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What is the proper form of the cosmological argument for God's existence? 

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Why is this the proper form of the argument? Because to argue that "this world exists, therefore, God, the necessary being exists," is either really to argue from the more abstract premise, "something exists/ ," or else the conclusion is not strictly necessary, in which case the unconditionally necessary being, God, is but conditionally necessary, and so not what the argument seeks after all (AD: 47f47f.).