1. What authority do the Rosh and the Kesef Mishneh have?

They don’t have any. But according to the view that the medieval authorities have authority, here we have them themselves saying they do not.

Obviously the Rosh isn’t supposed to hold that the medieval authorities have authority, but by the same token Rav Ashi didn’t hold that the Amoraim have authority. Authority is determined by public acceptance, after all. And if with the perspective of time their words were accepted, and all halakhic decisors view the words of the medieval authorities as binding to some extent, then that binds just like the acceptance of the Talmud does. (Unless you say that if their words weren’t accepted absolutely, then it’s no longer binding acceptance—even if people saw disagreement with them as possible only when there was a “well-known difficulty,” as the Shakh says.)

Completely agreed. Except that, as you say, they are “binding to some extent,” and that is exactly what I said.

Rabbi, is the Shulchan Arukh a binding authority? People argue to me that it is, because the nation (and especially the Sephardim) accepted it, and therefore there’s no possibility—and certainly not for simple people like me—even to think of challenging its words, because he knew much more than I do. Can I make an ad hominem argument here too? Of course, whenever I dare not to accept absolutely things written in the Shulchan Arukh, what I say is met with mockery and lack of respect (from almost every rabbi or friend). I’d be glad to hear your view on the matter.

The question of authority is complicated. In principle, there is no formal authority after the Talmud. But there are substantive authorities (that is, the professional authority of someone knowledgeable—a Torah scholar). But substantive authority is good advice, not an obligation. In principle, a person is supposed to rule for himself, but that is only if he is capable of it. A person who is not proficient in Jewish law and its methods cannot rule for himself or reject the accepted halakhic ruling (such as the Shulchan Arukh), not because he has no right to, but because it isn’t serious.
I would add that halakhic ruling is based not only on considerations of truth but also on considerations of autonomy (a person’s obligation to rule for himself, if he is capable of it). Therefore, even if the Shulchan Arukh were wiser than you, that would not necessarily mean that you must always obey him. The Talmud in Eruvin says that the law was not ruled in accordance with Rabbi Meir because his colleagues could not get to the depth of his reasoning. He was a far greater Torah scholar than all his colleagues, so it is reasonable that if there is a dispute, he is the one who is right. And yet the law is not in accordance with him, because they acted according to their own understanding (even though they themselves would admit that he was probably the one who was right).
See my articles here:

אוטונומיה וסמכות בפסיקת הלכה

And here:

האם ההלכה היא פלורליסטית?

Do you mean that they understood that they were mistaken and ruled that way because of considerations of autonomy?
On the plain meaning, it sounds like Rabbi Meir’s opinion was simply not relevant to them, somewhat like what some of the medieval authorities wrote about “these and those are the words of the living God,” that there are two facets to the matter. So too with Rabbi Meir: there is a facet according to which one can say as he does, and maybe in truth that is indeed the more correct and truer facet, and still in their lives it was not relevant. (Just as Maimonides rules not like the Holy One, blessed be He, regarding the question of whether the white patch came first.)

Oh, you brought proof from the Rosh that the medieval authorities have no authority? I thought you brought proof from him that the Talmud does have authority, and that’s why I asked where he gets the authority to distribute authority. Now you just need to bring the questioner some other proof that he can’t disagree with the Talmud.

Itai,
I don’t know what “not relevant to them” means. Either that is the Jewish law, and then that’s what should be done. That’s all. More than that: none of Rabbi Meir’s rulings were relevant to them? It wasn’t just one incidental ruling? Doesn’t that sound like a pretty surprising case to you?
It’s obvious that the meaning is that they could not get to the depth of his reasoning, and therefore, despite the fact that he was right, they did not rule in accordance with him because of autonomy in halakhic ruling.
And the ruling against the Holy One, blessed be He, in the case of the white patch is for that same reason. Not because the Holy One, blessed be He, is not right, and not because His ruling is irrelevant (what could possibly be relevant or irrelevant in the question of whether the patch came first?), but because we are obligated to rule according to our own understanding even if we are mistaken. That is also the meaning of the rule “It is not in heaven.” And these are the well-known words of the Maharal in chapter 15 of Netiv HaTorah:

“For it is more fitting and more proper that one should issue rulings מתוך the Talmud, and even though there is room for concern that he may not follow the path of truth and may not decide the law in its true form, so that the ruling would accord with the truth, nevertheless the sage has only what his own intellect yields and understands from the Talmud. And when his understanding and wisdom mislead him, even so he is beloved by God, may He be blessed, when he instructs according to what follows from his intellect. For the judge has only what his eyes see. And this is better than one who rules from a single compilation and does not know the reason for the matter at all, walking like a blind man on the road.”

