It is pointed out that some already-known inequalities (Bell's inequalities) and some new ones presented here can be used to test experimentally the validity of a general conception of the foundations of microphysics. This conception mainly consists in considering sets of propositions (having the structure of lattices but possibly of non-Boolean ones) and in assuming that when a proposition is true on a system S this constitutes an intrinsic property of S, which can be neither imparted to S nor withdrawn from S as long as S is "isolated." It is shown that if experiments of the type of those used to test Bell's inequalities turn out to corroborate the quantum-mechanical predictions, such a result could be used in order to invalidate directly the general conception just described. This is done without reference to the general principles of quantum mechanics. More generally, our derivation does not depend for its validity on assuming the truth of any particular physical theory abstracted by induction from experimental knowledge.