 Solution

Empirical equivalence must be stronger than agreement with the evidence already collected: relative to a stated domain, empirically equivalent theories yield the same possible observational consequences. If they nevertheless make incompatible claims about unobservable entities, observations in that domain cannot alone determine which ontology is correct. This is a strong form of scientific underdetermination, directed against a unique inference from empirical success to full theoretical truth.

The scientific realist has several responses. One may deny that every formally constructed alternative is a serious physical rival, appeal to independently justified explanatory virtues, or restrict commitment to the structure genuinely shared by the alternatives. If two descriptions are connected by a change of variables or a gauge transformation, apparent difference may be representational rather than a disagreement about the world. Before calling such a pair a counterexample, identify what incompatible physical claims remain.

Actual and merely possible rivals have different evidential force. An actual, comparably developed rival demonstrates that the current inference is nonunique under specified criteria. A merely possible rival refutes a claim of logical entailment if its possibility is established, but does not automatically defeat ordinary fallible justification: otherwise any unexcluded sceptical possibility would defeat almost every empirical belief. A distant conceivable alternative need not deserve the same prior probability or explanatory standing as a well-tested account.

Consequently, empirical equivalence is a serious challenge to unrestricted, uniquely determined theoretical belief. It is not a deductive disproof of all scientific realism. A convincing argument must say whether the target is certainty or defeasible warrant, whether equivalence covers all observations or only present data, and why the rivals are physically distinct. Merely announcing that another story could be invented leaves these crucial questions unanswered.