> The question is, are there any properties a biological system can have that are not encoded in its physical constituents? Anyone answering ‘yes’ to that question really needs to provide a very clear answer as to how they think that might be possible and how else that property might arise.

I believe the answer is that there are properties which only come into existence once you have the right physical arrangement, but these properties can't be predicted in advance from the physical constituents.

As to how it could be possible that truly novel properties come into existence, that's not really different than how it can be possible that QM can have indeterminate properties, or anything that's physically fundament for which we have no explanation. Something happens to exist, and we don't know whether there is answer to why anything exists.

There's also other possibilities, like the existence of abstract and universal entities, such as numbers or universals. How is it that every electron has the exact same charge and mass? Is electron a universal? Why does math work so well for physics? Are there laws of nature that govern the world (make it be a certain way as opposed to just being regularities)? That sort of thing.

>I believe the answer is that there are properties which only come into existence once you have the right physical arrangement, but these properties can't be predicted in advance from the physical constituents.

In order for such properties to not be predictable from the physical constituents, they must not be encoded in the physical constituents. If they are encoded in the physical constituents, then they must be predictable from them.

If these properties are not encoded in their physical constituents, where does the information come from and where is it represented?

Supervenience is the relation of being made of a substrate, but not predicted by its laws. Supervenience is distinct from entailment, you are conflating the two. https://en.wikipedia.org/wiki/Supervenience

Suggesting that the natural laws are such that all behavior must be entailed by "lower level" natural laws, is a stronger position than stating that all things follow natural law. I think it is hubristic to think that somehow our understanding of natural law is exempt from the same issues that are raised by the incompleteness theorem in math.

Can you always recover all physical information?

I would be interested in seeing if two neural network models with equivalent topology and weights could always be said to 'have' the same subject matter. (It's a better example than for-loops, because I think both brains and computers can embody what it means to have a neuron in a close-enough fashion).

I would expect the answer would be "no". You would have to know about the environment that trained them, which blows the door open for something which is irreducible without knowing about environmental conditions, and biology having too rich of an environment to be as precisely reducible as computers might ever be without them being also a computer system.

In my other posts in this thread I emphasize the "in-principle" and "in-practice" distinction because I don't believe it is the "in-principle" part of reductionism that ought to be at stake. It's if we can actually do it in a way that doesn't invite approximations.