inductive reasoning have been reduced by logicians to certain canons,
but these reduce themselves to two main methods, which depend on whether
in a given piece of reasoning we start from the likeness between the
instances or the differences between them. On these two methods, the
method of agreement and the method of difference, hang all the processes
of modern science, and most of our everyday arguments.

The method of agreement has been defined as follows:

If two or more instances of the phenomenon under investigation have
only one circumstance in common, the circumstance in which alone all the
instances agree is the cause (or effect) of the given phenomenon.[34]

A few examples, which might easily be multiplied, will show how
constantly we use this method in everyday life. Suppose that a teacher
is annoyed at somewhat irregular intervals by whispering and laughing in
the back of the schoolroom, for which he can find no cause, but that
presently he notices that whenever a certain pair of boys sit together
there the trouble begins; he infers that these two boys are the cause of
the trouble.

In the old days before it had been discovered that the germs of malaria
are carried by mosquitoes, the disease was ascribed to a miasma which
floated over low ground at night; and the innkeepers of the Roman
Campagna, where malaria had almost driven out the population, urged
their guests never to leave their windows open at night, for fear of
letting in the miasma. In the lights of those days this was good
reasoning by the method of agreement, for it was common observation that
of all the many kinds of people who slept with their windows open most
had malaria. We are constantly using this method in cases of this sort,
where from observation we are sure that a single cause is at work under
diverse circumstances. If the cases are numerous enough and diverse
enough, we arrive at a safe degree of certainty for practical purposes.
As the case just cited shows, however, the method does not establish a
cause with great certainty. No matter how many cases we gather, if a
whole new field related to the subject happens to be opened up, the
agreement may be shattered.

The method of difference, which in some cases does establish causes with
as great certainty as is possible for human fallibility, works in the
opposite way: instead of collecting a large number of cases and noting
the single point of agreement, it takes a single case and v