I think that Miller makes is clear that Proctor believes that there is no distinction between both realities in his mind. Proctor feels that his actions to maintain his reputation do feed into the larger obligation he has to his family. When he rescinds the confession, he offers up a variety of reasons to do so. One such reason what the lesson left to his children. Proctor believes that if he is unable to stand for what is right and defend his "name," then he will not be able to teach his children right from wrong. It is this moment in which Proctor believes that the actions to defending his name represent a moment of transcendent "goodness," that he has long sought, and something that he believes is important to transmit to his children. It is here where Proctor is not shown to be merely acting to save his reputation. It is not as if he is Parris, more concerned with how he is perceived than how he sees himself. Rather, Proctor understands that this conception of "reputation" is one where he must seek to stand for something to uphold a value or a transcendent notion in a world that discredits such elements. In doing so, Proctor believes that the lesson he teaches to his children and what he represents to his wife is worthy to accept the most dreadful of punishments.