In another sense, again, the whole of science is sometimes said to be
hypothetical, because it takes for granted the Uniformity of Nature; for
this, in its various aspects, can only be directly ascertained by us as
far as our experience extends; whereas the whole value of the principle
of Uniformity consists in its furnishing a formula for the extension of
our other beliefs beyond our actual experience. Transcendentalists,
indeed, call it a form of Reason, just because it is presupposed in all
knowledge; and they and the Empiricists agree that to adduce material
evidence for it, in its full extent, is impossible. If, then, material
evidence is demanded by any one, he cannot regard the conclusions of
Mathematics and Physical Science as depending on what is itself
unproved; he must, with Mill, regard these conclusions as drawn "not
from but according to" the axioms of Equality and Causation. That is to
say, if the axioms are true, the conclusions are; the material evidence
for both the axioms and the conclusions being the same, namely,
uncontradicted experience. Now when we say, 'If Nature is uniform,
science is true,' the hypothetical character of science appears in the
form of the statement. Nevertheless, it seems undesirable to call our
confidence in Nature's uniformity an 'hypothesis': it is incongruous to
use the same term for our tentative conjectures and for our most
indispensable beliefs. 'The Universal Postulate' is a better term for
the principle which, in some form or other, every generalisation takes
for granted.
We are now sometimes told that, instead of the determinism and
continuity of phenomena hitherto assumed by science, we should recognise
indeterminism and discontinuity. But it will be time enough to fall in
with this doctrine when its advocates produce a new Logic of Induction,
and explain the use of the method of Difference and of control
experiments according to the new postulates.
CHAPTER XIX
LAWS CLASSIFIED; EXPLANATION; CO-EXISTENCE; ANALOGY
§ 1. Laws are classified, according to their degrees of generality, as
higher and lower, though the grades may not be decisively
distinguishable.
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