Instances of Decision Theory in Plato's Alcibiades Major and Minor and in Xenophon's Memorabilia

This essay discusses Socrates' use of hypothetical choices as an early version of what was to become in the twentieth century the discipline of decision theory as expressed by one of its prominent proponents, F. P. Ramsey. Socrates' use of hypothetical choices and thought experiments in the dialogues is a way of reassuring himself of an interlocutor's philosophical potential. For example, to assess just how far Alcibiades is willing to go to attain his goal of being a great Athenian leader, we employ Ramsey's concept of Mathematical Expectation. Mathematical Expectation operates on the assumption that it is not enough to measure probability; we must also measure our belief to apportion our belief to the probability. In other words, it illustrates how strongly or to what degree a person holds a particular belief. If a person's belief in X lacks enough doubts to cancel the belief out, the probability of his acting on this belief is higher than if his belief in X was plagued by a greater number of doubts.