I have endeavoured to show in preceding chapters that all inductive reasoning is an inverse application of deductive reasoning, and consists in demonstrating that the consequences of certain assumed laws agree with facts of nature gathered by active or passive observation. The fundamental process of reasoning, as stated in the outset, consists in inferring of a thing what we know of similar objects, and it is on this principle that the whole of deductive reasoning, whether simply logical or mathematico-logical, is founded. All inductive reasoning must be founded on the same principle. It might seem that by a plain use of this principle we could avoid the complicated processes of induction and deduction, and argue directly from one particular case to another, as Mill proposed. If the Earth, Venus, Mars, Jupiter, and other planets move in elliptic orbits, cannot we dispense with elaborate precautions, and assert that Neptune, Ceres, and the last discovered planet must do so likewise? Do we not know that Mr. Gladstone must die, because he is like other men? May we not argue that because some men die therefore he must? Is it requisite to ascend by induction to the general proposition “all men must die,” and then descend by deduction from that general proposition to the case of Mr. Gladstone? My answer undoubtedly is that we must ascend to general propositions. The fundamental principle of the substitution of similars gives us no warrant in affirming of Mr. Gladstone what we know of other men, because we cannot be sure that Mr. Gladstone is exactly similar to other men. Until his death we cannot be perfectly sure that he possesses all the attributes of other men; it is a question of probability, and I have endeavoured to explain the mode in which the theory of probability is applied to calculate the probability that from a series of similar events we may infer the recurrence of like events under identical circumstances. There is then no such process as that of inferring from particulars to particulars. A careful analysis of the conditions under which such an inference appears to be made, shows that the process is really a general one, and that what is inferred of a particular case might be inferred of all similar cases. All reasoning is essentially general, and all science implies generalisation. In the very birth-time of philosophy this was held to be so: “Nulla scientia est de individuis, sed de solis universalibus,” was the doctrine of Plato, delivered by Porphyry. And Aristotle1 held a like opinion—Οὐδεμία δὲ τέχνη σκοπεȋ τὸ καθ’ ἕκαστον ... τὸ δὲ καθ’ ἕκαστον ἄπειρον καὶ οὐκ ἐπιστητόν. “No art treats of particular cases; for particulars are infinite and cannot be known.” No one who holds the doctrine that reasoning may be from particulars to particulars, can be supposed to have the most rudimentary notion of what constitutes reasoning and scíence.
At the same time there can be no doubt that practically what we find to be true of many similar objects will probably be true of the next similar object. This is the result to which an analysis of the Inverse Method of Probabilities leads us, and, in the absence of precise data from which we may calculate probabilities, we are usually obliged to make a rough assumption that similars in some respects are similars in other respects. Thus it comes to pass that a large part of the reasoning processes in which scientific men are engaged, consists in detecting similarities between objects, and then rudely assuming that the like similarities will be detected in other cases.
Distinction of Generalisation and Analogy.
There is no distinction but that of degree between what is known as reasoning by generalisation and reasoning by analogy. In both cases from certain observed resemblances we infer, with more or less probability, the existence of other resemblances. In generalisation the resemblances have great extension and usually