THE THEORY OF SYLLOGISM, ETC. 



85 



y is used after the manner of a universal term in logic, a> after the manner of a particular. 

 We must know the whole of y ; but we may be enabled to make the assertion by knowing 

 a part of ,v. A little consideration suggests as a necessary rule of inference, the right to sub- 

 stitute a larger term used particularly for a smaller one, however used, and a smaller, used in 

 either way, for a larger used universally. What we may affirm or deny of some or all men, 

 we may affirm or deny of some animals: what we may affirm or deny of all animals, we may 

 affirm or deny of all or some men. The second part of the rule is the dictum de omni et 

 nulla ; the first part has not, within my reading, been added to it : both might well be incor- 

 porated in one under the name of the dictum* de majore et minore. Observing that every 

 inference was frequently declared to be reducible to syllogism, with no exception unless in the 

 case of mere transformation, as in the deduction of ' No X is Y' from • No Y is XJ I gave 

 a challenge in my work on formal logic to deduce syllogistically from ' Every man is an animal' 

 that ' every head of a man is the head of an animal.' From the total absence of attempt to 

 answer this challenge, I conclude f that no one has succeeded in whose way it has fallen. 



I shall presently have occasion to pursue this subject a little further : I now proceed to 

 a new section. 



Section II. 



ON THE FORMATION OF SYMBOLIC NOTATION FOR PROPOSITIONS AND SYLLOGISMS. 



The commonly received method of denoting the affirmative and negative universals by 

 A, E, and the particulars by /, O, is rather mnemonical than instrumental : it suggests to 

 nothing but the memory. Of all the systematic deductions of the valid forms of syllogism, 

 not one came into general use : inductive selection and exclusion were employed, when any- 

 thing more than a mere declaration of results was given. The figure being given, the above 

 symbols are sufficient : thus AEI in the first figure can be nothing but the invalid mode 

 ' Every Y is Z, no X is Y, therefore some Xs are Zs.' 



In my former paper, and in my work since published, I borrowed from the above notation 

 the use and meaning of A, E, I, O, and added symbolic distinctions. So far I have nothing 

 to change: any system must use some mode of expressing its relation to the language of so 

 many centuries. I also adopted a more detailed mode of expressing propositions : and here it 

 would have been better if the detail had been greater at first, that it might have been ulti- 

 mately made still less. 



A fundamental symbol should not be of compound meaning : that is, should not expressly 

 signify more than one thing. Composite expressions should be reserved for symbols which are 



* Eveiy syllogism in the Aristotelian system is a direct use 

 of this dictum. 



+ This would be a very unsafe conclusion from the absence 

 of printed answer. But any one who writes on a controverted 

 subject gains a number of private correspondents, with and 



without names. When I advanced, in my discussion with Sir 

 William Hamilton, that a person kept close to Aristotle's 

 forms could not prove that some must have both coats and 

 waistcoats, if a majority have coats, and a majority waistcoats, 

 I had various ingenious attempts to disprove my assertion. 



