Examples for Analysis.

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

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.

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 theargument 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.

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?

There is a certain variety in the use of the word Enthymeme among logicians. In the narrowest sense, it is a valid formal syllogism, with one premiss suppressed. In the widest sense it is simply an argument, valid or invalid, formal in expression or informal, with only one premiss put forward or hinted at, the other being held in the mind (ἐν θυμῷ). This last is the Aristotelian sense.

It is only among formal logicians of the straitest sect that the narrowest sense prevails. Hamilton divides Enthymemes into three classes according as it is the Major Premiss, the Minor Premiss, or the Conclusion that is suppressed. Thus, a full syllogism being:—

All liars are cowards:Caius is a liar:... Caius is a coward:—

All liars are cowards:

Caius is a liar:

... Caius is a coward:—

this may be enthymematically expressed in three ways.

I. Enthymeme of the First Order (Major understood).

Caius is a coward; for Caius is a liar.

II. Enthymeme of the Second Order (Minor understood).

Caius is a coward; for all liars are cowards.

III. Enthymeme of the Third Order (Conclusion understood).

All liars are cowards, and Caius is a liar.

The Third Order is a contribution of Hamilton's own. It is superfluous, inasmuch as the conclusion is never suppressed except as a rhetorical figure of speech. Hamilton confines the word Enthymeme to valid arguments, in pursuance of his view that Pure Logic has no concern with invalid arguments.

Aristotle used Enthymeme in the wider sense of an elliptically expressed argument. There has been some doubt as to the meaning of his definition, but that disappears on consideration of his examples. He defines an Enthymeme (Prior Analyt., ii. 27) as "a syllogism from probabilities or signs" (συλλογισμὸςἐξ εἰκότωνἢσημείων). The word syllogism in this connexion is a little puzzling. But it is plain from the examples he gives that he meant here by syllogism not even a correct reasoning, much less a reasoning in the explicit form of three terms and three propositions. He used syllogism, in fact, in the same loose sense in which we use the words reasoning and argument, applying without distinction of good and bad.

The sign, he says, is taken in three ways, in as many ways as there are Syllogistic Figures.

(1) A sign interpreted in the First Figure is conclusive. Thus: "This person has been drowned, for he has froth in the trachea". Taken in the First Figure with "All who have froth in the trachea have been drowned" as a major premiss, this argument is valid. The sign is conclusive.

(2) "This patient is fever-stricken, for he is thirsty." Assumed that "All fever-stricken patients are thirsty,"this is an argument in the Second Figure, but it is not a valid argument. Thirst is a sign or symptom of fever, but not a conclusive sign, because it is indicative of other ailments also. Yet the argument has a certain probability.

(3) "Wise men are earnest (σπουδαῖοι), for Pittacus is earnest." Here the suppressed premiss is that "Pittacus is wise". Fully expressed, the argument is in the Third Figure:—

Pittacus is earnest.Pittacus is wise.... Wise men are earnest.

Pittacus is earnest.

Pittacus is wise.

... Wise men are earnest.

Here again the argument is inconclusive and yet it has a certain probability. The coincidence of wisdom with earnestness in one notable example lends a certain air of probability to the general statement.

Such are Aristotle's examples or strict parallels to them. The examples illustrate also what he says in hisRhetoricas to the advantages of enthymemes. For purposes of persuasion enthymemes are better than explicit syllogisms, because any inconclusiveness there may be in the argument is more likely to pass undetected. As we shall see, one main use of the Syllogism is to force tacit assumptions into light and so make their true connexion or want of connexion apparent. In Logic enthymemes are recognised only to be shown up: the elliptical expression is a cover for fallacy, which it is the business of the logician to strip off.

In Aristotle's examples one of the premisses is expressed. But often the arguments of common speech are even less explicit than this. A general principle is vaguely hinted at: a subject is referred toa class the attributes of which are assumed to be definitely known. Thus:—

He was too ambitious to be scrupulous in his choice of means.He was too impulsive not to have made many blunders.

He was too ambitious to be scrupulous in his choice of means.

He was too impulsive not to have made many blunders.

