460 



Mb DE morgan, ON THE SYLLOGISM, No. V. AND 



)) (•( < )•( > )■) (( 



W. included in P. excluded from W. excluded from = W. excluding P. excluding W. including 



(( )•) < (•) > (•( )) 



W. uncompleted by P. completed by W. completed by = W. completive of P. completive of W. incompletive of 



)) > () )•( < (( 



W. included in P. included in W. excluded from = W. excluding P. including W. including 



(( > )( (•) )( < )) 



W. uncompleted by P. uncompleted by W. completed, by = W. completive of P. incompletive of W. incompletive of 



)•( () < )) > )( (•) 



W. excluded from P. included in W. included in = W. incompletive of P. incompletive of W. completive of 



(•) )( < (( > () ).( 



W. completed by P. uncompleted by W. uncompleted by = W. including P. including W. excluding 



)•( > (•( )) (•( < (■) 



W. excluded from P. excluded from W. included in = W. incompletive of P. completive of W. completive of 



(•) > )•) (( )•) < )•( 



-W. completed by P. completed by W. uncompleted by = W. including P. excluding W. excluding 



In this table contradiction is denoted by a dotted line ; and ascent or descent by the 

 algebraic signs for less and greater. 



Common language proceeds as if the part were more worthy than the whole, as a notion 

 on which to base enunciation. Accordingly, we are familiar with inclusion, e.vclusion, and 

 partienc.e of both : but completion^ and coinadequacy are strange and heretical. I have 

 somewhere read of a speculator who maintained that every world has, in some other part of 

 space, a counterpart world of defects equal and opposite to its own. If his system be true — 

 all questions about other stars or planets are quite open — there is somewhere a planet in which 

 thought fixes upon whole in preference to part; in which the concept of penultimacy is more 

 familiar than that of singularity ; in which the demonstrative pronoun is not this, but some 

 word of the force of all else ; and in which, at this moment, some antimathematical logician — for 

 the mathematical tendency is in excess in the logic of our counterpart — endeavours to force 

 attention to exclusion and partience upon a community which is too exclusively familiar with 

 completion and coinadequacy. I have amused myself with constructing enunciations and syl- 

 logisms as they are in the exemplar-counterpart forms of our counterpart planet ; from which 



' Mr Spalding (viii. 16(i) says that all the eight forms are 

 set forth by Boethius. I cannot find them. Boethius does 

 indeed apply the /our to privatives, and so obtains equivalents 

 of the eight onymatic forms : but I cannot detect him evolving 

 relations between the given terms by help of their privatives. 

 But he is rather prolix ; and perhaps some reader may favour 

 me with a definite reference to something which will support 

 Mr Spalding's assertion. If not, that assertion is one of a very 

 numerous class, of the bad consequence of which no one can 

 fonn an idea who is not familiar with the history of discovery. 



Two things are affirmed to be the same because the passage 

 from one to the other is easy in the mind of the afiirraant, after 

 study of both : they are virtually the same, one amounts to the 

 other, &c. This was Solomon's practice, or he never would 

 have said that there is nothing new under the sun. I once had 

 a private discussion of several long letters which might have 

 been spared if my correspondent had said at first what he said 

 at last, that certain two methods were the same to all intents 

 and purposes: he began by saying they were the same; which 

 is quite a different thing. 



