220 Mb DE morgan, ON THE SYLLOGISM, No. Ill, 



complement of every partient. Now take () (•) which, the middle spicule? being erased, 

 gives (•), a universal; changing the second spicuia, (•( 



Every complement is a partient of every complement 

 Every exient is a partient of every complement. 



The first is only a strengthened form of the second. Syllogisms being combinations, these 

 relations may be called decomhinations. From the strengthened syllogisms proceed the 

 strengthened decomhinations : from the syllogisms in which universals give universals the 

 decomhinations in which a universal gives two universals. The sixteen remaining cases arise 

 from the particular syllogisms. The sixteen pairs, such as (•) () &c., and the eight )■) ) •) 

 &c. which are not decomhinations, are no doubt of some logical import which I do not now see. 

 These decomhinations are the contrapositives of the combinations. Thus ' Every external of. 

 any genus is an external ' gives every non-external (partient) is a non-external (partient) of any 

 genus, or ( ) gives ( ) ( (, as from the rule. 



XXXIX. The full stops and colons in the table denote that one of the syllogisms 

 between which they stand is formed from the other (proceeding from the middle column) by 

 altering the first or second premise. Thus (•) )•) is formed from (•) )•( by weakening the 

 universal )•( into )•). But (•) (•) is formed from (•))') by strengthening the second 

 premise )•) into (•). Accordingly, the eight strengthened syllogisms are those which are 

 under VVP. 



I shall write down and illustrate one syllogism in the three readings : namely ) •( (• ( which 

 gives ) (. 



Metaphysical. 



Arithmetical. 



X).(Y NoXisY. 



Y (.(Z Some Ys are not Zs. 



X) (Z Some things neither 

 Xs nor Zs, t. e. as many at 

 least as there are Ys which 

 are not Zs. 



Mathematical. 



X co-external of Y. 



Y exient of Z. 



X external of exient of Z, or 

 coinadequate of Z, by all the 

 extent at least by which Y 

 is exient of Z. 



X repugnant of Y. 



Y independent of Z. 



X repugnant of independent 

 of Z, or inalternative of Z, 

 by at least all the force of Z 

 which is not in Y. 



Take the instance of metaphysical reading previously given, " Courage (moral) and meanness 

 are inconsistent ideas, and courage is not dependent on personal strength, so that strength and 

 meanness are not necessary alternatives." Courage does not depend on strength : a man 

 wanting strength may therefore have courage, which puts meanness out of the question, so 

 that a man may have neither strength nor meanness, or we must not say he must have one or 

 the other or both. It is said that the force of this proposition is all the force of the word 

 strength which is not in courage. Courage not depending on strength, the latter has attri- 

 butes which are not in the notion of courage : say health. Ill health is a field of intensive 

 force for the verification of the proposition : the want of strength may arise from ill health, 

 which is consistent with courage, &c. 



It is impossible that the logician can fully represent this case of common thought in his 

 syllogism : — " All courageous is not mean, some courageous is not strong ; therefore some 

 not strong is not mean." 



XL. When quantity or force is particular or incomplete in a term of the conclusion, that 

 quantity or force is derived as follows : — 



