A man who employs a word quite correctly may be sadly posed by a request to explain or define it.

Moreover, so far as we are aware of the connotation of terms, the number and the kind of attributes we think of, in any given case, vary with the depth of our interest, and with the nature of our interest in the things denoted.

'Sheep' has one meaning to a touring townsman, a much fuller one to a farmer, and yet a different one to a zoologist.

But this does not prevent them agreeing in the use of the word, as long as the qualities they severally include in its meaning are not incompatible.
All general names, and therefore not only class-names, like 'sheep,' but all attributives, have some connotation.

'Woolly' denotes anything that bears wool, and connotes the fact of bearing wool; 'innocent' denotes anything that habitually and by its disposition does no harm (or has not been guilty of a particular offence), and connotes a harmless character (or freedom from particular guilt); 'edible' denotes whatever can be eaten with good results, and connotes its suitability for mastication, deglutition, digestion, and assimilation.
Sec.2.But whether all terms must connote as well as denote something, has been much debated.