The modal argument for dualism is really strong.What the modal argument does rest on is the definition of what constitutes identity. I don't know anyone who would disagree with that definition of identity. Nor am I aware of anyone even remotely studied in logic who would say that axiom S5 isn't valid, but since it's not even in question here, it's irrelevant.
1) Definition of identical: If x=y, then whatever is true of x is true of y and vice versa.
2) Possibly, my mind can exist without my body.
3) Therefore, my mind is not identical to my body.
The mind possesses the property of possibly existing without the body. Since the body lacks that property (since the body can't exist without the body) the mind can't be identical to the body, because it possesses the property that the body cannot posses. Therefore, the mind isn't identical to the body.
Not to mention the batch of questions and issues he has yet to respond to. Plus he hasn't presented any evidence to support his position, which I asked for. Plus he conveniently dropped his silly claim that, "All of this shows first that you don't understand modal logic and classical logic are not compatible," which is an odd claim, seeing as modal logic is simply an extension of classical logic.Then he, without saying how, accuses me of making a category mistake.
Yet I have addressed every single thing he mentioned. These are the signs of one who has clearly lost the argument, and in desperation is trying to save face by using emotive rhetoric. Let the reader decide.