regard ourselves obliged to answer to what we can best conceive to be the author's true meanings rather than to what he has explicitly said.
We do not conceive that he regards it as necessary to a definition that the defining assertions should be expressed "in the simplest manner that can be devised." We have also to take his use of the word "restrict" as importing completion as well as limitation, and his use of the word "requirements" as intending conditions that together are sufficient as well as necessary.
If we are right in our understanding of the meanings of our author he contemplates four cases, first, the definition of a name that has no denotation already known and that is not to form the basis of a deductive science, second, the definition of a name that has no denotation already known but which is to form the basis of a deductive science, third, the definition of a name that has a denotation already known but which is not to form the basis of a deductive science, and fourth the definition of a name that has a denotation already known and is to form the basis of a deductive science.
In this fourth case our author deems it requisite for a logical definition that there shall be made one or more assertions about the subject of definition that are not demonstrably incompatible with one another, that are independent of one another, that are commonly accepted as true in respect to the subject defined and that "restrict" the meaning of the name under definition exactly to its accepted denotation.
It seems to us that this last requirement dispenses with the necessity of all the rest. If we have provided an assertion or a set of assertions that do in fact complete and limit the meaning of the subject of definition exactly to its proper denotation that is a definition in full. It implies that the defining assertions are all consistent with one another, and in case any assertion is dependent upon one or more of the rest that is a circumstance wholly immaterial. Utile per inutile non nocetur.
Again, what is it to be commonly accepted as true? Does logical competence depend on the altering states of our knowledge or on the fluctuations of opinion? Was a whale logically defined as a fish before we learned that it was a mammal?
The third case allows of the application of the same comment as that made upon the fourth. But in the first and second cases the doctrines of the author as well as his suppositions are very notable. He supposes the anomaly of names without any known denotation, by which he may mean those which have no application whatever. In respect to such he propounds that they may be given a logical definition by making one or various consistent assertions as applicable to them or to their attributes.
"The proof of the pudding will be found in the eating," as our author says. So let us say that a troft may be perceived whenever our attention is excited, and that trofts are of multitudinous variety. Do these assertions constitute a logical definition? It is a prime requisite for a definition that the defining assertion or assertions shall have a meaning, which is the same as to say that names must be
