Paragraphs are found in nearly all writing systems, and are a standard subject in teaching writing. Nevertheless, there is no half-adequate account of what they are, though they are clearly related to (1) coherence and cohesion, (2) topics and/or topic sentences, and (3) the structure of the argument or discourse. We observe here that pronoun usage is significant.
Whereas pronouns (in European languages) are generally obligatory if a unique antecedent is available, a paragraph boundary is a general barrier to anaphora. In particular, a pronoun cannot find an antecedent embedded in a previous paragraph. Apparent counterexamples can be characterized, and appear to take the topics of preceeding paragraphs as antecedents. This work needs further generalizing to non-Indo-European languages, as well as to the other sorts of anaphora.
In explaining why anaphora is blocked, we can arrive at a notion of what a paragraph is, and the role it plays in speaking and understanding. This account then explains in turn a number of informal but indisputable facts about paragraphing, such as the effects of paragraphs that are too long or too short, why they support but do not match the logical structure of a discourse, and what the mechanism behind the perception of cohesion is.
This account of paragraphing also provides an upper limit on integrative semantic theories, theories in which the meaning of a sentence (and the words in it) are a function of the context that preceeds it. Also noted is the impossibility of ever observing this or other similar facts within a framework of syntax or semantics that is limited to sentences.
In short, we will observe some simple facts about pronouns that have escaped notice, and propose a general principle: paragraph boundaries are barriers to anaphora, with certain characterizable leaks, An explanation that accounts for this also accounts for a number of other observations about paragraphing. It also has interesting theoretical consequences.