128 



PROF. W. STANLEY JEVONS ON THE 



Refer- 

 ence 

 Number. 



Propositions expressing 



the general type of 

 the logical conditions. 



Number of dis- 

 tinct logical 

 variations. 



Number of com- 

 binations contra- 

 dicted by each. 



I. 

 II. 



III. 



IY. 



Y. 



YI. 



YII. 



YIII. 



IX. 



X. 



XI. 



XII. 



XIII. 



XIY. 



XV. 



A=B 



A=AB 



A=B, B=C 



6 



12 



4 



24 



24 

 24 

 24 



8 



24 

 8 



4 

 12 



8 



2 

 8 



4 

 2 

 6 



5 



4 

 4 

 3 



1 



3 

 4 

 2 



2 



3 

 4 

 5 



A=B, B=BC 



A=AB, B = BC 



A=BC 



A=ABC 



AB = ABC 



A=AB, aB = aBc 



A=ABC, ab = abC 



AB=ABC, ab-abc 



A=ABC|Afo 



A=BC-\-Abc 



A=BC-|.fo 



A=ABC, a=Bc\-bC 







192 





There are 63 series of combinations derived from self- 

 contradictory premises ; which; with the above 192 series 

 and the one case where there are no conditions or laws at 

 all; make np the whole conceivable number of 256 series. 



We learn from this table; for instance; that two pro- 

 positions of the form A=AB; B=BC; which are such as 

 constitute the premises of the old syllogism Barbara; nega- 

 tive or render impossible four of the eight combinations in 

 which three terms may be united, and that these proposi- 

 tions are capable of taking twenty-four variations by trans- 

 positions of the terms or the introduction of negatives. 

 This table then presents the results of a complete analysis 

 of all the possible logical relations arising in the case of 

 three terms, and the old syllogism forms but one out of 

 fifteen typical forms. Generally speaking; every form can 

 be converted into apparently different propositions ; thus 

 the fourth type A=B, B=BC may appear in the form 

 A= ABC; a—ab, or again in the form of three propositions 

 A=AB; B=BC; «B=«Bc; but all these sets of premises 

 yield identically the same series of combinations; and are; 

 therefore; of exactly equivalent logical meaning. The fifth 



