1. Logical Reasoning: Oedipus initially approaches the problem of Thebes' plague with a rational mindset. He sees the plague as a consequence of some offense against the gods and believes that identifying and punishing the culprit will resolve the issue.
2. Inquiry and Investigation: Oedipus employs rational methods of inquiry and investigation to uncover the truth. He gathers information from various sources, including the seer Tiresias and the shepherd from Corinth. He questions and cross-examines witnesses, seeking to establish a logical chain of events.
3. Deductive Reasoning: Oedipus uses deductive reasoning to piece together the evidence he gathers. He starts with the facts and uses logical inferences to arrive at conclusions. For instance, he concludes that the previous king, Laius, must have been killed at a crossroads based on the location where he encountered the mysterious traveler who attacked him.
However, it's essential to note that Oedipus' rationalism is limited and ultimately flawed. He becomes so obsessed with finding the truth and fulfilling the prophecy that he fails to consider alternative interpretations of the events. This leads to tragic consequences, as he ultimately discovers that he himself fulfilled the prophecy he sought to avoid.
In conclusion, while Oedipus demonstrates rationalistic tendencies in his pursuit of the truth, his limited perspective and overreliance on logical reasoning contribute to his downfall, highlighting the complexity and limitations of rationality in human affairs.