15. INDUCTIVE AND DEDUCTIVE METHOD.--Professor Henry Sidgwick has defined a method of ethics as "any rational procedure by which we determine what is right for individual human beings to do, or to seek to realize by voluntary action." [Footnote: _The Methods of Ethics_, Book I, chapter i, Sec I.] 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.