24 THE SCIENCE OF LOGIC 



cause&quot; ethical principles like &quot; Virtue is praiseworthy&quot; geo 

 metrical and mathematical axioms such as &quot; Two and two are 

 four&quot; ; and the whole vast body of truths that can be derived 

 from such principles by pure demonstration. These truths are all 

 in materia necessaria ; they have to do with abstract essences, or 

 objects of thought considered in a possible state, apart from the 

 changing conditions of actual existence in time and space. 



The process by which we come into possession of truths of 

 this class presents no logical difficulty. It is simply a process 

 of forming abstract and universal concepts ; of analysing and 

 comparing these with one another ; of thus seeing intellectually 

 self-evident, necessary relations between them ; of generalizing 

 these relations and formulating them in necessary or analytic 

 propositions. The process embraces conception and judgment, but 

 does not involve logical inference or reasoning proper. It is from 

 sense observation of a few instances that we form the concepts : 

 we need such observations in order to get, for example, the 

 notions of &quot;whole,&quot; and &quot;part,&quot; and &quot;greater&quot;. But having 

 once abstracted these intellectual notions from sense experience, 

 and compared them with one another, we have an immediate 

 intellectual intuition of the necessary truth that &quot; the whole is 

 greater than its part &quot; : and this truth we see to apply to every 

 whole, actual arid possible, known and unknown : we assent to it 

 not because we have examined all the instances for we have 

 not but because we perceive the relation to be universal because 

 it is necessary.^ 



Now, this simple process of abstraction, intuition, and general 

 ization, by which we attain to a knowledge of self-evident, 

 necessary principles, through the notions which we abstract from 

 sense experience, is sometimes called Induction. But this is 

 using the word in such a wide sense as to make it embrace every 

 mental process by which we ascend from or through the particular 

 to the universal. Aristotle used the equivalent Greek term in 

 this wide sense : ETraywyrj rj cnro rwv icad eKacrrov eVt ra tca66\ov 



e(f&amp;gt;o8o&amp;lt;?. 2 



1 Cf. JOSEPH, Logic, pp. 356, 363 (2), 508 sqq, 



*Top. i. 12. Truths oi the- class with which we are dealing are described in 

 Scholastic philosophy as per se notae (86), i.e. knowable in themselves, by a full 

 analysis of tlie notions involved in them. In some of these truths the notions are 

 so simple as to be within the reach of all who are endowed with ordinary intelli 

 gence. These are said to be per se notae quoad omnes. In other cases, however, 

 the notions may be so complex as, for instance, in the remoter mathematical con 

 clusions that although the truths embodying them are knowable in themselves 



