36. Logical Value of the Predicate of a Simple Proposition. -- The comprehension and extension of the predicate are a function of the form of the proposition. In an affirmative proposition they are in inverse ratio to what they are in a negative.

(1) In an affirmative proposition the predicate is taken in all of its comprehension, although this may be less than that of the subject; but only in a part of its extension. All the notes of the predicate, taken together or separately, apply to the subject; but the subject need not represent, and consequently does not, so far as the enunciation goes, represent more than a portion of the objects within the extension of the predicate. E. g., when I say, "the dog is a vertebrate", I mean to assert that the dog has all the properties included in the idea vertebrate, collectively or distributively; but not that there are no other vertebrates but the dog.

There is, however, this reservation to be made: that in essential definitions, the thing defined and its definition have the same extension and the same comprehension.

(2) In a negative proposition, on the contrary, the predicate is taken in its whole extension, but only in an indeterminate part of its comprehension. E. g., when I say, "The mollusc is not a vertebrate", I mean to say that the mollusc is not any one of the vertebrates, because it does not include all the attributes of the vertebrates; but that does not prevent its having some of the properties which belong to the vertebrates. I exclude all the subjects to which the idea of vertebrate applies, but I need not therefore exclude all the notes which that idea comprehends.