QUANTITATIVE INFERENCE. 359 



of experiments. If we inductively infer a general truth 

 from a collection of instances, our collection of instances 

 is never a complete one, and may not include some really 

 exceptional cases ; the law we infer from them is therefore 

 too broadly stated, and is so far an hypothesis. When also 

 we deductively infer the existence of a particular fact from 

 a general law which governs it, the instance is only an hy- 

 pothetical one until its existence is proved by experiment 

 or observation ; and our belief in it ought not to be certain 

 until it has been proved by actual observation of nature. 



Although quantitative reasoning is extremely im- 

 portant, little is here said about it, because this treatise 

 is almost entirely restricted to a qualitative view of re- 

 search. But quantitative inference may be superadded 

 to purely logical reasoning ; for instance, when we say, 

 most metals are fusible, and most metals are ductile ; or, 

 some ductile metals are fusible, and some fusible metals 

 are ductile, we begin to employ quantitative ideas, because 

 the equivalent idea of ' most ' is ' more than half ; ' and 

 the word ' most ' may mean any proportion more than fifty 

 or less than one hundred per cent. The quantification of 

 knowledge and inference is also of extreme value in ques- 

 tions of proof, and the fundamental question in such a case 

 is, what amount of evidence is sufficient ? Practically, a 

 preponderance of proof determines us, and the human 

 mind has no choice in the matter. 



As all departments of knowledge assist in developing 

 each other, so a searching study of the use of the reasoning- 

 power and other intellectual faculties in original scientific 

 research, shows that the developments of science, and the 

 ways in which they are effected, reflect much light upon 

 the proper functions and modes of action of each of our 

 intellectual powers. 