Each of these sentences contains a conclusion and an enthymematic argument in support of it. The hearer is understood to have in his mind a definite idea of the degree of ambition at which a man ceases to be scrupulous, or the degree of impulsiveness that is incompatible with accuracy.

One form of enthymeme is so common in modern rhetoric as to deserve a distinctive name. It may be called theEnthymeme of the Abstractly Denominated Principle. A conclusion is declared to be at variance with the principles of Political Economy, or contrary to the doctrine of Evolution, or inconsistent with Heredity, or a violation of the sacred principle of Freedom of Contract. It is assumed that the hearer is familiar with the principles referred to. As a safeguard against fallacy, it may be well to make the principle explicit in a proposition uniform with the conclusion.

The main use of the Syllogism is in dealing with incompletely expressed or elliptical arguments from general principals. This may be called Enthymematic argument, understanding by Enthymeme an argument with only one premiss put forward or hinted at, the other being held in the mind. In order to test whether such reasoning is sound or unsound, it is of advantage to make the argument explicit in Syllogistic form.

There have been heaps and mazes of discussion about the use of the Syllogism, much of it being profitable as a warning against the neglect of Formal Logic. Again and again it has been demonstrated that the Syllogism is useless for certain purposes, and from this it has been concluded that the Syllogism is of no use at all.

The inventor of the Syllogism had a definite practical purpose, to get at the simplest, most convincing, undeniable and irresistible way of putting admitted or self-evident propositions so that their implication should be apparent. His ambition was to furnish a method for the Yes and No Dialectician, and the expounder of science from self-evident principles. A question being put up for discussion, it was an advantage to analyse it, and formulate the necessarypremisses: you could then better direct your interrogations or guard your answers. The analysis is similarly useful when you want to construct an argument from self-evident principles.

All that the Syllogism could show was the consistency of the premisses with the conclusion. The conclusion could not go beyond the premisses, because the questioner could not go beyond the admissions of the respondent. There is indeed an advance, but not an advance upon the two premisses taken together. There is an advance upon any one of them, and this advance is made with the help of the other. Both must be admitted: a respondent may admit one without being committed to the conclusion. Let him admit both and he cannot without self-contradiction deny the conclusion. That is all.

Dialectic of the Yes and No kind is no longer practised. Does any analogous use for the Syllogism remain? Is there a place for it as a safeguard against error in modern debate? As a matter of fact it is probably more useful now than it was for its original purpose, inasmuch as modern discussion, aiming at literary grace and spurning exact formality as smacking of scholasticism and pedantry, is much more flabby and confused. In the old dialectic play there was generally a clear question proposed. The interrogative form forced this much on the disputants. The modern debater of the unpedantic, unscholastic school is not so fettered, and may often be seen galloping wildly about without any game in sight or scent, his maxim being to—

Spur boldly on, and dash through thick and thin,Through sense and nonsense, never out nor in.

Spur boldly on, and dash through thick and thin,

Through sense and nonsense, never out nor in.

Now the syllogistic analysis may often be of some use in helping us to keep a clear head in the face of a confused argument. There is a brilliant defence of the syllogism as an analysis of arguments in theWestminster Reviewfor January, 1828. The article was a notice of Whately's Logic: it was written by J. S. Mill. For some reason it has never been reprinted, but it puts the utility of the Syllogism on clearer ground than Mill afterwards sought for it.

Can a fallacy in argument be detected at once? Is common-sense sufficient? Common-sense would require some inspection. How would it proceed? Does common-sense inspect the argument in a lump or piecemeal? All at once or step by step? It analyses. How? First, it separates out the propositions which contribute to the conclusion from those which do not, the essential from the irrelevant. Then it states explicitly all that may have been assumed tacitly. Finally, it enumerates the propositions in order.

Some such procedure as this would be adopted by common-sense in analysing an argument. But when common-sense has done this, it has exhibited the argument in a series of syllogisms.

