Do those two sentences follow logically? Sure they do, even though you have skipped an essential point in the progression of the narrative — the fact that Joe was injured. It does not necessarily follow that Joe was injured by the fall, but we assume he was since he’s in the hospital. But if one of Joe’s wounds (from his fall off the cliff) got infected, and the doctor put him on antibiotics, what do you think of these two sentences?
“Joe fell off a cliff. The doctor put him on antibiotics.”
Strange, right? A non sequitur (literally, “It does not follow”), right? So we can sometimes skip one step in a logical progression of ideas, but two or three or four, and we’re going to get into trouble.
Of course, we would never skip so many steps in the progression of thought, would we? But I see writers do it all the time. And I do it all the time, though I don’t see it as clearly in my own writing as in the work of others. That’s why it is so important to let others look at your draft of an article or chapter or book. And when they say, “I’m not sure what you’re driving at,” ask them if they can identify the exact spot in the text where you lost them. Then in the revision, rethink those passages, looking for missing logical steps. Your writing will be much clearer and more readable.
Too often when you give people your manuscript to read, they proofread it! Tell them you aren’t interested in spelling and punctuation at this point, but logical progression of thought. And if they don’t know what you mean, tell them about poor old Joe.