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erroneous, for, as Mr. Johnson has most perspicuously shown, the series of propositions that Jevons desires to reach are only determinants of the data-are, that is to say, neither more general nor more conjectural than the data. Jevons' conception of Boole's idea of the scope of mathematics was, previous to the second edition of the Principles of Science, altogether mistaken, and hence the attempts in the earlier edition to "divest his (Boole's) system of a mathematical dress" could not result in much that is useful.* But even in the second edition the inaccurate notion has only partially disappeared. Boole's is still a quasi-mathematical system, still requires "the manipulation of mathematical symbols in a very intricate and perplexing manner." Jevons, in holding the view that the process of subtraction is useless because the same operation can be represented as one of restriction, passes over the fact that each may be useful at times. His objection that, because he admits the Law of Unity into his system, Boole must necessarily have done the same, is without force, since Boole was not guilty

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of any inconsistency in the omission. Jevons declared that cannot be understood without reference to the mathematics of quantity, an assertion which is refuted from the simplest logical considerations. His statement that inverse operations are impossible is contradicted by the history of Symbolic Logic. I do not profess that this list is complete, but it must be confessed that, though Jevons stimulated logical thought much more extensively than most men are enabled to do, his actual contributions to the development of Symbolic Logic were few and relatively unimportant. His great powers were, in short, less successfully occupied in the logical than in the mathematical realm. In pure economic theory and in currency investigations, where in both cases the argument is almost entirely concerning quantities, his work is of the utmost value,

* G. B. Halsted, in Mind, No. 9, p. 134.

and has placed him in the very first rank of thinkers upon such subjects.

To resume the main discussion of this section, we have said that Symbolic Logic does not directly lead us to any new truths in natural science. It is, however, by no means the case that no new truth at all, but only a recognition in another form of the information contained in the premises is reached by means of the calculus. For what is a new truth? It is an accurate subject-predicate combination that an individual forms, but which has never till then been formed in the history of the race. Now such a combination may be reached deductively or inductively. It was a new truth when the conclusion of Euc. I, 47, was for the first time reached, just as it was a new truth when Adams and Leverrier discovered the planet Neptune. In a second sense a truth may be said to be new when, though well known to science, the full force of the subject-predicate combination is for the first time grasped by the mind of a student. Here again the above-mentioned combinations may take equal rank in their claims to be designated new. And, just as in pure Mathematics the results may constitute new truths in both of the above senses, so in Symbolic Logic we may be said in the same senses to reach a new truth. For instance, the difficult problem that was first solved by Boole* gave a result that was true and altogether new, and this solution, which is well known to all symbolists, is the occasion of the experience of a new truth in the mind of each student of the subject.

Moreover, though it be correct, as we have seen, to say that Symbolic Logic cannot directly assist the individual in his scientific pursuits or in his daily affairs, the indirect help of the discipline in each of these regions is by no means insignificant. Mankind is consciously or semi-consciously much occupied with questions that turn upon the relations of classes,

* Boole, Laws of Thought, pp. 146-148.

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so that the manner of looking at things which the logical study makes habitual cannot fail to be of service in practical concerns. Instead of confining himself to things that are seen, the logician spontaneously is led to regard the things that are not seen. has become a custom with him to consider the as of equal value with the x. The truth is not that his logically-developed habits are not applicable to the affairs of ordinary life, but rather that he will so weigh the pros and cons of a question that his active forces will be apt to suffer from a certain paralysis. The man of strong will, who has a more or less vivid idea of one aspect of a practical problem, is much more likely to achieve a great deal than the man who sees accurately both sides. Hence the dilemma faces us whether it is better to act vigorously, and accomplish much that has to be revised and largely undone, or to produce only a small amount, but such as needs little alteration.

Now, if the study of Symbolic Logic is thus indirectly of use in natural science and in practical affairs, then a fortiori the study is of service to the philosopher. For I take it that we philosophize rather in order to know than in order to act, and therefore in philosophy there is no danger whatever arising from seeing the other side of a question. I think, moreover, that the principles of Symbolic Logic point in a striking manner to the fact that in philosophical researches we shall always be left with a duality, however far we press our investigations. Attempts to reduce the world to unityto God, to Self, to Nature, for instance-appear to be doomed to fail. In this extreme case our 1 means the totality of the existent, the universe in the common acceptation of that term. As before, x + x = 1 of necessity, and with this necessity we are obliged to stop. We cannot establish the existence of x only, for there is no premise available with the information that 2 = 0. For instance, let a stand for "God," then will stand for "not-God." Now, if we attempt to demonstrate the nonexistence of, we shall be proceeding in an absurd manner, for we shall be assuming, if not ourselves, at any rate our reasoning, which evidently is a part of the 7. An opponent of this argument might perhaps affirm that the human proof may well be regarded as a form of Divine reasoning. God would thus be proving His own exclusive existence. But it is obvious that the circumstances under which such Divine ratiocination would be taking place would be such that a human thinker was recognising the argument as his own construction. Hence the human mind and its reasoning would still be distinct from the Divine. And, similarly, in our other efforts to reach unity, the argument is based on the assumption of an ultimate duality.

The remarks that we have made with respect to the utility of the ordinary Symbolic Logic apply also to the so-called Logic of Relatives. In this further study we do not arrive at anything more general or conjectural than the multiply-quantified propositions with which we start. There is here, therefore, no instrument by which the problems of natural science may be solved. But the educational advantage and indirect assistance of the study, and the possibility of reaching new truths, in the sense that we have just mentioned, are the same as in the case of the Symbolic Logic that deals with singly-quantified propositions.

VI. THE PERSONAL ELEMENT IN PHILOSOPHY.

By CLEMENT C. J. WEBB.

IT is a complaint not unfrequently brought against philosophy by those who are entering upon the study of it that, unlike the physical sciences and unlike history, it seems to add no certain and positive facts to our knowledge; that, while one is told much of what this or that thinker has said, one is never told plainly which view is right. There often goes along with this complaint a true perception that the seemingly vague and unprogressive character of philosophy is not unconnected with the importance attached (in some seats of philosophical learning at least) to the opinions of ancient thinkers, such as Plato and Aristotle, whose work or that of their contemporaries in the natural sciences would never be mentioned by teachers of those sciences except for their historical or antiquarian interest. The teacher of philosophy has to meet these complaints; and he will probably begin to do so by pointing out that in the method of every natural science there is a complete abstraction made from everything except that special part or aspect of experience with which that science deals, and that in particular the relation of this aspect to the knowing subject of experience (although without a knowing subject there could be no such science) is not brought under consideration at all. If we suspect that the peculiarities of the observer of natural phenomena affect his observations, then, it is true, these peculiarities are taken into account, but only in order to discount them, to eliminate them from the result. Science, in the sense in which we distinguish it from philosophy, is impersonal; it is concerned with facts which can be detached

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