Islam has obviously had enormous influence on the West, but has never been an integral part of it.  I am not sure that there is any real Judeo-Christian-Islam tradition.  St. Paul warns Christians to remember that it is not we who support the "root", but the root (Judaism) that supports us.   Without the Jewish heritage Christianity would be a completely different religion.

Sorry about  that confusion.   Consider four statements:

1)  Objective morality requires the existence of God.   True.

2 ) Objective morality requires a belief in God.  False.

3) Posting on Ricochet requires electricity.  True.

4) Posting on Richocet requires a belief in electricity. False.

You might believe that your computer works because of millions of microscopic gremlins trained to carry out your commands, but having a false belief would not necessarily interfere with the use of your computer.  A belief in God is a religious assumption, and arguments based upon that belief are religious arguments.  Arguments based on an objective moral order are not, not per se,  religious arguments.

Deleting as a duplicate post.   Obviously Ricochet Servers actually do depend on millions of microscopic gremlins. 

Just to clarify.  I don't think natural law arguments depend on a belief in God, or anything other than a belief in objective morality.   Belief in God is an entirely separate conclusion that can be drawn from that same premise.   But arguments based on natural law do not depend for their validity on any conclusion about the existence of God. 

That reminds me.  Recently a defender of gay marriage told me that the consent of both partners is required for marriage.  But the idea that mutual consent is required for marriage was originally a Catholic idea,  Many Hindus and Muslims do not agree.    A co-worker of mine had an arranged marriage for example (both parties seem to be happy).   All of us who were brought up in the Western tradition are viewing that idea of consent through the lens of a tradition that does not seem persuasive to many other cultures in this world.   Should we abolish this idea of mutual consent as violating the separation of Church and State?

By Zafar's definition above natural law arguments would not be inherently religious.   The only assumption required is a belief in an objective moral order.  But that very assumption seems to lead to the conclusion that there is a God, independently of whatever conclusions are drawn about justice. 

When I took my Western history courses, many moons ago, Western Civilization was defined as that civilization growing up west of Greece which was comprised of Judeo-Christian religion, Greco-Roman culture, and some Germanic tribal customs.   The law of contracts has its origins in Germanic customs, for example.  Just to clarify.

I think natural law arguments are kind of like the trunk of a tree that supports two limbs.  One limb is belief in God, the other is a belief in justice.  It is possible to climb on one limb without climbing onto the other one.  Atheists can believe in justice, and obviously many do.  So in that sense natural law arguments don't "require" one to draw a religious conclusion in order to understand and agree with them.  

But it is intellectually inconsistent to believe in a morality that exists independently of the human mind without believing in God (the second limb, which you don't have to climb).   

Good for you!!!!

Good for you!!!!

Natural law arguments are not compatible with reductive materialism.  If there is an objective moral order (one that exists independently of the human mind) that means there are a bunch of "values" just hanging out there in space somewhere.   "Do unto others as you would have them do unto you" is an imperative sentence, -a command.   But who commands it?  Parents, or society?  But parents and society often command us to to return runaway slaves, or round up the Jews, which are against the Golden Rule.   Is the Golden Rule a result of evolution?   Ted Bundy is just as much a product of evolution as is Albert Schweitzer.   Only a good and perfect mind could make a perfect commandment.   True, many people believe in the Golden Rule without believing in God.   Atheists can adopt the Golden Rule as a premise for proposing a just law.   But that just means that atheists can be morally upright, without necessarily being philosophically consistent.

I would define the natural law as an objective moral order, existing independently of the human mind, just like the truths of mathematics exist independently of the human mind.   The Golden Rule would be an example.   It is "law" because it is a binding command, and "natural" because it was not invented by humans, only recognized by them.   Statutory law by contrast is "artificial" law.  Whether "natural law" actually exists or not, is controversial.   "Natural law" could be just a shared hallucination experienced by many or most humans.  

If natural law exists, and sound arguments based upon "right reason"   lead us to adopt a law, that law cannot be called unjust, since natural law is the very basis of justice.   On the other hand if no objective moral order exists, then that law is still not an unjust law, because there is no such thing as injustice.

I didn't think she was making an argument, but instead was introducing a question for discussion.  "What kind of argument is a religious argument that should be dismissed?"  One problem with that question is that it is really two questions.  1)  "What kind of argument is a religious argument?"   2)  "Should that kind of argument be dismissed?"  Maybe even that should be rephrased in the plural, "What kinds of argument are religious arguments?   Which of them (if any) should be dismissed?"

Natural law arguments were developed by the Greeks and Romans before there was any such thing as "theology".   They have a long history in Western tradition.   The Declaration of Independence is a natural law document.

Before you can identify arguments that are inadmissible to public debate, you first have to explain why they should be inadmissible.   Once you have defined the reason for religious arguments being inadmissible you can apply that reason as your litmus test.  A couple of thoughts:  1) Any group should be able to protest how its tax funds are spent.  Some Christian Scientists object to fluoridation for example.   I hope they lose the fluoridation fight, but since they have  to pay the taxes as well as drink the water they have the right to speak up, and their votes should count.   The same goes for Quakers voting on militray spending, and Catholics voting on condoms.  2)  Making arguments based solely on faith is self-defeating.     As you said  "arguments will be unpersuasive.... if they rest on assumptions that are not widely shared".   The best way to decide if an argument is inadmissible is to let people make it, and then see whether others are persuaded or not.

This raises a question:  What "signs" have been there since he was a little boy?    For example, I was uninterested in sports, but I am not gay.  Lack of interest in sports at one time would have been considered a "sign" of gayness.   What clues exist to enable someone to predict that a boy will be gay?