Before playing with any toy formal systems, I would like to take a moment to express another philosophical motivation for adopting Tegmark’s proposal. For a long time I have been bothered by the apparent distinction between actuality and possibility. In other words, what does it mean for something to be actual as opposed to merely possible? I have always felt that to make a substantial distinction between actuality and possibility, one is forced to invent strange modes of existence, one for some “diminished” level of existence or bizarre non-existing existence, and one for a “distinguished” level of existence or “real” existence. I cannot help feeling that this is quite artificial. In the set of all possible worlds, why should there be a distinguished member?
From our perspective, of course, this seems intuitive. We experience some things as “actual” and other things we recognize as possible, but they do not obtain in our world. In other words, some things could be, but are not. Yet, to draw a strong distinction seems a mistake akin to thinking that the Earth is the center of the universe because it appears that way from our perspective. In reality, there is no preferred point in space and, by analogy, it seems reasonable that there is no preferred possible world either.
Being a form of modal realism, this is the thesis of the MUH. All possible worlds exist on equal footing. They are all of the same kind as our world. Ironically, looking at matters this way gives coherent meaning to the terms “actual” and “possible”, but instead of inventing convoluted or mysterious modes of existence, these become relative terms. The term “actual” simply refers to the world in which we find ourselves and “possible” refers to any other world. Of course, in any other world, its inhabitants, if it has any, will consider their world to be actual and ours to be possible. Another way of saying this is that actuality is indexical. Again, one can use relativity as an analogy. Each system has its own “preferred” (with respect to itself) reference frame from which it judges everything else. Objectively speaking, however, no reference frame is preferred over another. Or think of how each person deems his/her location as ‘here’. There is no objective ‘here’, it depends on the observer.
This brilliant solution is just one of the many recommendations the MUH enjoys!