Ishay,
He asked what my opinion is, and I told him. I did indeed cite the Rosh for both purposes: 1. also to say that the medieval authorities have no authority; 2. and also to say that the Talmud does.
And the explanation is this. First, you understand that there cannot be an answer to your question from some source that proves the authority of the Talmud. Who would testify to that—the Talmud itself? the medieval authorities? the Holy One, blessed be He, in the Torah (which was written before there was a Talmud)? This is a question that essentially has no answer beyond reasoning one way or the other.
Therefore my claim is that the authority of the Talmud, as others have already written before me, is rooted in the agreement of the public (or of all halakhic decisors / Torah scholars), somewhat analogous to the agreement at the giving of the Torah (as Rabbi Shimon Fisher writes in Derashot Beit Yishai, no. 15, based on Rabbi Kook, though as usual he did not cite him).
Now you can understand that the words of the Rosh (who also brings all the other views) testify that this is the agreement of all the halakhic decisors, and from that you also learn the second conclusion.

That already makes more sense (and it wasn’t written that way at first).
I still have difficulty with the rationale of general agreement. The agreement at the giving of the Torah is a covenant with the Holy One, blessed be He, by which we obligate ourselves to keep His commandments. Here, by contrast, there is no covenant with anyone, just something that many people think, and maybe they are mistaken. If there is general agreement about man-made global warming, that obviously doesn’t obligate me if I think otherwise (assuming I know the material and have reason). Beyond that, if I think they are mistaken, then I think the act they tell me to do (in some cases, a positive action and passive omission) runs contrary to the obligation of the covenant with the Holy One, blessed be He.
In Islam there is a hadith saying that the community will never agree on an error (and from that is derived the halakhic force of consensus—ijma). There that makes sense because it comes from the source of authority (Muhammad). As I understand it, here too you need the source of authority. Maybe you’ll bring proof from Nachmanides about rabbinic commandments, but then your guarantor needs a guarantor. There too it really isn’t clear before whom we accepted upon ourselves to listen to the sages, and even less clear why to listen to them when they uproot something from the Torah.

Part of the covenant with the Holy One, blessed be He, was that the Torah is subject to the interpretation of the sages (“you shall not deviate”). That is the Torah to which we committed ourselves. Now the only remaining question is who the sages are, and that is determined by agreements—after the end of ordination. Ordination is not the result of agreement; it is determined “from above.”
By the way, Nachmanides on rabbinic commandments does not write that this is a result of agreement. Rabbi Elchanan Wasserman (in Kuntres Divrei Sofrim) claims that in his own approach (I never understood his words there, and this is not the place for it). The reason is that Nachmanides is dealing with enactments and decrees of the Sanhedrin, and he is not asking who the sages are. He is dealing with the essence of the authority, not with identifying who possesses that authority. Here we are dealing with the second question.

Why is the identity of the sages determined by agreement? And in general, if authoritative sages are needed in every generation, then such sages are needed today too (and have been for the last 1,500 years). If authoritative sages are not needed today and everyone interprets according to his own understanding, since there are no authoritative sages, then there is also no need to accept the Talmud. We should accept only what was interpreted by sages who were authoritative from above. If there is an obligation to follow sages even when there are no authoritative sages from above, then presumably each person will decide for himself who those sages are—so what does acceptance have to do with it?
Nachmanides says this in the view of the Halakhot Gedolot, based on the baraita, and that also seems to be his own view—except that unlike the Halakhot Gedolot he does not count it among the Torah’s commandments. In addition, according to Nachmanides, every decree requires acceptance by the public (Avodah Zarah 35b), which is even stronger.

There needed to be authoritative sages in order to determine the meaning of the Torah and to establish rabbinic rules. Today the Talmud serves that function. Maybe there is no need to accept the Talmud (in my opinion there very much is)—but in fact we did accept it. Mount Sinai too is the result of public acceptance that obligates all of us. And even if we needed sages today, what can we do? There are no agreed-upon sages whom we have accepted upon ourselves. So the fact that they are needed proves nothing.

Where did you see such a statement in Nachmanides in the name of the Halakhot Gedolot? I don’t recall it. He writes that there is a scriptural support from “you shall not deviate” (that’s how he explains the Talmudic passage “And where did He command us?” in Shabbat).

And as for every decree requiring acceptance—that is the law of the Talmud itself (that it spread among the majority of the public and they are able to abide by it). But that is a law within the laws of enactments and decrees, and it does not seem to me connected to the authority of the sages.

