Eruvin 105 Intellectual honesty opposed to a philosophy of leniencies

This short daf deals with various work needed for the maintenance of the מקדש , to remove impure items from it, and how and by whom it should be done.

This is based on a debate in the concluding Mishna of the Masechta regarding how to remove a dead שרץ  (creeping creature/bug) from the Temple.

The Masechta ends, however, by focusing on a rather cryptic statement in the final Mishna by Rabbi Shimon: מקום שהתירו לך חכמים משלך נתנו לך שלא התירו לך אלא משום שבות – “The place where the sages permitted it to you, they gave you from your own, as they only permitted it because of a rabbinical prohibition.”

Whatever the meaning of this statement, we might instinctively think that it has something to do with the debate in this Mishna itself.

Yet the Gemara understands this as a flashback to two other debates that Rabbi Shimon was involved in:

  1. Although the Chachamim hold that even if one stepped one אמה outside the תחום  (shabbos zone), it is forbidden to return, Rabbi Shimon allows a leeway of up to 15 אמות  because the people who measure the תחום  do not do so precisely and leave a safety net of this distance inside the תחום.

The first part of his cryptic statement thus reads:

“That which they (according to me) permitted you, ie 15 amos, was really yours to begin with, due to the safety net made by the measurers.”

  • Although Chachamim permitted retying a string that came loose on a musical instrument required for the Temple service, due to the rule of אין שבות במקדש , Rabbi Shimon forbade it, seeing as he held that this is a biblical prohibition, and only permitted tying it with a bow.

The second part of his cryptic statement thus reads:

“They only permitted  tying a bow which is a שבות, not tying a knot which (according to me) is a biblical transgression.

Rashi and Tosfos both explain that Rabbi Shimon makes these statements here because they are connected to his ruling regarding the string of an instrument.

Tosfos adds that this discussion was interrupted by listing the other things permitted because אין שבות במקדש  (there are no rabbinical prohibitions when it comes to Temple service) and Rabbi Shimon is now returning to explain his position there.

They both explain that Rabbi Shimon is going out of his way to stress that his leniency regarding the תחום  was not due to his taking shabbos lightly and a general policy of leniency, but because he felt it was objectively the correct ruling, seeing as the safety net was intentionally placed for that reason.

In contrast, when  it comes to making  a knot, he believed that a biblical prohibition was involved and only permitted a bow, in keeping consistently with the rule of אין שבות במקדש, even though the Chachamim were lenient.

Although both Rashi and Tosfos explain the positioning of Rabbi Shimon’s “clarification” of his approach based on the recent placement of the late dispute, it seems fitting that the Maseches concludes in this way.

After all, as we have seen so many times, Eruvin is not just about the technical and specific laws of Eruvin, but also about the power of rabbinical decrees as a whole and many global rules of psak halocho.

We have seen many leniencies when it comes to rabbinic decrees, such as ספק דרבנן לקולא, אין שבות במקדש, אין גוזרין גזירה לגזירה etc , as well as many exceptions to these rules.

Rabbi Shimon, in particular, is known for many leniencies in the rules of Shabbos, among them דבר שאין מתכוין מותר, מלאכה  שאינה צריכה לגופא פטור, לית ליה מוקצה,  גגות חצירות וקרפפים רשוצ אחת הן,  כתבי קודש  etc.

However, as we discussed early in the Maseches (see post on Eruvin 7,) halacha ideally should not be about having a philosophy of leniency or stringency, but rather about searching for the objective truth.

It is so fitting that such a Masechta should end with no other than the “lenient” Rabbi Shimon clarifying his position that his leniencies do not flow from any זלזול (making light of) the laws of Shabbos, chas veshalom, but from his objective view of the truth in each case.

Just like he was lenient so often in cases where he believed the truth required leniency, he was not afraid to be stringent against consensus when he felt that the truth required it.

Although a poseik might often be required to take local circumstances or even “meta-halachik” factors into account when issuing rulings, Rabbi Shimon, forever the idealist, seems to be teaching us that the ideal derech of a poseik and Talmid Chacham, namely intellectual honesty and objectivity, must never be forgotten.

הדרן עליך מסכת עירובין והדרון עליך

Its been an incredible journey, and we will miss you, as we temporarily move on to exciting new territory with Maseches Pesachim, Hashem willing, truly inspired and looking forward to the next round!

Eruvin 93-95  When the Eruv comes down, שבת הואיל דהותרא הותרא , and הלכה   כדברי המיקל בערוב revisited

When it comes to Eruv Techumim, we have seen that the golden rule regarding whether the eruv is valid is that if it is valid during the period of בין השמשות at the beginning of shabbos, it is valid the whole shabbos, even if the eruv food is later lost,eaten, or destroyed .

When it comes to ערוב חצירות and the מחיצות required for them, the situation is less simple.

At the bottom of Eruvin 93a, רב הושיעא asks what happens if new inhabitants enter a courtyard on shabbos?

Do we say that seeing as they were not there for the beginning of shabbos and their lack of participation in the eruv thus never invalidated everyone else’s eruv, the eruv remains valid for the whole shabbos despite their lack of participation therein, or do we say that seeing as they cannot join the eruv on shabbos, their presence now invalidates the eruv for the rest of the shabbos ?

Rashi gives the example of two courtyards separated by a common wall, who both make their own eruvin.

The wall then falls down, and each courtyard suddenly has a whole lot of new “inhabitants” that could render their eruv invalid.

Rav Chisda suggests a proof from the Mishna which says that if a large courtyard’s boundary wall with a smaller one is breached, the inhabitants of the large courtyard invalidate the eruv of the smaller courtyard.

He assumes that this is referring to if it was breached on shabbos, and we see from this that even if an eruv was valid for part of shabbos, it can be invalidated on shabbos through “new inhabitants.”

Rabbah, however, says that this Mishna might be referring to when the breach occurred before shabbos, and Abaya notes that according to Rabbah, it MUST be referring to such a case, as Rabbah himself had told Abaya that he has asked Rav Huna who in turn asked Rav Yehuda about a related case:

This was about two courtyards that made a joint eruv by means of an opening in their shared boundary wall which became sealed during the course of the Shabbos, possibly invalidating the eruv.

Rav Yehuda answered with the principle that שבת הואיל והותרה הותרה – Once Shabbos has been permitted (at its onset), it remins permitted (even if the entrance the eruv is based on becomes closed up.)

Similary in our case, once the smaller courtyard made its own eruv and the wall separating it from the neighboring larger courtyard was standing at the onset of shabbos, the eruv remains valid even if the wall falls down, introducing “new inhabitants.”

It follows that according to Abaya, Rabbah, and Rav Yehuda, we follow the rule of שבת הואיל והותרה הותרה  , and at least according to Abaya and probably Rabbah, this is a broad principle that applies both  in cases where a wall falls down (destroying a partition) and where a gap in the wall is filled (recreating the partition.)

The Gemara then records a debate between Rav and Shmuel regarding a similar case where the boundary wall between two courtyards that both made their own עירוב חצירות  falls down on Shabbos.

Rav holds that the inhabitants of each courtyard invalid the eruv of those of the other and carrying more than 4 amos within in the area is forbidden.

Shmuel, on contrast, holds that each courtyard’s inhabitants may carry up to where the boundary wall was, based on the rule of שבת הואיל והותרה הותרה .

Although we usually follow Rav against Shmuel, seeing as the later Amoraim like Abaya and Rabbah seem to hold like Shmuel, there is a strong argument at this point that we would do so too.

However, the discussion is far from over- In the Mishna at the bottom of Eruvin 94a, there is a debate between Rabbi Yehuda and Rabbi Yossi regarding what seems like related cases.