Such is Mill's early defence of the Syllogism. It is weak only in one point, in failing to represent how common-sense would arrive at the peculiar syllogistic form. It is the peculiar form of logical analysis that is the distinction of the syllogism. When you have disentangled the relevant propositions you have not necessarily put them in this form. The arguments given in text-books to be cast into syllogistic form, consist only as a rule of relevant propositions, but they are not yet formal syllogisms. But common-sensehad only one other step to make to reach the distinctive form. It had only to ask after analysing the argument, Is there any form of statement specially suitable for exhibiting the connexion between a conclusion and the general principle on which it is alleged to depend? Ask yourself the question, and you will soon see that there would be an obvious advantage in making the conclusion and the general principle uniform, in stating them with the same predicate. But when you do this, as I have already shown (p. 197) you state the argument in the First Figure of the Syllogism.

It must, however, be admitted that it is chiefly for exhibiting, or forcing into light, tacit or lurking assumptions that the Syllogistic form is of use. Unless identity of meaning is disguised or distorted by puzzling difference of language, there is no special illuminative virtue in the Syllogism. The argument in a Euclidean demonstration would not be made clearer by being cast into formal Syllogisms.

Again, when the subject matter is simple, the Syllogistic form is not really required for protection against error. In such enthymemes as the following for example:—

She must be clever: she is so uncompromisingly ugly.Romeo must be in love: for is he not seventeen?

She must be clever: she is so uncompromisingly ugly.

Romeo must be in love: for is he not seventeen?

it is plain to the average intelligence without any knowledge of Syllogism that the argument takes for granted a general proposition and what the general proposition is.

Another thing is plain to the average intelligence, perhaps plainer than to a proficient in the use of theSyllogism. Clearly we cannot infer with certainty that a woman is clever because she is ugly, unless it is the case that all ugly women are clever. But a Syllogiser, seeing that no certain conclusion can be drawn except upon this condition, is apt to dismiss the argument as altogether worthless. This may be specified as an error incident to the practice of the Syllogism, that it inclines us to look for necessarily conclusive premisses, and to deny all weight to anything short of this. Now in ordinary life it is comparatively seldom that such premisses can be found. We are obliged to proceed on maxims that are not of universal scope, and which lend only a more or less strong colour of probability to cases that can be brought under them. "A little learning is a dangerous thing;" "Haste makes waste;" "Slowness of speech is a sign of depth of thought;" "Vivacity is a sign of shallowness:" such are the "endoxes" or commonplaces of popular knowledge that men bring to bear in daily life. They are not true for all cases, but some of them are true for most or for a good many, and they may be applied with a certain probability though they are not rigidly conclusive. The plain man's danger is that he apply them unthinkingly as universals: the formal logician's danger is that, seeing them to be inapplicable as universals, he dismisses them as being void of all argumentative force.

It helps to fix the limits of Formal Logic to remember that it lies outside its bounds to determine the degree of probability attaching to the application of approximate truths, such as are the staple of arguments in ordinary affairs. Formal Logic, we may repeat, is not concerned with degrees of truth or falsehood, probability or improbability. It merely shows theinterdependency of certain arguments, the consistency of conclusion with premisses.

This, however, is a function that might easily be underrated. Its value is more indirect than direct. In showing what is required for a certain conclusion, it puts us on the road to a more exact estimate of the premisses alleged, a sounder judgment of their worth. Well begun is half done: in undertaking the examination of any argument from authority, a formal syllogism is a good beginning.

The justification of including these forms of argument in Logic is simply that they are sometimes used in debate, and that confusion may arise unless the precise meaning of the premisses employed is understood. Aristotle did not include them as now given in his exposition of the Syllogism, probably because they have no connexion with the mode of reasoning together to which he appropriated the title. The fallacies connected with them are of such a simple kind that to discuss as a question of method the precise place they should occupy in a logical treatise is a waste of ingenuity.1

A so-called Hypothetical Syllogism is thus seen to be a Syllogism in which the major premiss is aHypothetical Proposition, that is to say, a complex proposition in which two propositions are given as so related that the truth of one follows necessarily from the truth of the other.

Two propositions so related are technically called theAntecedentor Reason, and theConsequent.

The meaning and implication of the form, If A is B, C is D, is expressed in what is known as theLaw of Reason and Consequent:—

"When two propositions are related as Reason and Consequent, the truth of the Consequent follows from the truth of the Antecedent, and the falsehood of the Antecedent, from the falsehood of the Consequent".

