NATURE AND AXIOMS OF THE SYLLOGISM. 297 



discursive, since the false premisses may be dropped with the middle term, 

 and since the mind, after accepting the conclusion on false grounds while 

 inferring it, may now abandon the grounds altogether and assent to the 

 conclusion in itself and for its own sake, the mind may now be considered to 

 be accidentally of course in possession of the truth. 1 



Reverting again to the expression of the formal force of the syllogism by 

 the hypothetical &quot; If A is true and B is true C is true&quot; we see further that, just 

 as this proposition yields the contrapositive &quot; If C is false then either A or 

 B or both must be false&quot; and does not yield the simple converse &quot; If C is 

 true then A is true and B is true&quot; but only worthless one &quot; If C is ttue 

 then perhaps A and B are true or perhaps not &quot; : so, also, the nature of the 

 syllogism authorizes us to infer that if the conclusion of a formally valid 

 syllogism be false then one at least of the premisses must be false ; but it 

 does not authorize us to infer that if the conclusion is true the premisses 

 must be true. 



Notwithstanding all this, it is a very common fallacy for the controver 

 sialist to imagine that he has disproved or refuted his opponent s thesis 

 or contention when he has merely succeeded in showing that the reasons 

 alleged by his opponent in support of the latter are untrue. He forgets 

 that even if they are untrue this does not prove the contention itself to be 

 untrue. Many a good cause is supported by bad arguments. 



Scarcely less dangerous is the temptation to be too easily assured of the 

 soundness of one s own arguments and reasons from the mere conviction that 

 the position one maintains is a sound one. Though our cause be good, we 

 may be guilty of supporting, or rather injuring, it by bad arguments. 



Of course, in order that the syllogism be a means of discovering and 

 proving truth, not merely must it be formally valid, but its matter also, the 

 judgments embodied in it, must be true. The material requirements of the 

 syllogism will be treated in connexion with Demonstration (Part v.). Its 

 formal aspect alone will be treated in the present context* 



149. KINDS OF SYLLOGISM. Much of what has been said 

 so far in the present chapter applies primarily to that form of 

 syllogism which is constituted exclusively by simple categorical 

 propositions. But we have seen that there are other important 

 types of proposition most notably the hypothetical (or condi 

 tional) and the disjunctive (or alternative). It will be necessary 

 to treat explicitly the separate forms of syllogism intc which 

 these three kinds of proposition enter. If the two premisses of 

 a syllogism be of the same class, or Relation (83, 84), we have a 

 Pure Syllogism. Of this, therefore, there are three kinds : the 

 Pure Categorical, the Pure Hypothetical, and the Pure Disjunctive. 

 If the premisses be propositions of different classes, we have 

 a Mixed Syllogism. Of this also there are three kinds. The 



1 Of course, the mind, in so far as it retains the false premisses, is in error, and 

 may be led by them otherwise into further error. C/&quot;. JOSEPH, op. cit., p. 342. 



