Chapter 28

THE ANALYSIS OF ARGUMENTS INTO SYLLOGISTIC FORMS.

Turning given arguments into syllogistic form is apt to seem as trivial and useless as it is easy and mechanical. In most cases the necessity of the conclusion is as apparent in the plain speech form as in the artificial logical form. The justification of such exercises is that they give familiarity with the instrument, serving at the same time as simple exercises in ratiocination: what further uses may be made of the instrument once it is mastered, we shall consider as we proceed.

I.--FIRST FIGURE.

Given the following argument to be put into Syllogistic form: "No war is long popular: for every war increases taxation; and the popularity of anything that touches the pocket is short-lived".

The simplest method is to begin with the conclusion--"No war is long popular"--No S is P--then to examine the argument to see whether it yields premisses of the necessary form. Keeping the form in mind, Celarent of Fig. I.--

No M is P All S is M No S is P-- we see at once that "Every war increases taxation" is of the form All S is M. Does the other sentence yield the Major Premiss No M is P, when M represents the increasing of taxation, _i.e._, a class bounded by that attribute? We see that the last sentence of the argument is equivalent to saying that "Nothing that increases taxation is long popular"; and this with the Minor yields the conclusion in Celarent.

Nothing that increases taxation is long popular. Every war increases taxation. No war is long popular.

Observe, now, what in effect we have done in thus reducing the argument to the First Figure. In effect, a general principle being alleged as justifying a certain conclusion, we have put that principle into such a form that it has the same predicate with the conclusion. All that we have then to do in order to inspect the validity of the argument is to see whether the subject of the conclusion is contained in the subject of the general principle. Is war one of the things that increase taxation? Is it one of that class? If so, then it cannot long be popular, long popularity being an attribute that cannot be affirmed of any of that class.

Reducing to the first figure, then, amounts simply to making the predication of the proposition alleged as ground uniform with the conclusion based upon it. The minor premiss or applying proposition amounts to saying that the subject of the conclusion is contained in the subject of the general principle. Is the subject of the conclusion contained in the subject of the general principle when the two have identical predicates? If so, the argument falls at once under the _Dictum de Omni et Nullo_.

Two things may be noted concerning an argument thus simplified.

1. It is not necessary, in order to bring an argument under the _dictum de omni_, to reduce the predicate to the form of an extensive term. In whatever form, abstract or concrete, the predication is made of the middle term, it is applicable in the same form to that which is contained in the middle term.

2. The quantity of the Minor Term does not require special attention, inasmuch as the argument does not turn upon it. In whatever quantity it is contained in the Middle, in that quantity is the predicate of the Middle predicable of it.

These two points being borne in mind, the attention may be concentrated on the Middle Term and its relations with the extremes.

That the predicate may be left unanalysed without affecting the simplicity of the argument or in any way obscuring the exhibition of its turning-point, has an important bearing on the reduction of Modals. The modality may be treated as part of the predicate without in any way obscuring what it is the design of the syllogism to make clear. We have only to bear in mind that however the predicate may be qualified in the premisses, the same qualification must be transferred to the conclusion. Otherwise we should have the fallacy of Four Terms, _quaternio terminorum_.

To raise the question: What is the proper form for a Modal of Possibility, A or I? is to clear up in an important respect our conceptions of the Universal proposition, "Victories may be gained by accident". Should this be expressed as A or I? Is the predicate applicable to All victories or only to Some? Obviously the meaning is that of any victory it may be true that it was gained by accident, and if we treat the "mode" as part of the predicate term "things that may be gained by accident," the form of the proposition is All S is in P.

But, it may be asked, does not the proposition that victories may be gained by accident rest, as a matter of fact, on the belief that some victories have been gained in this way? And is not, therefore, the proper form of proposition Some S is P?

This, however, is a misunderstanding. What we are concerned with is the formal analysis of propositions as given. And Some victories have been gained by accident is not the formal analysis of Victories may be gained by accident. The two propositions do not give the same meaning in different forms: the meaning as well as the form is different. The one is a statement of a matter of fact: the other of an inference founded on it. The full significance of the Modal proper may be stated thus: In view of the fact that some victories have been gained by accident, we are entitled to say of any victory, in the absence of certain knowledge, that it may be one of them.

A general proposition, in short, is a proposition about a genus, taken universally.

II.--SECOND FIGURE.

For testing arguments from general principles, the First Figure is the simplest and best form of analysis.

But there is one common class of arguments that fall naturally, as ordinarily expressed, into the Second Figure, namely, negative conclusions from the absence of distinctive signs or symptoms, or necessary conditions.

Thirst, for example, is one of the symptoms of fever: if a patient is not thirsty, you can conclude at once that his illness is not fever, and the argument, fully expressed, is in the Second Figure.

All fever-stricken patients are thirsty. This patient is not thirsty. [.'.] He is not fever-stricken.

Arguments of this type are extremely common.

Armed with the general principle that ill-doers are ill-dreaders, we argue from a man's being unsuspicious that he is not guilty. The negative diagnosis of the physician, as when he argues from the absence of sore throat or the absence of a white speck in the throat that the case before him is not one of scarlatina or diphtheria, follows this type: and from its utility in making such arguments explicit, the Second Figure may be called the Figure of Negative Diagnosis.

