CHAPTER XLV. REMARKS ON THE LOGIC OF THE SCIENCES. As S we have seen in the preceding chapter, different methods of discovery belong to different sciences; thus, demonstration pre-eminently belongs to mathematics, and experiment to chemistry. Mathematical methods have not yet been successfully applied to chemistry, though perhaps it may some day be found possible to do so; but we may positively assert that they never can be applied to the science of life. Indeed it may be stated as a general truth, that the more special and complex are the facts which constitute the subject-matter of a science, the less susceptible is it of mathematical treata science, ment. Thus, general dynamics is altogether a mathemathe less is tical science; the secondary dynamical sciences (sound, radiance, heat, electricity, and magnetism) are so in great part; chemistry may perhaps become so; but the sciences that involve life can never by any possibility become mathematical. The more special and mathematics applicable to it. In connexion with this, the facts of life are in some degree in definite. This peculiarity of the sciences of life is connected with the truth that their facts, even when perfectly well ascertained, are not capable of being determined with the same kind of precision as those of the inorganic sciences. In chemistry, for instance, the proportions in which two substances combine are in many cases known with perfect numerical accuracy, and are in all cases capable of being so known. In biology, on the contrary, no such accurate determinations are possible: this is not because the quantitative relations are too difficult to determine; it is because they are variable, any un within moderate limits no doubt, but without any ascertainable law. Thus, in that branch of biology which is most nearly connected with chemistry, it is impossible to state the effect of medicines, or of poisons, with the same kind of accuracy to which we are accustomed in chemistry. We know that laudanum will produce sleep, and that strychnine will kill; but, even if the constitution of the patient is known, it is impossible to say how much laudanum will be sufficient to cause sleep, or how much strychnine will be sufficient to kill, with the same kind of precision with which we can say how much of an acid is required in order to saturate a given quantity of alkali. But the determinations of biological science, though thus This does inferior in precision to those of the inorganic sciences, are not imply in no sense, and in no degree, inferior to them in certainty. certainty. The same is true, and even more eminently so, in the higher branches of biology. Thus, the law that all actions tend to become habitual, is as well established as it is possible for such a law to be; but it is impossible, in any case whatever, to say how many times an action must be repeated in order to make it habitual, or, again, for how long it must be discontinued in order to destroy the habit by disuse. In the sciences of society also, in morals and The same in politics, there are laws of general tendencies, but no morals. quantitative laws; consequently there is certainty without precision. It is, for instance, as certain as anything can Certainty be, that the tendency of falsehood is injurious to human precision. happiness; but it is never possible to tell how much injury any particular falsehood will do, or has done. The ethical bearing of this truth is very important, but it does not belong to the subject of this work. is true of without We may enumerate four fallacies on the subject of the Four relation of mathematics and of logic to the other sciences. and their fallacies, They all, I believe, have their origin in the fact that origin: mathematics and logic were the earliest sciences in the field; and they are relics of the time when those were almost the only sciences, and when Pascal wrote of "the geometrical spirit," meaning the scientific spirit. These four fallacies are as follow: that logic 1. The fallacy that logic is an organon of discovery. This was the error of the scholastic philosophy, and was discovery: that against which Bacon's whole philosophical career was that mathematics is employed in contending. It is now so completely discredited that I need not spend many words in refuting it. I have stated in a former chapter1 what is now the universally received conclusion on this subject;—namely, that the function of logic, regarded as a science, is not to extend the structure of our knowledge, but to fix its foundations. 2. The fallacy that mathematics is the type of all science. Mathematics is altogether a deductive science; the type that is to say, it is a science of pure reasoning; and consequently it cannot possibly be the type of sciences of observation like anatomy and histology, or sciences of experiment like chemistry. Even if chemistry hereafter becomes in part a mathematical science, as the sciences of electricity and heat have done, yet, like them, it must always continue to be in part experimental, and in so far as it is experimental, it cannot be mathematical. of science: that clearness are tests of truth: 3. The fallacy that simplicity and intelligibleness are and intel- tests of truth. This was formularized as an axiom by ligibleness Descartes, who laid down as the foundation of his philosophy that what is conceivable with perfect clearness must be true. This was the error of a geometrician; for, in geometry, nothing can be clearly conceived unless it