NATURE AND CHARACTERISTICS OF INFERENCE 389 



To this class we would refer the arguments given by Father Joyce in 

 his Principles of Logic (p. 199) : 



&quot;The triangle ABC is equal to the triangle DEF. 



The triangle GHI is equal to the triangle DEF. 

 .-. The triangle GHI is equal to the triangle ABC. 

 and 



12 = 7 + 5 ; 12 = 20 - 8 ; .-. 7 + 5 = 20 - 8 &quot;. 



These arguments are based on the mathematical axiom &quot; Things which 

 are equal to the same thing are equal to one another.&quot; not on the logical 

 &quot; Dictum de omni &quot;. Father Joyce believes this view to be erroneous ; and 

 he gives two reasons : &quot; In the first place the data most certainly gives us a 

 subject-attribute relation : for this is inseparable from judgment &quot;. This we 

 admit ; but it is not from the combination of these subject-attribute relations 

 that we reach the respective conclusions. No doubt, as we pointed out above, 

 we can reach each of the conclusions by a syllogism the major of which em 

 bodies the very mathematical axiom on which the arguments are directly based. 

 Father Joyce gives such a syllogism : 



&quot; Any two quantities, each of which is equal to the same third quantity, 

 are equal to each other. 



&quot;ABC and GHI (as being equal to DEF) are two quantities, each of 

 which is equal to the same third quantity. 



.-. ABC and GHI are equal to each other.&quot; But this syllogism can hardly 

 be claimed to be an equivalent expression of the original argument. Nor can 

 it be fairly denied that when people do actually reason as in the two arguments 

 given above, the copula in their minds is not &quot; is&quot; but &quot; is equal to&quot; : &quot; the 

 word equals is a copula in thought and not a notion attached to a predicate V 



&quot; Secondly,&quot; continues Father Joyce, &quot; it is impossible that the axiom Things 

 which are equal to the same thing, etc., etc., should be a principle of inference. 

 It is a truth relating to the real order, not to the conceptual. It is necessary 

 to the inference, but it is not a canon governing the inferential process itself. 

 A canon of inference must have explicit reference to the conceptual order.&quot; 



We cannot allow that because the axiom in question relates &quot; to the real 

 order,&quot; therefore it cannot &quot; be a principle of inference &quot;. The Dictum de omni 

 relates to the real order : it is a self-evident intuition of the mind about the 

 nature of the real order, and not, as a Kantist might perhaps contend, an 

 empty, subjective form, revealing nought but the nature of thought itself : and 

 yet we recognize in the Dictum de omni a principle of inference. And why ? 

 Because it is conceptual as well as real : i.e. because it formulates a law based 

 on certain characteristics (intension and extension) of our concepts character 

 istics which these concepts derive front the nature of the reality which forms 

 their objects. But so is the other axiom in question conceptual as well as real. 

 It is because we intellectually conceive reality as constituted of classes of things, 

 and these things as endowed with attributes, that we are able to formulate 

 subject-attribute judgments, and to lay down the Dictum de omni and the other 

 dicta of syllogistic inference. Similarly, it is because we intellectually conceive 

 reality as embodying magnitudes and multitudes, and these as related in de 

 gree to one another, that we can form judgments having a quantitative or 

 mathematical copula (symbolized by = , &amp;gt;, &amp;lt;, etc.), and lay down distinct 



1 De MORGAN, Syllabus, pp. 31, 32 ; apud KEYNES, op. cit., p. 386, note. 