There, a house or courtyard collapses on two sides bordering the public domain on shabbos , or the pole or beam of a מבוי  collapse on shabbos.

Rabbi Yehuda holds that even though the מחיצות  that separate them from the public domain have collapsed, we apply the rule of שבת הואיל והותרה הותרה  and carrying within them remains permitted for the duration of that Shabbos.

In contrast, Rabbi Yossi holds that the duration of Shabbos is no different to the next shabbos, and the Gemara on Eruvin 95a understands this to mean that just like carrying within them will be forbidden the next shabbos, it is also forbidden for the duration of this shabbos and we do not apply the rule of שבת הואיל והותרה הותרה .

Rabbi Chiya bar Yosef rules like Rabbi Yosi, whereas Rav Yehuda quotes Shmuel as ruling leniently like Rabbi Yehuda.

The Gemara questions whether Shmuel could really have ruled leniently in this case.

In a different context, Rav Yehuda quoted Shmuel as saying that we always follow Rabbi Yehuda’s (lenient) rulings when in comes to eruvin, which at first glance appears to be consistent with the ruling quoted here.

However, Rav Chanan of Baghdad had asked Rav Yehuda to clarify whether Shmuel would even be lenient when it comes to the post or beam of a מבוי  being removed on shabbos, and Shmuel said that the lenient rule he had mentioned applied only to Rabbi Yehuda’s lenient views regarding the eruv itself, but not regarding the מחיצות  that are required for it.

As such, when it comes to disputes regarding whether מחיצות  are valid or not, the rule of   כדברי המיקל בערוב   הלכה does not apply- in our case, Shmuel would accordingly be stringent like Rabbi Yosi and not say שבת הואיל והותרה הותרה !

Rav Anan reconciles that apparent contradiction in Shmuel’s words by distinguishing between a private domain that opens to a רשות הרבים  and one that opens to a כרמלית .

In the former case, any dispute regarding the validity of the מחיצות  is effectively a dispute regarding a biblical prohibition, and being stringent is consistent with the general rule of ספק דאורייתא לחומרא.

In contrast, if only a רשות היחיד  and a כרמלית  are involved, the dispute only involves rabbinical matters, and the rule of ספק דרבנן לקולא  and its stronger “extension” of הלכה כדברי המקיל בערוב  should logically apply.

It could follow that according the conclusion of the sugya, if certain components of the מחיצות  that validate the eruv, such as a boundary wall, or the pole or beam of a מבוי, fall down on shabbos, the eruv remains valid for the duration of that shabbos, so long as  the previously enclosed area is not open to a biblically defined public domain.

This could be an extremely useful tool for many of our city eruvin which are based on the assumption that the public areas are not busy or large enough to be considered a biblically defined public domain ((רשות הרבים דאורייתא

Another huge נפקא מינה (practical ramification) could be when it comes to debates regarding the precise length of halachik measurements such as a טפח  and an אמה  which are used to measure the validity of מחיצות.

Assuming that the rule of הלכה כדברי המקיל בעירוב  applies to disputes amongst later authorities as well (which of course needs its own discussion,) then according to Rav Anan’s distinction, so long as no biblically defined public domain is involved, one might be permitted to rely on the more lenient opinions  (for example measure a לבוד  taking a טפח  as closer to 10cm rather than closer to 8cm when measuring the maximum gap between the wires of a fence.)

However, while Rav Anan has succeeded in reconciling the contradiction in Shmuel’s words, and he does seem to have the final word in this sugya, it is not a foregone conclusion that we follow Shmuel either in this particular case of שבת הואיל והותרה הותרה   or in his general rule (as understood by Rav Anan) that הלכה כדברי המיקל בערוב  applies even regarding מחיצות  when no רשות הרבים  is involved.

There are other sugyas that discuss this issue (see for example Eruvin 17a, Eruvin 70b,Eruvin 81b) which need to be put together with the various pieces on our three daf before a clearer idea of  the halacha can be seen, but we shall suffice for now to point out that Tosfos rules against Shmuel even when the previously enclosed area opens to a כרמלית  seeing as Rav rules like Rabbi Yosi. This seems to be the general consensus of other Rishonim as well, though a thorough study of their views is obviously required still, and as such, it seems that when a problem occurs on shabbos with the מחיצות , the rule of הואיל דהותרה הותרה  cannot be applied.

When the problem is created by the closure of a gap in the מחיצה  and not the lack of a מחיצה , however, Tosfos points out that even Rabbi Yosi agrees with the rule of שבת הואיל והותרה הותרה.

Whether Rav Anan’s extension of כלכה כדברי המיקל בערוב  to rabbinically required מחיצות  in other disputes where Rav does not rule against Shmuel requires further analysis, and could impact our second question regarding disputes over the sizes of the טפח  and אמה!

These posts are intended to raise issues and stimulate further research and discussion on contemporary topics related to the daf. They are not intended as psak halacha

Eruvin 91-92 Rabbi Shimon’s domains and הלכה כסתם משנה

In the previous post, we mentioned the three opinions regarding how unusual types of private domains such as roofs, courtyards, and קרפפים are treated when it comes to transferring from one to the other in the absence of an eruv. I refer to them  as “unusual” seeing as their main purpose is not for dwelling in-see  first Rashi 91a )

According to Rav Yehuda, the opinions are as follows:

1. Rabbi Meir allows free direct  transfer from roof to roof, courtyard to courtyard , and קרפף to קרפף so long as the one private domain is within 10 amos height of the other , even if each domain   has different owners.

2. The Chachamim consider each roof to be under the same domain as the house below and thus forbid transferring from one to the other .

3. Rabbi Shimon allows free transfer between all 3 of these special private domain types so long as the object was in one of them before Shabbos and not in one of the houses. He also does not have the 10-amah height limitation between domains that Rabbi Meir has.

We have discussed how Rav and Shmuel debated whether two roofs not separated by a partition can be considered separate as far as carrying on one of them according to Chachamim, or bringing things from the house onto them according to Rabbi Shimon.

We discussed how Samuel’s lenient ruling might not carry weight against Rav despite the rule of הלכה כדברי המיקל בערוב because Shmuel  himself holds that this rule only applies to requirements of the eruv itself and not disputes about the status of the מחיצות needed for the eruv, something we shall hopefully follow up on soon.

In this post, we discuss whether Rabbi Shimon’s lenient ruling is accepted in halacha. 

On the one hold, we would not normally follow Rabbi Shimon against the majority view in a Mishna.

On the other hand, the rule of הלכה כדברי המיקל בעירוב might apply here, seeing as the debate is not about what is considered a valid מחיצה but rather about whether an eruv itself is required between different types of irregular  private domains ( as opposed to houses which are specifically meant to live in)

Rabbi Yochanan indeed rules leniently like Rabbi Shimon.

There is another principle of psak, often quoted by Rabbi Yochanan himself, however, which the Gemara uses to question whether Rabbi Yochanan could indeed have ruled that way.

This is the rule of הלכה כסתם משנה ( the halacha follows an anonymous Mishna .)

Wherever a view of a Tana  is recorded in the Mishna without his name being mentioned , the law follows that view.

The reason for this is because when writing down the Mishna, Rebbe chose to use this method to record a view which he considered to be authoritative and not subject to dispute 

Seeing as there is such a סתם משנה which forbids moving things from one courtyard onto the top ( roof) of the wall between it and its neighboring courtyard, against Rabbi Shimons permission to transfer things from one private domain to another so long as a house is not one of the domains involved, it should follow that we do not accept his lenient opinion.

