276 



SCIENCE. 



[N. S. Vol. V. No. 111. 



pend upon different assumptions regarding dif- 

 ferent parts of the argument. 



Without going to the syllogistic part of the 

 argument, it can be said at the outset that it is 

 impossible to prove that £ is 4 if .4 is B. Such 

 a conclusion would violate the law of Conver- 

 sion, unless the proposition A is £ is a defini- 

 tion or exclusive. In the latter two alterna- 

 tives it could be proved by the law of conversion. 

 But Professor Jastrow gives an attempt to prove 

 it syllogistically, that is, by mediate instead of 

 immediate reasoning. As it is stated mediate 

 reasoning is not applicable, because no middle 

 term is given. Moreover, even immediate in- 

 ference can do nothing until we know what 

 kind of a proposition A is £ is supposed to be. 

 If it is the ordinary universal we cannot prove 

 that B is A, for the reason mentioned. If it is 

 a particular af&rmative, a definition, or an ex- 

 clusive proposition, it can be proved that i? is ^ 

 by immediate inference, and the error in the 

 argument would be that it is an attempt at 

 syllogistic or mediate reasoning where there is 

 no middle term and where the attempt to sup- 

 ply it may be a petitio principii. 



But, taking the syllogistic argument as it is 

 given, it is intended as a case of prosyllogism 

 and episyllogism connected with the disjunction 

 that B is either A or not A. It is supposed, 

 therefore, that the absurdity of the conclusion 

 in the prosyllogism justifies the conclusion in 

 the episyllogism, because that absurdity is as- 

 sumed to show the absurdity of the first term 

 of the disjunction, and hence the second would 

 follow. But we must raise the question first 

 whether the reasoning is formal or material. 



In the prosyllogism the formal reasoning is 

 perfectly correct. It is a case either of E A E 

 of the First Figure otAEE of the Fourth Figure 

 and is formally correct in either case. That is 

 to say, with the premises given, the conclusion 

 A is not A does follow, and there is no right to 

 call it absurd, as Professor Jastrow does. It is 

 an illustration of the fact that we must either 

 impeach the premise or accept the conclusion. 

 We cannot accept the premises and deny this 

 conclusion at the same time. Hence, we may 

 say either that one of the premises is a petitio 

 principii, or the statement ' which is absurd ' is 

 a petitio principii. 



There is only one way to establish a formal 

 fallacy in this syllogism, and it is to assume 

 that the major premises (major if the First Fig- 

 ure and minor if the Fourth Figure) is 0, a par- 

 ticular negative. This will give A of the 

 First Figure, or ^ of the Fourth Figure, in 

 both a case of undistributed middle. But then, 

 so far from making the conclusion absurd, as 

 assumed here, it cannot be drawn at all. No 

 conclusion whatever can be drawn under such 

 conditions. Hence, if the propositions that A 

 is not A be considered absurd it must be on 

 other grounds than the formal reasoning, 

 whether correct or incorrect. In fact, it is a 

 manifest contradiction, but is not so because of 

 the reasoning, but because the premise B is not 

 A contradicts A is B. Technically it is the 

 contradictory of the converse of A is B, and 

 this makes the second premise a contradictio in 

 adjeeto of the first and, therefore, a petitio prin- 

 cipii, a material fallacy. 



Again, granting, on any grounds, that the 

 conclusion of the prosyllogism is absurd, it is a 

 non sequitur to infer from this fact that B is A, 

 a material fallacy also. The temptation to ac- 

 cept it comes from the reflex influence of the 

 assumed absurdity of the conclusion in the 

 prosyllogism A is not A, upon the absurdity of 

 the premise B is not A, the proposition that 

 A is B not being questioned. But this only 

 throws us back to a disjunctive syllogism as the 

 only proper one in the case from which to at- 

 tempt to draw the conclusion B is A, and thus 

 nullifies the whole syllogistic procedure in the 

 prosyllogism, as an ignoratio elenehi. The argu- 

 ment should proceed disjunctively, with the 

 proposition B is not A as the minor premise of 

 a disjunctive syllogism, and it would appear as 

 follows: 



B is either A or not A. 

 B is not A 

 .-.Bis A. 



But in this reasoning we have a violation of 

 the principle in disjunctive reasoning ; namely, 

 the modus tollendo ponens. If we deny one term 

 we must afiirm the other. We deny the first 

 term in the minor premise, and, as the second 

 term is ' not A ' (instead of ^), when we affirm 

 it, the conclusion must be B is not A, the same 



