470 



Mb DE morgan, ON THE SYLLOGISM, N^o. V. AND 



The rules for detecting unrestricted readings are as follows : — 



1. (Lines 1 and 2.) When the primary and secondary spiculae are alike, as in )))), ))•((, 

 all the four readings are unrestricted. Thus X(-(Y follows from X((.((Y in every 

 case of 



some part , _,. . . any part 



, , of X IS not in , , 



any whole some whole 



( (•( ( 



ofY 



2. (Lines S and 4.) When the primary and secondary spiculae are both balanced, there 

 are two unrestricted readings, both unbalanced : when both unbalanced, two unrestricted 

 readings, both balanced. Thus ) () ( and ) (•) ( have the readings /jmj, wp, unrestricted: but 

 ) (( ) and ) (•( ( \\&\e pp and ww unrestricted. 



3. (Lines 5, 6, 7, 8.) When the primary and secondary spiculse are one balanced, and 

 the other unbalanced, one of the extreme spiculse is of a different curvature from its neigh- 

 bour: let this be the detached spicula. Two readings are unrestricted; and the detached 

 spicula has the same reading (part or whole) in both. That common reading is by part when 

 the other extreme is particular in an affirmative, or universal in a negative ; by whole, when 

 the other extreme is universal in an affirmative, or particular in a negative. Take notice 

 that the most Aristotelian combinations go together ; part, particular affirmative, universal 

 negative. Thus ())) has the first extreme spicula detached, the second particular in an 

 affirmative: accordingly, ())) gives () in the readings pp, pw. But ()•)) gives (•) in the 

 readings wp, ww. And ))•)(, in which the second spicula is detached has the readings 

 pp, wp. 



Interchange of primary and secondary spiculae produces no effect in any case on the 

 modes of unrestricted reading: thus )(•(( and ()•(( both give ^^, pw, for unrestricted 

 readings. 



Each relation is enunciated in ten ways : by secondary relation of its own name in four 

 ways, and in two ways by each remaining relation of the same quality. Thus species enun- 

 ciates species in four ways, and genus, partient, coinadequate, enunciate species in two ways 

 each. The following are the ways of announcing' that X is a species of Y. 



Any part of X is in some part of Y 

 Any part of X is in any whole of Y 

 Some whole of X is in any whole of Y 



Some whole of X is in some part of Y 



Any part of X does not complete any whole of Y 

 Any whole of X does not complete any whole of Y 

 Any part of X takes in some part of Y 

 Some whole of X takes in any whole of Y 

 Any part of X is not out of some part of Y 

 Any part of X is not out of any whole of Y 



' I use simple English verbs for the universal relations ; is 

 in, takes in, is out of, makes up or completes. To eke out is 

 the purest English for to make up all the rest: but it has in our 

 time too much the implication of pis alter and succedaneum. 

 The particulars are merely the negations of the universals : I 

 doubt if they ought ever to be anything else. I have made 



great use of these simple verbs, and with a feeling of relief 

 from the state trappings of technical terms; like the post-boy 't 

 horse in John Gilpin, 1 felt 



right glad to miss 



The lumbering of the wheels. 