From the question itself, it seems to follow that the Gemara assumes that this principle of הלכה כסתם משנה should override the rule of הלכה כדברי המיקל בערוב- this makes sense given the fact that Rebbe chose to record the stringent view anonymously  despite the later rule, clearly holding that the former rule does not apply .

The Gemara answers that the Mishna does not contradict Rabbi Shimon, as it could be referring to transferring things from the house VIA the courtyard to the top of the wall, which even Rabbi Shimon forbids.

As Tosfos points out, the very question of the Gemara is difficult , seeing as the rule of הלכה כסתם משנה has its limits.

If such a Mishna is followed by one which contains  dissenting opinions on the subject, the rule no longer applies, as we assume that Rebbe specifically recorded the later Mishna as a dispute in order to show that he no longer regards the anonymous Mishna as authoritative. 

This is referred to as סתם ואחר כך מחלוקת .

Seeing as the dispute between Rabbi Meir, Chachamim , and Rabbi Shimon is recorded later in the same Masechta than the סתם משנה against Rabbi Shimon, the סתם משנה should not be authoritative anymore .

The Rashba and Ritva suggest that the Gemara could indeed have answered that but preferred to answer the way it did .

Given that the answer given both went against the simple meaning of the Mishna  and Rabbi Chiya’s apparent interpretation thereof, this seems like a rather extreme approach, but perhaps making our principle of הלכה כדברי המיקל בעירוב  fit in with the סתם משנה was more important to the Gemara than interpreting it in the simplest way?

Tosfos in contrast suggests that the Gemara is not questioning Rabbi Yochanan’s support for Rabbi Shimon’s ruling regarding treating the three types of unusual private domains as one, as that is indeed סתם ואחר כך מחלוקת.

Rather the Gemara is questioning his support for Rabbi Shimon’s leniency regarding not being concerned about a 10 tefachim  difference in height between the relevant private domains as Rabbi Meir is , Something which is not explicitly permitted in our Mishna but rather deduced.

He suggests that the debate regarding this can be found in an earlier Mishna whereas the Mishna that discussed the wall between the courtyards and seems to be stringent like Rabbi Meir is both later and anonymous, making it סתם ואחר כך מחלוקות .

Whether the earlier Mishna is indeed connected to this issue or not depends on how the case under concern is interpreted, and the Ritva indeed views the two cases as completely different. 

In any case, it is seems to be concluded that we follow both leniencies  of Rabbi Shimon without compromising the rule of הלכה כסתם משנה, something which can be very useful under the correct circumstances, though the correct alignment of roofs, courtyards, and קרפפים  that Rebbe used to carry his towel to the spring is unlikely to be replicated in modern cities.

These posts are intended to raise issues and stimulate further research and discussion on contemporary topics related to the daf. They are not intended as psak halacha

Eruvin 89-90 The dispute over roofs and הלכה כדברי המקיל בערוב revisited

The new chapter opens with a fascinating dispute about various unusual private domains that are not primarily used for living in, but have some other, if not limited, use.

The opening Mishna starts with the view of Rabbi Meir who considers all roofs within a certain proximity to each other to be considered as if they are one large private domain, even if they are owned by different people.

We recall that even though on a biblical level, there is no problem with transferring something directly from one private domain to another, Chazal forbade transferring items between adjacent private domains owned by different people or from a private domain owned by one person to  a shared courtyard or vice versa, in the absence of an eruv chatzeiros.

This is in order that one should not become confused and think that transferring from any domain to another is permitted, thus coming to transfer things between a private and public domain and vice versa.

Rabbi Meir is of the view that this prohibition is limited to transferring from one house to that of another or one type of private domain to a different type of private domain, but that roofs (and we shall see soon, also courtyards and קרפפים  ) have limited use, are not affected by the dwellers below and do not share this concern( see Rashi ).  As such, one may transfer items  directly from one roof to another, so long as the one roof is not more than 10 tefachim below or above the other, a limitation the Gemara explains later.

The Chachamim on the other hand, do not agree with this leniency, and hold that the roofs have the same divided status as the houses underneath and one may not transfer things from one roof to another.

The third and most lenient view is that of Rabbi Shimon, who holds that so long as an item was on a roof, in a courtyard, or a קרפף on erev shabbos and not in a house, one is permitted to transfer it directly from anyone of these three types of private domain to another!  the Gemara brings the case where Rebbe said that they used to “carry” their towels and annointing oil through these kind of domains to the spring in which they would wash and back on shabbos!

Whereas I hope to focus on this view of Rabbi Shimon and whether it is authoritative in a later post, I would like to focus today on a dispute between Rav and Shmuel regarding the opinion of Chachamim, which might also be relevant to the view of Rabbi Shimon.

This debate is regarding an important principle regarding partitions, known as גוד אסיק מחיצתא  (the partition carries on upwards), the more widely applied cousin of the principle we discussed in the previous post, namely גוד אחית מחיצה  (the partition carries on downwards) and its sibling rule of  פי תקרה יורד וסותם (the edge of the ceiling continues downwards and seals.)

This rule might be what allows us to view a raised area such as a roof, higher than 10 tefachim vertically, or in a horizontal displacement of 4 amot, to be viewed as a private domain, seeing as the vertical rise below is considered to continue upwards enclosing the raised area.

The dispute centers around the status of a roof that is open to the neighbor’s roof.

According to Chachamim, it is forbidden to carry from the one roof to the other.

The Question is whether one may carry things around within the limits of the one roof itself?

This is because  being open to the neighboring roof means that it is open to a place to which items may not be transferred from it, and the rule is that any domain that is open to another domain to which items may not be transferred is itself considered similar to a כרמלית  in that one may only transfer within 4 amos even inside it.

Although each roof is viewed to be surrounded by the “rising” walls below, the area between the roofs might be viewed as open.

Whereas Shmuel holds that the boundary wall between the houses below is also consider to “rise upwards” and close the gap between the roofs, Rav is of the view that the rule of גוד אסיק  only applies where the partition below is noticeable from the top. In a case where there is no gap between the roofs, the roofs effectively hide the boundary wall below from the view of those on the roof, and the boundary wall cannot be said to rise and close the gap.

This would make a major difference as to how one can carry things on a roof according to Chachamim, and even according to Rabbi Shimon, it will also be relevant when it comes to items brought from the house to the roof on shabbos, to which his leniency does not apply.

When it comes to how to rule in this debate, we are faced by contradictory rules.

On the one hand, the halacha generally follows רב  against שמואל  except in 3 cases (see for example Shabbos 22a.) On the other hand, we also hold that הלכה כדברי המקיל בעירוב (the halacha is like the lenient opinion when it comes to eruvin,) even against a majority and against existing rules of psak (see Eruvin 46a.)

The Ritva rules that the halacha is like Rav as usual, because the rule of הלכה כדברי המקיל בעירוב  does not apply in our case.

He proves this from an earlier sugya (Eruvin 81b) which states that even though the halacha is like Rabbi Yehuda regarding Eruvin, this is only regarding the laws of the eruv itself, but when it comes to the laws of the מחיצות , the partitions required to define the status of the domains that the eruv is made for, this is not the case- it is in fact Shmuel who restricts this rule in that way.

The Ritva seems to understand that the rule that the halacha follows Rabbi Yehuda refers to his many leniencies and is an application of this rule of הלכה כדברי המקיל בערוב, and that its limitation to the laws of eruv proper and not those of the partitions, proves that its parent rule, namely הלכה כדברי המקיל בערוב  is similarly limited. This appears to be the understanding of the Yerushalmi too, which I hope to discuss in a later post.

