Question

I came across a formulation of the psychophysical problem presented as a paradox: four statements that all seem true, but apparently cannot all be held together.
(1) The mind is not physical. (2) The body is physical. (3) The body and the mind interact. (4) The physical and the non-physical cannot interact. First of all, does the Rabbi agree that this formulation, which seems not bad to me, defines it correctly?
At the second stage, I am trying to understand what the difficulty is with statement (4). (I assume the first three statements are fairly simple.) Seemingly, we have endless confirmations of the claim that the physical and the non-physical do in fact interact, no less than any other claim about reality. Why don’t they serve דווקא as evidence for this reality? Is it because there is no clear mechanism for this connection? How and why is that different from the famous story about Semmelweis, who proposed a solution to maternal mortality in maternity wards and implemented a solution even though he did not know how to propose a mechanism connecting the relevant factors?
In short, why is there any psychophysical problem at all beyond an ordinary scientific question, in light of all the confirmations of this connection? I have come across all kinds of strange explanations for this connection that seemingly stem from an unwillingness to accept the confirmed connection between the body and the mind.