Comment by Kim_Bruning

You elided the word "Empirical". Say his wife made it empirically as water-tight as she can: for instance she hires a PI who follows him 24/7. The PI finds nothing out of the ordinary. How is this even still cheating?

Maybe he was cheating before or after, sure, but not during. No court would buy that.

...At least, that's how I interpret 'empirical consequence' - something observable or detectable, at very least in principle. Do you mean something different?

(Right this minute I'm coming from an empiricist framework where acts require consequences. If you're approaching this from a realist or rationalist view -which I suspect-, I'd be interested to hear it!)