The reason for this distinction could be that whether an eruv is valid or not affects only rabbinical laws, the validity of a partition can also determine whether an area is biblically defined as a private or public domain (or neither) and this rule can therefore not be universally applied as an extension and further leniency in the general rule of ספק דרבנן לקולא  (assuming this is indeed what it is, ואכמ”ל)

Even though the affected halacha is not always biblically, to avoid confusion, the extended leniency of eruvin is inapplicable in all cases regarding מחיצות .

Seeing as many Rishonim and poskim apply the later rule to many undecided disputes regarding eruvin, this distinction would have a massive impact when it comes to any undecided disputes regarding partitions. 

There is much to write regarding the scope of  the rule of הלכה כדברי המיקל בעירוב and whether it also applies to partitions, and this is indeed the subject of much discussion and dispute amongst the Rishonim.

Before getting to the Rishonim and Poskim, there are many sugyas relevant to the discussion, and I hope to revisit this in a few days again the next time it comes up!  

These posts are intended to raise issues and stimulate further research and discussion on contemporary topics related to the daf. They are not intended as psak halacha

Eruvin 87-88 The hanging partition,the Kinneret, and strengthening דרבנן

One of the fascinating concepts we have seen over the past view daf is the concept of a מחיצה תלויה- a hanging partition.

The generally accepted view is that any partition that  a goat could get through is not considered a partition, and as such, it needs to be at least 10 tefachim high from the ground up.

It could also start a maximum of 3 tefachim above the ground, due to the rule of לבוד.

However, a מחיצה תלויה  (hanging partition) which extends 10 tefachim or more from the roof downwards but does not reach within 3 tefachim of the ground, is invalid.

This is the view of חכמים  regarding a Sukkah, though Rabbi Yosi dissents and allows it (Sukkah 16a)

However, there is an exception to this rule, and that is when it comes to a body of water.

Sometimes, people would build houses on the sea, river, or lake shore, and they would build balconies over the lake or sea , from which they could draw water.

They might also have a water-canal passing through their property.

Of course, this presents a problem on shabbos, seeing as the water body generally has the law of a כרמלית  (open area that does not qualify as a public domain), the balcony is a רשות היחיד (private domain), and transferring from the one to the other is rabbinically prohibited.

In order to circumvent this, a method was used whereby an area in the waterbody underneath the balcony was “partitioned” in order to become part of the same רשות היחיד  as the property.

In the case of an אמת המים (canal), a partition was built over the points where it entered and exited the courtyard.

In the case of the balcony, a mechitza would hang down from the balcony surrounding that area.

Although this would be a מחיצה תלויה , which is normally invalid, the sages were lenient when it came to the need for water supply, and allowed it, in the words of the Gemara:  קל הוא שהקילו חכמים במים.

In the Mishna at the bottom of Eruvin 86b, we discussed the case of a water-cistern that lies between 2 courtyards, where the wall between the courtyards passes over the pit.

Although the wall could perhaps be a מחיצה תלויה , dividing the pit between the two courtyards and allowing each courtyard to draw water from its side, the Mishna requires a special partition to be build in or over the pit. (see Gemara there for different views.)

Rabbi Yehuda, however, allows them to rely on the border-wall itself.

The Gemara assumes that Rabbi Yehuda follows the view of Rabbi Yosi regarding Sukkah, that a מחיצה תלויה  is valid even over dry land.

Although the wall passes over the cistern, which is clearly a body of water, Rashi explains that the leniency of allowing a hanging partition  over a body of water only applies when it is clear that it was built for that purpose, which is clearly not the case with the border-wall.

As such, this is the equivalent of a hanging partition over dry land, which is why the Chachamim do not accept it.

The Gemara counters that the two cases are not comparable:

Rabbi Yehuda is lenient in the case of the pit seeing as the requirement for eruv chatzeiros is only rabbinic, but would never be lenient when it comes to a Sukkah which is a biblical requirement.

Rabbi Yossi, on the other hand was lenient when it came to Sukkah, seeing as eating outside the Sukkah is only a בטול עשה  (going against a positive command), but would never be lenient when it comes to Shabbos transgression  which is a capital offense (at least under certain circumstances.)

Either way, the normative view seems to be that a מחיצה  תלויה  is only allowed over waterbodies.

The Beraisa discusses a case where a water-canal runs between two houses and can be accessed via windows from each house.

It says that if it is less than 3 tefachim wide (or 4 according to Rabban Shimon ben Gamliel,) one may draw water from it.

The Gemara first assumes that this is referring to the width of the canal  and that whereas below this width, it is a מקום פטור  from which water may be transferred directly to the house, above this threshold it is already a כרמלית  from which water may not be transferred.

However, as Rav Dimi had quoted Rabbi Yochanan as saying that a כרמלית  cannot be less than 4 tefachim wide, the Gemara prefers not to make these words subject to a tannaic debate.

It therefore explains that the Beraisa is referring to the width of the banks of the canal between it and the overlooking window of the house.

If the bank is less than 3 tefachim (or 4 according to Rabban Shimon ben Gamliel,) it would be considered a מקום פטור  and even if the canal itself is wide enough to be a כרמלית, it would be permitted to transfer the pitcher to the canal via the banks and back once filled with water via the banks.

This implies that the Beraisa permits transferring an item from two different domains via a מקום פטור.

However, Rav Dimi has also reported Rabbi Yochanan’s view who permits transferring an item from a private domain or a public domain to a מקום פטור  or vice versa, he does not permit using the מקום פטור  as a half-way station for transferring an item from  a private domain to a public one or vice-versa.

The Gemara explains that Rav Dimi’s case involved biblically forbidden transfers, and it is thus rabbinically forbidden even through a מקום פטור.

However, seeing as the canal is only a כרמלית and transferring directly from it to the private domain is only rabbinically forbidden, Rabbi Yochanan would permit doing so through a מקום פטור.

The Gemara then brings a case (that we have seen earlier)  where Rabbi Yochanan permits transferring something from one of the two adjoining courtyards to the top of the wall between, so long as it is less than 4 tefachim wide and thus considered a מקום פטור.

This is contrast to Rav who forbids doing so.

He does not, however, permit using the wall as a means of transferring from the one courtyard to the other, even though transferring from one private domain to another is only rabbinically prohibited (in the absence of an eruv!)

The Gemara concludes that that reflects Zeiri’s view, who forbids doing this even where the direct transfer is only rabbinical.

What is immediately obvious is that when it comes to using a מקום פטור  as a means of transferring from one domain to another, the Gemara is happy to suggest that Rabbi Yochanan is more lenient regarding rabbinical domains than regarding biblical ones.

Yet we have seen earlier )Eruvin 77a)  that not only does Rav not go along with this, but he is even stricter when it comes to rabbinical domains- not only does he not permit using the top of the wall (less than 4 tefachim wide) as a half-way station from one courtyard to the other, he even forbids carrying from one of the courtyards to the top of the wall itself or vice-versa, despite it being a מקום פטור which would be permitted even from a biblical private or public domain!

His reasoning was that precisely because we are dealing with rabbinical domains, we need to be extra stringent so that people do not take them lightly!

We have seen (85b) that Shmuel also followed that approach, and have also seen it in the beginning of the Maseches (see posts on Eruvin 3 and Eruvin 21)

Not withstanding the fact that that approach seems to fly in the face of the normal principle that advocates more leniency is rabbinic matters particularly regarding eruvin, Tosfos points out that Rabbi Yochanan clearly does not accept this approach even in these case, and follows the usual rule of treating rabbinical laws more leniently.

Given Rabbi Yochanan’s seniority in halachik rulings over both Rav and Shmuel, this could have major halachik ramifications wherever the idea of חכמים עשו חזוק לדבריהים  applies, and there is a need to understand the basis of these two different approaches, and whether Rabbi Yochanan’s rejection thereof is limited to this case or is a general objection to the entire concept.

