These questions are about Chapter 5 of Harry J. Gensler's book on FORMAL ETHICS (Routledge: 1996). These materials are copyrighted (c) 1998 by Harry J. Gensler; but they may be distributed freely.A golden rule theorem
This GR theorem is derivable from our axioms: Don't combine acting to do A to X with not consenting to the idea of A being done to you in an exactly similar situation.The place of the golden rule in morality
More simply (but not as precisely): Treat others only in ways that you're willing to be treated in the same situation.
To apply GR, you'd imagine yourself in the exact place of the other person on the receiving end of the action. If you act in a given way toward another, and yet are unwilling to be treated that way in the same circumstances, then you violate GR.
GR is a consistency principle. It doesn't tell us specifically what to do; and it doesn't replace regular moral norms. It only prescribes consistency -- that we not have our actions (toward another) be out of harmony with our desires (toward a reversed situation action). It tests our moral coherence. If we violate GR, then we're violating either conscientiousness or impartiality.Deriving the golden rule
To apply GR adequately, we need knowledge and imagination. We need to know what effect our actions have on the lives of others. And we need to imagine ourselves, vividly and accurately, in the other person's place on the receiving end of the action. When combined with knowledge and imagination, GR is a powerful tool of moral thinking.
If you're conscientious and impartial, then you'll follow GR. To see this, let's use these abbreviations:Elements in our GR formulation
1 = act to do A to XSuppose that you're conscientious and impartial. Then you won't do 1 unless you do 2, you won't do 2 unless you do 3, and you won't do 3 unless you do 4. So you won't do 1 (act to do A to X) unless you do 4 (consent to the idea of A being done to you in an exactly similar situation).
2 = believe that it would be all right for you to do A to X
3 = believe that in an exactly similar situation it would be all right for A to be done to you
4 = consent to the idea of A being done to you in an exactly similar situation
To avoid the absurd consequences of the literal golden rule, our GR uses a don't-combine form, a similar situation qualifier, and a present attitude to a hypothetical situation.
Many variations on GR are also theorems; for example, we could use a "relevantly similar" situation -- or have you imagine your son or daughter in the place of the other person.