The working definition of an arc
A character’s arc is the course, across a whole book, of the rule by which that character resolves dilemmas. Scene and Sequel (Chapter 2) gives the rule its name. To resolve a dilemma a character applies a rule about which cost is more bearable, loyalty over legality or the family over the self, and that rule is the criterion. Most decisions in a novel are made on a criterion the character already holds, so the plot advances and the person does not. The arc is what the reader sees when the criteria behind a character’s largest decisions are read in order: the same rule throughout, a rule replaced by a better or a worse one, or a rule tested to the edge of change and kept.
The point at which the criterion changes is the hinge, Scene and Sequel’s term (Chapter 2) for the moment within a decision at which a dilemma is resolved on a rule the character did not hold before, while the options themselves may stay the same. The old rule is usually outranked rather than refuted. Huckleberry Finn accepts his training’s verdict that he will be damned for helping Jim, and chooses Jim anyway; he has not stopped believing the rule, he has found one that matters more. That is the general shape of change in fiction, and it explains why arcs that work rarely feel like conversions to an argument. The character keeps the old belief and acts against it.
An arc defined in this way is a matter of decisions, not of feelings, knowledge or circumstances. A character can learn a great deal, suffer a great deal and end in a different place without an arc, if every choice along the way was made by the same rule. Equally, a character who ends in the same place can have a strong arc, if the last choice is made for a reason that could not have motivated the first. The definition is narrow on purpose, because it gives the writer something to look for on the page: a decision, and the rule behind it.
The working definition of a theme
A theme, in this chapter as in The Ending (Chapter 16), is a question the book tests rather than a proposition it asserts. It differs from a topic, which names what the book is about (grief, inheritance, a family shop), and from a thesis, which is one answer. The household novel’s topic is a family after a death; its theme, put as a question, is what the members of a family owe each other in the way of truth, a phrasing first given in The Dialogue Exchange (Chapter 3). The question form matters for revision, because a question can be answered differently by different characters, and a book argues by arranging their answers. A book that has only a topic gives the reader nothing to weigh, and a book that has only a thesis gives the reader nothing to decide.
The two definitions meet at the hinge. A theme is tested when characters choose under pressure, and the criterion behind each choice is, read from the other side, that character’s answer to the book’s question. Where the protagonist’s criterion changes, the book’s argument turns.
Adjacent terms
Several neighbouring words describe parts of the same structure. The want is what a character consciously pursues, the goal of Scene and Sequel’s goal–conflict–disaster sequence (Chapter 2); the need, in the screenwriting manuals, is what the character must change in order to live better, usually unknown to them. In this chapter’s terms the need is a criterion the character does not yet hold, and the hinge is where they come to hold it. Characterisation is the sum of a character’s observable traits, how they speak, dress and behave; the arc lies beneath it and is visible only in choices, a distinction set out in How It Works. Motif is a recurring element, an object, image or phrase, that carries a theme by being returned to in changing contexts; the ledger and the coat are the household’s. Premise and controlling idea are the names two widely used manuals give to a theme stated as a proposition, and the chapter treats them as one carrier among four in The Taxonomy.
Two terms from earlier chapters recur. The Ending’s constant (Chapter 16), something visibly unchanged against which a change can be read, is one of the conditions of an arc in The Mechanism. And The Subplot’s thematic counterpoint (Chapter 14), two threads that comment on each other by analogy, is the subplot’s version of what this chapter calls variation.
What the chapter leaves to other chapters
The single decision, with its dilemma and its criterion, belongs to Scene and Sequel (Chapter 2); this chapter takes it to the scale of the book. Whose mind the reader is granted, and therefore whose arc can be shown from inside, is The Viewpoint Shift’s question (Chapter 13). The completion of an arc and the closure of a theme at the last pages belong to The Ending (Chapter 16), and the midpoint at which a protagonist’s mode or knowledge changes to The Middle (Chapter 11). A change in what the reader understands, as distinct from what a character chooses, is a reveal, and belongs to The Reveal (Chapter 15). A character carried across several books, whose arc may be suspended or spread across volumes, is Series and Genre’s subject (Chapter 17).
See also: the full treatment, with a table relating the terms of the main arc models to this chapter’s.