Symmetries as by-products of conserved quantities

•The Received View (RV) is not a philosophically uniform interpretation.•Solution equivalent Lagrangians imply that a strong RV is wrong.•By fixing the Lagrangian, RV is not ruled out, but becomes redundant.•Prop: conserved quantities are sufficient conditions for symmetrical descriptions.•Proposal is philosophically uniform, and it is independent of Lagrangian choices.

There is general consensus among physicists in considering symmetries as a source of conserved quantities, a conclusion allegedly supported by Emmy Noether׳s theorems. Recently it has been pointed out that no arrow of explanation can be extracted from Noether׳s work, and there are also criticisms against the priority of particular symmetries over specific conserved quantities under Noether׳s ideas, but there are no general arguments against the aforementioned consensus, nor proposals promoting an explanation that leads from conserved quantities to symmetries. In this paper a general argument is built which favours conserved quantities over symmetries inasmuch as the presence of the former seems to allow (i.e. it seems to be a sufficient condition leading to) symmetrical descriptions.