The point, then, is this: if they are content to indicate the shared attributes by way of implication or necessary entailment, the differentia already does so. But should they demand an explicit, direct statement of those attributes, they have not provided it.

This shows that their insistence that only the proximate genus be included in a “complete definition” is nothing but arbitrary fiat. A parallel case is their claim that a demonstrative syllogism must be composed of exactly two premises—no fewer and no more. When a single premise suffices, they say the second is merely suppressed and call it an “implicit syllogism”; when additional premises are required, they dismiss them as “nested syllogisms.”

By such conventions they stipulate that every definition must contain two terms—a genus and a differentia—and that every syllogism must contain two premises. All of this is pure arbitrariness.

In reality, a proof may at times be complete with a single premise; at other times it cannot be completed without two; and still other cases may require three, four, or even five premises, depending on the needs of the disputant and on which premises are already known or unknown.

The same applies to their contentment with two words in a definition—one denoting the common element and the other the distinguishing element—and to their claim that a complete definition can be achieved only in this fashion, requiring no addition and unattainable without it. If by “complete definition” they mean one that lays out, in detail, all essential attributes, both common and distinctive, then the proximate genus together with the differentia does not accomplish that. But if they mean simply a designation that points to the essential attributes, even by implication or entailment, then the differentia alone—or even the proprium—already suffices.

And when they are challenged by someone who insists on mentioning every genus, or on omitting genera altogether, they have no reply except to say, “This is our convention and terminology.” Yet it is well known that genuine sciences do not vary with changing conventions. It is therefore clear that what they have set forth belongs merely to the realm of arbitrary convention.