Confused about the placement of commas in the following sentences

"I believe in no God, no invisible man in the sky. But there is something more powerful than each of us, a combination of our efforts, a Great Chain of industry that unites us." - Andrew Ryan

What are the rules that permit the use of commas after the words "God", "us" and "efforts"?

Solution 1:

These are all examples of non-restrictive appositive noun phrases, which require the use of commas.

Non-restrictive appositive noun phrases add additional information to further describe/quantify/specify/develop the preceding noun phrase. They are however, non-restrictive (rather than essential or restrictive) because they can be removed without significant change in meaning to the overall sentence. Removing them may lessen the detail or reduce the propositional impact, but the meaning is still clear.

I believe in no God, no invisible man in the sky [2]. But there is something more powerful than each of us, a combination of our efforts [3], a Great Chain of industry that unites us[4]

In the first sentence [2] can be removed. In the second sentence [4] can be removed. In the second sentence, however, it is more difficult to remove [3] without [4], as [4] seems to work in close logical apposition to efforts.