confined to the
most elementary relations.

Moreover it is to be remarked that while, on the one hand, we can
discover the laws of the greater proportion of phenomena only by
investigating them quantitatively; on the other hand we can extend the
range of our quantitative previsions only as fast as we detect the laws
of the results we predict. For clearly the ability to specify the
magnitude of a result inaccessible to direct measurement, implies
knowledge of its mode of dependence on something which can be
measured--implies that we know the particular fact dealt with to be an
instance of some more general fact. Thus the extent to which our
quantitative previsions have been carried in any direction, indicates
the depth to which our knowledge reaches in that direction. And here, as
another aspect of the same fact, we may further observe that as we pass
from qualitative to quantitative prevision, we pass from inductive
science to deductive science. Science while purely inductive is purely
qualitative: when inaccurately quantitative it usually consists of part
induction, part deduction: and it becomes accurately quantitative only
when wholly deductive. We do not mean that the deductive and the
quantitative are coextensive; for there is manifestly much deduction
that is qualitative only. We mean that all quantitative prevision is
reached deductively; and that induction can achieve only qualitative
prevision.

Still, however, it must not be supposed that these distinctions enable
us to separate ordinary knowledge from science, much as they seem to do
so. While they show in what consists the broad contrast between the
extreme forms of the two, they yet lead us to recognise their essential
identity; and once more prove the difference to be one of degree only.
For, on the one hand, the commonest positive knowledge is to some extent
quantitative; seeing that the amount of the foreseen result is known
within certain wide limits. And, on the other hand, the highest
quantitative prevision does not reach the exact truth, but only a very
near approximation to it. Without clocks the savage knows that the day
is longer in the summer than in the winter; without scales he knows that
stone is heavier than flesh: that is, he can foresee respecting certain
results that their amounts will exceed these, and be less than those--he
knows _about_ what they will be. And, with his most delicate instruments
and most elaborate calculations, all tha