 Tennant (1987) argues that a condition of adequacy for any logicist theory is to explain the applicability of the finite cardinals (see p. 234). Let ∃nxFx be the formula of first-order logic with identity, defined inductively in the usual way, that says that there are exactly n Fs. Let n be the numeral denoting the natural number n, that is, “s…s0”, with n occurrences of the successor symbol s. Schema N is the following biconditional, an instance of which is obtained by fixing on a particular natural number n and open formula Φ. 