no 



REASONING. 



philosophical precision, and explained 

 with remarkable perspicuity, the whole 

 of the common doctrine of the syllo- 

 gism. 



All valid ratiocination, all reason- 

 ing by which, from general proposi- 

 tions previously admitted, other pro- 

 positions equally or less general are 

 inferred, may be exhibited in some 

 of the above forms. The whole of 

 Eticlid, for example, might be thrown 

 without difficulty into a series of syl- 

 logisms, regular in mood and figure. 



Though a syllogism framed accord- 

 ing to any of these formulae is a valid 

 argument, all correct ratiocination 

 admits of being stated in syllogisms 



wise, poor, and a man, and we merely re- 

 peat the concurrence which is selected 

 from the whole aggregate of properties 

 making up the whole, Socrates. The case 

 is one under the head * Greater and Less 

 Connotation' in Equivalent Propositional 

 Forms, or Immediate Inference. 



" But the example in this form does not 

 do j ustice to 1 1 1 e syllogism of singulars. We 

 must suppose both propositions to be real, 

 the predicates being in no way involved m 

 the subject. Thus 



Socrates was the master of Plato, 



Socrates fought at Delium, 



The master of Plato fought at Delium. 



" It may fairly be doubted whetlier the 

 transitions, in this instance, are anything 

 more than equivalent forms. For the pro- 

 position ' Socrates was the master of Plato 

 and fought at Delium,' compounded out of 

 the two premises, is obviously nothing 

 more than a grammatical abbieviation. 

 No one can say that there is here any 

 change of meaning, or anything beyond a 

 verbal modification of the original form. 

 Tne next step is, 'The master of Plato 

 fouglit at Delium,' which is the previous 

 statement cut down by the omission of 

 Socrates. It contents itself with reproduc- 

 ing a part of the meaning, or saying less 

 than had been previously said. The full 

 equivalent of the affirmation is, 'The master 

 of Plato fought at Delium, Jind the master 

 of Plato was Socrates : ' ttie new form omits 

 til e last piece of information, and gives only 

 the first. Now, we never consider that we 

 have made a real inference, a step in 

 advance, when we repeat less than we are 

 entitled to Sfiy, or drop from a complex 

 statement some portion not desiied at the 

 moment. Such an operation keeps strictly 

 within the domain of equivalence, or Im- 

 mediut'^ Inference. In no way therefote, 

 can a syllogism with two singular premises 

 bs viewed as a genuine tyliogistic or de- 

 ductive inference" (Logic, i. 159). 



The first argument, aa will hav«> been 



of the first figure alone. The rules 

 for throwing an argument in any of 

 the other figures into the first figure 

 are called rules for the reduction of 

 syllogisms. It is done by the conver- 

 sion of one or other, or both, of the 

 premises. Thus an argument in the 

 first mood of the second figure, as — 



No C is B 



All A is B 



therefore 



No A is 0, 

 may be reduced as follows. The pro- 

 position, No C is B, being an universal 

 negative, admits of simple conversion, 

 and may be changed into No B is C, 

 which, as we showed, is the very same 



seen, rests upon the supposition that the 

 name Socrates has a meaning ; that man, 

 wise, and poor, are parts of this meaning ; 

 and that by predicating them of Socrates 

 we convey no information ; a view of the 

 sitrnification of names which, for reasons 

 already given,* I cannot admit, and which, 

 as applied to the class of names which 

 Socrates belongs to, is at war with Mr. 

 Bain's own definition of a Proper Name 

 (i. 148), "a single meaningless mark or 

 designation appropriuted to the tldng." 

 Such names, Mr. Bain proceeded to say, 

 do not necessarily indicate even human 

 beings: much less tlien does the name 

 Socrates include tlie meaning of wise or 

 poor. Otherwise it would follow that if 

 Socrates had grown rich, or had lost his 

 mental faculties by illness, he would no 

 longer have been called Socrates. 



The second part of Mr Bain's argument, 

 in which he contends that even when the 

 premises convey real information, the con- 

 clusion is merely the premises with a part 

 left out, is applicable, if at all, as much to 

 universal propositions as to singular. In 

 every syllogism the conclusion contains 

 less than is asserted in the two premises 

 taken together. Suppose the syllogism 

 to be 



All bees are intelligent, 

 All bees are insects, therefore 

 Some insects are intelligent : 

 one might use the same liberty taken by 

 Mr. Bain, of joining together the two pre- 

 mises a.s if they were one—" All bees are 

 insects and intelligent" — and might say 

 that in omitting the middle term bees we 

 make no real inference, but merely repro- 

 duce part of what iiad been previously 

 said. Mr. Bain's is really an objection to 

 the syllogism itself, or at all events to the 

 third figure : it has no special applicability 

 to singular propositions. 



• Note to 5 4 of the chapter on Definition, 

 tupra, p. 92, 



