348 NECESSARY TRUTH 



know, but which we think we can account for in terms of other 

 admitted truth. Moreover, it is always a truth which has been 

 or which can be reached otherwise than by simple enumeration 

 and which, therefore, can be tested in one or more ways, for 

 example by simple enumeration. Thus, after declaring that, 

 given certain conditions (e.g. universal gravitation, the rotating 

 earth, and the moon), a certain result must follow (e.g. the tides), 

 we can test our supposed necessary truth by appealing to instances 

 which occur in reality. Therein it differs from a truth which as 

 yet has been and can be founded only on simple enumeration (e.g. 

 the statement that all real bodies have extension) ; for such a truth, 

 which has not been deduced from any other, can be tested, if that 

 deserves to be called testing, only by continuing the enumeration. 

 586. We see then that a necessary truth is one which we have 

 reached by tracing the relation of cause and effect. We observe 

 that certain bodies in nature have certain properties or qualities, 

 for example extension and gravity, by means of which they are 

 brought into relation with one another and so affect one another. 

 A law of nature is a uniformity that we have observed in nature. 

 Usually we mean by the term a uniformity of sequence ; that is, a 

 uniformity in the way in which bodies affect one another. Uni- 

 formities of sequences imply uniformities of qualities and relations, 

 and, therefore, of consequences. Doubtless, it is this notion of 

 necessary consequences that has given rise to the term ' law.' l 

 Thus, if it be true that material bodies attract one another, it must 

 be true also that they tend to approach one another. A necessary 

 truth is merely a particular instance of a general uniformity, or 

 else it is a consequence correctly deduced from such a uniformity. 

 When we formulate such a truth, we declare, in effect, "If the 

 general law is true, then, since the bodies we are considering have 

 qualities and relations that bring them within the range of that 

 law, this particular instance or consequence of it must be true also." 

 In practice the term necessary truth is used, as a rule, in cases in 

 which the inference is not very obvious in cases in which conse- 

 quences rather than instances are dealt with, in which more than 

 one quality and relation and therefore more than one uniformity is 

 concerned, and in which, therefore, the conclusion is reached by 



1 " A law, then, in the strict scientific sense is a fully established statement 

 of universal and necessary connexion . . . more loosely, the term is frequently 

 used to denote mere empirical generalizations. . . . These, however, express no 

 necessity and, consequently, are not laws in the strict sense . . . ' empirical law ' 

 is, correctly speaking, almost a contradiction in terms." (Wei ton, Manual of 

 Logic, vol. ii. p. 200.) 



