Paragraphs should be constructed with some sense of internal order, whether through time, or space, or some other logical way or arranging information. Again, you have a lot flexibility in choosing an ordering scheme—as long as you choose something that will make sense to the reader.
It's common for writers to produce paragraphs that don't hang together, partly because we think as we write and don't always go back and revise thoughtfully. Here's an example, from an essay on Machiavelli's opinion about Christianity. This paragraph is really pasted together from two pieces (marked by italics):
Christianity was not always weak and without vigor and war. When it was a new religion it extinguished the old, Paganism, in order to become the only one. In this, according to Machiavelli, Christianity behaved as every new religion does. The Christians burned the works of poets, threw down statues, and forbade Pagan teachings. Their mistake in this overthrow was to keep the language of the Pagans, Latin. The Christians translated the Gospels into Latin, and Christian political leaders put wrote their civil codes in Latin. So, although they had blotted out all of the Pagan ceremonies and teachings, all was not forgotten. The works of great Pagan thinkers were still studied because the language was not extinguished along with the rest of Paganism.
When the reader reaches the italicized portion, he gets a bit confused. The topic is the same, true—the early history of Christianity. But two distinct argumentative points are being made: (1) Christianity was once a fierce religion, and (2) Early Christians erred in not eradicating the Latin language. Each of these points deserves its own paragraph.
The best test for deciding whether a paragraph hangs together is to read its topic sentence and see if it reasonably covers everything you discuss in the paragraph.
It's common for writers to produce paragraphs that don't hang together, partly because we think as we write and don't always go back and revise thoughtfully. Here's an example, from an essay on Machiavelli's opinion about Christianity. This paragraph is really pasted together from two pieces (marked by italics):
Christianity was not always weak and without vigor and war. When it was a new religion it extinguished the old, Paganism, in order to become the only one. In this, according to Machiavelli, Christianity behaved as every new religion does. The Christians burned the works of poets, threw down statues, and forbade Pagan teachings. Their mistake in this overthrow was to keep the language of the Pagans, Latin. The Christians translated the Gospels into Latin, and Christian political leaders put wrote their civil codes in Latin. So, although they had blotted out all of the Pagan ceremonies and teachings, all was not forgotten. The works of great Pagan thinkers were still studied because the language was not extinguished along with the rest of Paganism.
When the reader reaches the italicized portion, he gets a bit confused. The topic is the same, true—the early history of Christianity. But two distinct argumentative points are being made: (1) Christianity was once a fierce religion, and (2) Early Christians erred in not eradicating the Latin language. Each of these points deserves its own paragraph.
The best test for deciding whether a paragraph hangs together is to read its topic sentence and see if it reasonably covers everything you discuss in the paragraph.