If A is B, C is D, implies that If C is not D, A is not B. If this subject is educative, it quickens the wits; if it does not quicken the wits, it is not educative.

Admitted, then, that the law of Reason and Consequent holds between two propositions—that If A is B, C is D: admitted also the Antecedent, the truth of the Consequent follows. This is theModus Ponensor Positive Mode, where you reach a conclusion by obtaining the admission of the Antecedent. Admit the Antecedent and the truth of the Consequent follows.

With the same Major Premiss, you may also, under the Law of Reason and Consequent reach a conclusion by obtaining the denial of the Consequent. This is theModus Tollensor Negative Mode. Deny the Consequent and one is bound to deny the Antecedent.

But to guard against the fallacy technically known asFallacia Consequentis, we must observe what the relation of Reason and Consequent does not imply.The truth of the Consequent does not involve the truth of the Antecedent, and the falsehood of the Antecedent does not involve the falsehood of the Consequent.

"If the harbour is frozen, the ships cannot come in." If the harbour is not frozen, it does not follow that the ships can come in: they may be excluded by other causes. And so, though they cannot come in, it does not follow that the harbour is frozen.

(1)Are they properly called Syllogisms?This is purely a question of Method and Definition. If we want a separate technical name for forms of argument in which two terms are reasoned together by means of a third, the Hypothetical Syllogism, not being in such a form, is not properly so called. The fact is that for the purposes of the Hypothetical Argument, we do not require an analysis into terms at all: it is superfluous: we are concerned only with the affirmation or denial of the constituent propositions as wholes.

But if we extend the word Syllogism to cover all arguments in which two propositions necessarily involve a third, the Hypothetical Argument is on this understanding properly enough called a Syllogism.

(2)Is the inference in the Hypothetical Syllogism Mediate or Immediate?

To answer this question we have to consider whether the Conclusion can be drawn from either of the two premisses without the help of the other. If it is possible immediately, it must be educible directly either from the Major Premiss or from the Minor.

(a) Some logicians argue as if the Conclusion were immediately possible from the Major Premiss. The Minor Premiss and the Conclusion, they urge, aresimply equivalent to the Major Premiss. But this is a misunderstanding. "If A is B, C is D," is not equivalent to "A is B,thereforeC is D". "If the harbour is frozen, the ships cannot come in" is not to say that "the harbour is frozen, and therefore," etc. The Major Premiss merely affirms the existence of the relation of Reason and Consequent between the two propositions. But we cannot thereupon assert the Conclusion unless the Minor Premiss is also conceded; that is, the inference of the Conclusion is Mediate, as being from two premisses and not from one alone.

(b) Similarly with Hamilton's contention that the Conclusion is inferrible immediately from the Minor Premiss, inasmuch as the Consequent is involved in the Reason. True, the Consequent is involved in the Reason: but we cannot infer from "A is B" to "C is D," unless it is conceded that the relation of Reason and Consequent holds between them; that is, unless the Major Premiss is conceded as well as the Minor.

(3)Can Hypothetical Syllogism be reduced to the Categorical Form?

To oppose Hypothetical Syllogisms to Categorical is misleading, unless we take note of the precise difference between them. It is only in the form of the Major Premiss that they differ: Minor Premiss and Conclusion are categorical in both. And the meaning of a Hypothetical Major Premiss (unless it is a mere arbitrary convention between two disputants, to the effect that the Consequent will be admitted if the Antecedent is proved, or that the Antecedent will be relinquished if the Consequent is disproved), can always be put in the form of a general proposition, from which, with the Minor Premiss as applyingproposition, a conclusion identical with the original can be drawn in regular Categorical form.

Thus:—

If the harbour is frozen, the ships cannot come in.The harbour is frozen.... The ships cannot come in.

If the harbour is frozen, the ships cannot come in.

The harbour is frozen.

... The ships cannot come in.

This is a Hypothetical Syllogism,Modus Ponens. Express the Hypothetical Major in the form of the general proposition which it implies, and you reach a conclusion (inBarbara) which is only grammatically different from the original.

