Peter Leithart recently passed on observations from an article by J. Warren Smith:
Smith discerns similar motivations [of self-glorification] in early Christian martyr theology, but interprets the Martyrdom of Polycarp, which contrasts the evangelical martyrdom of Polycarp to the self-aggrandizing efforts of Quintus, as a very different sort of self-sacrifice.
Fundamentally, Christian martyrdom differs from Aristotelian self-sacrifice because martyrdom does not seek to establish the greatness of the martyr but to emphasize the greatness of God’s sustaining grace: “The true martyr—unlike the Noble Soul—does not seek greatness but is willing to be used by God to display the power of grace.” As a result, the Christian martyr doesn’t seek out death but waits patiently. The Christian martyr waits for the time, place, and circumstances of his death to be chosen, ultimately by God, rather than choosing them himself.
On these points, Polycarp’s is a model martyrdom: “Polycarp proves himself a true disciple of Jesus because he followed the pattern of Jesus’ proto-martyrdom in the gospels. He is a true disciple precisely because he waited to be arrested, thereby proving his election by God who gave the eighty-year-old bishop the grace sufficient to die nobly. The result was that Polycarp’s bold witness brought an end to the persecutions. Moreover, Polycarp’s martyrdom, which was not sought but even avoided, is an example of a martyrdom that breaks with the classical view of self-sacrifice for honor and glory (Homer) or of self-love that seeks nobility (Aristotle).”
See Leithart’s post for further explanation of Aristotle’s conception of self-sacrifice.