is true; and whatever is true must necessarily be clearly conceived as soon as it is fully understood. In physical science, on the contrary, truth is mere truth of fact, and error consequently involves no logical absurdity; and a conception may be clear and yet not true. But though it is not true that clearness is a test of truth, yet it is true that inability to attain to clearness is a proof of imperfect knowledge. Yet even this test must be applied with caution; for there are many subjects on which our knowledge must always be imperfect;-I do not mean merely limited in extent, but surrounded with a kind of haze of mystery: this is especially true of the mutual relation of the conscious and the unconscious life, and of all the facts 1 The chapter on the Classification of the Sciences (Chap. XLIII.). of unconscious intelligence. It is also true that selfcontradiction is a proof of error: but this test also needs caution in its application; for it is always necessary, and often difficult, to determine whether a contradiction is real or only verbal. cision certainty. 4. Lastly, the fallacy that precision is the criterion of that precertainty. I have insisted above at some length on the is the important truth that certainty without precision or definite- criterion of ness is characteristic of the facts of life. It is important clearly to conceive this distinction between certainty and precision, because a vague notion appears to be very common, that precision is the criterion of certainty, and that no truth can be perfectly certain unless it is capable of being stated with numerical accuracy; and consequently that the certainty which is attainable in the moral and political sciences is, inferior in degree to that which is attainable in the mathematical and the physical ones. This notion is never, I think, stated as a formula; indeed, it would refute itself if it were; for were it true that no numerically indefinite proposition can be quite certain, it would follow that because no man knows how long he has to live, it is therefore not quite certain whether he is to die at all: a conclusion which it would be impossible to accept. But the notion of some necessary connexion between certainty and precision is, I think, implied in such expressions as "mathematical certainty" and "mathematical precision;" and in the belief, which is often avowed and oftener implied, that no general truths are attainable concerning the social relations of man; that historical and political science are consequently impossible, and that history is, and ever must be, a mass of mere facts, and politics a chaos of mere opinions. The prevalent unbelief in the possibility of historical and political science, however, though it allies itself with the lingering notion that determinations cannot be certain unless they are also precise, is chiefly due to the fact that the political group of sciences is still in a very immature state. But, as I have remarked in the introduction to this work, the time 1 Vol. I. p. 6. 1 of the use of the word science. Extension is coming when the use of the word science in the sense of only mathematical and physical science will be extinct, or, if it survives, will survive merely as a relic of an extinct habit of thought. We have already begun familiarly to use such expressions as the science of language, the science of history, and the science of politics: a notion still survives that such a use of the word science is a somewhat inaccurate extension of the meaning of the word; but I believe that in another generation such expressions will come to be used with no more sense of inaccuracy or of paradox than we have when we speak of the science of chemistry or the science of astronomy. Double method in science. and deduction must It is an important truth, that perfect scientific method consists in the co-operation of the inductive and deductive Induction methods; and perfect scientific proof consists in the results of the two methods coinciding. Thus in astronomy the co-operate. results of induction and of deduction, that is to say of observation and of calculation, coincide within very small limits of error; and the same is true of the sciences of sound, radiance, heat, electricity, and magnetism. None of these sciences could have attained to anything at all comparable to their present perfection without the use of this double method: in which the calculated results of theoretical deduction are checked and verified by the results obtained by induction from observation and experiment; while at the same time, by the converse process, the results obtained by induction from observation and experiment are checked and verified by the calculated results of theoretical deduction.1 In language which is at once and obser- familiar and accurate, this is called the coincidence of the results of theory with those of observation. As was Theory vation. 1 It is usual to call the experimental result the verification of the theoretical one. According to Comte, in physical science the results of theory are verified by observation or experiment; but in historical science the results are first generalized from observation, and then verified by theory (the theoretical data in this case consist, of course, in the general laws of human nature). This may be true, but it is not very important. The important and universal truth on the subject is, that the results of the theoretical and of the experimental methods each need to be verified by the other. |