Of the two facts which, taken together, yield an inferred fact, one is often a general rule or principle, and the inference then consists in seeing how the general rule applies to a special case. A dealer offers you a fine-looking diamond ring for five dollars, but you recall the rule that "all genuine diamonds are expensive", and perceive that this [{467}] diamond must be an imitation. This also is an instance of indirect comparison, the yardstick being the sum of five dollars; this ring measures five dollars, but any genuine diamond measures more than five dollars, and therefore a discrepancy is visible between this diamond and a genuine diamond. You can't see the discrepancy by the eye, but you see it by way of indirect comparison, just as you discover the difference between the heights of Mary and Kate by aid of the yardstick.
If all French writers are clear, then Binet, a French writer, must be clear. Here "French writers" furnish your yardstick. Perhaps it would suit this case a little better if, instead of speaking of indirect comparison by aid of a mental yardstick, we spoke in terms of "relations". When you have before your mind the relation of A to M, and also the relation of B to M, you may be able to see, or infer, a relation between 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.