But if we suppose that the latter proposition is convertible, we shall have these propositions:
Elephant, horse, mule, &c., are long-lived.
All acholous animals are elephant, horse, mule, &c.,
from whence we infer, quite rigorously as to form,
All acholous animals are long-lived.
This mode of putting the Inductive inference shows both the strong and the weak point of the illustration of Induction by means of Syllogism. The strong point is this, that we make the inference perfect as to form, by including an indefinite collection of particular cases, elephant, horse, mule, &c., in a single term, C. The Syllogism then is
All C are long-lived.
All acholous animals are C.
Therefore all acholous animals are long-lived.
The weak point of this illustration is, that, at least in some instances, when the number of actual cases is necessarily indefinite, the representation of them as a single thing involves an unauthorized step. In order to give the reasoning which really passes in the mind, we must say
Elephant, horse, &c., are long-lived.
All acholous animals are as elephant, horse, &c.,
Therefore all acholous animals are long-lived.
This "as" must be introduced in order that the "all C" of the first proposition may be justified by the "C" of the second.
This step is, I say, necessarily unauthorized, where the number of particular cases is indefinite; as in the instance before us, the species of acholous animals. We do not know how many such species there are, yet we wish to be able to assert that all acholous animals are long-lived. In the proof of such a proposition, put in a syllogistic form, there must necessarily be a logical defect; and the above discussion shows that this defect is the substitution of the proposition, "All acholous animals are as elephant, &c.," for the converse of the experimentally proved proposition, "elephant, &c., are acholous."