  In this paper we propose an interpretation for self-referential propositions
in a "meta-model" N* of ZF. This meta-model N* is considered as an informal
model of arithmetic that mathematicians often use when working with number
theory. Specifically, we assume that within this meta-model, the axiom system
ZF is applied, interpretations for sentences can be offered, and natural
language can be used. We show that under the proposed interpretation, some
types of self-referential propositions that are considered legitimate in
mathematics turn N* into an inconsistent model, and examine the connection of
this result to a certain interpretation of godel's first incompleteness
theorem. Some general problems which follow from the above discussion are then
addressed.
