A perpetual motion machine is nomologically impossible. Yet if, per impossibile, one were to exist, it would have to be a physical object.
This is a useful example for looking at how reasoning per impossibile works, since it is clear and not controversial. The conjunction of 'A perpetual motion machine exists' and 'A perpetual motion machine is nomologically impossible' is a contradiction. Despite this we can (one might say) overlook the contradiction and say, without supposing any difference in the laws of the universe (which would be a messy and complicated thing to do, given how much reasoning would be required in order to be consistent about it), that if a perpetual motion machine were to exist, it would have to be a physical object. It follows simply from its being a motion machine of any sort that it would have to be a physical object.
Another example, from Vomit the Lukewarm:
If, per impossibile, I existed by essence or definition, then I could never cease existing, for definitions are always true.
The point here, of course, is that to exist by essence or definition is to exist, simply speaking; even if we assume an impossible case of existing by essence or definition, to make sense of it qua case of existing by essence or definition, we have to treat it as a case in which the thing supposed to exist simply exists, end of story.
I think that my suggestions for an account of reasoning per impossibile apply to examples like these quite well.
