384 THE SCIENCE OF LOGIC 



each prosyllogism. Every syllogism may have a reason assigned 

 for one, or for both, of its premisses. These reasons may be stated 

 as enthymemes. If a reason be thus assigned in support of both 

 premisses of the original episyllogism, we have a Double Epi- 

 cheirema. For example : 



Every M is P y because every Q is P ; 



Every S is M, because every S is R ; 

 . : Every S is P. 



If only one premiss of the original episyllogism be thus supported, 

 we have a Single Epicheirema. For example : 



All Ps are M s because they are Qs ; 



No Ss are M s ; 

 . . No Ss are Ps. 



In the first of these examples, the enthymeme proving the major 

 is of the second order, for it omits its minor (Every M is Q] ; 

 that proving the minor is of the first order, for it omits its major 

 (Every R is M\ The reason given for the major in the second 

 example is also an enthymeme of the first order, omitting its 

 major (All Qs are M s). 



Conceivably, the premiss of each enthymeme alleged in 

 support of either premiss of the original syllogism might be itself 

 supported by a new syllogism ; and each premiss of these simi 

 larly supported ; and so on, the syllogisms multiplying in geo 

 metrical progression. We rarely, however, find concrete examples 

 in which the supporting process is carried farther than one or 

 two steps backward. 



WELTON, op. cit., bk. iv., chap. vi. KEYNES, op. cit., pt. iii., chap. vii. 



