Chapter 25

THE SYLLOGISM.

We have already defined mediate inference as the derivation of a conclusion from more than one proposition. The type or form of a mediate inference fully expressed consists of three propositions so related that one of them is involved or implied in the other two.

Distraction is exhausting. Modern life is full of distraction [.'.] Modern life is exhausting.

We say nothing of the truth of these propositions. I purposely choose questionable ones. But do they hang together? If you admit the first two, are you bound in consistency to admit the third? Is the truth of the conclusion a necessary consequence of the truth of the premisses? If so, it is a valid mediate inference from them.

When one of the two premisses is more general than the conclusion, the argument is said to be Deductive. You lead down from the more general to the less general. The general proposition is called the Major Premiss, or Grounding Proposition, or Sumption: the other premiss the Minor, or Applying Proposition, or Subsumption.

Undue haste makes waste. This is a case of undue hasting. [.'.] It is a case of undue wasting.

We may, and constantly do, apply principles and draw conclusions in this way without making any formal analysis of the propositions. Indeed we reason mediately and deductively whenever we make any application of previous knowledge, although the process is not expressed in propositions at all and is performed so rapidly that we are not conscious of the steps.

For example, I enter a room, see a book, open it and begin to read. I want to make a note of something: I look round, see a paper case, open it, take a sheet of paper and a pen, dip the pen in the ink and proceed to write. In the course of all this, I act upon certain inferences which might be drawn out in the form of Syllogisms. First, in virtue of previous knowledge I recognise what lies before me as a book. The process by which I reach the conclusion, though it passes in a flash, might be analysed and expressed in propositions.

Whatever presents certain outward appearances, contains readable print. This presents such appearances. [.'.]It contains readable print. So with the paper case, and the pen, and the ink. I infer from peculiar appearances that what I see contains paper, that the liquid will make a black mark on the white sheet, and so forth.

We are constantly in daily life subsuming particulars under known universals in this way. "Whatever has certain visible properties, has certain other properties: this has the visible ones: therefore, it has the others" is a form of reasoning constantly latent in our minds.

The Syllogism may be regarded as the explicit expression of this type of deductive reasoning; that is, as the analysis and formal expression of this every-day process of applying known universals to particular cases. Thus viewed it is simply the analysis of a mental process, as a psychological fact; the analysis of the procedure of all men when they reason from signs; the analysis of the kind of assumptions they make when they apply knowledge to particular cases. The assumptions may be warranted, or they may not: but as a matter of fact the individual who makes the confident inference has such assumptions and subsumptions latent in his mind.

But practically viewed, that is _logically_ viewed, if you regard Logic as a practical science, the Syllogism is a contrivance to assist the correct performance of reasoning together or syllogising in difficult cases. It applies not to mental processes but to results of such expressed in words, that is, to propositions. Where the Syllogism comes in as a useful form is when certain propositions are delivered to you _ab extra_ as containing a certain conclusion; and the connexion is not apparent. These propositions are analysed and thrown into a form in which it is at once apparent whether the alleged connexion exists. This form is the Syllogism: it is, in effect, an analysis of given arguments.

It was as a practical engine or organon that it was invented by Aristotle, an organon for the syllogising of admissions in Dialectic. The germ of the invention was the analysis of propositions into terms. The syllogism was conceived by Aristotle as a reasoning together of terms. His prime discovery was that whenever two propositions necessarily contain or imply a conclusion, they have a common term, that is, only three terms between them: that the other two terms which differ in each are the terms of the conclusion; and that the relation asserted in the conclusion between its two terms is a necessary consequence of their relations with the third term as declared in the premisses.

Such was Aristotle's conception of the Syllogism and such it has remained in Logic. It is still, strictly speaking, a syllogism of terms: of propositions only secondarily and after they have been analysed. The conclusion is conceived analytically as a relation between two terms. In how many ways may this relation be established through a third term? The various moods and figures of the Syllogism give the answer to that question.

The use of the very abstract word "relation" makes the problem appear much more difficult than it really is. The great charm of Aristotle's Syllogism is its simplicity. The assertion of the conclusion is reduced to its simplest possible kind, a relation of inclusion or exclusion, contained or not contained. To show that the one term is or is not contained in the other we have only to find a third which contains the one and is contained or not contained in the other.

The practical difficulties, of course, consist in the reduction of the conclusions and arguments of common speech to definite terms thus simply related. Once they are so reduced, their independence or the opposite is obvious. Therein lies the virtue of the Syllogism.

Before proceeding to show in how many ways two terms may be Syllogised through a third, we must have technical names for the elements.

The third term is called the MIDDLE (M) ([Greek: to meson]): the other two the Extremes ([Greek: akra]).

The EXTREMES are the Subject (S) and the Predicate (P) of the conclusion.

In an affirmative proposition (the normal form) S is contained in P: hence P is called the MAJOR[1] term ([Greek: to meixon]), and S the MINOR ([Greek: to elatton]), being respectively larger and smaller in extension. All difficulty about the names disappears if we remember that in bestowing them we start from the conclusion. That was the problem ([Greek: problema]) or thesis in dialectic, the question in dispute.

The two Premisses, or propositions giving the relations between the two Extremes and the Middle, are named on an equally simple ground.

One of them gives the relation between the Minor Term, S, and the Middle, M. S, All or Some, is or is not in M. This is called the Minor Premiss.

The other gives the relation between the Major Term and the Middle. M, All or Some, is or is not in P. This is called the Major Premiss.[2]

[Footnote 1: Aristotle calls the Major the First ([Greek: to proton]) and the Minor the last ([Greek: to eschaton]), probably because that was their order in the conclusion when stated in his most usual form, "P is predicated of S," or "P belongs to S".]

[Footnote 2: When we speak of the Minor or the Major simply, the reference is to the terms. To avoid a confusion into which beginners are apt to stumble, and at the same time to emphasise the origin of the names, the Premisses might be spoken of at first as the Minor's Premiss and the Major's Premiss. It was only in the Middle Ages when the origin of the Syllogism had been forgotten, that the idea arose that the terms were called Major and Minor because they occurred in the Major and the Minor Premiss respectively.]