In Plato’s Euthyphro, we are presented with the conversation between Euthyphro and Socrates. The conversation begins when Socrates comes to find that Euthyphro is prosecuting his father on the charges of murder of a murderer. Euthyphro explains that his family and friends believe that his course of action on his father to be impious. He then explains that they have mistaken his impiousness and that they are ignorant to the true nature of piety. This entices Socrates, since he himself his being prosecuted for corrupting the young and not believing in the same gods as in which the city he lives. He believes that Euthyphro holds the answer to the definite “form” of piety and impiety. Socrates then begins to examine Euthyphro through the Elenchus; a way of asking questions in order to ascertain the Form; since Euthyphro should know all that is piety.
This is where we begin to see Socrates Elenchus being used to examine the true nature of both piety and impiety. He wants to discover what is each of their definite “Forms” by which nature can be captured in a unique definition; other wise known as, Ti Esti. An example of Ti Esti would be; what is the definite “account” or “Form” of a triangle? As explained by Professor Puniwai, the answer to this Ti Esti is that the definite “Form” of a triangle is a three-sided Polygon or a closed shape with straight sides whose angels all add up to 180 degrees. We now have the accurate account of a triangle in which no other shape expresses. This is what Socrates was ultimately seeking from Euthyphro in regards to piety. So, if one was to ask what is Elenchus and how does it pertain to Ti Esti, I would say that Elenchus was used to find the Ti Esti of both piety and impiety.