If the debate is purely local, we need to understand why Rabbi Yochanan did not feel the need to “strengthen” this particular rabbinical requirement of forbidden carrying from either domain to a כרמלית   or vice versa.

If on the other hand, this is his global position, we would need to explain why he never feels the need to “strengthen” rabbinical requirements and show that his position is consistent in other places where this principle is used.

Much to think about- hopefully more on this as our journey continues…

The “sea of Teverya” (Kinneret) as well as the inhabitants of Teverya get a special mention on Eruvin 87 as well as Eruvin 88.

We learnt on Eruvin 86-87 that Rabbi Chananya ben Akavya has an extra special leniency when it came to drawing water from a water-body under a balcony.

He held that if the balcony was at least 4 by 4 amos (24 by 24 tefachim,) one could cut a hole of 4 by 4 tefachim in the middle, and the rest of the balcony would be viewed as “bent partitions”  dropping the required 10 tefachim below the balcony on all 4 sides. Then, the rule of גוד אחית מחיצתא  (the partition continues downwards as a hanging partition) kicks in , making the water below the hole a private domain!

At the bottom of Eruvin 87b, the Mishna seems to disagree with this, seeing as it requires proper partitions on or below the balcony, not imaginary bent ones.

The Gemara notes this difficulty and explains (as it has suggested earlier) that this special double leniency of Chananya ben Akavya is limited to the sea of Teverya  (the Kinneret.)

This is because it is surrounded by banks, cities, and קרפפים , making it more similar to a private domain than a כרמלית.

Rashi explains that even though it was not מוקף לדירה (surrounded for the purposes of dwelling in it) and thus still has the law of a כרמלית  , It is still different to most bodies of water and Chananya applied this leniency to make it easier for the people of Teverya.

The Gemara then notes that this was one of 3 leniencies that he made for the people of Teverya.

The other two were as follows:

1.       Normally, when one collects material from outside early in the morning while the due is still on it, the material is considered susceptible to impurity because of the due. However, if one is not happy with it being damp, but only collected it early in order to get to work on time, the material is not susceptible. Chananya took note of the fact that the people of Teverya were hard workers and allowed them to treat the material they collected  as non-susceptible !

2.       He also permitted them to dry themselves with a towel  after washing (on Yom Tov or in cold water on Shabbos- see Rashi) without worrying that they might come to squeeze the towel, apparently as they were known to be careful with such things!

It is truly to live in a time and place where we are so close to so many of the holy places mentioned in the ancient sources and that we are able to enjoy the splendor of the “Sea of Teverya” like our sages did before us!

These posts are intended to raise issues and stimulate further research and discussion on contemporary topics related to the daf. They are not intended as psak halacha

Eruvin 85-86 The tenant and the rich man

The Mishna on Eruvin 85b tells us that someone who dwells in a store-room that opens to a courtyard needs to participate in the eruv chatzeiros, and if he does not do so, he forbids the courtyard to everyone else.

Rabbi Yehuda, however opines that if the owner of the courtyard has a תפיסת יד (hold) on it , it is not an issue.

Rashi explains that this means that if the owner uses some of the space inside the storeroom to store his own things, it is considered still to be his רשות (domain.)

The Gemara  here seems to understands this to be part of  a general rule that when the owner retains usage of the house, he can also be part of the eruv in place of the tenant.

The Gemara gives the example of a very wealthy man, Bunias, who owned courtyards and allowed others to stay in them on condition that he could keep some of his property in them.

Rashi seems to understand that he used to “lend” the houses to them, whereas the Ritva understands that he sometimes “lent” and sometimes rented them to people.

As a rental ostensibly confers a higher degree of quasi ownership than a loaned house where no money is paid, this could be very significant regarding whether some level of קנין  is required here or whether simply דירה  (long-term dwelling) is sufficient to make the inhabitant the deciding factor regarding eruvin. (See Meiri who relates this to the debate whether עירוב משום דירה או משום קנין  .)

While the possibility that a long-term inhabitant might be considered the quasi owner regarding eruvin even if he does not pay for his stay certainly seems to be assumed by Rashi, short-term guests in hotels or visitors that stay in their own cottages in one’s courtyard could well  have a different law, but see our post on Eruvin 65.

The Beraisa proceeds to tell how when Bunias arrived, Rebbe himself would tell everyone to make space for the man of “100 portions.”

When another wealthy man arrived, however, he told them to make space for the man of “200 portions.”

Rashi explains that Rebbe thought the second person was even wealthier and thus honored him according to his level of wealth!

רבי ישמעאל ברבי יוסי pointed out to Rebbe that Bunias was actually wealthier than the second person, and his father owned 1000 boats at sea and 1000 cities on land!

Rebbe responded that when רבי ישמעאל ברבי יוסי next went to visit Bunias’ father, he should tell him to send his son in fancier clothes next time (so he will know how wealthy he is and honor him accordingly [see Rashi])

The Gemara proceeds to tell us how not only Rebbe, but also Rabbi Akiva were particular about honoring the wealthy.

For those of us who are naturally put off by the idea of the wealthy in a community being giving some of the top honors, and the common practise of auctioning off the best honors to the highest bigger, it might seem difficult to accept how such great Tannaim seemed to go along with this approach?

Surely  a person should be given honors based on merit, rather than on the size of his wallet?

Surely the road to community leadership should not bypass the less fortunate?

We discussed in our post on Daf 49 that although the Torah takes social responsibilities very seriously, enforces charity and tithes, and certainly does not accept a libertarian “laizze faire” approach to economics, it also has total respect for individual property rights and for the right to generate personal wealth.

We also noted that according to one view, the entire institution of allowing one to send a messenger with bread for eruv techumin rather than having to go there oneself was to make it easier for the wealthy, and that the Torah actually treats the wealthy with great respect.

This case serves as a prime example of this  honor shown to wealthy people.

Yet by the end of the sugya, it becomes clear that this honor is not unconditional, and that it is not a contradiction to the merit based approach that the Torah is famous for(for example a learned Mamzer takes priority over an ignorant priest!)

In explaining Rabbi Akiva’s great honor for the wealthy, the Gemara brings a passuk (Tehillim 61/):

“ישב עולם לפני אלהים חסד ואמת מן ינצרהו”- read midrashically as “The world shall endure in front of Elokim,  kindness and truth will guard it”

The Gemara applies this passuk to a wealthy person and says- When will the world sit forever in front of Hashem (endure?)  When kindness and truth guard it (when the wealthy use their money to perform acts of kindness and truth.)

The Torah’s true attitude to wealth is that it was given to the wealthy in order to help the less fortunate, and that when they do this, they are actually sustaining and building the world, something very worthy of honor!

It is thus fitting that someone like Bunias should be used as an example of a wealthy man honored by Rebbe, given that he used to “lend” his properties to people, at least sometimes free of charge, to live in!

Whether a less generous wealthy man loses this right to honor completely, or should still be honored given his potential, or in the hope of encouraging him to fulfill his purpose, is of course subject to discussion, but it seems that Chazal had little tolerance for wealthy misers who refused to give some of their wealth to others, and in this regard  ממשכנין על הצדקה- we take collateral from people in order to force them to give tzedakah, sometimes in very large sums(B.B. 8b)

These posts are intended to raise issues and stimulate further research and discussion on contemporary topics related to the daf. They are not intended as psak halacha

Eruvin 82   Nature walks on Shabbos and אין מערבין אלא לדבר מצוה

This is one of those daf where there are so many different topics to choose from, (including some we have started dealing with already in previous posts,)  that having to choose one for the purposes of this post is particularly frustrating.

