Support functions $s(h,e)=p(h\backslash e)-p(h)$ are widely used in discussion of explanation, causality and, recently, in connection with the possibility or otherwise of probabilistic induction. With this latter application in view, a rather complete analysis of the variety of support functions, their interrelationships and their "non-deductive" and "inductive" components is presented. With the restriction to two propositions, three variable probabilities are enough to discuss such problems. The analysis is illustrated by graphs, a Venn diagram and by using the Laplace Rule of (...) Succession as an illustrative example. It is concluded that within this framework one cannot prove or disprove the possibility of probabilistic induction. (shrink)