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PROFESSOR DE MORGAN, ON THE SYMBOLS OF LOGIC, 



logician, followed by the algebraist, has restricted himself to one copula : the former uses is, 

 the latter = ; and both are used in some variety of sense. The algebraist, indeed, sometimes 

 goes a little further, and introduces the correlatives > and <, which might be generalized for 

 the purposes of logic into symbols of correlative copulse in general. In every kind of logic, 

 formal and applied, the transitive copula is insisted on. This however is not necessary : 

 inference may be seen without it. The perception of relations by means of relations does not 

 require us to use only one relation. If I can see that 



Every X has a relation to some Y 

 and Every Y has a relation to some Z, 



it follows that every X has a compound relation to some Z. Be the premised relations 

 what they may, there is a concluding relation, which may or may not be expressible by one 

 word. Thus if John can persuade Thomas, and Thomas can command William, we cannot 

 infer that John can either persuade or command William : but if we express by one word the 

 process of gaining an end by persuading one who can command — say we choose to use the word 

 control* for this purpose — then John can control William. We have then a bicopular 

 syllogism, in which the intransitiveness of the individual copulae is supplied by the invention of 

 a compound copula for the conclusion. This is the step by which we ascend to the general 

 theory of the copula : but those who proceed from a general copula to a particular one, will 

 merely see how to read the general conditions in the particular case. 



Can a bicopular syllogism be reduced to a compound process of unicopular syllogism ? In 

 the case before us the conditions are 



Postulate. Control includes the influence exerted over the governed by one who can 

 persuade the governor. 



Premises. John can persuade Thomas. 



Thomas can command William. 

 Conclusion. John can control William. 



The only way in which this can be reduced to unicopular syllogism is by the following 

 sorites. 



John is {one who can persuade Thomas}. 



{One who can persuade Thomas} is {one who can control all whom 



Thomas commands.} 



)ne who can control all whoml . ( One who can 1 

 Thomas commands. J (control William J ' 



John is {one who can control William}. 



The algebraical equation y = <px has the copula =, relatively to y and (f)x : but relatively 

 to y and x the copula is = (p. This is precisely the distinction of ' John can persuade 



Given premise. 

 Postulate. 



Second given premise, 

 and diet, de maj. et min. 



Conclusion. 



IOi 



* This is not an improper word ; for the compound relation, 

 as well as the original ones, enters in a particular, not a univer- 

 sal, manner. It is enough that persuading one who can com- 

 mand is one of the ways of controlling. And let there be any 

 number of forms of persuasion, and of command, it is enough 

 that one of the forms of persuasion procuring one of the forms 



of command, should be one form of control. And thus it may 

 happen that, legitimately, the copular word of the conclusion 

 may be that of the premise in a different sense ; a very com- 

 mon thing in the logic of common life. But in the negative 

 copula, the copular word must be universal. 



