O. The idea of scientific progress in contemporary philosophy of science. Explicating the concept of cognitive progress means at the same time articulating an ideal of science. A desirable ideal: explain a lot and offer certainty. 1. Working out the ideal with the "foundationalist-positivist" approach. If the question, "When is it rational to accept a theory?" is answered, "When it has sufficient inductive support," this leads to insoluble problems. Reactions to the collapse of this approach - especially relativism and theory (...) instrumentalism. 2. The Popperian alternative: rational theory preference despite fallibility of methods for determining truth or greater accuracy of representations. What good reasons can there be for the conjecture that one theory is superior to a competing theory in its achievement as a description? Achievements to date as fallible but objective indicators of strength in describing. The sorts of risks for a theory differ in explanation and in prediction. Corresponding to the risks are the chances for cognitive progress. Instead of a cumulative index, itemized indication of success and failure in explanation and prediction with regard for importance of the questions at issue. On the concept of the "scientific importance" of questions. Postscript: On the political consequences of the sceptical position in philosophy of science. (shrink)