Logic sets forth the premises and conclusion in the form of the "syllogism", as in the old stand-by:
Major premise: All men are mortal
Minor premise: Socrates is a man
Conclusion: Therefore, Socrates is mortal
The syllogism includes three "terms", which in the above instance are "Socrates", "mortal", and "man" or "men". Logic employs the letters, S, P, and M to symbolize these three terms in general. S is the "subject" (or, we might say, the "object" or the "situation") about which something is inferred. P is the "predicate", or what is inferred about S; and M is the "middle term" which corresponds to our "yardstick" or "point of reference", as we used those words at the beginning of the chapter. S is compared with P through the medium of M; or, S and P are both known to be related to M, and therefore (when the relations are of the right sort) they are related to each other. It is part of the business of logic to examine what relations are, and what are not, suitable for yielding a valid inference.
In symbols, then, the syllogism becomes:
Major premise: M is P
Minor premise: S is M
Conclusion: Therefore, S is P
Without confounding logic and psychology in the least, we may take this symbolic syllogism as a sort of map, on which to trace out the different exploratory processes that we have already described under the head of "varieties of reasoning". To do so may make these different processes stand out more distinctly.
In problem-solution, we start with S, a situation unsolved, i.e., without any P. P, when found, will be the solution. We explore the situation, and find in it M; i.e., we observe that S is M. Now M recalls our previously acquired knowledge that M is P. Having then before us the two premises, we perceive that S is P, and are saved.
In rationalization or explanation, we know, to start with, that S is P, and wish to know why this is so. As before, we explore S, find M, recall that M is P, and see that S, therefore, is P. Our final conclusion is, really, that S is P because it is M; that January is cold because it gets little sunlight.
In application, doubt or verification, we start with the major premise, M is P, and explore our memories for an S which, being M, should therefore be P according to our hypothesis. If we find an S which is not P, then our final conclusion is that the major premise is false.