The Gemara in Yevamos 47a says:
The Sages taught: The verse states that Moses charged the judges of a court: “And judge righteously between a man and his brother, and the convert with him” (Devarim 1:16). From here, based on the mention of a convert in the context of judgment in a court, Rabbi Yehuda said: A potential convert who converts in a court is a valid convert. However, if he converts in private, he is not a convert.
מעשה באחד שבא לפני רבי יהודה ואמר לו נתגיירתי ביני לבין עצמי א"ל רבי יהודה יש לך עדים? אמר ליה, לאו. יש לך בנים? א"ל הן. א"ל נאמן אתה לפסול את עצמך ואי אתה נאמן לפסול את בניך
The Gemara relates: There was an incident involving one who was presumed to be Jewish who came before Rabbi Yehuda and said to him: I converted in private, and therefore I am not actually Jewish. Rabbi Yehuda said to him: Do you have witnesses to support your claim? He said to him: No. Rabbi Yehuda asked: Do you have children? He said to him: Yes. Rabbi Yehuda said to him: You are deemed credible in order to render yourself unfit to marry a Jewish woman by claiming that you are a gentile, but you are not deemed credible in order to render your children unfit.
Tosfos asked:
Question: If we require three for conversion only l'Chatchilah, but b'Di'eved one is Kosher, if so (that he has witnesses), the conversion was not by himself! (It was in front of two, which suffices b'Di'eved.)
This is a wonder! Tosfos [מו: ד"ה משפט] discuss how we know that geirus is similar to גזילות and חבלות that require a court of three and not to הודאות והלוואות where one is enough [see the beginning of Meseches Sanhedrin] and they prove that it is more similar to גזילות and חבלות and if so there is no opinion that one suffices בדיעבד!? So what is Tosfos' question??!
The Shach [יו"ד סי' רס"ח סק"י] comments on what the Shulchan Aruch writes that according to the Rif בדיעבד it is enough to do מילה וטבילה in the presence of 2 people, that the number 2 is not precise and even one is enough and quotes our Tosfos. We see that he interpreted Tosfos as discussing מילה and טבילה and wrote that בדיעבד three are not necessary and one is enough. And so is explicit in Tosfos [קידשין ס"ב: ד"ה גר] that only קבלת מצוות requires three but for טבילה one is enough and they quoted the Gemara in Yevamos 45b that we cited earlier.
This is very difficult to understand!! ממה נפשך! However you spin it we are in hot water [not for טבילה though]. If the concept of משפט regarding geirus relates to מילה and טבילה then why is one enough for those while we need 3 for קבלת מצוות? How can we split up the meaning of משפט to mean 3 for קבלת מצוות and one for מילה וטבילה?? Also, how can קבלת מצוות be like גזילות וחבלות and מילה and טבילה like הודאות and הלוואות [that require one]. So it must be that "משפט" doesn't refer to מילה and טבילה and even one person isn't necessary - NOT like the Shach and Tosfos!! Also, how does the Tosfos we quoted above know that the Gemara is talking about מילה וטבילה [as the Shach understood] and therefore one is enough. Maybe when he said on the Gemara "נתגיירתי ביני לבין עצמי" he was referring to קבלת מצוות where 3 are required. If so - what is Tosfos' question that בידעבד one is kosher and therefore the עדים were enough??! For קבלת מצוות we need 3?!!
וכל זה צריך עיון גדול!!!!!!! 😔😕
כל הקושיות עפ"י דברי מו"ר הגאון הגדול רבי ד"י מן זצ"ל