This paper attempts to establish that ignorance is a necessary condition for science to have a purpose, just as it is a precondition for any kind of intentional learning or discovety. The author argues that those who find intrinsic value in science must necessarily attribute positive value to ignorance, for the relationship between the two is symbiotic rather than combative. He presents a number of ways in which scientific ignorance may be positively valued by scientists and non-scientists and lays down a framework for discussing ignorance. He finds accumulating evidence of a shift in scientists' values towards more tolerance of ignorance. The paper concludes by saying that although some trends and currents suggest a swing towards an insistence on certainty, safety and security of political agendas, this does not indicate which way the rest of society is going. The author points out the possibility that at least some sectors of society may be moving towards a realization that many kinds of ignorance are irreducible, and with that, a recognition of the need for scientists to cultivate their particular type of purposive ignorance. © 1996, Sage Publications. All rights reserved.