   During the period in which Russell was working on Principia Mathematica, most likely in 1907, Russell also radically revised his former realism about propositions understood as mind independent complexes. The motivations for the change are a matter of some controversy, but there are at least two possible sources. The first is that in addition to the logical paradoxes concerning the existence of classes, Russell was aware of certain paradoxes stemming from the assumption that propositions could be understood as individual entities. One such paradox was discussed already in Appendix B of POM (527–28). By Cantor’s theorem, there must be more classes of propositions than propositions.  However, for every class of propositions, m, it is possible to generate a distinct proposition, such as the proposition that every proposition in m is true, in violation of Cantor’s theorem. Unlike the other paradoxes mentioned above, a version of this paradox can be reformulated even if talk of classes is replaced by talk of their defining propositional functions.  Russell was also aware of certain contingent paradoxes involving propositions, such as the Liar paradox formulated involving a person S, whose only assertion at time t is the proposition All propositions asserted by S at time t are false. Given the success of the rejection of classes as ultimate entities in resolving the paradoxes of classes, Russell was motivated to see if a similar solution to these paradoxes could be had by rejecting propositions as singular entities.