As I said, acceptance of the Torah took place in a contract with someone, and therefore it is binding; it was not just acceptance. I don’t understand what this acceptance is or why it should be binding.
The Talmud too requires interpretation, and there is no binding interpretation. So either one can interpret on one’s own, or one can’t, and every generation needs authoritative sages. Since it is agreed that one can manage without authoritative sages, it follows that one can also manage with the Torah and the words of the authoritative sages (if there are any). Obviously there is an advantage to an interpretation from the fifth century over the words of the Torah themselves plus maybe whatever we can extract from authoritative sages, but there is also an advantage to the Mishnah Berurah over the Talmud. Advantage is not the issue here. Since there is no Torah obligation to listen to non-authoritative sages, we have no ability to choose sages and obligate ourselves to obey their voice.
Nachmanides’ words in the glosses: “And you have already shown from the words of the Rabbi that the sages expound concerning future commandments that were to be newly instituted, that Israel accepted them upon themselves, like the one he mentioned from the chapter Shevuat HaDayyanin: ‘And thus we find that when Moses adjured Israel, he said to them: Know that I am not adjuring you according to your own understanding, but according to my understanding and according to the understanding of the Omnipresent, as it says: “Neither with you alone do I make this covenant and this oath.” I have only the commandments that were commanded at Sinai; from where do we know future commandments that would be newly instituted, such as the reading of the Megillah?’—that is, from where do we know that Moses adjured them regarding these too according to the understanding of the Omnipresent and according to his own understanding? ‘Scripture therefore says: “The Jews confirmed and accepted upon themselves and upon their descendants”—they confirmed what they had already accepted.’ This is explicit for them, that the reading of the Megillah was accepted from Sinai and that a covenant was made concerning it, like the other commandments, and an oath came regarding it according to the understanding of Moses and the understanding of the Omnipresent. If so, why should they not say about it and the like that they were told to Moses at Sinai?”
Acceptance of a decree is not the law of the Talmud; the question there is whether it spread. As you said, there is a law in the laws of enactments that a decree that did not spread becomes null automatically or requires annulment. That does not at all have to be connected to agreement. In Maimonides it seems that the sages have authority to decree, but if the decree didn’t succeed, then it didn’t succeed. Nachmanides explains that it requires annulment if it did not spread, “for they did accept it upon themselves; but had they not accepted it upon themselves from the outset, it would not require annulment.” That is, in his view this is a case where the Jewish people accepted the decree but did not keep it, and therefore it requires annulment. But if they never accepted it upon themselves at all, the decree has no validity whatsoever.

I think we’re just getting tangled up here. Indeed, I’m not talking about advantage but about formal authority. If there is a source for the authority of the sages from “you shall not deviate,” then that is exactly like a contract. The question is to whom the verse we signed onto is directed—that is, who has the authority. Public acceptance can define the institution or the person to whom that was said, just like ordination from above. And according to Nachmanides, while it is indeed unclear what the source is for the sages’ authority to legislate, their authority to interpret does, even in his view, come from “you shall not deviate.” So even according to him, public acceptance can define to whom the matter applies.

I didn’t understand what you saw in Nachmanides’ words. They deal with acceptance (or being accepted) of the decree, not with acceptance of the authority of the sages that gives their words force. All the more so since there he is speaking under the assumption that there is a Torah source for the authority of the sages, and that this was done as part of acceptance of the Torah itself. If he were talking about authority based on acceptance, all the later authorities’ questions on him would fall away, and there would be no need to search for answers. But that is not what he means.

Regarding acceptance of the decree, in my opinion he means that it spread. “They accepted it, but it did not spread” means that it spread and then later lapsed. So here he is only repeating the words of the Talmud.

Right, so the question is whom the verse is speaking about. I see two possibilities: a. ordained sages; b. the sages of every generation according to public acceptance. What other possibility is there to interpret it?

The Nachmanides in the glosses that I quoted is not dealing with a decree becoming accepted. He brings the baraita that says that the oath at Sinai was also on the words of the sages (though not as part of the Torah), and therefore one can say of enactments that they were given to Moses at Sinai, and that is why the Halakhot Gedolot counts them among the commandments. Nachmanides himself accepts the principle that they should not be counted among the Torah’s commandments, but he still accepts the baraita (“This is explicit for them”), and in his view the source of the sages’ authority is that Israel accepted them upon themselves at the revelation at Sinai.

When Nachmanides says “it spread,” he is certainly meaning what the Talmud (in his understanding) calls “it spread,” namely that initially it did not spread. He says that a decree that did not spread requires annulment, and adds what in his opinion is not stated in the Talmud: that if they did not accept it, it does not require annulment at all.

Ishay (Y.A. or Y.M.?)—the public accepted upon itself to act in accordance with the Talmud; it did not accept upon itself that the Talmud is correct. So what you brought from global warming is not relevant.