From the early-1950s on, F.A. Hayek was concerned with the development of a methodology of sciences that study systems of complex phenomena. Hayek argued that the knowledge that can be acquired about such systems is, in virtue of their complexity (and the comparatively narrow boundaries of human cognitive faculties), relatively limited. The paper aims to elucidate the implications of Hayek's methodology with respect to the specific dimensions along which the scientist's knowledge of some complex phenomena may be limited. Hayek's fallibilism was an essential (if not always explicit) aspect of his arguments against the defenders of both socialism ( 1948,  1948) and countercyclical monetary policy ( 1978); yet, despite the fact that his conceptions of both complex phenomena and the methodology appropriate to their investigation imply that ignorance might beset the scientist in multiple respects, he never explicated all of these consequences. The specificity of a scientific prediction depends on the extent of the scientist's knowledge concerning the phenomena under investigation. The paper offers an account of the considerations that determine the extent to which a theory's implications prohibit the occurrence of particular events in the relevant domain. This theory of "predictive degree" both expresses and – as the phenomena of scientific prediction are themselves complex in Hayek's sense – exemplifies the intuition that the specificity of a scientific prediction depends on the relevant knowledge available.