relative importance of these two branches of reasoning, I shall have to point out that—
- Perfect Induction is a process absolutely requisite, both in the performance of imperfect induction and in the treatment of large bodies of facts of which our knowledge is complete.
- Imperfect Induction is founded on Perfect Induction, but involves another process of inference of a widely different character.
It is certain that if I can draw any inference at all concerning objects not examined, it must be done on the data afforded by the objects which have been examined. If I judge that a distant star obeys the law of gravity, it must be because all other material objects sufficiently known to me obey that law. If I venture to assert that all ruminant animals have cloven hoofs, it is because all ruminant animals which have come under my notice have cloven hoofs. On the other hand, I cannot safely say that all cryptogamous plants possess a purely cellular structure, because some cryptogamous plants, which have been examined by botanists, have a partially vascular structure. The probability that a new cryptogam will be cellular only can be estimated, if at all, on the ground of the comparative numbers of known cryptogams which are and are not cellular. Thus the first step in every induction will consist in accurately summing up the number of instances of a particular phenomenon which have fallen under our observation. Adams and Leverrier, for instance, must have inferred that the undiscovered planet Neptune would obey Bode’s law, because all the planets known at that time obeyed it. On what principles the passage from the known to the apparently unknown is warranted, must be carefully discussed in the next section, and in various parts of this work.