An introductory text-book of logic - Mellone, Sydney - Rare Books at ...

232 THE GENERAL NATURE OF INDUCTION.
of units in a very short time, so Perfect Induction is
absolutely necessary to enable us to deal with a great
number of particular facts in a very brief space."
The case of Imperfect Induction is very different. It
is a kind of inference which, as Bacon says, precarie
concludit, et periculo exponitur ab instantia contradictoria,
A simple negative instance will refute it. As regards
the example given, few people would care to assert that
a grey crow has never been seen. It cannot be too
strongly impressed on the mind of the student that no
mere counting of instances, however many they may be,
can make a conclusion more certain. We may know
that S and P are conjoined twice or two thousand or
two million times; but this does not warrant us in
saying that they are always conjoined
unless we have
something more than the mere number to go upon.
A mere enumeratio simplex, a mere assemblage of
positive instances, is simply worthless. Take an old
" The three interior angles of a triangle are
example :
together equal to two right angles." This is known to
be true universally, for it is proved from the definition
of a triangle. Suppose that this proof were not known,
and that we had to rely only on measurement of the
angles of particular triangles to discover what their sum
is in each case. Granting
that the measurement could
be made with sufficient accuracy to establish the pro
position in particular cases, there would be no warrant
for taking it to be true of any triangle whose angles
we had not measured. There is nothing in the mere
measurement of a triangle to show that the sum of its
angles must be of this particular magnitude. Another
example of the difference between the enumeration of
positive instances, and real proof, is found in the laws
of planetary motion. Newton proved deductively, from