Pancomputationalism is a term encompassing all paradigms of a computational world, which proceed from the realization that nature can successfully be explained by computable scientific models. It takes the concepts of functionalism and computationalism to its ultimate consequences, envisaging a world where all physical processes are carried out by a computer. In other words, it encompasses all paradigms that see the universe as a computer program. The strongest form of pancomputationalism is the paradigm of a digital Turing computable world, but there are opposing paradigms having their own computational models. – Pancomputation – Bibliography – PhilPapers
Your question is about all pancomputationalist models, so I'm going to construct a machine capable of computing all pancomputationalist models (and then some), and show that everything it can compute is compatible with informational realism.
This definition of "pancomputationalism" appears to use a non-standard definition of "computable", given that only the strongest form has a Turing-computable world. So I'll assume that the most powerful hypercomputer I can think of (which is obscenely more powerful than anything I've seen anywhere – far more powerful than could possibly be necessary for even an unimaginably-large computation) is more powerful than the "computable" in this definition. That computer is:
- A multi-tape Turing machine with an unlimited supply of (countably) infinite tapes with a finite number of possible symbols…
- with an arbitrarily-infinitely-large program, so the program size is never a limit…
- with self-consistent time travel of a kind allowing it to (be the sort of algorithm that would) execute a single step and send the modified tape(s) back in time, meaning it immediately receives a tape consistent with the end state of the (hyper*-)computation, making it able to solve halting supertasks – and, given the infinite tape, therefore able to perform calculations on the reals, hence perform calculations over the complex numbers, hence able to simulate countably-infinitely large quantum systems in constant time…
- with a special "contradiction" state that only comes out of time machine when it's absolutely necessary to avoid a contradiction (and is always passed back into the time machine when it comes out), thus making it an Oracle…
- with an unlimited supply of time machines, thus making it a hypercomputer one order higher than itself. (I don't understand infinities well enough to describe the implications of that, but it's at least the countable ordinals.)
This hypercomputer can compute, in constant time, every calculation you could possibly imagine the existence of,1 because the size of your brain is smaller than its unlimited maximum program size. That includes the question of whether it halts if it doesn't halt (which would output the "contradiction" symbol… so much for the halting problem!). It's so obscenely large that anybody trying to use it in a philosophical argument is not really doing philosophy, but pure mathematics.
Specifically, this hypercomputer can perform every finite-order hypercomputation, including just being a bog-standard boring Turing-machine.
Ironically, I couldn't find much information about what informational realism is; Luciano Floridi's 2005 paper cuts out in section 6 just after saying “We are ready for a definition:”. However, bits like:
The problem is deceptively elementary: what is the ultimate nature of reality? The answer is misleadingly simple: it is informational.
A straightforward way of making sense of these structural objects is as informational objects, that is as clusters of data, not in the alphanumeric sense of the word, but in an equally common sense of differences de re, i.e. mind-independent points of lack of uniformity.
In its simplest form, a datum can be reduced to just a lack of uniformity, that is, a binary difference, like the presence and the absence of a black dot, or a change of state, from there being no black dot at all to there being one.
Clearly OOP provides us with a concept of informational objects that is richer than our minimalist approach to informational realism may allow us.
suggest that Floridi is not using a weird non-standard definition of "information" here – or, at least, the standard definition is a subset of Floridi's. Hooray!
My ridiculously overkill hypercomputer has access to an unlimited number of tapes, each of which with a countably infinite number of cells, each of which with a finite number of symbols. If there are n possible symbols, an upper bound for the amount of information stored in each cell is log₂(n) bits. An upper bound for the amount of information in the hypercomputer's working memory is this times some
incomprehensible very large infinity (it is partially-counterfactual, after all), but it's still some amount of information.
Therefore, given the assumption that my hypercomputer can compute all pancomputationalist models (i.e. the accepted definition of pancomputationalism satisfies my constraints), all pancomputationalist models are compatible with informational realism.
This doesn't necessarily apply the other way 'round, because:
- I suspect “informational realism” might be defined more broadly2 than the information-theoretic definition of information; and
- It's almost certain that the accepted definition of pancomputationalism is narrower than my "for the sake of argument" interpretation, in which case it's trivially demonstrable that some models involving informational realism are not compatible with pancomputationalism.
- Even if the accepted definition of pancomputationalism is this insanely broad, I'm not certain (only pretty sure) that all possible informational realism models resembling our universe could be executed even by this hypercomputer; I certainly haven't proven that here.
- But note: informational realism isn't constrained to things resembling our universe (that I could tell; I didn't actually have a definition). The number of possible programs operating on n bits of information is on the order of 2^(2^n), so it doesn't take that much of a restricted definition (e.g. "finite program, infinite universe, otherwise still the ridiculous metahypercomputer") to make it trivially incompatible again.
TL;DR: If I'm talking about the same “pancomputationalism” as you, yes.
1: Assuming you can't construct an even more powerful hypercomputer… but even the finite end of this one's capabilities is larger than necessary for pancomputationalism, if I'm right about what “pancomputationalism” is; this unjustified assumption is not necessary for the argument.
2: Vaguely? It's talking about “a constitutive part of the datum itself” and “the fundamental relation of difference” and I'm not sure whether that's really specific or really broad; all I know is that symbols on tape are close enough to dots on paper to meet the criteria.