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The source that doubtful Tumah in a private domain is Tamei is the Gemara in Sotah (28b - see there for translation):

מה ת"ל והיא נטמאה והיא לא נטמאה אם נטמאה למה שותה אם לא נטמאה למה משקה מגיד לך הכתוב שהספק אסורה מכאן אתה דן לשרץ ומה סוטה שלא עשה בה שוגג כמזיד ואונס כרצון עשה בה ספק כודאי שרץ שעשה בו שוגג כמזיד ואונס כרצון אינו דין שיעשה בו ספק כודאי וממקום שבאת מה סוטה רשות היחיד אף שרץ רשות היחיד ומה סוטה דבר שיש בו דעת לישאל אף שרץ דבר שיש בו דעת לישאל ומכאן אמרו דבר שיש בו דעת לישאל ברשות היחיד ספיקו טמא ברה"ר ספיקו טהור ושאין בו דעת לישאל בין ברה"י בין ברה"ר ספיקו טהור

Now regarding the question of why one needs a verse to forbid a woman who's anyways doubtfully prohibited (as Safek DeOraisa LeChumra), Tosfos answers that it makes her "certainly" prohibited and not "doubtfully prohibited".

Fine.

Now, the Gemara talks about regular impurity.

Let's say there's no verse. What would the Halacha be?

Any doubtful case of Tumah would be a Safek DeOraisa LeChumra, wherever it is.

Now, we're learning a Kal Vachomer from Sotah. Good, so now instead of one being Tamei "out of doubt" he'll be "definitely Tamei".

Good.

But now the Gemara learns a leniency - As a Sotah happens only in a private domain, so too does this rule apply only in a private domains.

Why? Let's say there's no extra stringency of Sotah. Why doesn't it fall back to the old classical "Safek DeOraisa Lechumra"?

  • Why are you assuming that Sotah can only be a stringency? – mevaqesh Mar 8 '17 at 5:08
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    Have you consulted the first shmua of the shev shmaateta? – kouty Mar 8 '17 at 6:57
  • ראש יוסף מסכת חולין דף ט עמוד ב: אבל מדברי רש"י ז"ל בד"ה הלכתא גמירי מסוטה אין נראה כן, אלא שמפרש דברה"ר ספיקו טהור דגזירת הכתוב הוא, דהא ברה"י אזלינן לחומרא וכל ספק איסורא בעינן למיזל לחומרא יע"ש. יראה מדבריו דאה"נ דהלכתא מסוטה בפירוש נאמרה דברה"ר טהור, ולאו דמסברא ידעינן לה כיון דלא דמי לסוטה דברה"י הוא דראוי לסתירה, ומש"ה ברה"ר ממילא טהור דאזלינן בתר חזקה. – mevaqesh Mar 8 '17 at 13:29
  • Like what @kouty said. See the Shev Shamaysa. – TrustMeI'mARabbi Mar 8 '17 at 15:10
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    "The source... is the gemara in Sotah". No it isn't, it's the mishna in Taharot. – Shimon bM Mar 8 '17 at 20:45
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Why? Let's say there's no extra stringency of Sotah. Why doesn't it fall back to the old classical "Safek DeOraisa Lechumra"?

The summarized answer is "because of chezkat Tahara", but it is not understandable, a too length answer is not readable. I hope that the follow can help. If you want really study the topic, the first shmaata of the Shev Shmaateta adresses it. In Melo Haroyim you can find some short explanations.

The question is based on several premises, two of them is perhaps disputable (to learn safek isur or tum'a in private domain from Sota, safek deorayta lachumra min hatora). but some statements in Gemara say them and are apparently not controversed. This question may be an introduction to a great topic. To treat it is not easy and great Acharonim wrote great books for this. I will give some elements, and finally, in a footnote, the most important element of answer explained.

Any doubtful case of Tumah would be a Safek DeOraisa LeChumra, wherever it is.

  1. Safek deorayta lechumra is not necessarily a din deorayta.It is true, though, that in Gemara Chulin " Rava said, prohibition's doubt is a case of stringency".
  2. But the Gemara says that contrarily regarding doubt about danger. The doubt regarding prohibition and uncleanness may be treated by leniency according to a chezkat heiter **Sota has a chezkat Tahara, let's say that safek deorayta lechumra, it is not the rule in case of chezkat heyter (¹).
  3. Following this, the rule of sota in public domain is a standard rule of chezkat heyter, nothing is learned from the Parasha.

(¹): Here we have to explain an important detail. The first Tosfot in Sota 28b reports that In several places in talmud the Gemara says that two halachot are learned from sota,

. the first is that doubt about uncleanness in private domain is unclean,

. the second is that doubt about uncleanness in public domain is clean (Sota 28b, Chulin 9a, Nidda 3a for Rabbi Shim'on).

Regarding this second rule, Tosfot asks: Why need we an halacha lemoshe misinai, there is a reason to be lenient without h.l.m., the chezkat tahara of the sota.

Further Tosfot makes this question stronger: In Gemara Nidda 3a, we see that Rabbanan state that it is not possible to learn a leniency in reshut harabim when there is chezkat tum'a. In other words, the leniency of sota in public domain results perhaps from her chezkat tahara only. That's as if no special halacha is learned from sota in public domain.

So why the Gemara says that in public domain there is a special teaching for sota.

