Extension = breadth = compass = application = denotation.
Intension = depth = comprehension = implication = connotation.
Of these various expressions, 'application' and 'implication' have the advantage of most clearly conveying their own meaning. 'Extension' and 'intension,' however, are more usual; and neither 'implication' nor 'connotation' is quite exact as a synonym for 'intension.' (§ 164.)
§ 153. We now return to the division of terms into connotative and non-connotative.
§ 154. A term is said to connote attributes, when it implies certain attributes at the same time that it applies to certain things distinct therefrom. [Footnote: Originally 'connotative' was used in the same sense in which we have used 'attributive,' for a word which directly signifies the presence of an attribute and indirectly applies to a subject. In this, its original sense, it was the subject which was said to be connoted, and not the attribute.]
§ 155. A term which possesses both extension and intension, distinct from one another, is connotative.
§ 156. A term which possesses no intension (if that be possible) or in which extension and intension coincide is non-connotative.
§ 157. The subject-term, 'man,' and its corresponding attributive, 'human,' have both extension and intension, distinct from one another. They are therefore connotative. But the abstract term, 'humanity,' denotes the very collection of attributes, which was before connoted by the concrete terms, 'man' and 'human.' In this case, therefore, extension and intension coincide, and the term is non-connotative.
§ 158. The above remark must be understood to be limited to abstract terms in their singular sense. When employed as common terms, abstract terms possess both extension and intension distinct from one another. Thus the term 'colour' applies to red, blue, and yellow, and at the same time implies (i.e. connotes), the power of affecting the eye.
§ 159. Since all terms are names of things, whether substances or attributes, it is clear that all terms must possess extension, though the extension of singular terms is the narrowest possible, as being confined to one thing.