that of organic life as a continuous transformation into itself of elements given, not originally produced by it."* Every life is, or strives to be, a whole: and so far as it is successful it modifies, subdues, perhaps converts into their opposites the individual values with which it sets out. Some one interest, now relatively constant, now changing, will always be the dominant one, and will " in a higher or lower degree impress its stamp on all the elements of consciousness and give them their direction." It has already been indicated how these interests may come to consciousness: the series of valuations and impulses that in the lower animal subserve the taking in of food, although their union towards this end is not at all before its mind; a further series of which the issue is the building of the nest, the production and care of the young: each of these series becomes at a higher stage consciously systematised into a whole, of which the correlative is a more or less permanent "interest." They give rise accordingly to different categories of "values" which may at any given moment enter into competition one with another, until they on their part become merged in still higher syntheses of interest and value. But we cannot take the position of external observers towards our own activities or valuejudgments: we cannot say that our limited and still subjective valuations are instrumental to some higher, more comprehensive end, posited not by us but for us, just as the end of lifepreservation and the continuance of the species is one imposed upon the animal from without. At least, if analogy suggests that there is such an absolute end, we cannot say what it is: nor if we could, would it be necessarily binding upon us to pursue it. It is impossible à priori to say that it would appear an object of value to us: that is at most a judgment of faith, a value-judgment in Ritschl's sense, not a judgment capable of scientific demonstration, or of being regarded as a postulate either of theoretical or of practical reason. As von Hartmann agrees, although with a different end in view, there can be no objective or absolute end where there is no objective value. He holds that there is an objective value: "values are what they are, in and for themselves; they do not require recognition in order to become values. Values are made known to us through feelings (of pleasure and pain), but neither their existence nor their value depends on their being known to us as values." This is because with von Hartmann the essence of value lies in the idea or content which determines the will towards its realisation: the feeling which the content exciteș is merely an index of its value for the furtherance of the will's ends. An objective value thus attaches to the objective ideal system of ends which is realised by the objective will.* But no such objective system enters into our experience, and the whole conception of an objective will realising an objective system of truth is in direct contradiction with the valueexperience in particular, which emerges always as we have seen in the reactions of the living individual upon the world about him. * Höffding, Philos. Probleme, p. 11 V.-SOME CONTROVERTED POINTS IN SYMBOLIC LOGIC. By A. T. SHEARMAN. By any person commencing the study of Symbolic Logic it is not unnaturally soon concluded that there exist several "systems," marked off from one another by fundamental differences. Such systems he is inclined to describe according to the character of the view that the founder entertained as to the import of the proposition. Thus there is the compartmental view, the predication view, the mutual exclusion view, and so on. But subsequent study enables the reader to perceive that, in adhering to such a conception, he is hiding the points of likeness and magnifying the points of difference between the proposed methods of treating the subject, and he is thus led to look rather at the net result of the different efforts. That is to say, instead of continuing to speak of several isolated systems, he proceeds to study the calculus that is now available, and to the construction of which most symbolists are seen to have contributed. The interest of the subject then gathers round such questions as to whom we are most indebted for those rules of procedure that may be said now to constitute the calculus, what important differences of opinion have arisen as the subject has been gradually thought out, and which of the conflicting views do we find it correct to adopt. Our business in this paper is with the second and third of these questions. In other words, we shall be occupied not so much with an historical sketch of the progress of the subject as with a critical account of certain points that have arisen as the work has proceeded. SYMBOLS AS REPRESENTING CLASSES AND PROPOSITIONS. We cannot do better than to commence with the question as to whether the symbols operated upon in the calculus should refer to classes or to propositions: There are here three considerations that must be kept quite distinct if the subject is to be profitably discussed. In the first place, it is possible to affirm that symbols may under one set of conditions represent terms, and under another set of conditions represent propositions, and then it has to be decided which of the two available uses it is expedient primarily to adopt. Secondly, it may be held that it is a matter of indifference whether symbols stand for terms or for propositions. And, in the third place, the opinion may be maintained that only one of the two should be symbolized-on this view it is generally to designate propositions that symbols are exclusively utilised. As regards the question of expediency, it has been affirmed that we should commence with the symbolization of propositions, for then, firstly, our procedure throughout will be analytical; and, secondly, we shall avoid the "confusion" that is introduced through the identification of the "physical" comkination of propositions into a system with the "chemical " combination of subject and predication into a proposition.* The former of these reasons is undoubtedly a strong one, but I am inclined to think that the common method of beginning with the consideration of classes, and the operations that may be performed upon them, is the better one to employ. For one thing, the latter procedure is of a simpler character than the other. But a stronger reason than this is that during the process of considering the manner in which the analysis of propositions modifies the form of the synthesis, it is necessary to point out that the letters representing predications obey the simple laws of propositional synthesis ; it is, therefore, * Mind, vol. i, N.S., p. 6. † Ibid., p. 352. desirable to be able to refer to an earlier discussion of terms and the operations that may be performed upon them. With respect to the confusion that it is alleged is likely to arise from our allowing letters originally to represent terms, it is, I think, apt to be exaggerated; indeed, a careful analysis of what really happens during the employment of literal symbols in the two spheres will show that there is no good reason for confusion in any degree. The fact that contradictories are not the same in both regions has been declared to be a likely source of error. Now it is certainly true that the contradictories in the two cases are different, but this should not involve any uncertainty in the application of the old formulæ to the new use. All that is necessary is that we make allowance for the change in the character of the contradictory, i.e., we must not admit that propositions are sometimes true and sometimes false. Again, it has been said that those who utilise the old rules for the new subject-matter will be led actually to confuse a class with a proposition, inasmuch as on the class view the contradictory of x is the class 7, but on the propositional theory the contradictory of the proposition x is the affirmation true."* But this criticism loses its force if the distinction is 66 is drawn between the truth of a proposition and the statement that the proposition is true. When the old formulæ are applied to the new case, the correct procedure is to make the letter symbol represent the truth of a proposition, while such an expression as x = 1 is used to denote that such a proposition is true. Hence the contradictory of the truth of x does not leave us with a proposition, but simply with the truth of . There is thus a perfect analogy between this case and the case where the letters represent classes. And, just as the class may be declared to exhaust the universe, so it is possible to state that the truth of the proposition is the only possibility. In other words, in both cases we may say that = 1. * Mind, vol. i, N.S., No. 1, p. 17. |