KiDD. — Induction and Necessary Truth. xli 



in all which resemble the former, in what are regarded as the material 

 circumstances." 



In this definition of Induction Mr. Mill is in unison with Aristotle and 

 other ancient writers, and with the popular reviver of Logic, Archbishop 

 Whately. The definitions given by more recent expositors are tantamount. 

 Induction being thus defined, let us now notice explicitly, in order to decisive 

 clearness, some of the properties of Induction which are expressed or implied 

 in that definition. 



1. Let us observe, in the first place, that the propositions obtained by induc- 

 tion are general propositions. When Kelper tested, one after another, many 

 different positions of the planet Mars, and found that each position would be 

 comprised in the periphery of an ellipse, each of those positions, thus experien- 

 tially known, was an individual fact, and the statement of them collectively was 

 a statement of actual definite experience ; but the inference that all the positions 

 of the planet constituted, when combined, an elliptical orbit, this was an induc- 

 tive generalization. Further, that the planet Mars moves round the Sun in 

 such wise that the radius vector describes equal areas in equal times, and 

 that Mercury and Yenus do so likewise j these may be designated as indi- 

 vidual facts, or their statement as singular propositions : while it was an 

 inductive generalization, for Kelper and his contemporaries, to conclude that 

 this law of equal areas in equal times was a property of every planet, tested and 

 untested. These generalizations did, of course, cease to be immediately 

 inductive when Newton demonstrated them to be deducible from simpler and 

 more general principles. Again, in the case of numberless bodies of earth, 

 and of many bodies astronomical, it has been ascertained, whether from direct 

 experience or by inference, that matter gravitates to matter; but it is an 

 inductive^ generalization, and that of the widest kind, that not any matter 

 throughout the universe is devoid of the attribute gravitation. 



2. With reference to the definition of Induction, it is, in the second place, 

 to be noted distinctly, that the result obtained is not merely a general term, 

 or the conception of a class of things ; the result of an induction is a general 

 proposition, or the ascription to the class universally of some attribute other 

 than that by which the class is constituted. E.g., all matter gravitates : to have 

 obtained the conception of matter, and to have apprehended what is meant by 

 gravitation, are of course results of experience ; without experience we should 

 be devoid of those ideas, and of all knowledge of those things. But Induction 

 does something more than this j it conjoins the two conceptions or terms in a 

 universal proposition. Simple Experience presents to us individual facts, and 

 thus furnishes us with concepts ; but Induction leads on to beliefs. 



3. We are now, therefore, to observe, thirdly, that no inductive gene- 

 ralization whatsoever, no inference from the phenomena of experience, can 



