CHAP. VI.] OF INTERPRETATION. 85 



position out of a series of denials or negations ? From what 

 source is the positive element derived ? I answer, that the mind 

 assumes the existence of a universe not d priori as a fact inde- 

 pendent of experience, but either a posteriori as a deduction 

 from experience, or hypothetically as a foundation of the possi- 

 bility of assertive reasoning. Thus from the Proposition, " There 

 are no men who are not fallible," which is a negation or denial of 

 the existence of " infallible men," it may be inferred either hypo- 

 thetically, " All men (if men exist) are fallible," or absolutely, 

 (experience having assured us of the existence of the race), " All 

 men are fallible." 



The form in which conclusions are exhibited by the method 

 of this Proposition may be termed the form of " Single or Con- 

 joint Denial." 



FORM II. 



7. As the previous form was derived from the development 

 and interpretation of an equation whose second member is 0, the 

 present form, which is supplementary to it, will be derived from 

 the development and interpretation of an equation whose second 

 member is 1 . It is, however, readily suggested by the analysis 

 of the previous Proposition. 



Thus in the example last discussed we deduced from the 

 equation 



x - yz = 



the conjoint denial of the existence of the classes represented by 

 the constituents 



xy(\-z\ xz(\-y\ x(\-y)(\-z), (\-x)yz, 



whose coefficients were not equal to 0. It follows hence that 

 the remaining constituents represent classes which make up the 

 universe. Hence we shall have 



This is equivalent to the affirmation that all existing things be- 

 long to some one or other of the following classes, viz. : 



1st. Clean beasts both dividing the hoof and chewing the 

 cud. 



