 This Russellian constraint on class abstraction, however, had the consequence that with impredicative ‘class abstracts’ of the form “the class of all x such that Φ(x)”, the existence of such a class could not be guaranteed as a matter of logic. So Russell had to postulate that such classes existed. This came to be regarded as detracting from their status as would-be logical objects, and revealing them instead as no more than mathematical posits. Their existence was once again (at best) a synthetic a priori matter, rather than one of analytic necessity and certainty. 