I'm having trouble defining your definition of counterfactual. In "Information is a Counterfactual...", you define a counterfactual property as one which only conveys information if the property could have been in a different state. This makes sense relative to the previous uses of "counterfactual" I'm familiar with.

In this piece, you introduce the category of "counterfactual law in physics" including the one "that says ‘it is impossible to build a perpetual motion machine’." Are these two different uses of the word 'counterfactual', in which case can you explain what a counterfactual law is? 

Or (more likely) is the connection obvious and I'm too dense to see it, in which case, can you explain what the lamp's lightedness-status (first post) and the physics law (this post) have in common that makes them counterfactual?

I think this was well-written and clear, so good job there! I also happen to disagree with the contents.

First off, I'm highly suspicious of any definition of a "prevailing conception" of physics that excludes the second law of thermodynamics! It seems like in actual practice, sometimes people make predictions by simulation, (the "PC") sometimes they make predictions by generalizing about the character of physical law (the quantum gravity example), and sometimes they do something in between those things and make abstractions/generalizations but then treat those abstractions as tools to do simulation (condensed matter theorists I see you).

And so what does it mean to recast physics in a different picture? Does this mean people are going to be rendered unable to do simple simulations about what actually happens when you shoot a particle at a barrier? No, that would be madness - you either give people the tools to do such calculations, or you get laughed out of the room.

So then does it mean that we're going to be able to make new exciting arguments that physicists were unable to make before? I mean, I'd love it if this were true, but I'm skeptical. My cynical side expects that there will be few new sorts of arguments, but plenty of flag-planting on old sorts of arguments.

Explaining the Turing principle using the PC is difficult. In, fact it is difficult enough to state the Turing principle in the language of the PC

The Church Turing thesis is a fact about computation as well as physics. As such , there is no particular reason it should be easily expressed in physics.

They can all be broadly framed as: ‘How can we be sure that laws which apply in one situation generalise to other situations?’. These questions are solved by taking Karl Popper’s approach to science, where scientific theories are viewed as conjectures, tentatively put forward to solve problems

Emphasis added.

Poppers approach doesn't solve the problem as stated, because it disregards certainty. Other approaches can also address the problem of induction by replacing certainty with probability.

We know this because there is a broad counterfactual law in physics that says ‘it is impossible to build a perpetual motion machine’.

Well, it's not really a law as such , because it's an outcome of more general laws such as the second law of thermodynamics. And since the second law is a macroscopic law, it's only macroscopic perpetual motion machines that are impossible. Any stable atom is a little PM machine.

Because the claim that energy is bounded from below is itself a counterfactual principle

Sure, but that doesn't mean it isn't a physics principle, or needs some novel explanation. Any deterministic law makes a bunch of things impossible....the determined outcomes happens of necessity, everything else is impossible.

The reason for this is that the second law is also a counterfactual principle which cannot be expressed in the PC.

!!!!!!!

As it stands, reconciling the irreversible second law with reversible dynamical laws in the PC is impossible without resorting to some sort of averaging or coarse-graining

I can think of two other solutions:

1. The 2LT is only an approximation, and things actually do cycle round to a low entropy state after a sufficiently long period.

2. Reversible microphysical laws are only special cases of irreversible macrophysical laws.