A System of Logic: Ratiocinative and Inductive, 7th Edition, Vol. II — John Stuart Mill — John Shaqi
A System of Logic: Ratiocinative and Inductive, 7th Edition, Vol. II
John Stuart Mill · en
This process may evidently be legitimate on one supposition, namely, if
the nature of the case be such that the final step, the verification,
shall amount to, and fulfil the conditions of, a complete induction. We
want to be assured that the law we have hypothetically assumed is a true
one; and its leading deductively to true results will afford this
assurance, provided the case be such that a false law cannot lead to a
true result; provided no law, except the very one which we have assumed,
can lead deductively to the same conclusions which that leads to. And
this proviso is often realized. For example, in the very complete
specimen of deduction which we just cited, the original major premise of
the ratiocination, the law of the attractive force, was ascertained in
this mode; by this legitimate employment of the Hypothetical Method.
Newton began by an assumption, that the force which at each instant
deflects a planet from its rectilineal course, and makes it describe a
curve round the sun, is a force tending directly towards the sun. He
then proved that if this be so, the planet will describe, as we know by
Kepler's first law that it does describe, equal areas in equal times;
and, lastly, he proved that if the force acted in any other direction
whatever, the planet would not describe equal areas in equal times. It
being thus shown that no other hypothesis would accord with the facts,
the assumption was proved; the hypothesis became an inductive truth. Not
only did Newton ascertain by this hypothetical process the direction of
the deflecting force; he proceeded in exactly the same manner to
ascertain the law of variation of the quantity of that force. He assumed
that the force varied inversely as the square of the distance; showed
that from this assumption the remaining two of Kepler's laws might be
deduced; and finally, that any other law of variation would give results
inconsistent with those laws, and inconsistent, therefore, with the real
motions of the planets, of which Kepler's laws were known to be a
correct expression.