39 THE SCIENCE OF LOGIC 



self-evident principles of inference concerning magnitude and multitude. And 

 precisely the same may be said, in anticipation, about the principles underlying 

 the inferences of the classes (C), and (D), below. The intellect conceives, as 

 holding good in reality, certain groups of relations whether of origin (C), or 

 of location in space or time (D) which enable it to compare or relate certain 

 objects otherwise than by the logical copula of subject and attribute, and to 

 lay down concerning these objects certain self-evident truths on which inferences 

 about these objects are seen to be based. 



All such axioms of inference must be both conceptual and real. Father 

 Joyce admits that those other axioms besides the Dictum de omni are &quot; neces 

 sary to ... inference &quot;. They are therefore &quot; conceptual &quot;. They are even 

 explicitly conceptual : they do not, of course, refer to the &quot; extension &quot; aspect of 

 the concept, or regard it as a &quot; logical whole &quot; resolvable into &quot; logical parts &quot; : 

 but this is not the only aspect of the concept, nor is the Dictum de omni the 

 only axiom that can claim to be &quot; conceptual &quot; merely because it is the axiom 

 that does especially deal with this particular side of the concept. 



Neither can it be objected that the Dictum is the only axiom that is con 

 ceptual in the sense that it alone regards the concept as a &quot; secunda intentio 

 mentis &quot;. The &quot;extension &quot; aspect of the concept belongs, of course, to the 

 latter only in so far as the latter is considered to be a &quot; secunda intentio mentis &quot;. 

 The abstract concept is universalized only in and by the mind : the &quot; intentio 

 universal it at is &quot; results from the mental comparison of the abstract type with 

 the individuals from which it was abstracted, and thus makes the abstract type 

 a &quot; second intention &quot;. But precisely the same is true of the other relations, 

 superadded to the direct concept by the mind, in the case of the other axioms. 

 The mental act of relating one objective concept to others as an equal, greater, 

 or less, magnitude than others, or as related in time or space to others, also 

 makes such concept a secunda intentio mentis. And it is because there is a 

 foundation in reality for all those mental relations, which we establish between 

 our concepts, that our conceptual processes of inference are also real that the 

 application of the secunda intentio to \\\K. prima intentio is legitimate. 



(C) Another class of mediate inferences embraces all those 

 derived from judgments which establish between pairs of objects re 

 lations of such a character that these involve further similar relations, 

 which are thus inferred from the former. For example, &quot; A is the 

 brother of B, B is the sister of C, therefore A is the brother of C &quot;. 

 Not all relations, of course, are of this kind. For each class of 

 mediate inferences from those which evidently are of this kind, we 

 can frame some mediate axiom like this : &quot; Whoever is the brother 

 (or sister) of any individual is the brother (or sister) of all the 

 brothers and sisters of that individual &quot; : and this axiom we can 

 make the major premiss of a syllogism which is involved in each 

 particular inference of the class. 



(D) A still more familiar class of mediate inferences includes 

 those fro m judgments which express each a &quot;time&quot; or &quot;space&quot; rela 

 tion between two objects of thought. For example, &quot; Dublin is 



