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In Mark we read that Jesus said that Abiathar was priest when David received and ate some of the bread of the Presence from the tabernacle. In terms of the point that Jesus is making it really does not matter who was priest, for the issue is the breaking of the rule about a layperson eating consecrated bread and its application to Jesus' disciples breaking the sabbath regulations. However, when we look up the incident in 1 Samuel 21:1-6, the text reads "Ahimelech" rather than "Abiathar." Was Jesus mistaken? Surely the Pharisees would have caught the error?
The first point to note is that Abiathar and Ahimelech are son and father. The son, Abiathar, first appears in 1 Samuel 22:20 as the one son of Ahimelech who escaped when Saul slaughtered the priests of Nob and their families for having helped David. Abiathar then remains with David and later serves as high priest during his reign. It looks like the son has been switched with the father.
The second thing we should look at is the textual tradition. There is no evidence that this switch is a textual error. It is true that the Western text does omit the priest's name, but none of the other textual traditions do, and the Western text does sometimes correct or add to the text in various books. When the Western text's reading remains unsupported by other textual traditions, it is not taken as very weighty. In fact, the Western text actually follows the other Synoptics, for Matthew 12:4 and Luke 6:4 both drop this offending name. Thus there appears to be solid evidence that Mark wrote "Abiathar."
There have been attempts to solve the problem by arguing that "in the days of Abiathar the high priest" should be understood to mean "In the section [of Samuel] entitled `Abiathar,' " since this section explains how Abiathar joined David (and there were no chapter and verse numbers for citing Scripture in Jesus' day). However, if that is what it means, Mark found a most awkward way of expressing it. To mean this, the Greek phrase with "Abiathar" in it should have been placed in Mark 2:25 right after "Have you never read?"
Likewise some argue that the phrase means "when Abiathar who became high priest was alive." However, if this was what were intended (if Jesus had forgotten the name of Abiathar's father or thought his listeners would not recognize it), a phrase like "in the days of the father of Abiathar the high priest" or "in the childhood of Abiathar the high priest" would have expressed the thought clearly. The phrase as it stands would express such an idea so unclearly and awkwardly that it is unlikely that it means this.
What, then, are the possibilities? First, we can be fairly certain that Mark is not covering up the Pharisaic response to an error Jesus made. If Mark had been aware of such a problem, he would have omitted the whole story or changed the name rather than simply omitted the Pharisaic response. Mark probably did not see any other problem with this passage than the issue of Jesus' defending his disciples' breaking the sabbath regulations.
Second, if Mark did not see the problem, he did not see it for one of three reasons: (1) he actually wrote Ahimelech and the more familiar name crept into the text at a very early stage, perhaps as an error in the first copying (often texts were read aloud to scribes making copies, so an oral substitution of the more familiar name for the less familiar would be quite possible), or (2) he received the story as it is and did not himself realize that there was a problem with it (in the latter case, we do not know if Jesus actually said "Abiathar" or if he said "Ahimelech" and the more familiar Abiathar was substituted in the course of oral transmission), or (3) his view of historical accuracy was not bothered by such an issue, since the main point is not affected by it. Whatever the case, Mark apparently did not realize that there was a problem.
The truth is that this is one of the problems in Scripture for which we do not have a fully satisfactory solution. We do not have Mark's original edition to check which name was in it, nor do we have Mark here to question about his state of mind. We do not have a tape recording of the preaching of Peter (thought by many to be the source of Mark) to see if he was using the right or the wrong name. While many ancient historians would not have been bothered by such an innocuous slip, it did seem to bother Matthew and Luke, so we cannot be sure that it would not have bothered Mark. Thus we can either arbitrarily select one of the speculative solutions mentioned in the previous paragraph, perhaps choosing the one which pleases us the best, or we can say, "We honestly don't know what the answer is to this problem, nor are we likely to ever know." In that case, this verse makes plain that our knowledge is always partial so that our trust remains in God rather than in what we know.