OBp

~~OBp, can be derived in any system to be considered here.

Deontic Logic McNamara, Paul 2006

OBp does not imply A4 can be found in the supplemental document

Deontic Logic McNamara, Paul 2006

But then it would seem to follow from the theorem OBp

Deontic Logic McNamara, Paul 2006

So, there must be an i-acceptable world, say j, where OBp is true, but

Deontic Logic McNamara, Paul 2006

OB (OBp †’ p), we need the further requirement of “secondary seriality”: that any i-acceptable world, j, must be in turn acceptable to itself.

Deontic Logic McNamara, Paul 2006

OBOBp †’ OBp, a formula involving an iterated occurrence of our main operator. [

Deontic Logic McNamara, Paul 2006

So let's assume we add that as the first ingredient in specifying any deontic logic, so that, for example, OBp †’

Deontic Logic McNamara, Paul 2006

OB (OBp †’ p) must be true at all worlds, after all.

Deontic Logic McNamara, Paul 2006

A puzzle regarding OBp †’ —Š p can be found in the supplemental document A Puzzle Surrounding Kant's Law

Deontic Logic McNamara, Paul 2006

OBp †’ p) obligatory as a matter of deontic logic.

Deontic Logic McNamara, Paul 2006