Are equations like F=MA or e=mc squared metaphysical statements about energy and force or are they empirical observations about regularly occurring correlations?

I think you can safely take them either way. You could take them to be more or less definitional of the terms involved. In that case the empirical question would be whether the terms pick out real quantities in nature. Or you could take the terms to pick out independently identifiable quantities and then they would be empirical statements.

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