I assume you mean the metaphysical status of propositions. The propositional calculus doesn't give much insight into determining what a proposition is--after all, it takes propositions for granted and attempts to develop a formal analysis of them. Similarly, mathematics won't tell you what a set is, but simply stipulate set axioms that are intended to model what we already understand a set to be.
However, the question has been approached pretty famously by Frege, Russell, and many others--you may be interested to see the debates on the topic. While there isn't unanimity on the answer to the question, I would claim that the "intended proposition" of a simple sentence is the set of all equivalent thoughts which the speaker attempts to communicate; the "public proposition" actually expressed by a simple sentence is the set of equivalent thoughts that a linguistic community tends to agree are expressed by the sentence.
To give just two important other notions of what propositions are: For Frege, they are abstract objects that refers to their truth-conditions. For modal realist David Lewis, propositions are sets of possible worlds.