 This attitude required Church to accept not only first order logic but also the logic of second and higher orders, so that he could study logic in all its generality. It was not enough to accept, for example, “\((x) F(x) \supset F(y)\)”, because there are infinitely many sentences of this form requiring one to also accept “\((F)(y) \hdot (x) F(x) \supset F(y)\)” “by generalization from infinitely many analytic sentences of the appropriate form” (1962b [BE: 608]). (Note Church’s notational convention that a dot placed before a connective or (as above) a quantifier brackets a proposition.)