Lesson 17Varieties Of Syllogisms.The authorities in Logic hold that with the four kindsof propositions grouped in every possible order ofarrangement, it is possible to form nineteen differentkinds of valid arguments, which are called the nineteen moodsof the syllogism. These are classified by division into what arecalled the four figures, each of which figures may be known bythe position of the middle term in the premises. Logicians havearranged elaborate and curious tables constructed to showwhat kinds of propositions when joined in a particular orderof arrangement will make sound and valid syllogisms. We shallnot set forth these tables here, as they are too technical for apopular presentation of the subject before us, and because theyare not necessary to the student who will thoroughly familiarizehimself with the above stated Laws of the Syllogism and whowill therefore be able to determine in every case whether anygiven argument is a correct syllogism, or otherwise.In many instances of ordinary thought and expression thecomplete syllogistic form is omitted, or not stated at full length.It is common usage to omit one premise of a syllogism, inordinary expression, the missing premise being inferred by thespeaker and hearer. A syllogism with one premise unexpressedThe Art of Logical Thinking106is sometimes called an Enthymene, the term meaning inthe mind. For instance, the following: We are a free people,therefore we are happy, the major premise All free peopleare happy being omitted or unexpressed. Also in Poets areimaginative, therefore Byron was imaginative, the minorpremise Byron was a poet is omitted or unexpressed. Jevonssays regarding this phase of the subject: Thus in the Sermonon the Mount, the verses known as the Beatitudes consist eachof one premise and a conclusion, and the conclusion is put first.Blessed are the merciful: for they shall obtain mercy. The subjectand the predicate of the conclusion are here inverted, so thatthe proposition is really The merciful are blessed. It is evidentlyunderstood that All who shall obtain mercy are blessed, sothat the syllogism, when stated at full length, becomes: Allwho shall obtain mercy are blessed; All who are merciful shallobtain mercy; Therefore, all who are merciful are blessed. Thisis a perfectly good syllogism.Whenever we find any of the words: because, for, therefore,since, or similar terms, we may know that there is an argument,and usually a syllogism.We have seen that there are three special kinds of Propositions,namely, (1) Categorical Propositions, or propositions inwhich the affirmation or denial is made without reservationor qualification; (2) Hypothetical Propositions, in whichthe affirmation or denial is made to depend upon certainconditions, circumstances, or suppositions; and (3) DisjunctivePropositions, in which is implied or asserted an alternative.The forms of reasoning based upon these three severalclasses of propositions bear the same names as the latter.And, accordingly the respective syllogisms expressing theseforms of reasoning also bear the class name or term. Thus,a Categorical Syllogism is one containing only categoricalpropositions; a Hypothetical Syllogism is one containing one ormore hypothetical propositions; a Disjunctive Syllogism is onecontaining a disjunctive proposition in the major premise.Varieties Of Syllogisms107Categorical Syllogisms, which are far more common thanthe other two kinds, have been considered in the previouschapter, and the majority of the examples of syllogisms givenin this book are of this kind. In a Categorical Syllogism thestatement or denial is made positively, and without reservationor qualification, and the reasoning thereupon partakes ofthe same positive character. In propositions or syllogisms ofthis kind it is asserted or assumed that the premise is trueand correct, and, if the reasoning be logically correct it mustfollow that the conclusion is correct, and the new propositionspringing therefrom must likewise be Categorical in its nature.Hypothetical Syllogisms, on the contrary, have as one or moreof their premises a hypothetical proposition which affirms orasserts something provided, or if, something else be true.Hyslop says of this: Often we wish first to bring out, if onlyconditionally, the truth upon which a proposition rests, soas to see if the connection between this conclusion and themajor premise be admitted. The whole question will thendepend upon the matter of treating the minor premise. Thishas the advantage of getting the major premise admittedwithout the formal procedure of proof, and the minor premiseis usually more easily proved than the major. Consequently,one is made to see more clearly the force of the argument orreasoning by removing the question of the material truth of themajor premise and concentrating attention upon the relationbetween the conclusion and its conditions, so that we knowclearly what we have first to deny if we do not wish to accept it.By joining a hypothetical proposition with an ordinaryproposition we create a Hypothetical Proposition. For instance:If York contains a cathedral it is a city; York does contain acathedral; therefore, York is a city. Or: If dogs have four feet,they are quadrupeds; dogs do have four feet; therefore dogsare quadrupeds. The Hypothetical Syllogism may be eitheraffirmative or negative; that is, its hypothetical proposition mayeither hypothetically affirm or hypothetically deny. The partThe Art of Logical Thinking108of the premise of a Hypothetical Syllogism which conditionsor questions (and which usually contains the little wordif) is called the Antecedent. The major premise is the oneusually thus conditioned. The other part of the conditionedproposition, and which part states what will happen or is trueunder the conditional circumstances, is called the Consequent.Thus, in one of the above examples: If dogs have four feet isthe Antecedent; and the remainder of the proposition: they arequadrupeds is the Consequent. The Antecedent is indicated bythe presence of some conditional term as: if, supposing, grantedthat, provided that, although, had, were, etc., the general