 (Note the following notational conventions. Firstly, a connective can take a variable as subscript: that variable becomes a universal quantifier whose scope is precisely that of the connective. Secondly, a dot placed before a connective brackets a proposition. The stars are also Church’s notation.) Church decides to avoid the stronger axiom asserting that \(D\) is functional due to complications concerning identity in the ramified theory, but the effect is the same. The  axiom *  guarantees a weaker form of functionality: It is a function from words as individuals to extensions of propositional functions, assuming the axiom of extensionality for such extensions. Next Church invokes an informally stated principle that he describes as “reasonable”: