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Compatibilism and incompatibilisim re justice

As a compatibilist, DD wants first to convince us that our actions are predetermined by antecedent conditions, and after having done that, convince us that this conviction is compatible with our day-to-day conviction that we can choose how we shall act.  

Is there an analogous way of treating justice--that is, could one be a justice compatibilist?This position would maintain both a positivistic notion of justice that is somewhat counter-intuitive, yet also assert that this counterintuitive notion is compatible with important common sense convictions about justice.

Here are two ways in which a positivist might go against common sense notions of justice.  The first way would be to argue that science undermines the objectivity of justice, nevertheless, prudence dictates that we engage ourselves in day to day endeavors as if justice were objective, even though it isn't.  For it is objective in some qualified sense, etc.

Another positivist might contradict the former, maintaining instead that the objectivity of justice is supported rather than undermined by scientific inquiry.  But the same positivist might adopt a belief that goes quite against common sense (say, by maintaining that it is appropriate to eat babies for sport), and at the same time claim that this claim is scientifically based.  

How would DD respond to these positivists?  Would he fight fire with fire: that is, would he use science to defend both the objectivity of justice and the wrongness of eating children for sport?

If he does chose this method, then it would seem hard for him to deny that later on, thanks to a yet unforeseen scientific revolution, his present defense of the objectivity of justice might be totally undermined.  After all, perhaps our notion of justice may be just as illusory as phlogiston.

He might instead fight fire with water.  That is, he might acknowledge that science as such is inadequate for reasoning about  justice; nevertheless, common sense reasoning may suffice to address both controversies.  If he chooses the latter response, then he runs the danger of undermining his whole argument about free will and God.  For any path that he beats toward common sense in the defense of justice might be detected and then used by another to defend libertarianism and theism. 

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