In “By the Waters of Babylon,” you have a 1st person narrator. This is seen in that the main character is presenting the story from his personal point of view. We see the world through his eyes and know only what he knows.
It can be argued whether or not he is reliable. Many people will say no because he does not have a solid and clear grasp of what has really happened to the world around him. He believes that the world was walked upon by gods who possessed far more knowledge than he and his people have. He does not understand that these supposed gods were simply technologically advanced people. However, as far as the reliability of the story is concerned the narrator is reliable in the sense that he is well informed about the culture in which he lives. My personal view is that he is unreliable because of his misinformation about the prior culture, material objects, and other events.
Finally, his diction (how he speaks) and syntax (how his speech is formed) fit the character because they are less sophisticated than a “modern” character would be. He speaks in the way that Native Americans are stereotyped in having spoken when English was new to them. His manner of speaking reinforces his naivety and his innocence.
John, the story's first-person narrator, is a simple, straightforward person, brave enough to become a priest and travel to the post-apocalyptic ruins of New York City. He believes in the traditions of his people, for example, approving of the way that his father is more strict with him once it becomes clear he will be a priest. Although John says "why should I lie about it," usually a clue that a character is lying, in this case we have no reason to doubt the words and observations of this reliable, straight-arrow character. This story is not rocket science, meaning it is not full of complicated characterizations such as you might find in a Chekhov story. John says these words about not lying because to him, what he has discovered on his trip to the city is extraordinary: the inhabitants of this lost city are not gods (as he has been taught) but men. Rather than upsetting him, this knowledge fills him with hope that his people can rebuild civilization.
John's diction is simple and declarative, revealing him processing information in the context of the simple world he knows of hunting and animals. He uses basic words like "fish" (rather than naming the kind of fish in question). When he eats food from a jar in New York, he calls it "fruit" and says very simply that it is "sweet." This shows he is from an unsophisticated culture, but his ability to observe and interpret shows he is intelligent