What is the relation between Extension and Connotation in Logic?

There is also a relation of inverse variation between extension connections of terms. From the point of extension a higher class (genus) includes a lower (species). But from the point of view of connotation the lower class (species) includes to connotation of the higher class (genus). Thus, as we pass from a species to its genus the extension increases but the connotation decreases.

On the other hand, when we pass from a genus to species there is increase in connotation but decrease in extension. For example, if we increase the connotation of ‘humans beings’ adding anew property ‘educated’ then the new term ‘educates human being’ will have greater connotation but its extension will be less than that of the extension of ‘human being’.

Similarly, if we decrease the connotation of ‘human beings’ by taking out to property ‘rationality’ from it we get a new term ‘animal’ with greater extension, since the term ‘animal’ contains more subclasses than that of ‘human beings’.

In the above examples we notice that increase in connotation leads to decrease in extension and decrease in connotation leads to increase in extension.

Analogously we can notice that increase or decrease in extension will also lead to corresponding decrease or increase in connotation.