The claim that all squares are rectangles is unlikely to be true of all squares.
This is analogous to the conclusion of the above argument, not P1. An analogue to P1 would have to be something like 'Any argument of the form 'for all squares s:(X)s is unlikely to be true.' The question would then be this: does this analogue of P1 count as an argument of the form 's:(X)s'? That is, does it quantify over all squares?
You might think it doesn't, since it just talks about arguments. But my point isn't quite that it must count as such an argument, but rather that it must count as an argument of the same form as P2 (whatever that might be). The reason is that P2 is not like 'all squares are rectangles'. If it were, P2 would be a (purportedly) universally compelling moral argument. But P2 is rather the claim that there is such an argument. P2 is 'for all minds m:(Moral Argument X is compelling)m'.
I see what you're talking about. My confusion originates in your definition of P2, rather than P1, where I thought the confusion was originated.
Suppose two minds, A and B. A has some function for determining truth, let's call it T. Mind B, on the other hand, is running an emulation of mind A, and its truth function is not(T).
Okay, yes, this is an utterly pedantic kind of argument, but I think it demonstrates that in -all- of mindspace, it's impossible to have any universally compelling argument, without relying on balancing two infinities (number of possible arguments and number of possible minds) against each other and declaring a winner.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.