Axiom T for physical possibility

Here is an argument for naturalism:

1. Only states that can be described by physics are physically possible.

2. Non-natural states cannot be described by physics.

3. Physical possibility satisfies Axiom T of modal logic: If something is true, then it’s physically possible.

4. So, non-natural states are physically impossible. (1 and 2)

5. So, non-natural states do not occur. (3 and 4)

I am inclined to think (1) is true, though it is something worth pushing back on. I think (2) is close to trivial.

That leaves me a choice: accept naturalism or deny that Axiom T applies to physical possibility.

I want to deny that Axiom T is a good axiom for physical possibility. The reason isn’t just that I think (as I do) that naturalism is actually false. The reason is that I think the axioms of physical possibility should hold as a matter of metaphysical necessity. But if Axiom T for physical possibility held as a matter of metaphysical necessity, then naturalism would be metaphysically necessary. And that is really implausible.

Yet Axiom T is very plausible. What should we do about it? Here is one potential move: Axiom T holds when we restrict our statements to ones formulated in the language of physics. This escapes the implausible conclusion that non-natural states are metaphysically impossible. But holding even this restricted axiom to be an axiom, and hence metaphysically necessary, still rules out the metaphysical possibility of certain kinds of miracles that I think should be metaphysically possible. So I think my best bet is to throw out Axiom T for physical possibility altogether. As a contingent matter of fact, it holds typically for statements formulated in the language of the correct physics. But that’s all.

Physical possibility

Here is an interesting question: How can one tell from a physics theory whether some event is physically possible according to that theory?

A sufficient condition for physical possibility is that the physics assigns a non-zero chance to it. But this is surely not a necessary condition. After all, it is possible that you will get heads on each of infinitely many tosses of an indeterministic die, while the chance of that is zero.

Plausibly, a necessary condition is that the event should be describable within the state space of the theory. Thus, the state space of classical mechanics simply cannot describe an electron being in a superposition of two position states, and hence such a superposition is physically impossible. But this necessary condition is not sufficient, as Newtonian mechanics bans various transitions that can be described within the state space of classical mechanics.

So, we have a necessary condition and a sufficient condition for physical possibility relative to a physics theory. It would be nice to have a necessary and sufficient condition.