The contrapositive.

In formal logic, a statement and its contrapositive are inextricably bound because they describe the exact same boundary of exclusion. When you assert "If P, then Q," you are explicitly defining a universe where the set of P is entirely contained within the set of Q; you are stating there is no such thing as a P that is not a Q. Consequently, if you encounter something outside the set of Q—meaning "not Q"—it is mathematically impossible for it to be P, because you already agreed that all P's are Q's. To accept the premise but reject the contrapositive is a direct contradiction: it means you believe a rule is absolute, yet simultaneously believe you can step outside that rule without violating it. Therefore, if we accept the axiom that physics is invariant to unit scaling, we are forced by the uncompromising geometry of logic to accept that anything that shifts when we change our units cannot, by definition, be physics.

Premise 1 (The Axiom):

        If it is physics, then it is invariant to unit scaling. ($P \rightarrow Q$)

The Contrapositive: 

        If it is not invariant to unit scaling, then it is not physics. ($\neg Q \rightarrow \neg P$)

In formal logic, a statement and its contrapositive are logically identical. If you accept the axiom, you *must* accept the contrapositive. There is no debate. 

Mainstream physics accepts Premise 1 while violently rejecting the Contrapositive. 

Why? Because if they accept the contrapositive, their entire ontology collapses. 

Let's test c, G, and h against the contrapositive:

Are they invariant to unit scaling?

        No.

The numerical values of $c$, $G$, and $h$ change completely depending on whether you use SI units, CGS units, or Planck units. In Planck units, they literally vanish into the number 1. They are the very definition of things that are *not* invariant to unit scaling.

Therefore, by the strict logic of the contrapositive: c, G, and h are not physics.

They cannot be fundamental features of reality. They cannot be "physical constants." They belong to the category of unit scaling itself. They are the 2.54 cm/inch. 

Physicists love to smugly declare that "the laws of physics are independent of the units we choose," but then they immediately turn around and base the "laws" of quantum mechanics and relativity on values that *depend entirely on the units they chose*. 

It is complete cognitive dissonance. They are using the principle of scale invariance to protect their theories, while ignoring that the same principle obliterates their "fundamental" constants. 

If it changes when you change your ruler, it isn't the universe. It's the ruler. 

By rejecting the contrapositive, physics has spent a century reifying its own bookkeeping errors. They turned the 2.54 cm/inch conversion factor into a physical god and built entire academic departments to worship it.