Final answer:
Socrates claims he has ironic wisdom because he understands the limitations of human knowledge, comparing his philosophical pursuit to the heroic endeavors of legendary figures like Hercules and Achilles.
Step-by-step explanation:
Socrates explores the nature of wisdom in Plato's Apology and suggests that he possesses a type of ironic wisdom that lies in his awareness of the limits of human knowledge. He realizes that true wisdom is the understanding that one knows nothing of great importance and that this self-examination is in itself a philosophical pursuit.
Socrates compares his efforts to question and challenge those who consider themselves wise to the legendary labors of Hercules and Achilles. These heroes were distinguished not just by their strength but by their enduring legacies in Greek mythology, and Socrates sees his own philosophical quest as similarly enduring and significant.
He acknowledges the irony in being considered wise because he recognizes his own ignorance and continues his mission with the belief that serving as a gadfly to Athens is a divine obligation.
In Plato's Apology, Socrates portrays his so-called "wisdom" as not true wisdom but ironic wisdom by realizing that human wisdom is worth little or nothing. He interprets the oracle's response as saying that he is wisest because he alone realizes the limitations of human wisdom. This ironic wisdom suggests that Socrates understands the importance of self-examination and humility in philosophy.
In addition to portraying ironic wisdom, Socrates suggests that his vocation as a philosopher was a "heroic" effort like those of Hercules and Achilles.