Philosophy of Being and Knowledge

Logic (Philosophy of Thought)

Operations on Concepts

The human mind not only employs concepts in thinking but also performs certain operations on them:

• Generalization: This operation reduces the content of a concept by removing attributes, thereby increasing its scope. Generalization transforms a more specific concept into a more general one. For instance, the concept of "square" has the general attribute "geometric figure" and specific attributes "having four right angles" and "having four equal sides." If the attribute "having four equal sides" is removed, the concept becomes "rectangle," which is broader in scope. Further generalization by removing "having four right angles" results in the concept "geometric figure."
• Restriction: This operation increases the content of a concept by adding specific attributes, thus decreasing its scope. Unlike generalization, which removes attributes, restriction involves adding them. There are two types of restriction:

✵ Restriction by substitution: Replacing a specific attribute with a subtype (e.g., the concept "quadrilateral" characterized by the general attribute "geometric figure" and the specific attribute "having four sides"; replacing "four sides" with "four pairs of parallel sides" results in the new concept "rhombus").

✵ Restriction by addition: Adding an additional attribute to a concept (e.g., the concept "rectangle" characterized by "geometric figure" and "having four right angles"; adding "having four equal sides" results in the new concept "square").

• Division: This operation results in the creation of sub-concepts that are types of the original concept being divided. There are three types of division:

✵ Division by characteristic: Dividing concepts based on a single criterion (e.g., "state" can be divided by the form of government into "monarchy" and "republic").

✵ Dichotomous division: Dividing a concept into two contradictory (opposing) concepts (e.g., the concept "color" can be divided into "white" and "non-white"; the concept "human" can be divided into "man" and "woman").

✵ Classification: A form of division that organizes all its types systematically (e.g., in biology - classification of living organisms, in linguistics - classification of parts of speech, in mathematics - classification of numbers). The rules for division are:

✵ The division must be based on a single criterion.

✵ The division must be exhaustive, meaning the sum of the scopes of the subdivisions should equal the scope of the original concept.

✵ The subdivisions should be mutually exclusive, having no common elements.

✵ The division should be sequential, with the subdivisions being concepts of the same level of generality.