________ . 



ward* BOO) to all argument- ; and nono can be valid which 

 cannot be proved to be in conformity with it. The whole key- 

 tone of reasoning, M explained by Logic, in thin very niraple 

 principle, ao aimplo that upon that very ground it has been 

 Mini and ridiculed by many. T .t, a* some 



MI; :! to pro re that a ayllogUm in conclusive in its 



inferi'!:<-e, but only to account for the fact, that any argument 

 which happens to bo capable of being thrown into the form of a 

 correct syllogism ia valid, while io argument can be valid which 

 oatr dealt with. If wo attempt t-> re.luoo mi invalid 



argument into a regular ayllogiam, we muat, it is true, fail ; 

 then the more nearly it ia made to approach in form to the 

 syllogistic, the more easy of dotoction will be ita fallacy, tho 



ire clearly we shall bo able to perceive that it violates aomo 

 uireinont of tho dictum above given. 



There are certain general rules applicable to all syllogisms 

 alike, which are founded on theso two canons : first. Terms 

 which agree with one and tho same third term agree with one 

 another; .SVruiicZ, Terms, one of which agrees and tho other 

 disagrees with one and tho samo third term, disagree with one 

 another. Those are too self-evident to require, or, in fact, 

 admit of pn>of, and are consequently clashed by Euclid, in a 

 more general form, amongst tho axioms of Geometry. Tho 

 il of the general rules deduced from thorn aro these : 



1. In every syllogism there are three terms, and three only. 

 For every syllogism proves some conclusion, in which there are 

 two terms only (usually called extremes), and unless theso are 

 both (one in each of the two promises) compared with ono and 

 the same third term, they cannot be proved either to agree or 

 disagree with ono another. The predicate of the conclusion ia 

 called the Major term ; its subject, the Minor term ; and tho 

 third term, with which they are each separately compared, is 

 called tho Middle (or Argument, in the language of tho older 

 logicians). 



2. In every syllogism there are three propositions, and 

 threo only, viz. : 1, the Major Premise (in which the major 

 term i* compared with tho middle) ; 2, the Minor Premise (in 

 which the minor term is compared with the middle) ; and 3, the 

 Conclusion (in which the minor term ia compared with tho 

 major). 



3. The middle term must not be ambiguous ; for in this 

 case, although there may be only ono middle tarm in sound, 

 there will bo two in sense, and the extremes not being each com- 

 pared with one and the same third term, it cannot be pronounced 

 either that they agree or that they disagree with ono another. 

 Tho ambiguity may arise from the middle being an equivocal 

 term used in different senses in the two premises, or from its 

 being undistributed in loth premises. In the latter case the 

 two extremes may have been compared each with a different 

 part of the signification of tho middle ; so that, in reality, there 

 will hare been two middle terms instead of one. Hence it is 

 all important that the middle should be distributed once, at 

 least, in the premises ; which we now know happens when it is 

 the subject of a universal proposition, or the predicate of a 

 negative. It is, however, sufficient for it to be distributed 

 once ; because if ono extreme has been compared to a part, and 

 the other to the whole of tho middle term, they must have been 

 both compared to the same thing. 



4. No extreme may bo distributed in the conclusion which 

 was undistributed in the premises. This would be, in reality, 

 to introduce a fourth term ; for it would bo to compare a part 

 only of the extreme with tho middle, and then to compare tho 

 whole of it in tho conclusion with tho other extreme; e.g., " All 

 men aro mortals ; fishes are not men ; therefore, fishes are 

 not mortal." Here the major term, though undistributed in ita 

 premise, is distributed in tho conclusion, and the argument, 

 therefore, is invalid. This is an example of what is called an 

 "illicit process of the Major" term; an "illicit process of the 

 Minor " occurring where the same fault occurs with respect to 

 tho Minor term. 



5. From two negative premises nothing can be inferred. 

 This is obvious ; for the middle is then a term with which 

 each extreme disagrees, and not one with which one extreme 

 agrees and the other disagrees : e.g., " Men are not stones ; 

 Men aro not angels," is a combination of propositions which 

 does not warrant any conclusion at all. 



