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Assume we have a theory of everything. Now, consider an electron e with all the relevant properties. Now, our theory of everything, being mathematical in form, can capture perfectly everything about the electron ex hypothesi.

But it cannot tell whether this electron actually exists. What is the difference within the TOE between electron e that I am observing now in my lab and electron e* that is exactly the same in all mathematical respects but is just theoretical?

It seems to me that the theory, whatever it turns out to be, cannot tell the difference between the two and thus cannot really be said to explain or even describe everything physical. This is precisely due to its purely mathematical form. With an existing physical objection there seems to be something more than just a math. description. But that "something more" no TOE can really have anything to say about.

What are some objections to this argument? Is there anything it simply overlooks? And, if it is sound, what does it imply for a TOE?