D.), syllogism would argue, that what is true of G. is true of any one of the four; but perfect induction would reason, that what we can prove true of A. B. C. D. separately, we may properly state as true of G., the whole genus. This is evidently a formal argument, as demonstrative as syllogism. But the imperfect or rhetorical induction will perhaps enumerate three only of the species, and then draw the conclusion concerning G., which virtually includes the fourth, or what is the same thing, will argue, that what is true of the three is to be believed true likewise of the fourth.” Newman’s Lectures on Logic, p. 73 (1837). The same distinction between perfect and imperfect induction is made in the Encyclopédie Françoise, art. Induction, and apparently on the authority of the ancients. It may be observed, that this imperfect induction may be put in a regular logical form, and is only vicious in syllogistic reasoning when the conclusion asserts a higher probability than the premises. If, for example, we reason thus: Some serpents are venomous--This unknown animal is a serpent-Therefore, this is venomous; we are guilty of an obvious paralogism. If we infer only, This may be venomous, our reasoning is perfectly valid in itself, at least in the common apprehension of all mankind, except dialecticians, but not regular in form. The only means that I perceive of making it so, is to put it in some such phrase as the following: All unknown serpents are affected by a certain probability of being venomous: This animal, &c. It is not necessary, of course, that the probability should be capable of being estimated, provided we mentally conceive it to be no other in the conclusion than in the major term. In the best treatises on the strict or syllogistic method, as far as I have seen, there seems a deficiency in respect to _probable_ conclusions, which may have arisen from the practice of taking instances from universal or necessary, rather than contingent truths, as well as from the contracted views of reasoning which the Aristotelian school have always inculcated. No sophisms are so frequent in practice as the concluding generally from a partial induction, or assuming (most commonly tacitly) by what Archbishop Whateley calls “a kind of logical fiction,” that a few individuals are “adequate samples or representations of the class they belong to.” These sophisms cannot, in the present state of things, be practised largely in physical science or natural history; but in reasonings on matter of fact they are of incessant occurrence. The “logical fiction” may indeed frequently be employed, even on subjects unconnected with the physical laws of nature; but to know when this may be, and to what extent, is just that which,