The Inductive Theories. 25 



the domain of mathematics, therefore, we must look elsewhere 

 for inductive inquiry. 



Mr. Mill here introduces his doctrine of Natural Kinds, ac- 

 cording to which there are in Nature classes of objects whose dis- 

 tinguishing common properties are innumerable. Among such 

 Natural Kinds, possessing countless properties in common which 

 are not possessed by other objects, we tind the chemical elements 

 as sulphur, phosphorus, etc., and also animals and plants, while 

 white things or cold things are examples of classes which are 

 probably united by only the single property whiteness or cold- 

 ness. In many departments of nature these Natural Kinds 

 will be marked out for us by their common possession of mul- 

 titudes of qualities; and as this fact makes it very likely that 

 an observation will hit upon generic qualities, an observed uni- 

 formity of co-existence may be generalized to the limits of the 

 Kind with some degree of assurance. And especially will this 

 be so if the qualities are of a kind which we have generally 

 found to be generic. 



In closing his discussion of Induction, Mill devotes some 

 attention to the question as to what degree of credence, if any, 

 is to be given to a generalization when we have none of the 

 foregoing aids in estimating its worth, but when we know 

 simply the number of cases of the uniformity which have been 

 properly observed. 



To what degree can we eliminate chance ; how far can we be 

 sure that a certain run of coincidences is more than casual. His 

 first conclusion is that the mere number of observations gives 

 no ground for a generalization; but he afterwards admits that 

 the probability of such a number of coincidences by chance is 

 calculable and if very small we have reason to infer from the 

 observations an empirical law. 



The theory of Induction thus sketched considers the process, 

 as we have seen, to be that operation of the mind by which from 

 certain observed concomitances of phenomena we infer that one 

 of the concomitants is an unfailing sign of the other; and the 

 greater part of the theory has to do with the conditions under 

 which we are justified in making that inference. The theory 