All frozen harbours exclude ships.The harbour is frozen.... It excludes ships.

All frozen harbours exclude ships.

The harbour is frozen.

... It excludes ships.

Again, take an example of theModus Tollens—

If rain has fallen, the streets are wet.The streets are not wet.... Rain has not fallen.

If rain has fallen, the streets are wet.

The streets are not wet.

... Rain has not fallen.

This is reducible, by formulating the underlying proposition, toCamestresorBarokoof the Second Figure.

All streets rained upon are wet.The streets are not wet.... They are not streets rained upon.

All streets rained upon are wet.

The streets are not wet.

... They are not streets rained upon.

Hypothetical Syllogisms are thus reducible, by merely grammatical change2, or by the statement ofself-evident implications, to the Categorical form. And, similarly, any Categorical Syllogism may be reduced to the Hypothetical form. Thus:—

All men are mortal.Socrates is a man.... Socrates is mortal.

All men are mortal.

Socrates is a man.

... Socrates is mortal.

This argument is not different, except in the expression of the Major and the Conclusion, from the following:—

If Socrates is a man, death will overtake him.Socrates is a man.... Death will overtake him.

If Socrates is a man, death will overtake him.

Socrates is a man.

... Death will overtake him.

The advantage of the Hypothetical form in argument is that it is simpler. It was much used in Mediæval Disputation, and is still more popular than the Categorical Syllogism. Perhaps the prominence given to Hypothetical Syllogisms as syllogisms in Post-Renaissance text-books is due to the use of them in the formal disputations of graduands in the Universities. It was the custom for the Disputant to expound his argument in this form:—

If so and so is the case, such and such follows.So and so is the case.... Such and such follows.

If so and so is the case, such and such follows.

So and so is the case.

... Such and such follows.

To which the Respondent would reply:Accipio antecedentem, nego consequentiam, and argue accordingly. Petrus Hispanus does not give the Hypothetical Syllogism as a Syllogism: he merely explains the true law of Reason and Consequent in connexion with the Fallacia Consequentis in the section on Fallacies. (Summulæ. Tractatus Sextus.)

A Disjunctive Syllogism is a syllogism in which the Major Premiss is aDisjunctive Proposition,i.e., one in which two propositions are declared to be mutually incompatible. It is of the form Either A is B, or C is D.3

If the disjunction between the alternatives is really complete, the form implies four hypothetical propositions:—

(1) If A is B, C is not D.(2) If A is not B, C is D.(3) If C is D, A is not B.(4) If C is not D, A is B.

(1) If A is B, C is not D.

(2) If A is not B, C is D.

(3) If C is D, A is not B.

(4) If C is not D, A is B.

Suppose then that an antagonist has granted you a Disjunctive Proposition, you can, using this as a Major Premiss, extract from him four different Conclusions, if you can get him also to admit the requisite Minors. The Mode of two of these is technically calledModus Ponendo Tollens, the mode that denies the one alternative by granting the other—A is B,thereforeC is not D; C is D,thereforeA is not B. The other Mode is also twice open, theModus Tollendo Ponens—A is not B,thereforeC is D; C is not D,thereforeA is B.

Fallacy is sometimes committed through the Disjunctive form owing to the fact that in common speech there is a tendency to use it in place of a merehypothetical, when there are not really two incompatible alternatives. Thus it may be said "Either the witness is perjured, or the prisoner is guilty," when the meaning merely is that if the witness is not perjured the prisoner is guilty. But really there is not a valid disjunction and a correct use of the disjunctive form, unless four hypotheticals are implied, that is, unless the concession of either involves the denial of the other, and the denial of either the concession of the other. Now the prisoner may be guilty and yet the witness be perjured; so that two of the four hypotheticals, namely—

If the witness is perjured, the prisoner is not guilty,If the prisoner is guilty, the witness is not perjured—

If the witness is perjured, the prisoner is not guilty,

If the prisoner is guilty, the witness is not perjured—

do not necessarily hold. If, then, we would guard against fallacy, we must always make sure before assenting to a disjunctive proposition that there is really a complete disjunction or mutual incompatibility between the alternatives.

