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