416 INDUCTION. 



Uniformities of co-existence, then, not only when they ave consequences 

 of laws of succession, but also when they ave ultimate truths, must be 

 ranked, for the purpose of logic, among empirical laws ; and are amenable 

 in every respect to the same rules with those unresolved uniformities which 

 are known to be dependent on causation.* 



CHAPTER XXIII. 



OF APPKOXIMATE GENERALIZATIONS, AKD PROBABLE EVIDEKCE, 



§ 1. In our inquiries into the nature of the inductive process, we must 

 not confine our notice to sucli generalizations from experience as profess to 

 be universally true. There is a class of inductive truths avowedly not uni- 

 versal ; in which it is not pretended that the predicate is always true of 

 the subject; but the value of which, as generalizations, is nevertheless ex- 

 tremely great. An important portion of the field of inductive knowledge 

 does not consist of universal truths, but of approximations to such truths ; 

 and when a conclusion is said to rest on probable evidence, the premises it 

 is drawn from are usually generalizations of this sort. 



As every certain inference respecting a particular case implies that there 

 is ground for a general proposition of the form, every A is B ; so does ev- 

 ery probable inference suppose that there is ground for a proposition of the 

 form. Most A are B ; and the degree of probability of the inference in an av- 

 erage case will depend on the proportion between "the number of instances 

 existing in nature which accord with the generalization, and the number of 

 those which conflict with it. 



§ 2. Propositions in the form. Most A are B, are of a very different de- 

 gree of importance in science, and in the practice of life. To the scientific 

 inquirer they are valuable chiefly as materials for, and steps toward uni- 

 versal truths. The discovery of these is the proper end of science ; its work 

 is not done if it stops at the proposition that a majority of A are B, with- 

 out circumscribing that majority by some common character, fitted to dis- 

 tinguish them from the minority. Independently of the inferior precision 

 of such imperfect generalizations, and the inferior assurance with which 

 they can be applied to individual cases, it is plain that, compared with ex- 

 act generalizations, they are almost useless as means of discovering ulterior 



* Dr. M'Cosh (p. 32t of his book) considers the laws of the chemical composition of bodies 

 as not coming under the principle of Causation ; and thinks it an omission in this work not 

 to have provided special canons for their investigation and proof. But every case of chem- 

 ical composition is, as I have explained, a case of causation. When it is said that water is 

 composed of hydrogen and oxygen, the affirmation is that hydrogen and oxj^gen, by the ac- 

 tion on one another which they exert under certain conditions, generate the properties of wa- 

 ter. The Canons of Induction, therefore, as laid down in this treatise, are applicable to the 

 case. Such special adaptations as the Inductive methods may require in their application to 

 chemistry, or any other science, are a proper subject for any one who treats of the logic of 

 the special sciences, as Professor Bain has done in the latter part of his work ; but they do 

 not appertain to General Logic. 



Dr. M'Cosh also complains (p. 325) that I have given no canons for those sciences in which 

 "the end sought is not the discovery of Causes or of Composition, but of Classes; that is, 

 Natural Classes." Such canons could be no other than the principles and rules of Natural 

 Classification, which I certainly thought that I had expounded at considerable length. But 

 this is far from the only instance in which Dr. M'Cosh does not appear to be aware of the 

 contents of the books he is criticising. 



