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A presupposition is a particular belief that must be held for a particular rhetorical structure, such as a sentence, to be understood as correct in a given context. Both the speaker or writer and the listeners or readers must share this background belief in order to effectively communicate and understand ideas. The sentence "Jane goes to the grocery store after she finishes work," for instance, includes the presupposition that there is a unique individual named Jane; that she is physically capable of getting to the grocery store; and that she does, indeed, work. Presuppositions do not need to be profound, and it is often unnecessary to state them explicitly, but if different people make different presuppositions, understanding may be difficult to achieve.
Presupposition is specifically studied in a subfield of linguistics known as "pragmatics." This subfield primarily examines the connection between context and meaning. One of the main concerns of pragmatics is understanding the implicit meaning in statements. Presupposition is in the domain of pragmatics, then, because presuppositions are seldom explicitly communicated and are instead generally understood implicitly. The sentence "Carl fell out of the tree," for instance, demands the presupposition that Carl was, in fact, in a tree, though it is not necessary to state this explicitly, as it can be understood without such a statement.
A presupposition may be considered "actual" or "potential" based on the presentation of the information being presupposed. The statement "Sarah said that Dave just got back from Florida" presupposes that there is a unique entity called "Sarah" and that there is a unique entity called "Dave" who was, until recently, in Florida. The presupposition that there is a unique entity called "Sarah" is necessary for the sentence to make sense and is considered to be actual. The notions that there is a unique entity called "Dave" and that that entity was, until recently, in Florida are potential presuppositions because they were reported by a third party. It is possible that Sarah did, indeed, make that claim and that she was completely wrong, thereby making the presuppositions about Dave and Florida false.
There are many different words and linguistic constructions, called presupposition triggers, that can be used to identify presuppositions. Many verbs, for instance, often indicate the presence of one or more presuppositions. In the sentence "Jacob realized that his bicycle was broken," the verb "realized" is a trigger. The realization presupposes that there is a bicycle and that it is broken. Such triggers exist in many different forms, including comparisons, questions, and temporal clauses.