<p>Starting from revealing the mathematical conceptual dilemmas of classical measurement theory and based on rigorous mathematical concepts, this study deduces the correct mathematical principles of measurement error theory. In contrast to the mathematical cognition of classical measurement theory, this study regards the measured values as constants and the true values of the measurands as variables and strictly distinguishes the differences between constant equations and variable equations, thus deriving a new measurement concept system without error categories, redefining the concept of measurement uncertainty, and improving measurement quality. This study negates the conceptual logical system of classical measurement theory, leading to a global change in human measurement concepts.</p>