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,