138 EEASONING. 



And again, 



The attributes of man are a mark of the attribute mortality, 

 The attributes of a king are a mark of the attributes of man, 



therefore 

 The attributes of a king are a mark of the attribute mortality. 

 And, lastly. 



The attributes of man are a mark of the absence of the attribute 

 omnipotence, 



The attributes of a king are a mark of the attributes of man, 



therefore 



The attributes of a king are a mark of the absence of the attribute 

 signified by the word onmipotent 

 (or, are evidence of the absence of that attribute). 



To correspond with this alteration in the form of the syllogisms, the ax- 

 ioms on which the syllogistic process is founded must undergo a corre- 

 sponding transformation. In this altered phraseology, both those axioms 

 may be brought under one general expression ; namely, that whatever has 

 any mark, has that which it is a mark of. Or, when the minor premise as 

 well as the major is universal, we may state it thus : Whatever is a mark 

 of any mark, is a mark of that which this last is a mark of. To ti-ace the 

 identity of these axioms with those previously laid down, may be left to the 

 intelligent reader. We shall find, as we proceed, the great convenience of 

 the phraseology into which we have last thrown them, and which is better 

 adapted than any I am acquainted with, to express with precision and force 

 what is aimed at, and actually accomplished, in every case of the ascertain- 

 ment of a truth by ratiocination.* 



* Professor Bain {Logic, i., 157) considers the axiom (or rather axioms) here proposed as 

 a substitute for the dictum de omni, to possess certain advantages, but to be "unworkable as 

 a basis of tlie syllogism. The fatal defect consists in this, that it is ill-adapted to bring out 

 the difference between total and partial coincidence of terms, the observation of which is the 

 essential precaution in syllogizing correctly. If all the terms were co-extensive, the axiom 

 would flow on admirably ; A carries B, all B and none but B ; B carries C in the same man- 

 ner ; at once A carries C, ^v'ithout limitation or reserve. But in point of fact, we know that 

 while A carries B, other things carry B also ; whence a process of limitation is required, in 

 transferring A to C through B. A (in common with other things) carries B ; B (in common 

 with other things) carries C ; whence A (in common with other things) carries C. The ax- 

 iom provides no means of making this limitation ; if we were to follow A literally, we should 

 be led to suppose A and C co-extensive : for such is the only obvious meaning of ' the attri- 

 bute A coincides with the attribute C" 



It is certainly possible that a careless learner here and there may suppose that if A carries 

 B, it follows that B carries A. But if any one is so incautious as to commit this mistake, the 

 very earliest lesson in the logic of inference, the Conversion of propositions, will correct it. 

 The first of the two forms in which I have stated the axiom, is in some degree open to Mr. 

 Bain's criticism : when B is said to co-exist with A (it must be by a lapsus calami that Mr. 

 Bain uses the word coincide), it is possible, in the absence of warning, to suppose the meaning 

 to be that the two things are only found together. But this misinterpretation is excluded by 

 the other, or practical, form of the maxim ; Nota notce est nota rei ipsius. No one would be 

 in any danger of inferring that because a is a mark of b, b can never exist without a ; that 

 because being in a confirmed consumption is a mark of being about to die, no one dies who is 

 not in a consumption ; that because being coal is a mark of having come out of the earth, 

 nothing can come out of the earth except coal. Ordinary knowledge of English seems a 

 sufficient protection against these mistakes, since in speaking of a mark of any thing we are 

 never understood as implying reciprocity. 



A more fundamental objection is stated by Mr. Bain in a subsequent passage (p. 158). 

 "The axiom does not accommodate itself to the t3-pe of Deductive Reasoning as contrasted 

 with Induction — the application of a general principle to a special case. Any thing that fails 

 to make prominent this circumstance is not adapted as a foundation for the syllogism." But 