6. If one of the premises be negative, the conclusion will 

 be negative. For the remaining premise is affirmative (by 



LKSSOXS ix Lo<nr 



COfl 



Bui* 5) ; therefore, on* of the extremes acres with the middle 

 term, and the other disagrees w jjj, ft ; and therefore the ex- 

 tremes disagree with one another, i.e., the conclusion is nega- 

 tive. It can also be shown, in a similar manner, thai one of 

 tho premises most be negative, if the conclusion is negative. 



7. If both premises are particular, nothing can be inferred. 

 In thin case ono of the premises would be affirmative (bj 

 Bole 5) ; and in it, therefore, both subject and predicate 

 (ono of which is the middle) would be undistributed. Hence, 

 the middle to be onoe distributed (in accordance with Bale 3), 

 would hare to be the predicate of the other premise, which 

 would consequently be negative. This (by Rule 6) would 

 mako tho conclusion negative. The predicate of this (the 

 major term) would then be distributed, although undid 



in ita premiae (for in the premises the only term which could 

 have been distributed waa the middle), and thus there would 

 result a violation of Kule 4. 



8. If one of tho premises is particular, the conclusion will 

 be particular. It will easily appear on examination that the 

 violation of this rule would, in every case where the premises 

 are otherwise correct, involve an " illicit process of the minor," 

 a fault we have already explained. 



Tho last two rules are sometimes stated together in this 

 form : the conclusion follows the weaker part the negative 

 being regarded as weaker than the affirmative, and the parti- 

 cular than the universal. 



We have next to see in how many different ways three pro- 

 positions can be combined so aa to make a regular and valid 

 syllogism. 



Tho determination or designation of the three propositions of 

 a syllogism in their order, according to their quantity and 

 quality, is called its Mood. Now, as there are the four kinds 

 of propositions (A, E, I, 0), and there are throe in each syllo- 

 gism, it is obvious that the number of possible moods is sixty- 

 four in all ; for any ono of tho four may bo a major premise, 

 each of which may, in like manner, have four minors. This 

 gives sixteen pairs of premises, each of which may have four 

 conclusions ; so that there are altogether sixty-four waya of 

 combining the three propositions (4x 4 = 16 X4= 64). The 

 majority of these, however, although arithmetically possible, 

 are logically invalid, from violating some of the above rules. 

 For instance, E E A is excluded for having two negative 

 promises, and fifteen other combinations are inadmissible for 

 the same reason. I I A and eleven others have two particular 

 premises ; twelve violate Bule G ; eight, Rule 8 ; and four 

 the latter part of Rule 6, having a negative conclusion with 

 two affirmative premises. 



By this means fifty-two modes altogether are excluded, aa 

 each offending against ono at least of tho general rules. In addi- 

 tion, one mood, I E O, is inadmissible, as it always involves an 

 " illicit process of tho major ; " for the major term is distri- 

 buted in the conclusion, which is negative, but undistributed 

 in the major premise, whether it be its subject or predicate. 

 There remain, then, ultimately only eleven modes, which can 

 be used in a legitimate syllogism. These are A A A, A A I, 

 A E E, A E O, A 1 1, A 0, E A E, E A O, E I O, I A I, and 

 OAO. 



The Figure of a syllogism is determined by the situation of 

 the middle term with reference to the extremes in the twc 

 premises. Hence, there result four figures : inasmuch as the 

 middle term may be the subject of both premises, or the predi- 

 cate of both, or the subject of either and the predicate of the 

 other. When tho middle is the subject of the major premis 

 and tho predicate of the minor, the figure is called the First. 

 In the /Second figure the middle is the predicate of both 

 premises ; in the Third, the subject of both ; and in the 

 Fourth, the predicate of the major premise and subject of the 

 minor. Thus, let "M" represent the major term, "m" tho 

 minor, and " j- " the middle ; we may exhibit the four figures 

 thus : 



1. 2. 3. 4. 



;. M M ^ pM MI* 



m n r.\ /j. ft m. ft m 



m M m M mM m M. 



Out of tho eleven modes enumerated above all are not admis- 

 sible in every figure. Thus All, which is legitimate in the 

 first and third figures, would have the middle undistributed in 

 the second and fourth ; and A E E would involve an " illicit 



