tween A and B. M is the common point of reference to which
A and B are related. Binet stands in a certain relation to "French
writers", who furnish the point of reference; that is, he is one of
them. Clear writing stands in a certain relation to French writers,
being one of their qualities; from which combination of relations we
perceive clear writing as a quality of Binet.

Just as an illusion is a false sense perception, so a false inference
is called a "fallacy". One great cause of fallacies consists in the
confused way in which facts are sometimes presented, resulting in
failure to see the relationships clearly. If you read that

"Smith is taller than Brown; and
Jones is shorter than Smith; and therefore
Jones is shorter than Brown,"

the mix-up of "taller" and "shorter" makes it difficult to get the
relationships clearly before you, and you are likely {468} to make a
mistake. Or again, if Mary and Jane both resemble Winifred, can you
infer that they resemble each other? You are likely to think so at
first, till you notice that resemblance is not a precise enough
relation to serve for purposes of indirect comparison. Mary may
resemble Winifred in one respect, and Jane may resemble her in another
respect, and there may be no resemblance between Mary and Jane.

Or, again,

"All French writers are clear; but
James was not a French writer; and therefore
James was not a clear writer,"

may cause some confusion from failure to notice that the relation
between French writers and clear writing is not reversible so that we
could turn about and assert that all clear writers were French.

The reasoner needs a clear head and a steady mental eye; he needs to
look squarely and steadily at his two given statements in order to
perceive their exact relationship. Diagrams and symbols often assist
in keeping the essential facts clear of extraneous matter, and so
facilitate the right response.

To sum up: the process of reasoning culminates in two facts being
present as stimuli, and the response, called "inference", consists in
perceiving a third fact that is implicated in the two stimulus-facts.
It is a good case of the law of combination, and at the same time it
is a case where "isolation" is needed, otherwise the response will be
partly aroused by irrelevant stimuli, and thus be liable to error.

Varieties of Reasoning

Reasoning as a whole is a process of mental exploration culminating in
inference. Now,