Clash of titans?

Are Mises's definition of "economics" and Hayek's definition of "market" incompatible with each other? Mises defines economics as the science whose study subject is purposeful behavior. On the other hand, Hayek stresses the fact that a spontaneous order is by itself purposeless, it doesn't have a purpose of its own. Relating these two odeas, one could be led to the perplexing conclusion that economics doesn't deal with the analysis of the spontaneous order of the market. Since this doesn't seem to match common sense or the usefulness of economics, then either Mises or Hayek or both have not the most useful definition of their respective concepts, or the relation above between the definitions of economics and spontaneous order is not the most suitable. I feel that the problem is with Mises.