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The paper discusses a possible way of justifying the existence of a multiplicity of cryptomorphic axiomatic theories. It is argued that what renders this multiplicity inevitable are the applications of the theory. They give rise to difficulties whose solution necessitates the application of different conceptual tools. The paper is organized as follows: (§1) introduces the concept of cryptomorphism and the canonic example for the phenomenon: matroid theory; (§2) discusses five cryptomorphic approaches to the definition of rationality in the framework of decision theory: through utility functions, weak orders, choice operators, layered permutations, and pop-stack sortability; (§3) shows that each of these different approaches can serve as a basis for the introduction of a different modification of the original theory. This establishes the heuristic value of cryptomorphic approaches in the domain of decision theory. [ABSTRACT FROM AUTHOR]

The present paper introduces a novel formalism for analysis of practical arguments, called reason-based decision theory. In (§1) I provide an analogy between logic and decision theory, motivated by the role that reasons play in both fields of inquiry. (§2) elaborates on the idea of reason-based choice proposed by Shafir, Simonson, and Tversky (1993). In (§3) I illustrate ho this idea can be applied to the analysis of the famous paradox of Allais. (§4) s etches the logical formalism of reason-based decision theory, hile (§5) presents the different forms of practical argumentation. It is shown that they are sufficient for the solution of any dilemma. Finally, (§6) provides a game-theoretical semantics of the logical formalism and discusses the possibilities for its further elaboration. [ABSTRACT FROM AUTHOR]