But the problem says: high in at least 5 of the 3 categories — which is logically impossible.

Tue, 05 May 2026 19:20:22 +0000

Why Saying “High in at Least 5 of the 3 Categories” Is Logically Impossible When trying to describe or categorize complex ideas, people often use phrases like “high in five or more of the three main categories.” At face value, this sounds impressive—but logically, it’s impossible. Tools that rely on structured classification—whether in data analysis, AI, or reporting—cannot reliably assign more than three distinct categories when only three are defined. Let’s explore why this claim breaks fundamental logic and what it means for clarity in communication. ### The Logical Foundation of Categorization Categories define boundaries between groups. If you establish three clear categories, each item or concept can fall into one or only those categories. Totaling “five or more” within only three groups contradicts the basic principles of set theory: the number of categories cannot exceed their total count. This is not just a linguistic flaw—it’s a structural impossibility.