3 i2 THE SCIENCE OF LOGIC 



to the sum of the squares on the remaining sides, the same 

 is true of all triangles inscribable in semi-circles : for in this case 

 we know that the acddens &quot; inscribable in a semi-circle &quot; is com 

 mensurate with the subject &quot; right-angled triangle &quot; ; that what we 

 can predicate of the former we may predicate of the latter ; that 

 the proposition, &quot; right-angled triangles are inscribable in semi 

 circles,&quot; being a reciprocal proposition, is simply convertible. Wher 

 ever the fallacy occurs it will be found to lie in the assumption 

 that some proposition is simply convertible, which is really con 

 vertible only per accidens. Hence the name of the fallacy. Take 

 the inference : &quot; This dog is yours ; this dog is a terrier ; there 

 fore this terrier is yours &quot; ; evidently a valid inference. But is 

 there not illicit process of the minor term ? Apparently there 

 is ; and apparently the conclusion should be &quot; a terrier (or some 

 terrier) is yours &quot; ; but really the minor premiss contains the 

 information &quot; this dog is this terrier &quot; which justifies the defi 

 nite conclusion. 



We have seen that the fallacy a dicto simpliciter ad dictum 

 secundum quid is committed when we attach the predicate of a 

 genus to some subject which is not really contained in, or subordin 

 ate to, that genus. We now see that the fallacy of the accident 

 is committed by unlawfully equating a genus and its subordinate 

 notions (species or individuals), either as subjects of the same 

 predicate (&quot; All men are rational ; all angels are rational ; there 

 fore all men are angels &quot;) ; or as predicates of the same subject 

 (&quot; All men are rational ; all men are bipeds ; therefore, all bipeds 

 are rational &quot;). 



(e) CONSEQUENS. The fallacy of the consequent is the mis 

 take of inferring the truth of the antecedent from the truth of 

 the consequent, or the falsity of the consequent from the falsity 

 of the antecedent, of a hypothetical proposition. 1 It is therefore 

 illicit conversion, or contraposition, or inversion, based on the 

 erroneous supposition that the hypothetical judgment is al 

 ways reciprocal. &quot; If a religion can elevate the soul it will sur 

 vive persecution ; therefore if a religion survives persecution it 

 must elevate the soul ; and if it does not elevate the soul it will 

 not survive persecution.&quot; &quot; This man has no visible means of 

 support ; therefore he is a professional thief.&quot; There is an ob- 



1 Another mistake is that of interpreting the antecedent of a hypothetical as 

 necessarily giving a causa essendi of the consequent : it need only give a ratio cog- 

 no$cendi, a symptom, or effect, of the latter. 



