbable hypothesis of a "Scythian" culture to which the nations of the dolmens supposedly belong and which is held to have preceded Aryan civilisation. Under the name of Scythism would be classed the doctrine which takes for granted the primordial existence of two coeternal causes: (1) a spirit which exists by itself and alone is active; (2) a matter composed of absolutely passive molecules; the result being that the universe is the product of the constant action of the first principle upon the second. To this doctrine we should have opposed the ontological doctrine of the Aryan mind with its different developments, and the spiritualistic idea which both represent would finally give way before the atomic doctrine which slowly developed by their side and has won the adherence of so many great minds.

I recommend the perusal of this volume, which bears witness to a distinguished mind. The reader will find here, in the first part, enlightened and liberal views upon Judaism and Christianity, for example, and in the second part a very compact criticism of spiritualistic systems, where the logic and common sense of the author easily triumphs over the subterfuges of transcendent dialectics.

*

There still remain to be mentioned: L'immanence de la raison dans la connaissance sensible, by M. GÉDÉON GORY; Le socialisme et la science sociale, by M. GASTON RICHARD, a careful criticism of facts and theories, written with great moderation; L'éducation intellectuelle dès le berceau, by M. BERNARD PÉREZ, the concluding volume of a series of works, in which the author displays his oft proved mer

1F. Alcan, publisher.

its; a new edition of the L'homme de génie,1 by M. LOMBROSO; and a translation of La femme criminelle et la prostituée, an important work of which I reserve the privilege of speaking again. I have been guilty of neglect also in not mentioning the volume of M. RENÉ WORMS, Organisme et société, and in doing so to-day I am sorry I cannot devote to it extended criticism.

LUCIEN ARRÉAT.

PARIS.

1 George Carré, publisher. The last works mentioned are published by Felix Alcan.

CRITICISMS AND DISCUSSIONS.

THE THEORY OF MATHEMATICAL FORM.

A CORRECTION AND EXPLANATION.

In his interesting communication to The Monist of January last on "The Logic of Relatives," Mr. C. S. Peirce, while alluding in flattering terms to my "Memoir on the Theory of Mathematical Form," takes exception to the opinion, which he conceives to be there put forward, that "a relationship" is "nothing but a complex of bare connexions of pairs of objects," and accordingly states that "while I have learned much from the study of Mr. Kempe's Memoir, I am obliged to modify what I have found there so much that it will not be convenient to cite it, because long explanations of the relation of my views to his would become necessary if I did so."

Any criticism which comes from so distinguished a logician as Mr. Peirce must of course have great weight; but in the present instance I fear that bonus dormitat Homerus, for I am confident that I have never held or expressed, either directly or by implication, any such opinion as he attributes to me. On the contrary, I regard it as quite inconsistent with the fundamental principles formulated in the Memoir. I am fully alive to the many defects of my essay, and am glad of this opportunity of expressing my gratitude to Mr. Peirce for a long and valuable letter of criticism, which he sent me on January 17, 1887, a letter which led to my inserting a "Note" in the Proceedings of the Royal Society, Vol. 42 (1887), p. 193, containing some very necessary corrections and emendations of the Memoir. But as that Memoir has now for the second time been called to the attention of the readers of The Monist, Mr. F. C. Russell having referred to it with appreciation in the issue of April, 1894, I have become solicitous to maintain its reputation here at as high a pitch as possible, and am anxious, therefore, that no undeserved criticism should pass unnoticed. Mr. Peirce's article fortunately affords me abundant evidence wherein it is that he has mistaken my views, and with the permission of the Editor I propose to indicate the nature of his misconception. In doing this I may be pardoned if I seize the opportunity to state concisely and without reference to details,