106 PROFESSOR DE MORGAN, ON THE SYMBOLS OF LOGIC, 



Extension given. Intension deduced. 



Every X is F. Every existing part of all Ys is an existing part of all Xs. 



No X is Y. No sufficient* part of any Y is an existing part of any X. 



Some Xs are Ys. Every existing part of all Ys is an existing part of some Xs. 



Some Xs are not Fs. No sufficient part of any F is an existing part of some Xs. 



Intension given. Extension deduced. 



A sufficient part of some one Y is an existing part of every X. Every X is Y. 



An existing part of any Y is not an existing part of any X. No X is Y. 



A sufficient part of some Fs is an existing part of some Xs. Some Xs are Fs. 



An existing part of any F is not an existing part of some Xs. Some Xs are not Fs. 



By treating the predicate itself as one attributive notion, the modes of reading both kinds 

 of propositions intensively may be assimilated : but not without losing sight of an important 

 distinction. In the affirmative, any portion of the intension of the predicate may be affirmed 

 of the subject ; in the negative, it is not true that any portion of the intension of the predicate 

 may be denied of the subject. Thus ' no planet moves in a circle' gives us a right to deny 

 any constitutive attribute of circular motion to that of a planet, but not any attribute ; not, 

 for instance, the progression through every longitude. 



Leaving the distinction of extensive and intensive reading entirely out of view, as not 

 connected with the theory of the copula, I proceed to inquire into the connexion of the 

 doctrine of figure with that of the copula ; a connexion which I take to be the most im- 

 portant part of the former doctrine. And first, I take the system from which contraries are 

 excluded. Looking at the two copular conditions, the transitive and the convertible, I ask 

 what inferences hold good when only the transitive condition holds : for this one must hold, 

 as long as there is but one species of copula ; we shall presently see that it is the condition of 

 permanence of the copula. As a representative of a transitive but inconvertible copula, let 

 us take the verb give, assuming that he gives who gives that which gives. Then ' X gives F, 

 F gives Z, therefore X gives Z' is legitimate, being the mere expression of the transitive 

 hypothesis. And the opponent forms of this must be legitimate. Thus i X gives F, X does 

 not give Z' leads to F does not give Z: for if F gave Z, X giving F, X would give Z : this 

 is in the third figure. Again, 'AT does not give Z, F gives Z' leads to ' X does not give F:' 

 for if X gave F, F giving Z, X would give Z : this is in the second figure. When these 

 propositions are made cumulative, with quantities proper for inference, the usual inferences are 

 obtained. Accordingly, + meaning affirmative, and — negative, all + + syllogisms in the 

 first figure, h — syllogisms in the second figure, and — i- syllogisms in the third figure 

 (reading premises in the Aristotelian order) do not need a convertible copula. They are 

 I. II. III. 



Barbara )))) Camestres ).((( Felapton (().( 



Darii ())) Baroko (.((( Ferison ()).( 



Bokardo (((.( 



* Meaning part sufficient to determine it to be K. I do not say attribute, because the inference does not depend upon the 



metaphysical meaning of that word. 



