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A new question for the new Euthyphros

Given that brains change structure when our opinions change, the question of how the two are related to each other naturally arises. We can pose that question in the same manner that Socrates once did to Euthyphro. Just as Socrates asked, is something good because the gods say it is, or do the gods say it is because it is good? And just as that question allowed for four answers (the first, the second, both, neither) so to does the following:

Does the opinion change because of the change in brain structure, or does the structure change because of the change in opinion? Or are both alternatives partially true? Or are both entirely false?

So the four alternatives are as follows:
1. opinion changes because of change in brain structure;
2. brain structure changes because of change in opinion;
3. both influence each other;
4. neither influences the other because the two are identical.

It is easy to guess at how an epiphenomenalist would answer (1), as well as how a dualist would (2). And I think I know how an eliminative reductionalist would answer as well (4). That is, the last sort of philosopher would say that the question itself is bogus or unfair, because the distinction between the physical and mental is itself a fiction.

I would respond by asking the eliminative reductionist if it's possible to wire a human brain to be convinced that 3x4=11. I would then apply the following destructive dilemma to their answer:

If the reductionist answers yes, then we don't really know the truths of math and logic are universal. We just think that they must be truth because we are wired to do so. In that case, science loses its claim to objectivity.

If the reductionist answers no, then I would ask, "On what basis do you know that no is the correct answer?" The presumption is because the respondent knows about 3 itself, x itself and 4 itself, as well as 11 (and 12) themselves. But where is the object of mathematical knowledge?Are these numbers and operations biochemical processes or states in your brain? Then how can you and I think about them without special neurogazing equipment?

Goofy addendum: Add to this, if I were to look at your brain while you are thinking 3x4=12 and were, per impossibile, able to see that this is what you're thinking, then would I also be able to see that this thought must be true? Or would I have to think of 4 itself, 3 itself, x itself, etc.?

Come to think of it, the new materialists are themselves Euthyphros--ready to kill their father.
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