Chapter 44

He points out that many methods are natural and are habitually used, but claims that only one can be rational. By which he means that the several methods of determining right conduct urged by the different schools of the moralists must be reconciled, or all but one must be rejected. [Footnote: _Ibid_., chapter i, Sec 3.]

In this chapter I shall not discuss in detail the schools of the moralists and the specific methods which characterize them. I am here concerned only with the general distinction between the scientific methods of deduction and induction, and its bearing upon ethical investigations.

How do we discover that, in an isosceles triangle, the sides which subtend the equal angles are equal? We do not go about collecting the opinions of individuals upon the subject, nor do we consult the records of other peoples, past or present. We do not measure a great number of triangles and arrive at our conclusion after a calculation of the probable error of our measurements. The appeal to authorities does not interest us; that measurements are always more or less inaccurate, and that all actual triangles are more or less irregular, we freely admit, but we do not regard such facts as significant. We use a single triangle as an illustration, and from what is given in, or along with, that individual instance, we deduce certain consequences in which we have the highest confidence. Here we follow the method of deduction. We accept a "given," with its validity we do not concern ourselves; our aim is the discovery of what may be gotten out of it.

In the inductive sciences the individual instance has an importance of quite a different sort. It is not a mere illustration, unequivocally embodying a general truth to which we may appeal directly, treating the instance as a mere vehicle, in itself of little significance. Individual instances are observed and compared; uniformities are searched for; it is sought to establish general truths, not directly evident, but whose authority rests upon the particular facts that have been observed and classified.

It is a commonplace of logic that both induction and deduction may be employed in many fields of science. We may attain by inductive inquiry to more or less general truths, which we no longer care to call in question, and which we accept as a "given," to be exploited and carried out in its consequences. Indeed, we need not betake ourselves to science to have an illustration of this method of procedure. In everyday life men have maxims by which they judge of the probable actions of their fellow-men and in the light of which they direct their dealings with them. Such maxims as that men may be counted upon to consult their own interests have certainly not been adopted independently of an experience of what, on particular occasions, men have shown themselves to be. But, once adopted, they may be treated as, for practical purposes, unquestionable; men are concerned to apply them, not to substantiate them. In so far, men reason from them deductively and pass from the general rule to the particular instance.

16. THE AUTHORITY OF THE "GIVEN."--Obviously the "given," in the sense indicated, may possess, in certain cases, a very high degree of authority, and, in others, a very low degree.

In the case of the mathematical truth referred to above, men do not, in fact, find it necessary to call in question the "given," though they may be divided in their notions touching the general nature of mathematical evidence and whence it draws its apparently indisputable authority. In certain of the inductive sciences, as in mechanics, physics and chemistry, generalizations have been attained in which even the critical repose much confidence. In other fields men are constantly making general statements which are promptly contradicted by their fellows, and are drawing from them inferences the justice of which is in many quarters disallowed. There are axioms and axioms, maxims and maxims. The confidence felt by a given individual in a particular "given" does not guarantee its acceptance by all men of equal intelligence. Where, however, the evidence upon which a disputed "given" is based is forthcoming, there is, at least, ground for rational discussion.

Not a few famous writers have treated moral truths as analogous to mathematical. [Footnote: See the chapter on "Intuitionism," Sec 90, note.] To take here a single instance. Sidgwick, in his truly admirable work on "The Methods of Ethics," maintains [Footnote: Book III, chapter xiii, Sec 3.] that "the propositions, 'I ought not to prefer a present lesser good to a future greater good,' and 'I ought not to prefer my own lesser good to the greater good of another,' do present themselves as self-evident; as much (_e.g._) as the mathematical axiom that 'if equals be added to equals the wholes are equals.'"

But it is one thing to claim that we are in possession of a "given" with ultimate and indisputable authority; it is another to convince men that we really do possess it. Locke's efforts at deduction fall lamentably short of the model set by Euclid. "Professor Sidgwick's well-known moral axiom, 'I ought not to prefer my own lesser good to the greater good of another,' would," writes Westermarck, [Footnote: _Op_. _cit.,_