A Dilemma is a combination of Hypothetical and Disjunctive propositions.

The word has passed into common speech, and its ordinary use is a clue to the logical structure. We are said to be in a dilemma when we have only two courses open to us and both of them are attended by unpleasant consequences. In argument we are in this position when we are shut into a choice between two admissions, and either admission leads to a conclusion which we do not like. The statement of the alternatives as the consequences hypothetically of certain conditions is the major premiss of the dilemma: once we admitthat the relations of Antecedent and Consequent are as stated, we are in a trap, if trap it is: we are on the horns of the dilemma, ready to be tossed from one to the other.

For example:—

If A is B, A is C, and if A is not B, A is D. But A either is or is not B. Therefore, A either is C or is D.If A acted of his own motive, he is a knave; if A did not act of his own motive, he is a catspaw. But A either acted of his own motive or he did not. Thereupon A is either a knave or a catspaw.

If A is B, A is C, and if A is not B, A is D. But A either is or is not B. Therefore, A either is C or is D.

If A acted of his own motive, he is a knave; if A did not act of his own motive, he is a catspaw. But A either acted of his own motive or he did not. Thereupon A is either a knave or a catspaw.

This is an example of theConstructiveDilemma, the form of it corresponding to the common use of the word as a choice between equally unpleasant alternatives. The standard example is the dilemma in which the custodians of the Alexandrian Library are said to have been put by the Caliph Omar in 640A.D.

If your books are in conformity with the Koran, they are superfluous; if they are at variance with it, they are pernicious. But they must either be in conformity with the Koran or at variance with it. Therefore they are either superfluous or pernicious.

Where caution has to be exercised is in accepting the clauses of the Major. We must make sure that the asserted relations of Reason and Consequent really hold. It is there that fallacy is apt to creep in and hide its head. The Alexandrian Librarians were rash in accepting the first clause of the conqueror's Major: it does not follow that the books are superfluous unless the doctrines of the Koran are not merely sound but contain all that is worth knowing. The propounder of the dilemma covertly assumes this. It is in the facility that it affords for what is technically known asPetitio Principiithat the Dilemma is a useful instrument for the Sophist. We shall illustrate it further under that head.

What is known as theDestructiveDilemma is of a somewhat different form. It proceeds upon the denial of the Consequent as involving the denial of the Antecedent. In the Major you obtain the admission that if a certain thing holds, it must be followed by one or other of two consequences. You then prove by way of Minor that neither of the alternatives is true. The conclusion is that the antecedent is false.

We had an example of this in discussing whether the inference in the Hypothetical Syllogism is Immediate. Our argument was in this form:—

If the inference is immediate, it must be drawn either from the Major alone or from the Minor alone. But it cannot be drawn from the Major alone, neither can it be drawn from the Minor alone. Therefore, it is not immediate.

In this form of Dilemma, which is often serviceable for clearness of exposition, we must as in the other make sure of the truth of the Major: we must take care that the alternatives are really the only two open. Otherwise the imposing form of the argument is a convenient mask for sophistry. Zeno's famous dilemma, directed to prove that motion is impossible, covers apetitio principii.

If a body moves, it must move either where it is or where it is not. But a body cannot move where it is: neither can it move where it is not. Conclusion, it cannot move at all,i.e., Motion is impossible.

The conclusion is irresistible if we admit the Major, because the Major covertly assumes the point to beproved. In truth,ifa body moves, it moves neither where it is nor where it is not, but from where it is to where it is not. Motion consists in change of place: the Major assumes that the place is unchanged, that is, that there is no motion.

Footnote 1:For the history of Hypothetical Syllogism see Mansel'sAldrich, Appendix I.

Footnote 2:It may be argued that the change is not merely grammatical, and that the implication of a general proposition in a hypothetical andvice versâis a strictly logical concern. At any rate such an implication exists, whether it is the function of the Grammarian or the Logician to expound it.

Footnote 3:Some logicians prefer the form Either A is, or B is. But the two alternatives are propositions, and if "A is" represents a proposition, the "is" is not the Syllogistic copula. If this is understood it does not matter: the analysis of the alternative propositions is unessential.

