As we learned on yesterday’s daf, the third perek of Massekhet Makkot focuses on the punishment of malkot (lashes). According to the Mishna (13a) someone who engages in a variety of incestuous relationships is liable to receive malkot. The Gemara on today’s daf tries to establish whether someone who engaged in a number of different forbidden unions would receive a separate punishment for each one, or, perhaps, a single punishment would suffice for all.
The Gemara quotes a baraita that relates that this question was not raised in the beit midrash, rather that Rabbi Akiva posed the matter to Rabban Gamliel and Rabbi Yehoshua when he chanced upon them in the itliz in the city of Emmaus (the city was situated about 30 kilometers west of Jerusalem and was a popular vacation spot thanks to its thermal pools). According to the baraita, Rabban Gamliel and Rabbi Yehoshua could not answer this question directly, and their attempts to cite comparable cases with clear rulings as precedent were rejected.
In modern Hebrew an itliz is a butcher store, and it is likely that that was where these Sages met. The source for the word in Latin may be a marketplace, or, perhaps a duty-free zone, which eventually became interchangeable with a market.
According to Tosafot, the detail describing that the interaction took place in the itliz was brought in order to teach that even while busy in the marketplace the Sages were open to discuss topics of Torah. Furthermore the Tiferet Yisrael points out that according to this story even though they were standing in a public place with crowds of people watching, Rabban Gamliel and Rabbi Yehoshua were not embarrassed to admit that they did not know the answer to Rabbi Akiva’s question (when this story appears in Massekhet Keritot there is a list of questions to which they admit that they did not know the answer).