346 NECESSARY TRUTH 



class which is content with such a catalogue as a grocer makes of 

 his stock. But consider the improvement effected by Darwin, 

 when, deducing necessary truths from given data, he linked 

 together plants and animals by chains of causation. Knowledge 

 was then supplemented by understanding. Something more than 

 a mere memory of perceptions came into play. That something 

 was Reason. 



583. What, then, do we mean by the expression 'necessary 

 truth ' ? How is it to be distinguished from ' invariable ' occur- 

 rence? A necessary truth is not one reached by intuition. 

 Apparently no such truths are known to us. Nor is it one reached 

 by induction from simple enumeration ; for that merely endows us 

 with a sense of probability, of expectancy. It is always one which 

 we have reached through what seems to us valid reasoning from an 

 apparently complete consideration of all the relevant properties and 

 relations of real things. It is not, of course, more certainly true 

 than the existence of those real things and of their properties and 

 relations ; but, given those existences, those properties, and those 

 relations, it is certainly true provided we have reasoned correctly 

 and taken all that is essential into consideration. It is an effect 

 that we have inferred from its cause, or a cause that we have in- 

 ferred from its effect. It is a conclusion drawn from premises 

 antecedently formulated or implied, and true zy the premises are true. 



584. If the reader will try to think of any notion the truth of 

 which appears necessary to him, he will always find that it bears 

 this character of an inference from premises which have previously 

 been granted. For example, though we are told that every axiom 

 of geometry is a ' self-evident ' and * fundamental ' truth ; " that is, 

 its truth should not be deducible from any other truth more simple 

 than itself " ; yet, as a fact, we do, in every instance, derive 

 geometrical axioms from truths which we regard as more funda- 

 mental, simple, and self-evident than themselves from the 

 qualities and relations of the things we are considering. Some reason- 

 ing is always done before we admit the truth of an axiom. Thus the 

 axiom that " Things which are equal to the same thing are equal 

 to one another," is but another way of saying that "^things are 

 equal to the same thing they are equal to one another, for the 

 reason that they will then have identical properties and relations." 

 The reasoning may be so swift and easy that only more think- 

 ing reveals its existence, so swift and easy that an attempted 

 exposition of it appears like stating the same thing in another and 

 a more involved way ; the inference may be so obvious that only 



