334 THE SCIENCE OF LOGIC 



No rule of logic can help him here : he must fall back on his 

 own knowledge and ingenuity. In the example, perhaps &quot; sup 

 pressions of tyranny &quot; will suffice. 



But this very example shows that the so-called &quot; proof,&quot; here 

 demanded, is not a demonstration (252) at all ; for a demon 

 stration requires not only that the conclusion follow from the 

 premisses and be itself true, but that the premisses also be true ; 

 whereas here all three propositions are false. The premisses 

 constitute what we may call a &quot;formal proof&quot; of the conclusion, 

 i.e. they are such that if they were true the conclusion would 

 necessarily be true also. So, in constructing &quot; formal proofs &quot; or 

 &quot; formally valid syllogisms,&quot; or in &quot; finding combinations of 

 premisses from which a given conclusion would necessarily follow,&quot; 

 the student has not to take into account the truth or falsity of the 

 propositions he deals with. He is, ex hypothesi, dealing not with 

 the &quot;material&quot; or &quot; truth&quot; aspect, but only with the &quot; formal&quot; 

 or &quot; consistency &quot; aspect, of the reasoning process. If, for instance, 

 he were asked to construct a formally valid syllogism, having as 

 its conclusion the proposition All men are mortal&quot; he might 

 construct such a syllogism as the following : 



All horses are mortal, 



All men are horses ! 



Therefore, All men are mortal 



which is an apt illustration of the maxim, Ex f also sequitur quod- 

 libet (148). 



WELTON, Logic, bk. iv., chap. iii. KEYNES, Formal Logic, pt. iii., 

 chap. ii. JOSEPH, Logic, chap. xii. JOYCE, Logic, pp. 172 sqq. MELLONE, 

 Introd. Text-Book of Logic, pp. 164 sqq. 



