SECTION 24.- VERIFICATION AND PROOF. 365 



instrumental observation and scrutiny; (b) simple and instru- 

 mental experiment; (c) enumeration, measurement, and calcula- 

 tion; (d) obvious or involved deductive testing; (e) confirmation 

 of a prediction by discovering its basis or awaiting its fulfil- 

 ment ; (/) special tests, such as are commonly applied or other- 

 wise prove effective; and (g) applying all or more than one 

 of the above methods. Indirect proof, especially referring to 

 causes, may be obtained by noting in a virtually interminable 

 series of cases drawn from exhaustively varied sources and 

 circumstances, (a) invariable agreement, (b) invariable difference, 

 (c) invariable concomitant variation, (d) invariable residue, and 

 (e) applying, in any particular case, several or all of these 

 methods in conjunction, as in Bacon's method of investigation. 

 The dialectical procedure recommended in Conclusion 28 should 

 be also applied, and, failing complete proof, the degree of proof 

 should be stated. In respect of the matter of the proof, no- 

 thing short of ascertaining the unmistakably precise static or 

 dynamic constituents (mechanical, ethereological, physical, chemi- 

 cal, crystalline, biological, and cultural) should be aimed at, or, 

 if this cannot be satisfactorily achieved, the degree of com- 

 pleteness of the apparent proof needs to be recorded. 



To verify a fact is not necessarily to explain it, e.gr., we 

 possess much verified knowledge concerning the law of gravi- 

 tation; but few scholars are satisfied that the law is an ex- 

 planation of the facts. Yet a particular fact is for all intents 

 and purposes explained when it can be shown to be in agree- 

 ment with some established fact more general than itself. 1 

 Consequently, the student should strive not only to establish 

 comprehensive laws of nature, but to prove given statements 

 by producing satisfactory evidence that they are special cases 

 of an acknowledged general fact. This is the ideal to be 

 aspired to; but, as we saw earlier, large working hypotheses, 

 and any kind of established propositions, may be utilised in 

 proving or explaining given facts. In other words, we should 

 first seek to verify, and then to explain, facts. We should, 

 however, remember that accord with theory is only to be 

 regarded as complete proof if no other theory is admissible 

 which would equally well or better explain an order of facts. 



1 "An individual fact is said to be explained by pointing out its cause, 

 that is, by stating the law or laws of causation of which its production is 

 an instance. Thus a conflagration is explained when it is proved to have 

 arisen from a spark falling into the midst of a heap of combustibles; and, 

 in a similar manner, a law of uniformity in nature is said to be explained 

 when another law or laws are pointed out, of which that law itself is but 

 a case, and from which it could be deduced." (Mill, Logic, bk. 3, ch. 12, 1.) 



"The truth of a given proposition is finally to be proved only by showing 

 that it is not inconsistent with any other propositions which we profess to 

 hold as certain." (J. M. Robertson, Letters on Reasoning, 1905, p. 237.) 