The traditional treatment of Fallacies in Logic follows Aristotle's special treatiseΠερὶσοφιστικῶνἐλέγχων—Concerning Sophistical Refutations—Pretended Disproofs—Argumentative Tricks.

Regarding Logic as in the main a protection against Fallacies, I have been going on the plan of taking each fallacy in connexion with its special safeguard, and in accordance with that plan propose to deal here with the two great types of fallacy in deductive argument. Both of them were recognised and named by Aristotle: but before explaining them it is worth while to indicate Aristotle's plan as a whole. Some of his Argumentative Tricks were really peculiar to Yes-and-No Dialectic in its most sportive forms: but his leading types, both Inductive and Deductive, are permanent, and his plan as a whole has historical interest. Young readers would miss them from Logic: they appeal to the average argumentative boy.

He divides Fallacies broadly into Verbal Fallacies (παρὰτὴν λέξιν,in dictione), and Non-Verbal Fallacies (ἔξω τῆς λέξεως),extra dictionem).

The first class are mere Verbal Quibbles, and hardly deserve serious treatment, still less minute subdivision. The world was young when time was spentupon them. Aristotle names six varieties, but they all turn on ambiguity of word or structure, and some of them, being dependent on Greek syntax, cannot easily be paralleled in another tongue.

(1) Ambiguity of word (ὁμωνυμία). As if one were to argue: "All cold can be expelled by heat: John's illness is a cold: therefore it can be expelled by heat". Or: "Some afflictions are cheering, for afflictions are sometimes light, and light is always cheering". The serious confusion of ambiguous words is met by Definition, as explained at length in pt. ii. c. i.

(2)Ambiguity of structure(ἀμφιβολία).

"What he was beaten with was what I saw him beaten with: what I saw him beaten with was my eye: therefore, what he was beaten with was my eye."

"How do you do?" "Do? Do what?" "I mean, how do you feel?" "How do I feel? With my fingers, of course; but I can see very well." "No, no; I mean, how do you find yourself?" "Then why did you not say so? I never exactly noticed, but I will tell you next time I lose myself."

(3)Illicit conjunction(σύνθεσις).

Socrates is good. Socrates is a musician. Therefore Socrates is a good musician.

(4)Illicit disjunction(διαίρεσις).

Socrates is a good musician. Therefore he is a good man.

(5)Ambiguity of pronunciation(προσῳδία),fallacia accentus).

Analogies to words that differ only in accent, such asοὖandοὔ, may be found in differences of pronunciation. "Hair very thick, sir," said a barber to a customer, whose hair was bushy, but beginning to turn grey. "Yes, I daresay. But I would rather have itthick than thin." "Ah, too thick to-day, sir." "But I don't want to dye it." "Excuse me, sir, I mean the hair of the hatmosphere, t-o-d-a-y, to-day."

"He said, saddle me the ass. And they saddledhim."

(6)Ambiguity of inflexion(σχῆμα τῆς λέξεως,Figura dictionis).

This is not easy to make intelligible in English. The idea is that a termination may be ambiguously interpreted, a neuter participle,e.g., taken for an active. Thus: "George is ailing". "Doing what, did you say? Ailing? What is he ailing? Ginger-aleing?"

Non-Verbal Fallacies, or Fallacies in thought, are a more important division. Aristotle distinguishes seven.

Of these, three are comparatively unimportant and trifling. One of them, known to the Schoolmen asFallacia Plurium Interrogationum, was peculiar to Interrogative disputation. It is the trick of putting more than one question as one, so that a simple Yes commits the respondent to something implied. "Have you left off beating your father?" If you answer Yes, that implies that you have been in the habit of beating him. "Has the practice of excessive drinking ceased in your part of the country?" Such questions were unfair when the Respondent could answer only Yes or No. The modern disputant who demands a plain answer Yes or No, is sometimes guilty of this trick.

