Can we do better? I think we can if we directly refer to scientific experimentation instead of coming up with an abstract reconstruction of empirical adequacy. Empirical adequacy should simply be framed in terms of the good predictions of models when they apply to various situations. Thus I suggest the following definition:
A theory is empirically adequate exactly if, for all its models, and for all concrete situations in the world, if the model applies to the situation, then its predictions are correct.
Here it is: that's a pretty simple definition. Now, of course, I need to expand a bit what all this means. This is the aim of the present post. But let me begin with an illustration.
Take as a concrete situation the evolution of the solar system during a certain period of time. A Newtonian model of the solar system applies to this situation if it correctly describes the planets and the sun, with their respective initial positions and masses. It makes good predictions if the evolution of the position of planets in the model correspond to the positions that we could observe in this situation. If this is so, then our model of the solar system is empirically adequate for this situation. If all models of the theory that we could apply in the world are empirically adequate for all situations to which they apply in the world, then our theory is empirically adequate.
I will now explain in more details what I mean by situation, application and prediction.