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

3OO
THE THEORY OF INDUCTION
has shown how it may suggest an mediate causation.
hypothesis
We find the event P in a number
of instances A, B, C, D, &c. ; examining further, we
of im
find that the fact S is the only other material circum
stance in which they agree, hence a connection of
S and P is suggested. This differs from simple enum
eration ; for we do not merely count the instances,
we begin to weigh them. They
must differ as much
as possible from each other, except as regards the
presence of P and S. Expressed syllogistically, the
argument becomes
A, B, C, D, &c., have the property P ;
A, B, C, D, &c., have the property S ;
. . S and P are or may be causally connected.
The student will notice that as
"
A, B, C, D, &c.," may
be regarded as a collective singular term, the argument
is an Aristotelian Enthymeme in fig. in., whose prob
ability depends on the number and variety of the
instances which collectively form the subject in both
premises. In fact, Aristotle s
"Enthymeme in the
third figure" expresses the principle of Mill s Method
of Agreement more correctly than Mill himself did.
There are two ways in which we may endeavour to
make this conclusion universal, in the form
"
Every S
is P."
(i) By counting
all the instances of S in order to
see if P is present in each. If so, then by complete
enumeration every S is P. The instances are 100
per cent ; the total is limited, and we have reached it.
This is usually impossible ; hence if we do not go
beyond counting, we cannot show that every S is P.
All that remains is to estimate the probability of S
being always P. This leads to the calculation of
chances and the quantitative Theory of Probability.