From gambling and אסמכתא  , to the role of קטן, disputes, ברירה  revisited, דעת בערוב, the food used for the eruv, Talmudic measurements, and more, this is no “one-sugya” daf.

Yet I decided to focus on the ruling of Rav Yosef that an eruv techumim may only be made for the sake of a mitzva.

He derives this from the Mishna on this daf which discussed how a person can make an eruv techumim on behalf of other people in his town.

He places the barrel containing the eruv in the chosen place and states that the eruv is  for all inhabitants of his city that want to go to a mourner’s house or בית המשתה  (place of drinking, sometimes used to refer to wedding feast.)

Noting that both examples given are for the purposes of mitzvos (comforting mourners and making the bride and groom happy,) Rav Yosef deduced that it is only for the purposes of a mitzva that an eruv can be made.

This deduction could be questioned for a few reasons:

i.                     Perhaps the Mishna is only mentioning the most common reasons someone would walk that far on shabbos ( אורחא דמילתא ) but does not intend to exclude דבר הרשות  (voluntary or non-mitzva related purposes.)

ii.                   Perhaps the permission to make the eruv on behalf on everyone in the city is limited to דבר מצוה  (matters of a mitzva) but making an eruv for one’s own purposes is allowed even לדבר הרשות?

iii.                 Perhaps this limitation only applies to when one uses food for one’s eruv, but if one is מערב ברגל (makes the eruv by being at the site of eruv just before shabbos,) it may be done even for דבר הרשות.

Whereas the Gemara acknowledges the first point and admits that Rav Papa’s deduction is indeed a חדוש, it does not question his ruling, and he appears to have the final word on the matter.

The second two points are not mentioned at all in the Gemara. While I have not seen any of the Rishonim mentioning the second point, there is indeed a strongly represented view amongst them that makes the distinction raised in the third case (see  among others Rabbenu Yonatan on the Rif, Meiri)

While it seems from this daf that the matter is settled, there are various other sources that show that it is far from simple.

For example, back on Eruvin 31, we saw a debate between Rabbi Yehuda and Chachamim regarding whether one may place the eruv food on a grave- this could be  because one is not allowed to benefit from a grave and the eruv might be considered  benefit seeing as it allows one to walk further than one could without it.

During the שקלא ותריא  (flow of the sugya,) Rava suggested that the debate is dependent on whether one is allowed to make an eruv techumim for something other than a mitzva.

If one is only allowed to do so for a mitzva, then seeing as מצוות לאו להנאות נתנו (mitzvos were not given to derive benefit from,) the eruv is not considered a benefit, and it is fine. This could be the view of Rabbi Yehuda who allows placing the eruv on a grave.

In contrast, Rava explains that the Chachamim hold that one may make an eruv techumin even for דבר רשות, and that the eruv is thus considered a forbidden benefit from the grave.

It could then follow that seeing as Rava was later than Rav Yosef  (הלכה כבתראי אבל צ”ע אם נאמר כלל  זה אפילו בתלמיד נגד רבו ) , and according to him, the chachomim allowed making an eruv for a non-mitzva purpose, this could indeed be the halacha.

Further support for this could be derived from the  Mishna (Pesachim  49a. )  It rules that if someone forgot to burn his chametz on erev pesach and was on his way to make an eruv techumim for a דבר רשות  (voluntary matter,) he needs to go back and burn the chometz, and  simply doing בטול  (nullification) in his heart is not sufficient. This seems to clearly indicate that it is permitted to make an eruv techumim for a דבר רשות.

Although none other than the Or Zarua (brought by  הגאות אשרי עירובין פרק 8 אות 1)  rules leniently and permits this, he appears to be virtually alone.  Virtually all other Rishonim understand that seeing as the Gemara went out of its way to explain the dispute earlier in Eruvin even according to Rav Yosef in a way that all Tannaim agree with him, and that the final word on our daf went to Rav Yosef with no mention of any dispute, the halacha is indeed like Rav Yosef (see for example Rif, Rosh, Rambam Eruvin 6/17, Meiri)

 The above-quoted  Mishna in Pesachim will thus need to be dealt with separately, and hopefully we shall have opportunity to do so when we get there!

Several important questions remain, are discussed in the Rishonim and Poskim, but time does not allow us to go into them in this post. Among them:

1.       What is considered a mitzva regarding this rule? Does even a rabbinical mitzva count, or something that involves a קיום  (implementation) of a  mitzva if done but is not obligatory, or a mitzva that can be fulfilled in a different way?

2.        Is the above definition unique to eruv techumim, or applicable to anything that is permitted for the sake of a mitzva (for example nullifying certain types of vows or a שבות דשבות  on shabbos?)

3.       If one made an eruv techumim for a forbidden purpose, does it work בדיעבד?

4.       If one made an eruv techumim for a mitzva, may it be used for a non-mitzva related purpose as well?

5.       What about community needs and other urgent needs? Do they also have the law of a דבר מצוה  as far as this rule is concerned?

One common practical ramification of this discussion relates to taking pleasurable nature-walks outside the techum on Shabbos .

 Is the “oneg shabbos” involved in the walk enough to be considered a mitzva purpose, or could we argue that “oneg shabbos” is only a rabbinical mitzva or/and could be fulfilled in so many different ways that it does not qualify?

If such a walk does qualify, is it also considered enough of a mitzva to allow one to ask a non-Jew to perform any rabbinically forbidden task to make it possible, safe or more enjoyable (such as carrying water through a כרמלית,) under the rule of שבות דשבות לדבר מצוה?

Although most Rishonim do not seem to list this as an example of a דבר מצוה, in a response on the topic, the תרומת הדשן (responsa number 77) seems to permit it, and this is indeed the ruling of the Rema (O.C. 416/1.)

As far as the later question is concerned, given the huge amount of disagreement regarding the heter for a שבות דשבות  altogether (see posts on the subject on Eruvin 66-68,) it might be a  little more complex, but if people are already going on such a walk in hot weather and water is a necessity, there certainly seems to be room for leniency in allowing a non-Jew to bring water along or meet one along the route, so long as all other halachik requirements are fulfilled, and it is done in consultation with an expert in the laws of shabbos.

UThese posts are intended to raise issues and stimulate further research and discussion on contemporary topics related to the daf. They are not intended as psak halacha

Eruvin 77-78 Chazal and Science III- Ladders and more square roots

We have learnt that two courtyards sharing a common wall  may make one eruv together, only if there is a suitable window or opening in the wall- otherwise, the wall serves as a closed מחיצה (partition) between the two courtyards and the eruv does not work.

The minimum size of a halachik opening is 4 tefachim by 4 tefachim, and at least some of it needs to be below 10 tefachim in height.

We also discussed the complex issue of how to ensure that a circular window fits the minimum size and concluded that it need to be large enough for a square of 4 by 4 tefachim to be inscribed inside it.

Although Rabbi Yochanan seemed to require a circle with a circumference of 24 tefachim, Assuming π equaling 3 and Ö2 equaling 1.4, the Gemara concludes that one with a circumference of 16.8 tefachim is sufficient, and that Rabbi Yochanan was relying on the judges (or Rabbis) of Caesaria’s different formula in his ruling, who believed that in order to circumscribe a square, the perimeter of a circle must be twice the perimeter of the square.

 We saw different views as to how to understand what seems like such a large error on the part of the judges of Caesaria and Rabbi Yochanan, as well as how to understand what appears to be a lack of mathematical precision on behalf of both the Rishonim and Chazal.