Two others, the fallacies known asA dicto simpliciter ad dictum secundum quid, andA dicto secundum quid ad dictum simpliciter, are as common in modern dialectic as they were in ancient. The trick, conscious or unconscious, consists in getting assent to a statement with a qualification and proceeding to argue as if it had beenconceded without qualification, andvice versâ. For example, it being admitted that culture is good, a disputant goes on to argue as if the admission applied to some sort of culture in special, scientific, æsthetic, philosophical or moral. The fallacy was also known asFallacia Accidentis. Proving that the Syllogism is useless for a certain purpose, and then claiming to have proved that it is useless for any purpose is another example. Getting a limited admission and then extending it indefinitely is perhaps the more common of the two forms. It is common enough to deserve a shorter name.

TheFallacia Consequentis, orNon-Sequitur, which consists specially in ignoring the possibility of a plurality of causes, has already been partly explained in connexion with the Hypothetical Syllogism, and will be explained further in the Logic of Induction.

Post hoc ergo proper hocis a purely Inductive Fallacy, and will be explained in connexion with the Experimental Methods.

There remain the two typical Deductive Fallacies,Petitio Principii(Surreptitious Assumption) andIgnoratio Elenchi(Irrelevant Argument) about which we must speak more at length.

The phrase of which Petitio Principii or Begging the Question is a translation—τὸἐνἀρχῇαἰτεῖσθαι—was applied by Aristotle to an argumentative trick in debate by Question and Answer. The trick consisted in taking for granted a proposition necessary to the refutation without having obtained the admission of it. Another expression for the same thing—τὸἐνἀρχῇλαμβάνειν—taking the principle for granted—is more descriptive.

Generally speaking, Aristotle says, Begging theQuestion consists in not demonstrating the theorem. It would be in accordance with this general description to extend the name to all cases of tacitly or covertly, unwittingly to oneself or to one's opponent, assuming any premiss necessary to the conclusion. It is the fallacy of Surreptitious Assumption, and all cases of Enthymematic or Elliptical argument, where the unexpressed links in the chain of argument are not fully understood, are examples of it. By contrast, the articulate and explicit Syllogism is anExpositio Principii. The only remedy for covert assumptions is to force them into the light.1

Ignoratio Elenchi, ignoring the refutation (τοῦἐλέγχουἄγνοια), is simply arguing beside the point, distracting the attention by irrelevant considerations. It often succeeds by proving some other conclusion which is not the one in dispute, but has a superficial resemblance to it, or is more or less remotely connected with it.

It is easier to explain what these fallacies consist in than to illustrate them convincingly. It is chiefly in long arguments that the mischief is done. "A Fallacy," says Whately, "which when stated barely in a few sentences would not deceive a child, may deceive half the world if diluted in a quarto volume." Very rarely is a series of propositions put before us in regular form and order, all bearing on a definite point. A certain conclusion is in dispute, not very definitely formulated perhaps, and a mixed host of considerations are tumbled out before us. If we were perfectly clear-headedpersons, capable of protracted concentration of attention, incapable of bewilderment, always on the alert, never in a hurry, never over-excited, absolutely without prejudice, we should keep our attention fixed upon two things while listening to an argument, the point to be proved, and the necessary premisses. We should hold the point clearly in our minds, and watch indefatigably for the corroborating propositions. But none of us being capable of this, all of us being subject to bewilderment by a rapid whirl of statements, and all of us biased more or less for or against a conclusion, the sophist has facilities for doing two things—taking for granted that he has stated the required premisses (petitio principii), and proving to perfect demonstration something which is not the point in dispute, but which we are willing to mistake for it (ignoratio elenchi).

It is chiefly in the heat of argument that either Petitio or Ignoratio succeeds. When a fallacy continues to perplex us in cold blood, it must have in its favour either some deeply-rooted prejudice or some peculiar intricacy in the language used, or some abstruseness in the matter. If we are not familiar with the matter of the argument, and have but a vague hold of the words employed, we are, of course, much more easily imposed upon.

The famous Sophisms of antiquity show the fascination exercised over us by proving something, no matter how irrelevant. If certain steps in an argument are sound, we seem to be fascinated by them so that we cannot apply our minds to the error, just as our senses are fascinated by an expert juggler. We have seen how plausibly Zeno's argument against the possibility of motion hides a Petitio: the Fatalist Dilemma is another example of the same sort.

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