Let us make the supposition that it is in the nature of man to doubt the completeness of his expectations; to admit in all humility that, no matter how accurate his perception is of the past and of the present, a complete list of possible futures cannot be produced in thought today; to acknowledge that "the unexpected may happen" (Marshall, 1920, p. 347); to admit, in other words, that the presently unimagined is possible. It follows from this that "human decisions affecting the future, whether personal, political or economic, cannot depend on strict mathematical expectation since the basis for making such calculations does not exist" (Keynes, 1936, pp. 162-163) and that "individual initiative will only be adequate when reasonable calculation is supplemented and supported by animal spirits" (Keynes, 1936, p. 162) -by "a spontaneous urge to action rather than inaction" (Keynes, 1936, p. 161).
The presently unimagined is subjectively possible. This Fundamental Uncertainty Principle is the premise on which we propose to construct an axiomatic theory of individual choice. In a substantive sense, our theory can be viewed as an axiomatization of Shackle's (1949Shackle's ( , 1961Shackle's ( , 1966Shackle's ( , 1978Shackle's ( , 1979) ) decision theory. In a purely formal sense, it can be viewed as an extension of Arrow and Hurwicz's (1972) axiomatic theory of choice under complete ignorance to that of what Knight (1921) calls 'partial ignorance'. Under this condition, Shackle argues that preference over imagined courses of action will be a reflection of the chooser's preference over their corresponding focus-values. What he calls the 'focus-values' of a course of action is an ordered pair of numbers, the first of which represents the worst threat the action appears to make possible, and the second of which represents the best hope which the action appears to offer. Our analysis shows that the acceptance of a plausible set of desirable properties of an optimally criterion under uncertainty implies the acceptance of Shackle's focus-values choice criterion. The core of this set of properties may be referred to as the Principle of Non-additive Theory and Decision 22 (1987) 49-69.