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The article focuses on the ongoing debate regarding the measurement of psychological attributes. The aim is to clarify different uses of the term theory and key points of agreement and disagreement among participants. In addition, the article addresses misinterpretations of key points in recent articles and notes an apparent paradox arising in the representational theory of measurement. Substantive theory is contrasted with both item response theory and the representational theory of measurement. Emphasis is placed on the direct dependence of the measurement of physical attributes on substantive quantitative theory as opposed to any form of separate measurement theory. It is concluded that the primary challenge faced in quantitative psychology is to posit testable substantive theories or laws which form a foundation for measurement.

Psychological measurement: Theory, paradoxes, and prototypes