88 



PROFESSOR DE MORGAN, ON THE SYMBOLS OF LOGIC, 



Let the middle name of a syllogism be placed in the middle, and when the two premises 

 are formed, let the extents which enter into the conclusion be signified by thicker lines, or 

 thicker dots. Thus it will appear what the conclusion is, and also whether the quantities in 

 the conclusion be those which entered into the premises, or whether, by the character of the 

 inference, either be curtailed. Thus in the diagram before us 



X 

 Y 

 Z 



(•))')-() 



we see the pictorial and arbitrary notation for the following syllogism : — Everything is either 

 Zor F; some Zs are not Ys; therefore some Zs (as many as entered the premise) are Xs 

 (not necessarily as many as in the premise). We also see that the real middle term of agree- 

 ment is a portion (or what may be only a portion) of the extent of y : and that the affirmative 

 form of the syllogism is X((y()Z = X()Z. References to figure might easily be added. 



I should here close this section, if it had not been that Sir William Hamilton's scheme of 

 notation has been published by an acute writer, with such commendations*, that I must not 

 appear to shun the comparison. This system is certainly so simple, that a person who knows 

 the premises and inference well, would write down any case of it immediately. I exhibit 

 one case of it in the three figures : premising that Sir William Hamilton rejects the distinction 

 of major and minor, and draws two conclusions in the second figure and in the third : but does 

 not permit the fourth figure to append itself to the first, nor to appear in any way. 



X 



,Y: 



Z X : 



>,Y: 



First Figure. 



Some Y is all X. 

 Some Z is all Y. 



Some Z is all X, or 



Second Figure. 

 All X is some Y. 

 Some Z is all F. 



Some Z is all X. 

 All X is some Z, 



or 



Third Figure. 

 Some Y is all X. 

 All Y is some Z. 



Some Z is all X. 

 All X is some Z. 



,Z 



Negation is expressed by drawing a vertical line through the sign of predication. When 

 the thin end of this sign is made the subject, the syllogism is read by intension. 



It would appear at first that this notation is almost identical with what I have proposed 

 above, as to principle. Leave out the lines of predication, and the above syllogism would be 



" " A mode of notation proposed by Sir William Hamil- 

 ton, is, beyond doubt, one of the most important contributions 

 to pure Logic which has ever been made since the science was 

 put forth ; and I am fortunate in being permitted to annex it. 

 Its excellences are — that it is very simple, that it shews the 

 equivalent syllogisms in the different figures at a glance, that it 



shews as readily the convertible syllogisms in the same figure, 

 that it enables us to read each syllogism with equal facility 



according to extension and intension, " Outline of the 



Necessary Laws of Thought. By William Thomson, M.A. 

 (2nd. Edition, 1849, p. 265.) A work to be strongly recom- 

 mended. 



