The expression "תדע" in the Gemara

Question

The expression Teda, תדע, is often found in Gemara, we can translate it as "you have to know". It is a weak argument, not as a proof from a Mishna or a proof ab absurdo or a logical argument. But it is a kind of argument. I don't understand the utility of the word in its second occurrence of the following Gemara, the Amora can say what he thinks simply without the word Teda:

Yevamot 92.1

ורב נחמן אמר הוראה היא א"ר נחמן תדע דהוראה היא דבכל התורה כולה עד אחד לא מהימן והכא מהימן מ"ט לאו משום דהוראה היא אמר רבא תדע דטעות הוא דאילו הורו ב'ד בחלב ובדם להיתירא והדר חזו טעמא לאיסורא כי הדרי ואמרי להיתירא לא משגחינן להו ואילו היכא דאתא עד אחד שרינא אתו תרי אסרנא כי הדר אתא עד אחרינא שרינן לה מ"ט לאו משום דטעות הוא

Rav Nahman, however, stated: [Such an authorization] is [to be regarded as] a ruling. Said Rav Nahman: You can have proof that it [is to be regarded as] a ruling. For throughout the Torah a single witness is never believed while in this case he is believed. But why? Obviously because [such an authorization is regarded as] a ruling. Rava said: You can have proof that it is [to be regarded as a mere] error. For were Beth din to issue a ruling in a case of some forbidden fat or blood that it is permitted, and then find a [strong] reason for forbidding it, [their subsequent ruling], should they retract and rule again that it is permitted, would be completely disregarded; whereas here, it should one witness present himself, the woman would be permitted to marry again, and should two witnesses [afterwards] appear the woman would be forbidden to marry again, but should another witness subsequently appear the woman would again be permitted to marry. But why? Obviously because it [is regarded as a mere] error.

The translation above is from Soncino. He translates תדע by "you can have a proof". But apparently this is not an accurate translation, because Rav Nachman and Rava both don't give a proof from a Berayita or a Mishna. They disagree and say if we have a case A, the behavior of the Bet din will be X. I understand that there is a disagreement between Rav Nachman and Rava in the case described here. An Aguna was permitted by one witness. Further two witnesses contradict the words of the first witness. In a third step, a second single witness came and says that the husband died, but later, his testimony is not identical to the testimony of the first witness. According to Rav Nachman, I assume that this woman loosed this Chazaka Isha Dayika Uminseba, but according to Rava, she didn't lose it, and she can marry, thanks to the second single witness. For Rava there is an error of testimony, for Rav Nachman an error of ruling. I understand the Pshat from Rashi

Can someone explain the meaning of Teda of Rava when this statement is itself the topic of the discussion?

Below i give some examples of Teda I understand:

Berachot 53.2

א"ל ר' נהוראי השמים כן הוא תדע שהרי גוליירין יורדין ומתגרין [במלחמה] וגבורים יורדין ומנצחין

Pesachim 16.1

וסבר רבי אלעזר משקין אית להו טומאה בעולם והתניא רבי אלעזר אומר אין טומאה למשקין כל עיקר תדע שהרי העיד (יוסף) בן יועזר איש צרידה על איל קמצא דכן ועל משקין בית מטבחיא דכן

I understand that "Teda" needs to be a weak proof based in a probably but not necessarily link to an admitted truth, not as Ta Shma or Shma Mina, or Matnitin Hee, that are direct proofs.

Answer 1

Both R. Nachman and Rava introduce their statements with the word "teda" because both of them are attempting to provide evidence for their immediately preceding statements.

R. Nachman had alleged that in the case in the Mishnah where a woman remarried based on the court's permission (based on the testimony of a single witness that her husband was dead) the woman can be said to have followed a court ruling, and thus be exempt from an offering.

Rava had argued that in this case the woman cannot be said to have followed a court ruling, because the court's permission for her to remarry did not constitute a ruling at all; it was merely a factual error akin to the case in the Beraita cited by Zeiri where the court permitted Shabbat desecration on the assumption that the sun had already set, which turned out to be a factual error.

Each amora has to provide evidence to their respective positions. It's very nice to assert that the court's permission was or wasn't a "ruling", but how do we know that. Each amora therefore marshals evidence to support his position. R. Nachman points out that in general we do not accept testimony of a lone witness. Thus, here where we do accept the testimony of a lone witness it is perforce a court ruling that we can accept a lone witness's testimony (due to the presumption that a woman will investigate before remarrying). If the woman ended up remarrying without investigating and then it turned out that her husband was actually still alive, the court did not make a factual error (i.e. assuming that the husband was alive when he was in fact dead); rather the court had made an erroneous ruling that the testimony of a lone witness can be relied upon in this situation. This argument is prefaced with the word "teda" because "teda" introduces the evidence.

Rava constructs a different argument. He notes that in a standard case where a court retracts an erroneous ruling and then tries to reinstate it, they can't reinstate it (at least without new evidence to support the original ruling). Yet in the case of the woman who remarried, if two witnesses later testify that her husband is alive we forbid her (to both men), but if then a new lone witness testifies that her husband has now died, we permit her. If the permission for her to remarry is a court ruling that a lone witness can be relied upon then how could they allow her to remarry again? The fact that two witnesses testified that the husband was still alive after the first witness's testimony demonstrates that the first ruling was erroneous. If so, the court would merely be returning to an erroneous ruling with no new evidence, which we do not allow them to do. Perforce, then, the original permission was not a court ruling; it was merely a factual error promulgated by the lone witness (that the husband was dead when in reality he was alive). Rava's argument is prefaced with the word "teda" because he too is citing evidence for his position.

Moreover, Rava's argument and R. Nachman's argument do not have to be read as responding to each other. Each one can stand on it's own in explicating whether the Mishnah is indeed contradicted by Zeiri's Beraita. They would still each say "teda" to introduce their arguments because they are declaring evidence.

(The above is all according to Rashi's understanding of the passage.)

Answer 2

I think that the answer is what I hear from a friend. Since the Mishna doesn't give any restriction to the din permitting a wife by one witness, so this is true even when occurring repetitively. So, the case of Rava is obvious and Rav Nachman can argue against it that this is not a strong proof, and the logical argument is stronger.

And the Teda of Rava is understood easier following the Pshat or the Rav Moshe reported in Ramban, that the second single witness comes to be added to the first to make his testimony a two witnesses testimony and this is universally accredited. But the question was about the Pshat of Rashi.