rue is because in every instance where observations or
experiments have been made, the results have tallied precisely
with expectations based upon the generalization. We can, to
a certain extent, determine the reliability of a generalization
before comparing our predictions with subsequent events.
If a generalization made contradicts laws that have been
established in so many instances that they are practically
beyond peradventure, it is suspect. A law, for example, that
should be an exception to the laws of motion or gravitation,
is _a priori_ dubious.

If an induction conflicts with stronger inductions, or with conclusions
capable of being correctly deduced from them, then, unless on
reconsideration it should appear that some of the stronger inductions
have been expressed with greater universality than their evidence
warrants, the weaker one must give way. The opinion so long prevalent
that a comet, or any other unusual appearance in the heavenly
regions, was the precursor of calamities to mankind, or to those at
least who witnessed it; the belief in the veracity of the oracles of
Delphi or Dodona; the reliance on astrology, or on the weather
prophecies in almanacs, were doubtless inductions supposed to be
grounded on experience.... What has really put an end to these
insufficient inductions is their inconsistency with the stronger
inductions subsequently obtained by scientific inquiry, respecting the
causes on which terrestrial events really depend.[1]

[Footnote 1: Mill: _Logic_ (London, 1872), vol. I, pp. 370-71.]

THE QUANTITATIVE BASIS OF SCIENTIFIC PROCEDURE. Science _is_
science, some scientists insist, in so far as it is mathematical.
That is, in the precise determination of facts, and in their
repetition with a view to their exact determination, quantities
must be known. The sciences have developed in exactness,
in so far as they have succeeded in expressing their
formulations in numerical terms. The physical sciences, such
as physics and chemistry, which have been able to frame their
generalizations from precise quantities, have been immeasurably
more certain and secure than such sciences as psychology
and sociology, where the measurement of exact quantities is
more difficult and rare. Jevons writes in his _Principles of
Science_:

As physical science advances, it becomes more and more accurately
quantitative. Questions of simple logical fact resolve themselves
after a while into questions of degree,