Explanation #1: Rashi explains that the Torah writes "be'Tzedek Tishpot", and that this Tana holds 'Ein Eiruv Parshiyos kasuv Ka'an.

Question #1: In that case, why does the Gemara not query R. Avahu, who holds that 'Shenayim she'Danu, Ein Dineihem Din' is unanimous, from here?

Question #2: Secondly, if, as Rashi say, those who hold Eiruv Parshiyos ... ' hold that a judge cannot judge on his own, how come that, on the one hand, Rav Yosef holds in Perek ha'Megaresh (Gitin, Daf 88ab that 'Hoda'os ve'Halva'os Avdinan Shelichusaihu' (in which case he holds 'Eiruv Parshiyos ... '), whilst on the other, that a Yachid Mumcheh may judge on his own (as is implied from the episode with Mar Zutra that the Gemara will cite shortly)?

Question #3: And thirdly, when he says there that 'If he does not receive permission to judge, his rulings are not valid, this implies that he concurs with R. Avahu, yet he nevertheless holds that a Yachid Mumcheh may judge (because according to Shmuel even a Yachid who is not an expert is permitted to judge).

Alternative Explanation: 'It therefore seems to me' that, even according to those who require three experts min ha'Torah, the Chachamim instituted that a Yachid Mumcheh is permitted judge on his own.

Ramifications #1: according to this, when the Gemara says that his rulings are not valid, this does not refer to the 'K'gon Ana' of R. Nachman, who, later in the Sugya, holds like Shmuel (that Shenayim she'Danu Dineihem Din), but to the 'K'gon Ana' of R. Chiya, who holds ('Ein Dineihem Din') - not like Shmuel.

Ramifications #2: according to this explanation, when the Gemara will later query R. Avahu from "Dan es ha'Din', it could have answered by establishing the case by a Mumcheh le'Rabim.

Question: The problem with this is from the Gemara in Perek Ra'uhu Beis-Din (Rosh Hashanah, 25b), which implies that a Mumcheh le'Rabim may judge single-handedly min ha'Torah?

Answer: The Sugya there is asking and answering according to the opinion that validates even one Dayan on his own.

Clarification: Even though, as we conclude, 'Mumcheh le'Rabim' implies that he is learned and knowledgeable in Halachah, when the Gemara states in 'Zeh Borer' (Daf 23a) that a litigant is permitted to disqualify his disputant's judge until he accepts him in front of a Beis-Din that is Mumcheh le'Rabim, it does not mean that the judges need to be experts like R. Chiya and R. Nachman ...

Reason: ... because there, the Gemara is talking about an official Beis-Din, which bears the title 'Mumcheh le'Rabim' even if the Dayanim are ordinary people; whereas here, it is talking about an iniviual Dayan, who only falls under the category of 'Mumchah le'Rabim' if he is an expert, as we explained.

Clarification: And he is even permitted to force the litigant to appear before him against his will; because had the latter accepted his jurisdiction, he would be obligated to do so even if he would not be a Mumcheh.

Ramifications #1: From here we learn that three people are permitted to judge a person against his will, in the event that he refuses to appear before Beis-Din - seeing as three ordinary people stand in place of a Yachid Mumcheh.

Ramifications #2: In fact, even two people may do so, only they are branded 'a Beis-Din Chatzuf'.

Implied Question: When the Mishnah in the third Perek (on Daf 23a) rules that each litigant picks one judge, implying that a judge can only judge with the litigant's consent, but not against his will.

Answer Part: .. it speaks where the litigant agrees on principle, to go to Beis-Din, only he is fussy about which judge will adjudicate, whereas our Sugya is speaking where he refuses to appear before Beis-Din at all.

Implied Question: How will we reconcile our Gemara with the Mishnah in Pirkei Avos, which warns against judging single-handedly?

Answer: The Mihnah is only advising against doing so (in case one comes to err), but does not actually forbid it.

Implied Question: Nevertheless, how can the Amora'im ignore the Tana's sound advice.

Answer #1: The Amora'im did not actually adjudicate on their own, but merely expressed their ability to do so.