Though the issue of why Chazal did not use more accurate measures for rational numbers like  π and Ö2 is also essential to our discussion, even more difficult was the far greater “error” (at least according to the way Rashi explained it) of Rabbi Yochanan and the judges he relied on that the hypotenuse of an isosceles right-angled triangle is equal to the sum of the other two sides, whereas according to the ancient theorem of Pythagoras, it equals Ö2 times the width of one of the sides, less than 75% of what they claimed.

We noted that even if Rabbi Yochanan and/or the judges of Caesaria and/or Rashi were unaware of this theorem, it is so easy to see that a factor of 2 is completely off by the simplest of measuring, and that ascribing such an error to any of them is extremely problematic, even without dealing with the question of whether and what type of “ruach hakodesh” they might have had.

I suggested that it might make more sense to explain that everyone understood that the length of the hypotenuse is less than the sum of both sides, but because measuring the precise length was difficult and involved square roots which were often irrational, they preferred to use the highest possible value of the hypotenuse of a right-angled triangle, which approaches (but never reaches) the sum of its’ width and height as the ratio between them decreases. (see chart below plotting hypotenuse on the y access and width on the x axis) assuming a constant height of 10)

We also mentioned that the Gra has another approach, which “seems” not to fit the text so well, but interprets the view of the judges of Caesaria and Rabbi Yochanan in a way that fits the maths perfectly- He claims that when the judges said that the square inside the circle is half, it does not refer to the perimeter of the square but to its area, and is not comparing it to the area of the circle it is inscribed in, but the square which superscribes the circle it is inscribed in (something Tosfos suggested was the intention of the judges of Casearia but misunderstood by Rabbi Yochanan and the Gemara!) and that Rabbi Yochanan’s requirement for 24 tefachim was also referring to the perimeter of the outer square.

On our daf, we have yet another instance of this issue, and seeing how the Rishonim handle it here, might shed some light on the earlier discussion, as well as its parallel discussion in Sukkah 8a (regarding the minimum circumference of a circular sukkah.)

On Daf 77, we have been discussing other options for linking the two courtyards, and one of them is by using a ladder that allows easy access.

On daf 78, Rav Yehuda quotes Shmuel as ruling that if a wall is 10 tefachim in height, it requires a ladder of 14 tefachim to permit it (serve as the equivalent of an opening.)

Rashi explains that seeing as the ladder cannot be placed vertically and still provide easy access, its base  needs to be at least 4 tefachim away from the wall, and that given its diagonal position (forming a hypotenuse,) it needs to be at least 14 tefachim (the sum of the two sides of the right-angled triangle formed) in order to reach the top of the wall.

Once again, we see that Rashi seems to assume that the hypotenuse of a right-angled triangle equals the sum of the other two sides, which we clearly know to be incorrect.

Once again, it is hard to believe that Rashi could make such a large error. It is also perplexing that what the earlier sugya and the sugya in Beitza seemed to view as an error of Rabbi Yochanan based on the judges of Caesaria, Rashi is now attributing to Shmuel, without even saying that it was an error.

This might strengthen what we suggested that at least some of Chazal preferred to use one general rule for all right-angled triangles, and err on the side of caution using the maximum the “hypotenuse” could ever be, assuming a collapsed triangle consisting of two lines at 180 degrees to each other.

Instead of having to constantly work out square roots that vary according to the ratio between the lengths of the other two sides, the simple measure of over-estimating the hypotenuse as the sum of the other two sides is then used across the board according to this view.

It would still be difficult why Rav Yehuda would be quoting Shmuel as expressing this stringent cautious view that was seemingly rejected in the earlier sugya and in Sukkah.

Further, the Gemara itself in Sukkah suggests that perhaps Rabbi Yochanan was simply לא דק  (not being precise) and rejects that suggestion based on the size of the imprecision being way too much to contemplate.

Tosfos on our daf, however, claims that Rashi was indeed “לא דק” (not being precise,) given that the ladder would need to be placed at a distance of 10 tefachim from the wall (forming an isosceles right-angled triangle) in order for it to have to be 14 tefachim in length, given the ratio of 1.4:1 of the hypotenuse to the other side ( Tosfos on Eruvin 57a  already offered his own proof that it is slightly more than 1.4, showing  independent mathematical ability but perhaps at the same time  unfamiliarity with the theorem itself.)

Though Tosfos’ understanding of Rashi might backup my suggestion that the inaccuracy in our case  was intentional and not due to ignorance, it remains difficult why Rashi would assume that Shmuel was being imprecise to a level that the sugya in Sukkah dismissed as implausible (using Pythagoras, the required length of the wall would be Ö116 or about 10.77, far closer to the height of the wall itself!)

Either way, we seem to see that according to Rashi, using the sum of the two sides as an “estimation” of the length of the hypotenuse was not limited to Rabbi Yochanan and/or the judges of Caesaria regarding the hypotenuse of an isosceles  right-angled triangle, but extends also to Shmuel’s treatment of the hypotenuse of any right-angled triangle!

The journey continues…

These posts are intended to raise issues and stimulate further research and discussion on contemporary topics related to the daf. They are not intended as psak halacha

Eruvin 76 Chazal and Science- PI, circumscribed circles, and square roots

In an earlier post (Eruvin 14,) we saw how the Mishna teaches that the ratio between the circumference and the diameter of a circle is 3.

The Gemara derived this from the ים  של שלמה  (circular water-feature) which was 10 amos wide and 30 amos in circumference.

We raised the obvious issue that the actual value of this ratio is π, an irrational number equal to slightly more than 3.14, and we saw two basic approaches amongst the Rishonim:

  1. The Tosfos brought evidence that Chazal were being precise in their measurements, pointed out that the mathematical experts hold that it is not precise, and leave it as a difficulty.
  2. The Rambam and Tosfos haRosh both understand that this is an approximation.

On our daf, we encounter this ratio once again.

Our Mishna discusses how large a “window” in the boundary wall between two neighbors’ properties needs to be for them to be able to make one eruv between the two of them.

It rules that the window needs to be at least four by four tefachim to qualify as a פתח

(opening) and that at least part of it needs to be within 10 tefachim of the ground.

Rabbi Yochanan brings up the case of a round window and how large it needs to be.

We should recall that in the context of daf 13b, the Mishna ruled that a round pole used for the beam of a מבוי does not have to be large enough to contain a tefach-wide square beam within it- it merely needs to be a tefach wide at the diameter, or 3 tefachim in circumference. (רואים כאלו היא מרובעת)

The Gemara initially seems to have thought  that the same should be the case with our window, and that so long as it is 4 tefachim at the diameter, or 12 tefachim in circumference, it counts as if it was a square window of 4 by 4 tefachim- after all, this could just be a symbolic opening in any case.

Yet There is a strong argument to be made that this case should be different seeing as the opening might actually need  to function as a פתח, and one could never squeeze through a circular hole that is only 4 tefachim wide at the diameter.

Rabbi Yochanan, citing the famous 3 to 1 ratio, rules that it needs to be 24 tefachim in circumference, and that slightly more than 2 of them need to be below the 10 tefachim line of the wall, so that if the circle is squared, part of the square will be under the line.

This rather cryptic statement of Rabbi Yochanan has pages and pages of commentary trying to explain.

After attempting to make some sense of it myself with the little high-school math I remember and some diagram, I was immediately overwhelmed by the complexity and length of the discussion.

I knew it would not be one day’s work to even scratch the surface, but decided to take my time and try get at least some idea of what is going on, and what we can take from it into the general topic of Torah and Science that we keep coming back to.

First – the “simple” flow of the Gemara,  (if there is such a thing:)

  1. The Gemara notes the usual 3 to 1 rule, and notes that in order to get a diameter of 4 tefachim, the circle should only need to be 12 tefachim in circumference.
  • The  Gemara answers that this rule replies to a circle, but for a square, more is needed.

