image: Molière's Tartuffe, Comédie Française
When we judge that a person has acted on the basis of character in a given situation, we are implying a judgment about his or her inner constitution, and we are judging that the action derived "authentically" from the individual's underlying traits. Character and authenticity go hand in hand.
So what is "authenticity" when it comes to action? It seems to come down to this. When we talk about authenticity, we are presupposing that a person has a real, though unobservable, inner nature, and we are asserting that he/she acts authentically when actions derive from or reflect that inner nature. This is a kind of moral psychological realism: we work on the assumption that there are real inner features of personality and character that influence (portions of) the individual's behavior.
There are many other kinds of judgments that we make about other people's actions that suggest the opposite of authenticity: pretense, guile, manipulation, scripted, self-flattering, role-playing, acting. What these descriptors have in common is the idea of an individual choosing a series of actions and a style of action that is intended to convey a particular impression of the actor, irrespective of the actor's "true" nature, thoughts, and intentions. There is a disjunction between semblance (based on actions) and self (based on the actor's inner subjective reality). Tartuffe's actions in Molière's comedy are inauthentic and insincere; Tartuffe skillfully shapes his behavior to evoke specific reactions from others. Politicians come to mind as we consider this list of features of action -- persons who seem always to be playing a role to cultivate positive reactions from others for the sake of electoral gain, with no evidence of authenticity.
Consider the example of Will Kane in High Noon, played in 1952 by Gary Cooper. Will Kane is a small-town marshall who is placed in a position of having to decide whether to stand and fight the armed men coming to kill him, or to slip out of town with a good head start -- and leave the town to the violent depredations of the outlaws. He strives first to gain a collective defense of the town, but all the town worthies suddenly find that they have other urgent appointments. And his deputy Harvey Pell takes this moment to allow his long-standing grievances to boil over and to walk away. So it is either stand alone or flee. He stays.
So how are we to understand Kane's choice? The movie's original poster gives one interpretation: "the story of a man who was too proud to run!" This isn't a particularly satisfying interpretation, though, in that it seems to trivialize his choice. Pride seems like a superficial motivation -- along the lines of "Robert was too proud to ask his boss for a loan for taxi fare when he realized he had forgotten his wallet." Pride seems to be a motivation that has to do with avoiding embarrassment rather than the loftier motivations of character and sacrifice.
Here is a somewhat different line of thought: Kane has learned to become a certain kind of person -- a person who doesn't bow easily to threats, a person who cares about his neighbors and friends, a person who loathes the violent bullying of the outlaw. On this line of thought, Kane has grown into a certain kind of character, which leads him to act in ways that seem contrary to his self-interest. He resists intimidation; we would also expect him to resist subornment or bribery.
Another possibility is that Kane possesses a deeply engrained role responsibility: it is his job as marshall to take risks to defend the town. (It's no longer his job, in fact, since he has resigned in deference to the pacifist convictions of his soon-to-be wife, Amy Fowler, before the crisis began.) But we might speculate that his sense of duty prevails over the fact of risk and the coincidence of having given up his badge; he is the only person on the scene who can or will oppose Frank Miller's gunmen.
There are several entwined complexities in this short discussion. One is the fact that the examples used here are drawn from fiction; so Tartuffe and Will Kane are both played by actors representing their actions and motivations. Certainly it would be a category mistake to judge that "Gary Cooper displayed great character in High Noon"; it is the depiction rather than the performer that needs analysis here.
Second, there is the realism point made above: the idea that the individual has a core set of characteristics that are "really" part of his or her makeup. Without this assumption, the idea of authenticity doesn't have traction. But this takes us in the direction of a real "self" which is the author of one's actions; and there are many reasons for thinking that this is an over-simplification of action and agency. Briefly, it is plausible that an actor's choices derive both from features of the self and the situation of action and the interplay of the actions of others. So script, response, and self all seem to come into the situation of action.
Moreover, even if the realism assumption is justified, character is only one part of the "real" self. One can be inauthentic by violating the impulses of his/her character; but likewise inauthenticity can derive from a deviation between beliefs and thoughts and actions. Iago is inauthentic because he pretends loyalty to Othello, whereas he is secretly disloyal.
And third, it is possible that the relation between "character" and "role" is not as contradictory as is suggested here. It may be that the role sets some of the parameters of the character and serves to reinforce one set of actions over another in particular circumstances of choice. The fact that Will Kane was regarded by others as an honorable and courageous man may be part of the explanation of the fact that he behaved in an honorable and courageous way.
(Here is an interesting source that provides examples of action driven by character in real life -- Bob Blauner's account of the professors in the University of California who resisted McCarthyism at the cost of their jobs; Resisting McCarthyism: To Sign or Not to Sign California's Loyalty Oath.)