Answer #2: Alternatively, they were so experienced in this field, that they were not worried about erring.

Explanation: Rashi explains 'If not' to mean - that they said to him 'Judge us according to Torah law!'

Question: In that case, what is R. Chiya coming to prove, bearing in mind that, even if he would not be 'Gamir ve'Savir' the Din would be that his ruling is valid and he is obligated to pay from his pocket' - as is evident from the Gemara later (Daf 6a), which queries R. Avahu from 'Dan es ha'Din', and answers that they accepted him as a judge, even though it is speaking about someone who is not an expert (seeing as the Seifa continues 'Whereas if he was an expert in Beis-Din, he would be Patur [see Maharam]).

Alternative Explanation: It therefore seems that 'If not' means that they refused to accept him at all.

Implication: This implies that 'Sheivet' (Bavel) is superior.

Implied Question: But the Gemara in 'Makom she'Nahagu' (Pesachim, 51a and 5b) which states 'However, from Eretz Yisrael to Bavel (if someone from Eretz travels to Bavel, it doesn't matter if he does not adhere to the Minhagim of Bavel), seeing as we in Bavel, are subservient to the Chachmei Eretz Yisrael', implies the opposite?

Answer (Part 1): Rabeinu Tam explains that the Gemara in Pesachim is speaking with reference to Isur ve'Heter, based on the fact that the Chachmei Eretz Yisrael were wiser than their Babylonian counterparts, for, the fact that the very air of Eretz Yisrael makes a person wise, and as the Gemara says here they are called 'Mechokek' because they teach Torah in public ...

Answer (Part 2): ... whereas with regard to the power to extract money (regarding the Din of 'Hefker Beis-Din Hefker'), the Chachmei Bavel are superior. In fact, they are called 'Sheivet', because they rule over the people with a staff.

Reason: And this is because the exilarchs descended from the dynasty of David ha'Melech via their fathers, whereas the Princes in Eretz Yisrael descended from the royal dynasty via their mothers, as the Gemara states in the Yerushalmi.

Text: This is the correct text. Rabah bar bar Chanah is not correct, since that would make him the grandson of Chanah, whereas here it is implied that he was the nephew (brother's son) of R. Chiya, and Chanah was R. Chiya's brother, as we shall see later; whereas Rabah bar bar Chanah throughout Shas lived in the days of R. Yochanan, and was Chanah's grandson, which explains the term 'bar bar'. (It transpires that Chanah had a son and a grandson by the name of Rabah.

Alternative Explanation: Some explain that the name of Rabah's father was bar Chanah (though it is not clear how that will reconcile the two Gemaros).

Refutation: But this is not correct, since the Gemara in 'ha'Mocher es ha'Sefinah' states that every bar bar Chanah is a fool (see Maharam).

Clarification: meaning that Aba Mari (Rav Huna) received permission from Rav - because someone who has permission has the authority to give permission, just as we find later in connection with Semichah, where a Samuch can give Semichah and permission to judge Dinei Kenasos, as the Gemara states there 'However, may that man (R. Yehudah ben Bava) be remembered for the good, for, were it not for him, the laws of K'nas would have been forgotten ... '.

Implied Question: Why did R. Chiya (who had himself received permission from Rebbi) find it necessary to obtain permission on behalf of Rabah bar Chanah and of Rav?

Answer: Perhaps that was because in the town were Rebbi lived, nobody was allowed to grant permission other than Rebbi

Final point: It is not logical however, to say that Rabah bar Huna lived in the time of Rebbi.

Implied Question: Bearing in mind the Gemara in Perek Echad Dinei Mamonos' (later, Daf 33a), which requires express consent in order to be Patur from paying should he err in Dinei Isur ve'Heter, why does the Gemara not answer that he needs permission in order to be Patur from paying ...

Answer: ... because if that was the reason why, then he would not have required permission both for Hora'ah ('Yoreh Yoreh') and for Din ('Yadin Yadin'); one of them would have sufficed, since that would cover anything that he would be Chayav to pay.

