“Porphyry’s tree” is used to illustrate this doctrine.  It begins with a summum genus, ‘Substance,’ and descends by adding differences, step by step, to the infima species, ‘Man.’  It also illustrates Division by Dichotomy.

SUBSTANCE
/ \
CORPOREAL || INCORPOREAL
||
BODY
/ \
ANIMATE || INANIMATE
||
LIVING BODY
/ \
SENSIBLE || INSENSIBLE
||
ANIMAL
/ \
RATIONAL || IRRATIONAL
||
MAN
//||\\
// || \\
// || \\
// || \\
// || \\
// || \\
// || \\
Socrates Plato Aristotle

Beginning with ‘Substance,’ as summum genus, and adding the difference ‘Corporeal,’ we frame the species ‘Body.’  Taking ‘Body’ as the genus and adding the difference ‘Animate,’ we frame the species ‘Living Body;’ and so on till ‘Man’ is reached; which, being infima species, is only subdivisible into individuals.  But the division of Man into individuals involves a change of principle; it is a division of the denotation, not an increase of the connotation as in the earlier steps.  Only one side of each dichotomy is followed out in the ‘tree’:  if the other side had been taken, Incorporeal Substance would be ‘Spirit’; which might be similarly subdivided.

Genus and species, then, have a double relation.  In denotation the genus includes the species; in connotation the species includes the genus.  Hence the doctrine that by increasing the connotation of a name we decrease its denotation:  if, for example, to the definition of ‘lion’ we add ‘inhabiting Africa,’ Asiatic lions are no longer denoted by it.  On the other hand, if we use a name to denote objects that it did not formerly apply to, some of the connotation must be dropped:  if, for example, the name ‘lion’ be used to include ‘pumas,’ the tufted tail and mane can no longer be part of the meaning of the word; since pumas have not these properties.

This doctrine is logically or formally true, but it may not always be true in fact.  It is logically true; because wherever we add to the connotation of a name, it is possible that some things to which it formerly applied are now excluded from its denotation, though we may not know of any such things.  Still, as a matter of fact, an object may be discovered to have a property previously unknown, and this property may be fundamental and co-extensive with the denotation of its name, or even more widely prevalent.  The discovery that the whale is a mammal did not limit the class ‘whale’; nor did the discovery that lions, dogs, wolves, etc., walk upon their toes, affect the application of any of these names.

Similarly, the extension of a name to things not previously denoted by it, may not in fact alter its definition; for the extension may be made on the very ground that the things now first denoted by it have been found to have the properties enumerated in its definition, as when the name ‘mammal’ was applied to whales, dolphins, etc.  If, however, ‘mammal’ had formerly been understood to apply only to land animals, so that its definition included (at least, popularly) the quality of ‘living on the land,’ this part of the connotation was of course lost when the denotation came to include certain aquatic animals.