 Church’s philosophy of logic was shaped not only on the one hand by a belief in the generality of logic but also on the other by the need to avoid the paradoxes to be discussed in  section 4.  In order to avoid the paradoxes to which Frege’s position lead, Church was forced to work primarily within a type-theoretic framework—the logic of second, third and higher orders up to and including w—with different kinds of variables, with different restricted domains of individuals, classes, relations, etc. (Church’s type theory is described in  supplement D.)  Moreover, as we will now see, Church departed even further from Frege and Russell by presenting these ideas in terms of conventional model theory.