It is to be observed, however, that the character of the argument is best disclosed when the Major Premiss is expressed by its Converse by Contraposition. It is really from the absence of a symptom that the physician concludes; as, for example: "No patient that has not a sore throat is suffering from scarlatina". And the argument thus expressed is in the First Figure. Thus the reduction of Baroko to the First Figure by contraposition of the Middle is vindicated as a really useful process. The real Middle is a contrapositive term, and the form corresponds more closely to the reasoning when the argument is put in the First Figure.

The truth is that if the positive term or sign or necessary condition is prominent as the basis of the argument, there is considerable risk of fallacy. Sore throat being one of the symptoms of scarlatina, the physician is apt on finding this symptom present to jump to a positive conclusion. This is equivalent technically to drawing a positive conclusion from premisses of the Second Figure.

All scarlatina patients have sore throat. This patient has sore throat.

A positive conclusion is technically known as a Non-Sequitur (Doesn't follow). So with arguments from the presence of a necessary condition which is only one of many. Given that it is impossible to pass without working at the subject, or that it is impossible to be a good marksman without having a steady hand, we are apt to argue that given also the presence of this condition, a conclusion is implicated. But really the premisses given are only two affirmatives of the Second Figure.

"It is impossible to pass without working at the subject."

This, put into the form No not-M is P, is to say that "None who have not worked can pass". This is equivalent, as the converse by contraposition, with--

All capable of passing have worked at the subject.

But though Q has worked at the subject, it does not follow that he is capable of passing. Technically the middle is undistributed. On the other hand, if he has not worked at the subject, it follows that he is not capable of passing. We can draw a conclusion at once from the absence of the necessary condition, though none can be drawn from its presence alone.

THIRD FIGURE.

Arguments are sometimes advanced in the form of the Third Figure. For instance: Killing is not always murder: for tyrannicide is not murder, and yet it is undoubtedly killing. Or again: Unpleasant things are sometimes salutary: for afflictions are sometimes so, and no affliction can be called pleasant.

These arguments, when analysed into terms, are, respectively, Felapton and Disamis.

No tyrannicide is murder; All tyrannicide is killing; Some killing is not murder.

Some afflictions are salutary things; All afflictions are unpleasant things; Some unpleasant things are salutary things.

The syllogistic form cannot in such cases pretend to be a simplification of the argument. The argument would be equally unmistakable if advanced in this form: Some S is not P, for example, M. Some killing is not murder, _e.g.,_ tyrannicide. Some unpleasant things are salutary, _e.g.,_ some afflictions.

There is really no "deduction" in the third figure, no leading down from general to particular. The middle term is only an example of the minor. It is the syllogism of Contradictory Examples.

In actual debate examples are produced to disprove a universal assertion, affirmative or negative. Suppose it is maintained that every wise man has a keen sense of humour. You doubt this: you produce an instance of the opposite, say Milton. The force of your contradictory instance is not increased by exhibiting the argument in syllogistic form: the point is not made clearer.

The Third Figure was perhaps of some use in Yes and No Dialectic. When you had to get everything essential to your conclusion definitely admitted, it was useful to know that the production of an example to refute a generality involved the admission of two propositions. You must extract from your opponent both that Milton was a wise man, and that Milton had not a keen sense of humour, before you could drive him from the position that all wise men possess that quality.

_Examples for Analysis._

Scarlet flowers have no fragrance: this flower has no fragrance: does it follow that this flower is of a scarlet colour?

Interest in the subject is an indispensable condition of learning easily; Z is interested in the subject: he is bound, therefore, to learn easily.

It is impossible to be a good shot without having a steady hand: John has a steady hand: he is capable, therefore, of becoming a good shot.

Some victories have been won by accident; for example, Maiwand.

Intemperance is more disgraceful than cowardice, because people have more opportunities of acquiring control of their bodily appetites.

"Some men are not fools, yet all men are fallible." What follows?

"Some men allow that their memory is not good: every man believes in his own judgment." What is the conclusion, and in what Figure and Mood may the argument be expressed?

"An honest man's the noblest work of God: Z is an honest man": therefore, he is--what?

Examine the logical connexion between the following "exclamation" and "answer": "But I hear some one exclaiming that wickedness is not easily concealed. To which I answer, Nothing great is easy."

"If the attention is actively aroused, sleep becomes impossible: hence the sleeplessness of anxiety, for anxiety is a strained attention upon an impending disaster."

"To follow truth can never be a subject of regret: free inquiry does lead a man to regret the days of his childish faith; therefore it is not following truth."--_J. H. Newman._

He would not take the crown: Therefore 'tis certain he was not ambitious.

As he was valiant, I honour him; as he was ambitious, I slew him.

The Utopians learned the language of the Greeks with more readiness because they were originally of the same race with them.

Nothing which is cruel can be expedient, for cruelty is most revolting to the nature of man.

"The fifth century saw the foundation of the Frank dominion in Gaul, and the first establishment of the German races in Britain. The former was effected in a single long reign, by the energy of one great ruling tribe, which had already modified its traditional usages, and now, by the adoption of the language and religion of the conquered, prepared the way for a permanent amalgamation with them." In the second of the above sentences a general proposition is assumed. Show in syllogistic form how the last proposition in the sentence depends upon it.

"I do not mean to contend that active benevolence may not hinder a man's advancement in the world: for advancement greatly depends upon a reputation for excellence in some one thing of which the world perceives that it has present need: and an obvious attention to other things, though perhaps not incompatible with the excellence itself, may easily prevent a person from obtaining a reputation for it." Pick out the propositions here given as interdependent. Examine whether the principle alleged is sufficiently general to necessitate a conclusion. In what form would it be so?