GENERAL RULES OR CANONS OF THE SYLLOGISM 3&amp;lt;&amp;gt;7 



The following English rhymes may help the student to remember these 

 rules (cf. infra, 158): 



Of terms have but three ; proposition as term ; 



Distribute the middle in this be most firm ; 



Distribute no term in conclusion, beside, 



Unless in a premiss tis equally wide ; 



One premiss affirmative, this you must learn, 



For negative premisses nothing affirm ; 



A negative head has a negative tail, 



And the converse of this is of equal avail. 1 



155. EXAMINATION OF THE GENERAL RULES OF SYLLOGISM. 

 A (i), (2). The two rules of structure are not, properly speaking, 

 rules of the syllogism, but rather a statement of its essential 

 requirements, of its very nature. If there be valid forms of 

 mediate inference which, as they stand, are not in keeping with 

 these requirements, eg. &quot; B is greater than C ; A is greater than 

 B ; therefore A is greater than C&quot; and which cannot be reduced 

 to any form in which they will conform to these requirements 

 (147), then they are not syllogisms. When, however, a mediate 

 reasoning does conform to these requirements, by having three 

 terms and three propositions connecting those terms as subject 

 and predicate by the logical copula is (are, not), then it is not 

 valid unless it also conforms to the four remaining rules. 



The first rule of structure, however, is of great practical utility 

 as a canon or guide to correct reasoning, inasmuch as it explicitly 

 forbids ambiguity in the use of the terms of a syllogism. It puts 

 us on our guard against apparent syllogisms which really contain 

 four (or more) terms instead of three, because of some term or 

 terms being used in different senses in the different propositions. 

 This apparent syllogism with four (or more) terms masked as 

 three, is a very familiar form of fallacy, technically called Quaternio 

 Terminorum or the Fallacy of Four Terms? 



&quot;A good example of an ambiguous middle is given by De Morgan 

 (Formal Logic, pp. 241-2) : 



All criminal actions ought to be punished by law ; 



Prosecutions for theft are criminal actions ; 



* . . Prosecutions for theft ought to be punished by law ; 



Here the middle term is doubly ambiguous, both criminal and action 

 having different senses in the two premisses .&quot; 



The reason why the middle term must be the same, have the 

 same sense, in both premisses, is sufficiently obvious : otherwise 



1 Questions on Logic, HOLMAN and IRVINE, p. 65. 



2 Also nicknamed &quot; the logical quadruped&quot;. s WELTON, op. cit., p. 290. 



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