I. Placement of the Concept (3)

2.2 Properties of the concept: Comprehension and extension

a) Definition

Let us consider the concept 'man'. Even if it constitutes an intelligible unity which expresses the same human nature in all men, we can nevertheless submit this concept to an analysis, from which will emerge a certain number of intelligible aspects whose totality will distinguish the concept of man from every other; for example: 'substance', 'corporal', 'living', 'endowed with sensibility', 'endowed with reason'. In the more universal concept of 'animal', we will have: 'substance', 'corporal', 'living', 'endowed with at least one sense'. We call known of a concept the intelligible aspects which the mind discerns so in it, and which pertain to it necessarily. On the other hand, the same concept 'man' can be considered no longer in the aspects which it contains, but with regard to the individuals of which it can be said, like 'Peter', 'Paul', 'Italian', 'Mexican', 'dentist', 'boy', 'bishop', etc.

We are now ready to borrow from Maritain the following definitions of comprehension and extension:

1) The comprehension of a concept is its breadth with regard to the notes which characterize it.
2) The extension of a concept is the complete set of subjects (real or not) to which this can be attributed.

These definitions explain well comprehension and extension in their ontological foundation. It seems useful here to try two parallel definitions which are located on the formally logical plane:

1) The comprehension of a concept is the complete set of essential predicates which can be attributed to it.
2) The extension of a concept is the complete set of subjects (real or not) to which it can be attributed.


b) Laws of comprehension and extension

1) Statement:

Comprehension and extension are inversely related concepts.

2) Explanation:
The comprehension of the concept 'animal' is less than that of the concept 'man', since the note 'endowed with reason' with all its implications, does not pertain to 'animal'; Therefore this concept can be attributed to individuals (animals without reason) of which the concept 'man' cannot be said; therefore the extension of 'animal' will be greater than 'man'.