Logically equivalent concept structures can differ sharply in theoretical meaning.

Evidence

In formal terms we can convert a structure of OR at the indicator level and AND at the secondary to the converse because (x1 + x2 + x3) ∗(y1 + y2 + y3) = (x1 ∗y1) + (x1 ∗ y2) + · · · + (x3 ∗y3), but this rarely makes any theoretical sense. — Gary Goertz, Social Science Concepts, 333

Categorization

• DEFINE: Illustrates that conjunctive and disjunctive normal forms are algebraically convertible yet semantically non-equivalent for concept-building.
• DEEPTHINKING: A small but load-bearing point: formal equivalence does not cash out as conceptual equivalence, which undermines purely algebraic treatments of concept structure.