The Origins of Cardinal and Ordinal in Economics: A Deep Dive

When discussing the fundamental concepts in economics, cardinal and ordinal measures have proven indispensable. These measures have helped economists understand and analyze economic phenomena in a precise manner. However, their origins predate the development of modern economics and exist within the broader context of mathematical concepts. This article aims to explore the historical roots of cardinal and ordinal measures, their evolution, and their significance in economic analysis.

Introduction to Cardinal and Ordinal Measures

In economics, cardinal and ordinal measures are crucial for understanding various economic variables and phenomena. Cardinal measures involve the use of exact numerical values to quantify economic attributes. For example, a cardinal measure would assign specific monetary values to goods and services. On the other hand, ordinal measures rank economic variables based on a qualitative order, such as preference in utility theory. Both measures have distinct applications and are often used in conjunction to provide a more comprehensive analysis.

The Genesis of Mathematical Concepts

The concepts of cardinal and ordinal measures have their roots deeply embedded in the history of mathematics. These concepts predate the development of economics as a distinct discipline and are considered fundamental elements of mathematical theory. Historically, the earliest records of these concepts can be traced back to ancient civilizations, such as the Greeks, who made significant contributions to mathematics and logic.

Cardinal Numbers: Cardinal numbers are used to indicate the quantity or magnitude of something. The concept of cardinal numbers was well-established by mathematicians like Euclid, who explored the properties of numbers in his Elements. The use of cardinal numbers allows for precise measurement of economic quantities, such as the GDP, which is a cardinal measure.

Ordinal Numbers: Ordinal numbers, on the other hand, are used to indicate the position or order of something. The origin of ordinal numbers can be attributed to the work of philosophers and mathematicians who sought to understand the nature of order and ranking. For instance, Aristotle discussed the concept of ordinal numbers in his work on metaphysics, and later mathematical thinkers like Cantor formalized these ideas in the context of set theory.

Integration into Economics

The application of cardinal and ordinal measures in economics was a natural consequence of the evolving field of mathematics. As mathematics became more sophisticated, economists began to adopt these concepts to model and analyze economic phenomena. The integration of these measures into economic theory significantly enhanced the accuracy and depth of economic analysis.

Cardinal Measures in Economics: Cardinal measures are often used in economic models that require exact numerical values. For example, in microeconomics, cardinal measures are used to quantify the utility derived from a set of goods. The concept of utility is cardinal, meaning that the exact numerical value assigned to a unit of utility is significant. Economists like Léon Walras and Vilfredo Pareto used cardinal measures to develop theories of general equilibrium and consumer behavior.

Ordinal Measures in Economics: Ordinal measures are critical in economic theories that focus on preferences and rankings. In utility theory, for instance, consumers' preferences are ranked without implying any cardinal difference in satisfaction. The ordinal approach, popularized by John von Neumann and Oskar Morgenstern in their work on game theory and decision-making under uncertainty, allows economists to model consumer behavior more flexibly.

Challenges and Alternative Measures

While cardinal and ordinal measures have proven invaluable in economic analysis, they also present certain challenges. One major challenge is the issue of cardinal utility, which assumes that the difference between two utility levels is meaningful and constant, even without a monetary context. This assumption has been criticized for its lack of empirical validation.

In response to these challenges, alternative measures such as revealed preferences and choice-based models have gained prominence. These approaches focus on observable choices and preferences rather than hypothetical utility values. The work of Herbert A. Simon and George J Stigler, among others, has emphasized the importance of pragmatic utility, which is more aligned with real-world economic behavior.

Conclusion

The origins of cardinal and ordinal measures in economics are closely tied to their long-standing presence in mathematical theory. While their exact origins are lost in the annals of history, the contributions of ancient mathematicians and philosophers laid the foundation for these concepts. As economics continues to evolve, the integration of cardinal and ordinal measures remains a cornerstone of economic analysis, providing a methodical approach to understanding and predicting economic behavior.

References

1. Euclid. The Elements. D. E. Joyce, translator. Clark University, 1997. 2. Aristotle. Metaphysics. Richard Kraut, editor. Princeton University Press, 2009. 3. Cantor, Georg. Contributions to the founding of the theory of transfinite numbers. Dover Publications, 1955. 4. Walras, Léon. Cours d'économie politique. Guillaumin, 1874. 5. Von Neumann, John, and Oskar Morgenstern. Theory of Games and Economic Behavior. Princeton University Press, 1944.