The big philosophical problem is the question of what is the true nature of existence. In the context of the present discussion, there are two ideas that I think we should exclude upfront.
Pretty much all of philosophy is unfalsifiable, at least the valid views. I agree with your list (both versions of solipsism) because indeed, both render empirical evidence meaningless. Perhaps MUH does as well, per my post just above. To you list I would add any kind of anthropocentrism. Both in your list are versions of it, and I name the more general case. Nothing can really be known about the nature of reality if reality is all about me.
The first idea is the problem of hard solipcism. Solipcism is the claim that we cannot be sure that
anything exists, apart from our own minds. Actually,
you can't be sure that
my mind exists, except as some notion in your mind. This means that there's no way to know whether ducks - or anything else normally considered external to your mind - actually exist separately from your mind.
We come, then, to Tegmark's claim that the universe is mathematics. One thing to note, before we go on, is that if the simulation hypothesis is correct, that doesn't support Tegmark's hypothesis.
What you described in your post is a VR hypothesis, a version of solipsism. Tegmark does not seem to suggest anything of the kind. He says mathematics is fundamental. Both the simulation and the VR thing posit a more fundamental reality on which our reality is being implemented. So no machine under the mathematics. Nobody seems to get that.
[/QUOTE]So, let's step away now from these unfalsifiable philosophical hypotheses and accept, for the sake of argument, that you really do exist separately from ducks (that they aren't just things in your head) and that, as far as we can tell, our universe is "real"[/QUOTE]The universe doesn't have to 'be real' in order for me to be separate from the duck, for the duck to not depend on me or any other observer to be a duck. I suppose it depends on humans to have the human name 'duck' attached to it, but that's about as far as it goes.
I find it more useful to define 'real' or 'exists' as a relation of A measures B. So the duck is real relative to anything that measures it, like say the water. The water is affected by the displacement of the duck, so the duck exists in relation to the water. That's seems a more useful definition, a relation instead of a property. But that's just me. Tegmark is pretty obviously a realist, and says the duck is part of the universal structure, and so are you, so there cannot be a duck without you since you're both part of the same thing. But the universe, being real, exists as much as any other mathematical structure. That's the level-4 multiverse thing going on. His assertions, not mine, but more mainstream (and also naive in my opinion).
in the sense that it will go on existing after you're no longer aware of it.
You seem to have a presentist definition of existence, that things stop existing after a time. Just something I notice. The MUH thing seems incompatible with presentism since it would entail the mathematical structure existing within time, making time more fundamental than the mathematics, a contradiction of the premises.
Let us also agree that, even if we are in a simulation, there appear to be certain rules and regularities that we can investigate from inside the simulation, even if we can never look outside it. Let's do what we can do.
Now we're into the realm of observation and science. We observe that that there are two types of things in our world - physical objects and ideas. Put simply, physical objects are things that can be touched or otherwise sensed. They exist outside our minds which, for the sake of argument, we are accepting as separate from one another and from the universe at large. Ideas, on the other hand, are thoughts in our heads. They are information. We can communicate them to other people, to a certain extent using physical media, but they cannot be touched or otherwise sensed.
This again is the VR idea, with artificial inputs to real minds. Dualism does indeed have empirical falsification tests, which nobody seems to pursue since I suspect the proponents fear the falsification. It becomes a matter of faith. All the arguments seem to be faith and incredulity based. If I am a real mind controlling a simulated avatar body, it is pretty easy to show that the decisions made by the avatar do not come from the avatar itself, but from outside.
What is mathematics? Is it a physical object (or collection of physical objects) that we can touch or otherwise sense? I say: it is not. It is a collection of ideas.
The mathematics in context of the MUH is not about ideas or abstractions. Once again, nobody seems to get that, and thus the incredulity. The hypothesis is not suggesting that the universe is the product of any abstracting entity, a sort of higher level universe implementing the lower one.
Tegmark, on the other hand, says that mathematics and physical objects are one and the same. He wants to abolish the distinction.
That's a misrepresentation of what he says. A tesseract for instance is not physical. To us, it is an abstraction, an idea, the map so to speak. An actual tesseract would be neither of these things. A physical approximation of a triangle could be made, but our physics does not support the creation of an actual physical triangle.
In Tegmark's world, the number 3 is on the same ontological footing as a real-life duck.
That's a begging statement since you're implying that the duck is real life and 3 is not. Attack the hypothesis on its own ground instead of adding your own premises. The duck is part of a mathematical structure, and 3 is a valid mathematical structure on its own, so perhaps in Tegmark's world, 3 is on somewhat more solid ontological footing than is the duck, a mere component of a far more complex structure. The duck is physical because anything that is part of our structure is considered 'physical' by other parts of that same structure. The word 'physical' is merely a means of self reference in that regard. I saw no suggestion that 3 was a physical thing.
The main problem I have with Tegmark's hypothesis is that I think it's a dead end in terms of suggesting any useful programme of research to better understand the universe in which we find ourselves (simulated or otherwise, as the case may be).
Agree there. It's philosophy, and almost all of philosophy has this problem. Research is for science. MUH is not science.
What follows? Having abolished the distinction between ideas and physical objects,
This distinction has never been abolished. The hypothesis is not about ideas at all. So much of your post here obviously assumes otherwise. You cannot critique the hypothesis if you don't get that.
