Kripke notoriously argues against the mind as being identical to the brain roughly as follows.
Saul Kripke
My being in a pain is identical my brain state.
If my being in a pain state is identical to my brain state, then necessarily my being in a pain state is identical to my brain state. (rigid designation)
Hence, necessarily my being in a pain state is identical to my brain state.
However, we can imagine imagine disembodied minds or brain-states with no pains.
But, it follows that it is not necessary that my being in a pain state is identical to my brain state.
Therefore, my being in a pain state is not identical to my brain state.
Questions: How would a materialist respond to this argument? How would they "explain away" the appearance of contingent identity mentioned in (4)?