You're all over the place at least that's how it seems to me. Can you break up what you said into two sections 1) Modal logic and 2) Deontic logic and then explain how it's weird that diamond operator should refer to possibility? — TheMadFool
There's nothing weird about the diamond operator meaning possibility,
in an alethic modal logical, wherein box means necessity. What's weird is if you
mix alethic and deontic modes like you suggest.
If diamond means possibility, then box has to mean necessity -- alethic necessity,
not deontic obligation -- or else you get problems like the example I gave, where nothing you can do is forbidden.
Conversely, if box means obligation, then diamond has to mean permission -- deontic permission,
not alethic possibility -- or else you get the same problem.
It's still possible to argue about whether or not obligation requires possibility, but you can't just mix together deontic and alethic modes like that to "prove" it without causing strange consequences like "nothing you can do is forbidden".
It's not possible that (you shouldn't lie AND you should save your friend) — TheMadFool
The way you've phrased it, that's not so. It can be the case both that you
shouldn't lie, and that you
should save your friend; intuitively we'd usually agree it is, both of those "should" claims are true, since those are both good things, and since they
are both true they
can be both true.
But it simultaneously might be the case that you
can't both not lie and also save your friend. Note the absence of "should"s here. Maybe it can't be that you
don't lie and you
do save your friend. "Do", rather than "should".
It's possible for both states of affairs to be
moral (for both "should" statements to be correct), but it might not be possible for both states of affairs to be
real (for both of the corresponding "do" statements to be correct).
There is still room here to argue about whether or not the impossibility of that combined state of affairs means it must be an omissible (non-obligatory) state of affairs too, but you don't get the conclusion that it does for free just out of the structure of the logic.
One hint, One word, universalizability. — TheMadFool
Universalizability means that it applies for all similarly-situated moral agents.
Or to quote Wikipedia, "the most common interpretation is that the categorical imperative asks whether the maxim of your action could become one that everyone could act upon
in similar circumstances".
The circumstances can be accounted for without compromising the universalizability.