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SATURDAY, APRIL 4, 1874.
THE PRINCIPLES OF SCIENCE.
The Principles of Science: a Treatise on Logic and Scientific Method. By W. Stanley Jevons, M.A. (Macmillan & Co.) THE mathematicians have been avenged on their formidable assailant, the late Sir William Hamilton. It is well known with what fierce and passionate energy the Scotch metaphysician, in his controversy with Dr. Whewell, strove to reduce the value of mathematics as an intellectual discipline. The great master of Logic would admit no comparison between the science of mind and the science which deals with quantity and its laws. What many counted the glory of mathematics was represented by Hamilton to be the symbol of their comparative degradation. They dealt with certainties, with processes of a more or less mechanical character, which, if faithfully performed, could not fail to produce their results. Metaphysics, on the other hand, far more profoundly, and after a much more varied fashion, exercised the faculties of the human mind, because their materials were contingent. The greatest mathematicians might well be-nay, had often been-either the most credulous or the most sceptical of men, whereas metaphysicians were guarded from either extreme by the catholic intellectual training of which they were the subjects. Since Hamilton maintained these views, doing battle for them in his usual sledge hammer fashion, the Science of Logic, of which he deemed himself the great renovator and reformer, has been more diligently cultivated in England than perhaps ever before. Hamilton doubtless applied a powerful stimulus to its cultivation, and there have been diverging schools of Logic, according to the different metaphysical or philosophical proclivities of those who dealt with it. Hamilton distinguished himself by the earnestness with which he reiterated (after Kant) the assertion of the formal character of Logic as a science of the Laws of Thought. His great distinction, however, in his own eyes, and in those of some of his followers, was the discovery of the Quantification of the Predicate. By this addition to the old doctrine of the Syllogism, he had achieved, it was alleged, a greater work than any logician since Aristotle. A new Analytic of Logical Forms was required to supplement the old, though, unfortunately, it has not been supplied to this day. The new Analytic, of which we have only partial and incomplete accounts, would bring to light a side of Logic not hitherto recognized, by showing that it is pervaded by the distinction between comprehension and extension, and that the one implies the other. Logic, as the science of the fundamental Laws of Thought, requires that "we should state explicitly what is thought implicitly." And Hamilton promised, and in part gave, a system of symbolical notation, which he claimed would exhibit with the utmost mechanical simplicity the various forms of syllogisms and propositions in all their applications. Through the quantification of the predicate reasoning was re
duced to a statement of quantitative relations, and the laws which form the subject matter of logic are only the modes in which that which is implicit in thought are stated or made to appear explicitly. The work of applying the new view of the character of formal logic has been ably performed since Hamilton's time, by writers with whom he would have had scant sympathy. While Dr. Boole, by great ingenuity, has formed a theory of symbolical reasoning, developed from fundamental laws and expressed in mathematical terms, Prof. Jevons has improved upon Boole, and supplied us with a logic which makes reasoning mechanical. Dr. Boole converted logic into a mathematical calculus, and Prof. Jevons has shown how it may be made a purely mechanical process. So perfectly has he done this, that he has constructed a logical machine, or Abecedarium, which performs with infallible accuracy, by means of symbolical terms, all the processes of analytical reasoning. Surely the mathematicians are avenged on their adversary.
In previous works Prof. Jevons has explained the principles of his system, and described the instrument by which logical inference may be mechanically performed. In the two volumes before us, he has taken a wider sweep, and sought to extend the rules of reasoning with which he deals to a scientific method. His aim is to point out for the guidance of the scientific inquirer the processes or methods of inductive investigation. It is the aim of science to discover the like in the unlike amid diversity to trace identity; and in every act of scientific inference (he says) we are engaged in tracing some likeness or analogy, some equivalence or equality. The multitude of phenomena presented to our observation are either like or unlike, and in reasoning we recognize the likenesses and associate them together. By this observation of identity the mind passes from case to case in inference, acting always on the assumption that what is true of one thing will be true of its equivalent. The one supreme rule of inference consists in the direction to affirm of any thing what is known of its like, equal, or equivalent. This replacement of objects by their equivalents the author calls "the Substitution of Similars." This Substitution as the true principle in reasoning he claimed to have discovered, though, as has been pointed out by Prof. Lindsay in his edition of Ueberweg's Logic, and is now admitted by Prof. Jevons, it was long ago enounced by Dr. Beneke, who sought to prove that it was the fundamental principle of Deductive Reasoning. Prof. Jevons, however, was an independent investigator, as he was quite unaware he was using Beneke's property when, on his own account, he applied the principle of Substitution which he supposed he had discovered. Of course, the writer is only able to bring Induction within the scope of his principles by reducing it under Deduction; and, therefore, he maintains that Induction and Deduction are essentially the same, the one being only the inverse application of the other. His whole system thus rests on the doctrine of the Quantification of the Predicate, a doctrine accepted by few logicians, and to which there are formidable objections. Mr. Mill's criticism in his work on Hamilton has not been answered, and it may be doubted if it will be. Prof. Jevons, following Hamilton, of
course holds that the logical postulate explicitly what is thought implicitly" involves the Quantification of the Predicate. He is satisfied, that is to say, that the Predicate is always implicitly thought to be a Quantity, a position which has not been proved. It naturally follows that every Proposition is an equation of Subject and Predicate, and Predication is the affirmation or negation that one class comes under another class. In cases in which the Predicate cannot be quantified, that is to say, when the Predicate cannot be taken substantively, it is obvious that the rule will not hold good.
It follows, from what has been said, that it is necessary to lay the foundations of the scientific method sought by a system of Formal Logic. A statement of the fundamental laws of thought and the manner in which reasoning proceeds, according to the principle of substitution, forms the first portion of the work. In connexion with the processes of inductive inquiry, the writer describes the mechanical arrangements by which his logical machine operates, and by which what he terms "the combinational system of Formal Logic" is "rendered evident to the eye and easy to the mind and hand." By means of letter combinations, which stand for the terms of propositions in syllogisms, the treatment of propositions is illustrated as equations. Since Induction is but an inverse employment of Deduction, it may be surmised that Prof. Jevons does not side with the philosophers who, professedly following the Baconian method, insist on discarding hypothesis. the contrary, he maintains that hypothetical anticipation of nature is an essential part of Inductive inquiry, and (as he says in his Preface) that it is "the Newtonian method of Deductive Reasoning combined with elaborate experimental verification which has led to all the great triumphs of scientific research." The sciences of both Number and Quantity are made to spring from the more general science of Logic. It hardly seems consistent with this that no Inductive conclusions are more than probable, but this is the author's view, and accordingly he includes a theory of Probability under Logical Method. In no case of inductive research do we attain to conclusions that are more than probable. The phenomena of nature are manifested in quantities of Space, Time, Force, &c.; and as their laws are quantitative, we must bear in mind the degree of quantitative approximation to the truth probably attained. A theory of approximation is considered a part of scientific method; on which a chapter is added. The use of hypothesis, generalization, and analogy and classification, are also treated with some fullness, and the work concludes with an investigation and appreciation of the logical value of our knowledge of nature.
We have given, we fear, an imperfect idea of the nature of the work under review; but we have said enough to show that the author's principles unsettle every scientific doctrine or law, and bring us back to a régime of speculation. We are taught to regard the universe as an infinite ballot-box, out of which are being constantly drawn ball after ball. By means of close observation we may form some notion of the contents of this vast ballot-box of nature, and science shows us the order of succession in which balls of various