JMC : Elements of Logic / by Cardinal Mercier

18. Comprehension and Extension of Concepts. -- There are relations of subordination between various predicables. To understand these it is necessary to establish two logical properties of abstract concepts: their comprehension and their extension.

The comprehension of an idea is its content, the sum of the characteristics or notes which analysis can find in it. Take the abstract idea of man. When we consider what this idea represents, we find in it different characteristics taken by abstraction from the individuals. The extension of an idea is its range of applicability, the sum of the subjects to which the abstract idea is applied or can be applied, extends or can extend.

We thus consider the abstract and universal concept as a whole, whether metaphysical or logical. Man is a metaphysical whole, which comprises corporeality, life, sensibility, reason, as so many metaphysical parts.{1}

The idea of man is attributable to all men, past, present, future, or merely possible; it forms a logical whole of which men, taken distributively, are the logical parts.

The Latin words totus and omnis correspond to the two members of this distinction.

An idea is more or less comprehensive accordingly as it embraces more or fewer notes. It has greater or less extension accordingly as it applies to a greater or smaller number of subjects.

These two properties of the idea are in inverse ratio to each other: the greater the comprehension of an idea, the less its extension, and vice versa.

When we compare two or more ideas in the twofold respect of their extension and their comprehension, certain relations are seen to arise between them.

{1} See General Metaph., no. 48.

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