Perhaps it’s illuminating to turn the reasoning around: What if physical and logical possibility do not coincide? Then, it would seem, we would have logical possibilities that are not physical (owing to the logical possibilities superseding the physical ones). But what then chooses which possibility to realize physically? Is there some sort of selection principle? Of what sort, of what status would this be? If it was dictated by logic, then the laws of logic would uniquely determine the laws of physics. But, if it was a physical law (however that might be possible), then, although the laws of logic underdetermine the laws of physics by themselves, those possible physical laws somehow ‘determine themselves’, in which case, again, the laws of logic suffice to set the laws of physics.

The other possibility (barring supernatural intervention, about which to try to reason would be useless) would be that there is an element of fundamental randomness in what physics is selected from logic. But then, one is faced with some difficulty: what, among all the possible physics, sets the ‘real’ one apart from the rest? What breathes fire into the equations? This posits a curious élan vital that a certain set of physical laws needs to possess (or be possessed by?) in order to be ‘actual’, rather than merely ‘possible’. This isn’t an attractive position, for this animating force can neither be physical nor logical, as in both cases, physics would follow uniquely from logic, and the randomness posited would merely be apparent.

Another way to look at this is that there is, in fact, little difference between the merely logically possible, and the physically actual: Let’s say logic allows certain mathematical structures – those which are consistent, to impose some minimal criterion. What would the difference ‘from the inside’ be for a structure that is physically real, that contains physical possibilities, as opposed to one that is merely a logical possibility, one that ‘might have been’ physical? Well, in both cases, we certainly can do the same things we do in the ‘real world’ in order to abstract predictions from the underlying physical laws: where, in the real world, we might get a prediction for the decay of a free neutron into a proton, an electron, and an electron-antineutrino, in the merely possible world, we could do similar things to arrive at an x-particle decaying into y and z-particles. We could study their interactions, how they, perhaps, bind together, form new structures of increasing complexity with emergent properties, and in the real world, this would eventually lead us to ourselves, to our interactions with the environment, and to the observations we make about it.

But the same thing is, in principle, possible in the fictional, logically possible world (although it’s possible that no sufficient complexity can be achieved in whatever structures we’re studying). There, too, we would arrive at some sort of (fictional) ‘beings’ that interacted with their (fictional) environments, and that can make (fictional) observations, and, if you believe that consciousness is nothing more than a suitably complicated computer program, i.e. a mathematical structure, they might be just as conscious of these things as we are – fictionally, of course. But what’s the difference between fictional and real consciousness? Well, to them, there can’t be any – just as in the real world we might arrive at some mathematical expression describing our being conscious of, say, a neutron decaying, in our fictional world, we arrive at a mathematical expression of our fictional beings being conscious of an x-particle decaying, and there’d be no way of deciding, from these expressions alone, which one applies to the real, and which to the fictional world. The subjective perception of the beings in the fictional world does not differ from our own subjective perception – like wrestling, it’s real to them!

This is more or less what Max Tegmark calls ‘self-aware substructures’ in his mathematical universe hypothesis, which is one framework in which indeed logical and physical possibilities coincide.

So the conclusion it seems this is meandering towards is that either the logically and physically possible are equivalent, or one needs a selection principle, something to breathe fire into the equations, some vital spirit that is of neither kind to distinguish one from the other; this, to me, however, is just the same as an appeal to the supernatural, which is, as far as the quest of finding things out is concerned, utterly devoid of content.