In this paper, I address two connected issues that arise when one considers a rational agent facing a decision problem. One is whether or not the agent may find that the dictates of rationality are such that they cannot all be followed. For example, one may ask whether or not the requirements on the agent's actions imposed by rationality can conflict in an irreconcilable way, making it impossible to satisfy all of them. Put differently, one may ask whether or not any apparent conflict of this type must in fact be capable of rational resolution. I shall say that an agent who is in a position in which the requirements of rationality cannot all be satisfied faces a feasibility dilemma, and I shall characterize certain conceptions of rationality that differ according to whether or not they admit such a possibility. A second issue concerns the number of options that may be deemed rational in a decision problem. Is rationality sufficiently determinate that it always dictates precisely one choice, or may there be more than one rationally permissible option? Is there anything about rationality itself that guarantees that any of the possible options could rationally be chosen? I shall call this issue – whether the concept of rationality itself places any limits on the number of options that may be deemed rational in a given problem – the numbers problem.

One calls a lot of things propositions. If one sees this, then one can discard the idea Russell and Frege had that logic is a science of certain objects – propositions, functions, the logical constants – and that logic is like a natural science such as zoology and talks about these objects as zoology talks of animals. Like a natural science, it could supposedly discover certain relations. For example, Keynes claimed to discover a probability relation which was like implication, yet not quite implication. But logic is a calculus, not a natural science, and in it one can make inventions but not discoveries.

Giving grounds, however, justifying the evidence, comes to an end; – but the end is not certain propositions' striking us immediately as true, i.e. it is not a kind of seeing on our part; it is our acting, which lies at the bottom of the language-game. (Wittgenstein, 1969, §204)

Hysteresis means literally “that which comes later,” being derived from the Greek verb ύστερέω. Thus, hysteresis effects, generally defined, are those that persist after the initial causes giving rise to the effects are removed.

During the course of the 1980s, it became increasingly fashionable to invoke hysteresis effects to explain economic phenomena. Two of the main areas of application were to unemployment and international trade. In the case of unemployment, distinctive features of labor markets, such as social norms that rule out wage-cutting in the face of rising unemployment, imply that “increases in unemployment have a direct impact on the ‘natural’ rate of unemployment” (Blanchard and Summers, 1988, p. 15). The implication for macroeconomic systems is that “temporary shocks can have a permanent effect on the level of employment” (Ibid., p. 307). In the case of international trade, hysteresis effects arise from the industrial economics of sunk costs: “the argument is that firms must incur sunk costs to enter new markets, and cannot recoup these costs if they exit.… thus foreign firms that entered the U.S. market when the dollar was high do not abandon their sunk cost investments when the dollar falls.” The implication for trade flows is “an effect which persists after the cause that brought it about has been removed” (Dixit, 1989, p. 205).

We consider two reasons why firms should be owned and run democratically by their workers. The first concerns accountability: Because the employment relationship involves the exercise of power, its governance should on democratic grounds be accountable to those most directly affected. The second concerns efficiency: The democratic firm uses a lower level of inputs per unit of output than the analogous capitalist firm.

Although it may seem from its formalism that game theory must have sprung from the mind of John von Neumann as a corollary of his work on computers or theoretical physics, it should come as no real surprise to philosophers that game theory is the articulation of a historically developing philosophical conception of rationality in thought and action. The history of ideas about rationality is deeply contradictory at many turns. While there are theories of rationality that claim it is fundamentally social and aims at understanding and molding all facets of human psychological life, game theory takes rationality to be essentially located in individuals and to concern only the means to achieve predetermined ends. Thus, there are some thinkers who have made important contributions to this history who do not appear in the story of game theory at all, among them, Plato, Kant, and Hegel. There is, however, a clear trail to follow linking theories of instrumental rationality from Aristotle to the nineteenth-century marginalist economists and ultimately to von Neumann and Morgenstern and contemporary game theorists, that historically grounds game theory as a model of rational interaction.