The numerical value of a dimensionful constant depends on the system of units you're measuring it in; that of a dimensionless constant doesn't.
Well yes, but who cares about the numerical value? Hold the system of units constant and look at the actual physics!
New Salt Compounds Challenge the Foundation of Chemistry
The title is overblown (it depends on what you think the foundation is), but get a load of this:
And here's the philosophical bit:
The obvious example of local truth is relativistic effects being pretty much invisible over the durations and distances that are normal for people, but there's also that the surface of the earth is near enough to flat for many human purposes.
Any suggestions for other truths which could turn out to be local?