If we assume a prexisting algorithm for the universe already (which most people here seem to do), then everything else could be derived from that, including all axioms of natural numbers, since we assume the algorithm to be more powerful then them at the start. Step b) is simply postulated to be already fulfilled, with the algorithm just being there (and “just being there” is not an algorithm), so that we already have an algorithm to start with (the laws of nature).
The “laws of nature” simply have to be taken as granted. There is nothing deeper than that. The problem is that then we face a universe which is essentially abitrary, since from what we know the laws could be anything abitrary else as well (these laws would just be the way they are, too). But this is obviously not true. The laws of nature are not abitrary, there is a deeper order in them which can’t stem from any algorithm (since this would just be another abitrary algorithm).
But if this is the case, I believe we have no reason to suppose that this order just stopped working and lets do one algorithm all the rest. We would rather expect it to be still continuously active.
Then the argument works. The non-algorithmic order can always yield more powerful seed AIs (since there is no single most powerful algorithm, I think we can agree on that), so that AI is not sufficient for an ever increasing general intelligence.
So we face a problem of worldview here, which really is independent of the argument and this is maybe not the right place to argue it (if it is even useful to discuss it, I am not sure about that, either).
I see in which case my argument fails:
If we assume a prexisting algorithm for the universe already (which most people here seem to do), then everything else could be derived from that, including all axioms of natural numbers, since we assume the algorithm to be more powerful then them at the start. Step b) is simply postulated to be already fulfilled, with the algorithm just being there (and “just being there” is not an algorithm), so that we already have an algorithm to start with (the laws of nature).
The “laws of nature” simply have to be taken as granted. There is nothing deeper than that. The problem is that then we face a universe which is essentially abitrary, since from what we know the laws could be anything abitrary else as well (these laws would just be the way they are, too). But this is obviously not true. The laws of nature are not abitrary, there is a deeper order in them which can’t stem from any algorithm (since this would just be another abitrary algorithm). But if this is the case, I believe we have no reason to suppose that this order just stopped working and lets do one algorithm all the rest. We would rather expect it to be still continuously active. Then the argument works. The non-algorithmic order can always yield more powerful seed AIs (since there is no single most powerful algorithm, I think we can agree on that), so that AI is not sufficient for an ever increasing general intelligence.
So we face a problem of worldview here, which really is independent of the argument and this is maybe not the right place to argue it (if it is even useful to discuss it, I am not sure about that, either).