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Classically, risk aversion is equated with concavity of the utility function. In this work we explore the conceptual foundations of this definition. In accordance with neo-classical economics, we seek a definition that is based solely on the decisions maker's preference order, independent of numerical values. We present two such definitions, based on simple, conceptually appealing interpretations of the notion of risk-aversion. We then show that when cast in numerical form, these definitions coincide with the classical Arrow-Pratt definition - once the latter is defined with respect to the appropriate units -thus providing a conceptual foundation for the classical definition. The implications of the theory are discussed, including, in particular, to the understanding of insurance.