It's a statement that describes (and predicts) empirical phenomena.

I echo Marchesk's response. 'e=mc2' cannot be understood as an empirical statement. It says in ordinary language something like 'energy equals mass multiplied by the speed of light squared'. None of these bar the speed of light is empirically observable, and even whether that is is arguable.

My point is just that if the statement is not intelligible as an empirical statement, that is in terms of observable phenomena, then how is it intelligible; that is, what entities are being posited in order to render it intelligible?

It is not even strictly a statement that predicts observable phenomena as those predictions are not explicit in the statement but are inferences to what might be expected if the hypothetical entities or properties 'energy' and 'mass' ( as well as other hypothetical entities such as uranium atoms, electrons, protons and neutrons and so on) actually are and behave as the formula says they should be and behave. I believe most physicists would interpret the extraordinary success of the predictions to count as empirical evidence ( the only kind of evidence in this kind of connection we could ever have) that the 'extra-empirical' (causal) 'realm' is ( more or less) as we have modeled it.

Although there can never be 'proof' that such an interpretation is correct, I can see no serious reason to doubt that it is.

The fact is that you cannot give any ordinary English interpretation of this formula that does not involve a position of the existence of these hypothetical (meta-empirical) entities and properties. Unless you can come up with an alternative account then I think intellectual honesty demands that you owe allegiance to belief in their existence.

I believe most physicists would interpret the extraordinary success of the predictions to count as empirical evidence ( the only kind of evidence in this kind of connection we could ever have) that the 'extra-empirical' (causal) 'realm' is ( more or less) as we have modeled it. — John

Right, so as I said before you're adopting scientific realism. But the internal realist wouldn't adopt scientific realism. They'd adopt something like instrumentalism or model-dependent realism.

Well, I said "most physicists" not "I", but it is true that I don't see any serious alternative. The fact that I don't see any serious alternative does not, though, mean that I have to "adopt scientific realism". In other words 'accepting' is not the same as 'adopting'.

You still haven't explained how any other position would render 'e=mc2' as an intelligible sentence in ordinary language.

You haven't explained, that is. how a (philosophical) adoption of instrumentalism or model-dependence could be really, as opposed to merely superficially appearing to be, coherent.

You still haven't explained how any other position would render 'e=mc2' as an intelligible sentence in ordinary language.

You haven't explained, that is. how a (philosophical) adoption of instrumentalism or model-dependence could be really, as opposed to merely superficially appearing to be, coherent. — John

I'm not here to defend instrumentalism or model-dependent realism. I'm just explaining internal realism to you as you asked about it.

It's a statement that describes (and predicts) empirical phenomena. — Michael

Right, but it employs math and theoretical entities, as John mentioned.

Right, so as I said before you're adopting scientific realism. But the internal realist wouldn't adopt scientific realism. They'd adopt something like instrumentalism or model-dependent realism. — Michael

In the context of scientific laws and theories, it's more a matter of rationalism vs empiricism, where empiricism alone can't get you to something like e=mc2. And it also goes back to Plato and the universalism debate. The shadows on the cave wall don't give you the forms. In scientific terms, the empirical data doesn't provide the theory. That's something humans add to make sense of the data. The realist question is whether that addition exists independent of us, or is made up by us, or is due to our constitution as cognitive agents (Kantian categories).

In the context of scientific laws and theories, it's more a matter of rationalism vs empiricism, where empiricism alone can't get you to something like e=mc2. And it also goes back to Plato and the universalism debate. The shadows on the cave wall don't give you the forms. In scientific terms, the empirical data doesn't provide the theory. That's something humans add to make sense of the data. The realist question is whether that addition exists independent of us, or is made up by us, or is due to our constitution as cognitive agents (Kantian categories). — Marchesk

The question is a mistake in the first instance. Relationships like e=mc2 are an expression of the functioning empirical world. To ask whether, for example, e=mc2 exists doesn't make sense. It's not a state of the world. As a logical expression of states of the world, it is not an existing object itself. We can't look out in the world and find and e=mc2 anymore than we can find the meaning of "red" sitting on the road.

Relationships like e=mc2 are an expression of the functioning empirical world. To ask whether, for example, e=mc2 exists doesn't make sense. It's not a state of the world. — TheWillowOfDarkness

Maybe. It is curious though how well something like e=mc2 works. As if there is something more than just the observables.