Scholars typically interpret Justin Martyr's "old man" historically as a Christian teacher or figuratively as a literary device, and some argue that Justin paints him into the narrative specifically as a figure of Christ. Andrew Hofer takes this latter approach in "The Old Man as Christ in Justin's 'Dialogue with Trypho,'" and his summary of previous scholarship proves helpful as well.
Scholars preferring a historical old man include Oskar Skarsaune, who claims that "the Old Man may have been a Palestinian or Syrian Christian," and L. W. Barnard:
Barnard defends his historicity and considers that Justin's account of conversion at the hands of an old Christian "has a ring of truth about it and gives an adequate explanation of his later work as a Christian philosopher."
Others prefer a figurative old man. Niels Hyldahl draws parallels with similar characters in the writings of non-Christian philosophers and suggests that the old man himself is not a Christian. J. C. M. van Winden is among those who dispute this:
[T]he old man is a literary figure. He personifies wisdom, here Christianity. He is a Christian, not a 'barbarous stranger', a figure blindly copied by Justin from post-classical literature. Granted for the sake of argument that Justin followed a literary tradition, he certainly did so in a remarkably personal manner.
Edmond Robillard extends van Winden's analysis and connects the old man with the Ancient of Days of Daniel and suggests "that the old man symbolizes either God the Father or the Word of God." In turn, Andrew Hofer elaborates on Robillard, and argues that Justin's old man is a figure of Christ.
To defend this thesis, Hofer points to 15 parallels between Justin's story and the Road to Emmaus story of Luke 24, such as the unexpected appearance of a stranger, the teacher's apparent feint of ignorance, and the use of the prophets to teach the truth. To defend the idea of Christ being portrayed as "old," Hofer points to the biblical connection between Jesus and the Ancient of Days in Revelation 1, as well as other early Christian writings that portray Christ, the Lord of time, as elderly. Hofer offers many other evidences, some more technical and some merely suggestive, but generally emphasizing the similarities between Christ and Justin's portrayal of the old man as a wise, humble, and authoritative teacher.
Hofer is careful to clarify that it would be excessive to say that Justin physically saw Jesus, as the apostles did. "Justin need not claim a singular vision," he says, "but a common teaching given by the first-begotten, pre-existing Christ about how to read the scriptures." He summarizes his position:
Justin Martyr draws the old man as a figure for Christ. The pre-existent Son of God has interpreted the scriptures for Justin and given him the grace to understand, just as it was done for the first disciples after the resurrection.