This is an approach I considered back in 1990something actually, and at the time I actually considered it correct. I get the idea. We say that the "finding algorithm" somehow detracts from what is running. The problem is, this does not leave a clearly defined algorithm as the one being found. if X is found by F, you might say that all that runs is a "partial version of X" and that X only exists when found by F. This, however, would not just apply to deeply hidden algorithms. I could equally well apply it your brain. I would have to run some sort of algorithm, F, on your brain to work out that some algorithm corresponding to you, X, is running. Clearly, that would be nothing like as severe as the extreme situations discussed in that article, but what does it mean for your status? Does it mean that the X corresponding to you does not exist? Are you "not all there" in some sense?

Here is a thought experiment:

A mind running in a VR system (suppose the two are one software package to make this easier) gradually encrypts itself. By this I mean that it goes through a series of steps, each intended to make it slightly more difficult to realize that the mind is there. There is no end to this. When does the mind cease to exist? When it is so hard to find that you would need a program as long as the one being hidden to find it? I say that is arbitrary.

You suggest that maybe the program running the mind just exists "partially" in some way, which I fully understand. What would the experience be like for the mind as the encryption gets more and more extreme? I say this causes issues, which are readily resolved if we simply say that the mind's measure decreases.

I can also add a statistical issue to this, which I have not written up yet. (I have a lot to add on this subject. It may be obvious that I need to argue that this applies to everything, and not just minds, to avoid some weird kind of dualism.).

Suppose we have two simulations of you, running in VRs. One is about to look in a box and see a red ball. The other will see a blue ball. We subject the version that will see the blue ball to some process that makes it slightly harder to find. You don't know which version you are. How much will you expect to see a blue ball when you look in the box? Do you say it is 50/50 that you will see a red ball or a blue ball? We keep increasing the "encryption" a bit each time I ask the question. If your idea that somehow the mind is only "partial" by needing the finding algorithm to find it is right, I suggest we end up with statistical incoherency. We can only say that the probability is 50/50 when the situations are exactly the same, but that will never be the case in any real situation. For any situation, one mind will need a bit more finding than the other.

In other words, if you think the length of the finding algorithm makes the algorithm running a mind somehow "partial", in a statistical question in which you had two possibilities, one in which your mind was harder to find than the other, and you don't know which situation you are in, when would you eliminate the "partial" mind as a possibility? If you say, "Never. As the encryption increases I would just say I am less and less likely to be in that situation" you have effectively agreed with me by adopting an approach where each mind is as valid as the other (you accept either as a candidate for your situation but treat them differently with regard to statistics - which is what I do). If you say that one mind cannot be a candidate for your situation then you have the issue of cut-off point. What cut-off point? When would you say, “This mind is real. This mind is only partial so cannot be a candidate for my experience. Therefore, I am the first mind?”

I would point out that I do not ignore these issues. I address them by using measure. I take the view that a mind which takes more finding exists with less measure, because a smaller proportion of the set of all possible algorithms that could be used to find something like it will find something like it.

Finally, this only deals with one issue. There is also the issue of combining computers in the statistical thought experiments that I mentioned in the first article of that series. My intention in that series is to try to show that these various issues demand that we take a particular view about minds and reality to maintain statistical coherency.