Question: How can one confuse 'Beitzim' (eggs) with 'Be'tza'im' (a muddy pond)?

Answer: They actually thought that he said not 'Mei Beitzim' (with a 'Yud'), but 'Mei Bitzim' (without a 'Yud') - like we find in the Pasuk in Iyov, 8 "ha'Yig'eh Go'me be'li Bitzah" - and they erred between Bitzim an Beitzim.

Question: The Gemara in Perek ha'Mocher es ha'Sefinah (Bava Basra, Daf 74b) implies that Karmiyon and of Pigah are rivers (so why is their water not eligible for Mei Chatas)?

Answer: Of course they are rivers, answers Rabeinu Tam, and they are Pasul because the water is not clear, and are mixed with earth and mud, which would be a Chatzitzah between the water and the vessels, whereas the Torah writes in Chukas "Mayim Chayim el Keli" (indicating that there may no interruption between the water and the vessel).

Implied Question: But according to the Gemara in Perek Hadar (Eruvin, 62b and 63a), as long as Rav Huna was alive, Rav Chisda would ask Rav Huna even 'eggs cooked in milk' (which most people know is permitted), without issuing an independent ruling?

Answer: The Gemara there is speaking when he was actually in Rav Huna's presence (see Maharam).

Proof: ... since the Gemara itself informs us there that Rav Chisda issued rulings in Kafri during Rav Huna's lifetime.

Question: The Gemara there explains that Rav Hamnuna desisted from issuing rulings in Charta de'Argiz during Rav Huna (the Gemara there says Rav Chisda)'s lifetime, because he was his Talmid; whereas in our Gemara it is implied that beyond three Parsah it is permitted?

Implied Answer #1: And one cannot answer that our Sugya is confined to a Talmid Chaver, which is permitted outside three Parsah, like Rav Chisda there ...

Refutation: ... since we learn the concession from Moshe Rabeinu, as Rashi explains here, implying that it is speaking about a Talmid.

Implied Answer #2 and Refutation #1: And to answer that Charta de'Argiz was within three Parsa'os, because it is a Dochek (forced interpretation).

Refutation #2: Furthermore, we say there that, in one's Rebbe's presence, it is forbidden and carries with it the death-penalty, whereas not in his presence, it is forbidden but there is no death penalty - and it is implied there that within three Parsah is considered in his Rebbe's presence; whilst beyond that is not.

Answer: It therefore seems that the Gemara there (concerning Rav Hamnuna) is speaking where he did not obtain permission.

Clarification: This is the correct text and not R. Chiya, as Rashi explains.

Proof: Because the Yerushalmi cites these episodes in connection with Rebbi, who witnessed them in Ako; and the Gemara there goes on to extrapolate from there that Ako is part of Eretz Yisrael, since he wanted to eat there Taharos; whilst on the other hand, it is also partially in Chutz la'Aretz, since he was angry with a Kohen who was standing in the section that was outside Eretz Yisrael. And the text there reads 'Rebbi saw a certain man standing in the Land of the Nations'. Earlier too, the text reads 'And they thought that he meant the water in which eggs had been boiled (see Tosfos ha'Rosh).

Clarification: The reason that Shmuel mentions 'two' is because even two is called a 'Beis-Din Chatzuf'` but in fact, even the rulings of one Dayan is accepted ...

Proof #1: ... since the Gemara will shortly query R. Avahu (who requires three Dayanim) from 'Dan es ha'Din', but not Shmuel.

Proof #2: And one can also prove it from the Beraisa later (Ibid.), which cites the Chachamim who say 'P'sharah be'Yachid', and the Gemara suggests that this is because we compare P'sharah to Din.

Question: In what way is P'sharah stronger than Din? Din too, when, like P'sharah, it is performed with the litigants' consent, once the two Dayanim have adjudicated, they (the litigants) cannot retract.

Answer: The Gemara is speaking where the litigants approached two people and asked them to judge them in the usual fashion (in which case, they are allowed to retract [See also Tosfos ha'Rosh]).