This essay argues that beneath the superficial linearity of the history of neoclassical price index theory lie important conceptual ruptures that are linked to the ordinal revolution, including a radical transformation in the core objective for cost-of-living indexes. Revealing these ruptures produces a more accurate history of both the development of neoclassical price index theory and its reception. Furthermore, we can recognize how transformations in this theory have made cost-of-living indexes more coherent with existing traditions of empirical macroeconomics even as they may have reduced the indexes’ suitability for other functions, notably adjusting income payments.