|Equivalence: Relation between sentences. It exists if both sides have the same truth value, so that they are both true or both false.|
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Empirical equivalence: about empirical adequacy: there is a model so that all phenomena are identifiable with movements in the model (also historical, not perceived ones) - empirically equivalent: are two theories if they have both models that do that.
Relative equivalence/Fraassen: (relative to background knowledge): we recognize sodium because it has - a) this spectrum - b) this atomic structure - asymmetry: the spectrum does not generate the atomic structure. However, there is equivalence. Yet, only one equivalence is relevant. Equivalent propositions are true in the same possible world. - Nevertheless, we can say that some possible worlds are excluded - (in which the proposition is irrelevant).
Equivalence: has indistinguishability, due to the same set of possible worlds - solution: distinction by means of making it true - e.g. a) either it rains or it does not rain - b) ...snows or does not snow - difference: a) is made true by the fact that it rains, b) by the fact that it does not snow - relevance of propositions depends on deeper relevances.
B. van Fraassen
The Scientific Image Oxford 1980