I'm doing a MOOC on mathematical philosophy and the lecturer drew a distinction between a proposition and a statement. This is very puzzling to me. My background is in math and I regard those two words as synonymous. I looked on Wikipedia and it says:
Often propositions are related to closed sentences to distinguish them from what is expressed by an open sentence. In this sense, propositions are "statements" that are truth bearers. This conception of a proposition was supported by the philosophical school of logical positivism.
This also went right over my head. I (naively) regard both a proposition and a statement to be well-formed formulas that, once a suitable interpretation is chosen, have the ability to be either true or false. For example 2 + 2 = 4 is a proposition or statement because once I assume the Peano axioms along with the usual interpretations of the symbols '2', '4', '+', and '=', this statement is capable of being determined to be true or false.
Can anyone shed some light?