senseand meaning of such terms being that of the little word if. TheConsequent has no special indicating term.Jevons gives the following clear and simple Rules regardingthe Hypothetical Syllogism:I. If the Antecedent be affirmed, the consequent may beaffirmed. If the Consequent be denied, the Antecedent may bedenied.II. Avoid the fallacy of affirming the consequent, or denyingthe antecedent. This is a fallacy because of the fact that theconditional statement made in the major premise may not bethe only one determining the consequent. The following is anexample of Affirming the Consequent: If it is raining, the skyis overclouded; the sky is overclouded; therefore, it is raining.In truth, the sky may he overclouded, and still it may not beraining. The fallacy is still more apparent when expressed insymbols, as follows: If A is B, C is D; C is D; therefore, A is B.The fallacy of denying the Antecedent is shown by the followingexample: If Radium were cheap it would be useful; Radium isnot cheap; therefore Radium is not useful. Or, expressed insymbols: If A is B, C is D; A is not B; therefore C is not D. Intruth Radium may be useful although not cheap. Jevons givesthe following examples of these fallacies: If a man is a goodteacher, he thoroughly understands his subject; but John Jonesthoroughly understands his subject; therefore, he is a goodVarieties Of Syllogisms109teacher. Also, If snow is mixed with salt it melts; the snow onthe ground is not mixed with salt; therefore it does not melt.Jevons says: To affirm the consequent and then to infer thatwe can affirm the antecedent, is as bad as breaking the thirdrule of the syllogism, and allowing an undistributed middleterm. To deny the antecedent is really to break the fourthrule of the syllogism, and to take a term as distributed in theconclusion which was not so in the premises.Hypothetical Syllogisms may usually be easily reduced to orconverted into Categorical Syllogisms. As Jevons says: In reality,hypothetical propositions and syllogisms are not different fromthose which we have more fully considered. It is all a matterof the convenience of stating the propositions. For instance,instead of saying: If Radium were cheap, it would be useful, wemay say Cheap Radium would be useful; or instead of saying:If glass is thin, it breaks easily, we may say Thin glass breakseasily. Hyslop gives the following Rule for Conversion in suchcases: Regard the antecedent of the hypothetical propositionas the subject of the categorical, and the consequent of thehypothetical proposition as the predicate of the categorical. Insome cases this change is a very simple one; in others it can beeffected only by a circumlocution.The third class of syllogisms, known as The DisjunctiveSyllogism, is the exception to the law which holds that all goodsyllogisms must fit in and come under the Rules of the Syllogism,as stated in the preceding chapter. Not only does it refuse toobey these Rules, but it fails to resemble the ordinary syllogismin many ways. As Jevons says: It would be a great mistake tosuppose that all good logical arguments must obey the rulesof the syllogism, which we have been considering. Only thosearguments which connect two terms together by means of amiddle term, and are therefore syllogisms, need obey theserules. A great many of the arguments which we daily use are ofthis nature; but there are a great many other kinds of arguments,some of which have never been understood by logicians untilThe Art of Logical Thinking110recent years. One important kind of argument is known as theDisjunctive Syllogism, though it does not obey the rules of thesyllogism, or in any way resemble syllogisms.The Disjunctive Syllogism is one having a disjunctiveproposition in its major premise. The disjunctive propositionalso appears in the conclusion when the disjunction in themajor premise happens to contain more than two terms. Adisjunctive proposition, we have seen, is one which possessesalternative predicates for the subject in which the conjunctionor (sometimes accompanied by either) appears. As forinstance: Lightning is sheet or forked; or,Arches are eitherround or pointed; or, Angles are either obtuse, or right angled,or acute. The different things joined together by or are calledAlternatives, the term indicating that we may choose betweenthe things, and that if one will not answer purpose we may takethe other, or one of the others if there be more than one other.The Rule regarding the Use of Disjunctive Syllogisms is that:If one or more alternatives be denied, the rest may still beaffirmed. Thus if we say that A is B or C, or that A is either Bor C, we may deny the B but still affirm the C. Some authoritiesalso hold that If we affirm one alternative, we must denythe remainder, but this view is vigorously disputed by otherauthorities. It would seem to be a valid rule in cases where theterm either appears as: A is either B or C, because there seemsto be an implication that one or the other alone can be true.But in cases like: A is B or C, there may be a possibility of bothbeing true. Jevons takes this latter view, giving as an examplethe proposition: A Magistrate is a Justice-of-the-Peace, a Mayor,or a Stipendiary Magistrate, but it does not follow that onewho is a Justice-of-the-Peace may not be at the same time aMayor. He states: After affirming one alternative we can onlydeny the others if there be such a difference between them thatthey could not be true at the same time. It would seem thatboth contentions are at the same time true, the example givenby Jevons illustrating his contention, and the proposition TheVarieties Of Syllogisms111prisoner is either guilty or innocent illustrating the contentionsof the other side.A Dilemma is a conditional syllogism whose Major Premisepresents some sort of alternative. Whately defines it as: Aconditional syllogism with two or more antecedents in themajor, and a disjunctive minor. There being two mutuallyexclusive propositions in the Major Premise, the reasoneris compelled to admit one or the other, and is then caughtbetween the two horns of the dilemma.The Art of Logical Thinking112113