Tosfot answers that the leniency in public domain is needed in a second step of the learning. After the novelty of doubt about uncleanness in private domain is unclean, we need to be sure that in private domain only the chezkat tahara is not effective, but in private domain the chazaka makes the din lenient.

איצטריך הלכתא להעמיד ספק טומאה ברשות הרבים אחזקתה דלא מחתינן ליה טומאה מספק

--> So in such cases, there is no old safek deorayta lechumra.

However, according to Rabbi Shim'on, the chezkat heyter of the sota is weakened even in public domain and we need a source to allow without chazaka. Rabbi Shim'on thinks that safek without chazaka is allowed and learns this from Sota.

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This answer is build from Tosfot in Nazir 57a (see also the Tosfot in Chulin 9b and Tosfot Nidda 2a).

But now the Gemara learns a leniency - As a Sotah happens only in a private domain, so too does this rule apply only in a private domains. Why? Let's say there's no extra stringency of Sotah. Why doesn't it fall back to the old classical "Safek DeOraisa Lechumra"?

First, you seem to assume that this rule of safek deorayta lachumra is a rule deorayta, it is not obvious.

Anyway according to Tosfot in Nazir there is a simple answer to Why doesn't it fall back to the old classical "Safek DeOraisa Lechumra"? I assume that you ask for sota in public domain. You will see below that no particular leniency is learned from sota according to Rabanan and that safek deorayta lechumra is not said when there is Chezkat tahara. Here is a stuff from this Tosfot:

באומר ראיתי שנזרקה טומאה ביניכם. והוא עומד מרחוק דהוי ספק טומאה ברשות היחיד ואם תאמר אם כן יביא כל אחד קרבן טומאה ודאי דכל ספק טומאה ברשות היחיד שורפין עליה [תרומה] ויש לומר דלא גמירי מסוטה אלא דבר שאפשר להיות כסוטה דאפשר שנטמאת אבל הכא לא אפשר לטמאות שניהם דודאי אחד טהור

One of two nezirim became unclean, they were alone, in a private domain. Despite that the din of doubt about uncleanness in a private domain should apply for each of them, since we know that only one of them is unclean, and we learn from Sota only a possible interpretation of the doubt, each Nazir is safek unclean and cannot make offer a Korban Tum'a.

ואם תאמר אם כן מאי פריך מעיקרא והא ספק טומאה ברשות הרבים הוא כלומר ויביאו שניהם קרבן טהרה והא ספק טומאה ברשות הרבים דמטהרינן נמי מסוטה גמרינן לה ולא ילפינן אלא דבר שאפשר להיות והכא בודאי אחד טמא

If it's clear for the Gemara that we learn from Sota with a restriction, so in public domain too, they cannot be regarded as both clean, because we know that one of them is unclean.

ויש לומר דספק טומאה ברשות הרבים לאו מסוטה גמרינן ליה

Tosfot explains that the novelty learned from Sota is the din of safek tum'a in private domain, not the din in public domain. {this is congruent with the opinion of Rabanan in Nidda 3a, following which the chiddush of Sota is the Vaday tame in case of safek. In reshut harabim, case sota shenistera is not a safek}

אלא כל חד וחד מוקמינן אחזקתיה וילפינן ליה מקרא פרק קמא דחולין (דף י:) להעמיד כל דבר אחזקתיה** אף על גב דודאי אחד טמא כיון דלא ידעינן ליה

In public domain, the safek nezirim treatment doe's not result from Parshat Sota, each of both nezirim benefits from his chezkat tahara.

ואף על גב דבפרק קמא דחולין (דף ט' עמוד ב') למאי דקא סלקא דעתיה קאמר התם הילכתא גמירי לה ומשמע התם דספק טומאה ברשות הרבים לאו משום חזקה אלא נגמר מסוטה

There is a Gemara in Chulin 9b which states that safek tum'a birshut harabim tahor when we have chezkst tahara is learned from Sota.

במסקנא לא קאי הכי ובמקום אחר [בריש מסכת נדה.] מפורש באורך:‏

This Gemara in Chulin doesn't follow the conclusion of suggia for the opinion of Rabanan. But for Rabbi Shim'on, this is the final rule, to learn from sota in public domain for a safek without chezkat tahara, because Rabbi Shim'on regards the chezkat tahara of the sota as cancelled.

The point that addresses your question is that Safek Tum'a in private domain is the "natural case of safek", which can be influenced by the Chezkat tahara. (this din doesn't result from halachot Sota according to rabanan).

The Gemara does not learn any leniency from Sota in reshut harabbim. The leniency is generated by the Chezkat tahara.

In masechet nidda at the first two dapim, there is a discussion between Rabbi Shim'on and Rabanan regarding the learning from Sota. Sota has objectively two features.

  1. There is a great reason to be suspicious because she did wish to be with this man against the prohibition of her husband {raglayim laddavar} so this is a little worst than a simple case of doubt.
  2. A second feature is that in the presence of someone else man and woman would probably not do nothing {this gives a special reason to see the safek sota in public domain with a special leniency}.

One of the two features would restrict the comparison between Sota and different cases of doubt. For Rabanan the leniency of Sota in public domain is not comparable to other doubts, and is not a source of learning. In the footnote of my second answer, you can see that this principle for rabanan is less clearly explained in other sugiot out of masechet nidda, but the Talmud is congruent with itself and the public domain for sota is a paradigm of safek + chezkat tahara.

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