Objective Moral Truth Without God

Rob asks:  "If there are certain observable truths about human nature (whether it's a created nature or an accidental nature that has taken hold at this stage of our evolution), those truths have moral implications, don't they?" 

My answer (and I am open to being persuaded otherwise) is "no" in the absence of created nature.  If there is a "moral law giver," then the truths He placed in human nature have moral implications.  But, if all of this is an accident, why should I be morally bound by what is observable in human nature at this stage of our evolution? In other words, why does accidental nature have a claim on how I ought to live and treat other human beings, animals, the environment, etc.?  Grotius posited that the natural law held whether or not God existed.  Am I being overly simplistic to suggest that the Enlightenment and modernity were a long attempt to work out Grotius' hypothesis?  Am I wrong to think that the postmodernists have shown the hypothesis to be false?

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