We need to understand what the Gemara means to say, as it is clear that we are dealing with a circle and not a square.

One possibility is that although we are dealing with a circle, Rabbi Yochanan requires a circle with a circumference equal to a square of 4 by 4, in order for it to be considered an equivalent valid opening to the square.

  • The Gemara answers that a square that circumscribes a circle is only a quarter more than the circle itself , so 16 tefachim should be sufficient. (It does not say what attribute of the square is a quarter more than the circle, but the Gemara seems to assume that this is the circumference, and to be referring to a quarter of the resulting square.)
  • The Gemara answers that this is the case with a square that circumscribes a circle (is inscribed by a circle). The internal circle is 3 (PI) times the diameter in circumference, namely 12 tefachim,  whereas the square is 4 times its width, or 16 tefachim.

However, what we need here is a square of 4 times for tefachim to be able to fit inside the circle, which means the circumference of the circle needs to be even more to cover the parts of the circle outside the square.

  • The Gemara uses another apparent approximation, the length of the hypotenuse of a right-angled triangle formed by cutting a square in two by its diagonal. Although this is the square route of two (an irrational number) times by the width, the Gemara treats it as 1.4 (1 and two fifths.) This would also be the circumference of the required circle.

Using this, it works out that circumference of our circle need only be 16.8 tefachim, in order to be able to have square of 4 by 4 tefachim inscribed in it. (using precise modern measurements, this would be 4Ö2*π, rounded to 17.77)

So why does Rabbi Yochanan require such a large circle!

  • The Gemara replies that Rabbi Yochanan was following the judges of Caesarea (some versions say “The Rabbis of Caesarea)  who said that “a circle inside a square is a quarter, a square inside a circle is a half.”

This cryptic statement is  itself subject to interpretation of course.

There are multiple ways to learn the flow of the Gemara, starting from the requirement for “2 of them and a bit” to be below the 10 tefachim line, and ending with this view of the judges of Caesarea, and it would take pages and pages to go through.

Some essential reading in in the Rishonim include  Rashi, Tosfos, Rashba, Ritva, and the Meiri who has a particularly extensive treatment of the subject.

As we have already addressed the issue of PI being approximated by 3 by Chazal, we shall not focus on that right now, although it would be in place to analysis whether the flow of the sugya here indicates that Chazal were aware of this approximation and using it intentionally or not.

What we see here in addition to this is another “approximation” of Chazal (also encountered elsewhere), namely the square root of 2, but even more significantly, that it is used in combination with the approximation of PI, creating quite a large combined “rounding error.”- after all, there is a significant different between a circumference of 16.8 and one of 17.6 (see picture and formula,) and even according to the view of Rambam and Rosh that approximation is sometimes acceptable, relying on a double approximation seems to be a significantly greater novelty.

Another fascinating issue here is the question of the accuracy of the mathematical knowledge of Chazal and the Rishonim.

The simple explanation of the sugya, as understood by Rashi and Tosfos (see also the parallel sugya on Sukkah 8a,) seems to be  that Rabbi Yochanan relied on a mistaken mathematical formula used by the judges (or Rabbis) of Caesarea which according to Rashi seems to calculate the diagonal as twice the width, rather than 1.4 times the width of the Gemara or the root of 2 used by mathematicians.

Tosfos is bothered by how the judges of Caesarea  could have erred in something that is so obviously easy to ascertain.  Interestingly enough, he seems less bothered by the fact that Rabbi Yochanan followed in their error. He even goes so far to suggest that it was not the judges who erred, but Rabbi Yochanan who erred in his interpretation of what they said!

In contrast, the Rashba seems more bothered by the fact that Rabbi Yochanan could have made such an era, and the Gra notes that we should not “chas veshalom” say that they made any era, choosing to interpret their ruling differently to most of the Rishonim.

In addition, Tosfos disagrees with Rashi’s interpretation of the “2 and a bit” rule stated earlier given that his claims are not mathematically correct and proposes another explanation which using the correct formula also does not seem mathematically correct (though in fairness to both Rashi and Tosfos, they are merely commenting on the meaning of Rabbi Yochanan and the judges of Caesarea, not on mathematical reality!)

The temptation to simply say that Rishonim did not understand basic mathematics should not be taken lightly.

Rashi’s ability to make complex calculations is well known, and the Tosfos were brilliant enough to provide their own proof that the length of the  hypotenuse of an isosceles right-angled triangle is slightly more than 1.4 times the length of its other sides- It is hard for us to imagine that people with such minds did not know mathematical formula that even the ancient Greeks were aware of so long ago.

Yet despite the above,  it might not be necessary to assume that all Rishonim were well-versed in all mathematical formula and knowledge that was known to man at the time.

Medieval Europe was not the most “enlightened” part of the world by any means, communications were not what they are today, and much knowledge that the ancient Greeks had access to was inherited by the Islamic world to the South and East, rather than France and Germany.

The Rishonim might have been brilliant enough to work out mathematical theory on their own had they dedicated their time to it, but they clearly had other priorities and did not go all the way.

It is also not so outlandish to posit that whereas some Chazal were very exposed to and familiar with the scientific knowledge of the Greek and Roman worlds, others were less so, and sometimes needed to be corrected by their colleagues or even later authorities.

This does not even have to contradict the view of the Ramban, discussed in earlier posts, that ascribes a form of wisdom-induced “ruach hakodesh” to great Talmidei-Chachomim.

As we mentioned before, this does not necessarily mean that they ALWAYS experienced this “ruach hakodesh” nor that this “ruach hakodesh” has anything to do with awareness of scientific facts through supernatural means- rather it seems from the examples given in the relevant sugya (Bava Basra ) that it has more to do with intellectual “siyata dishmaya” which allows them to come up with ideas only far greater people would normally have come up with, while still basing these ideas on the information available to them at the time.

However, I am extremely hesitant at over-using such explanations- while they can possibly account for a lack of precision regarding the root of 2 or the value of PI, Chazal and the Rishonim certainly knew how to learn things from simple observation, and larger errors, such as viewing the hypotenuse of an isosceles right-angled triangle as the sum of the two other sides, essentially treating root 2 as the same as 2, simply defy rational explanation.

As such, I tend to believe that at least in such cases, the errors made were more strategic than mathematical, and that for reasons of convenience, the judges of Caesaria chose to be stringent and require the maximum possible length of the third side of ANY “triangle” (ie approaching a straight line with 180 degrees between the two sides) which is the sum of the other two sides. It is important to stress that this is not necessarily Rashi’s view, but his explanation of their view, but it could also explain other issues where Rashi takes this approach (or make it more difficult!)

The Gra, of course, has his own novel approach to the sugya, and whereas it seems somewhat forced in the text and out of line with most of the Rishonim on the subject, the Gra most certainly was a complete expert in all of Torah as well as in mathematics, making a study of his approach particularly appealing.

There are indeed SO many questions raised in this sugya and the way  that the Rishonim handle them, and its awfully frustrating to have to leave the discussion for a different forum and start catching up on the daf, but such is life- maybe we shall get to revisit this discussion sooner than we think!

These posts are intended to raise issues and stimulate further research and discussion on contemporary topics related to the daf. They are not intended as psak halach

Eruvin 69-71  The Lomdus of “Bittul Reshus”

Eruvin 69-71  The Lomdus of “Bittul Reshus”

The main theme of this daf relates to the concept of  בטול רשות  and how and when it applies.
We have mentioned before that the mechanism of choice for multiple inhabitants of one courtyard is to make an עירוב חצרות  whereby food is set aside on behalf of everyone in one of the houses, symbolically “joining” them all into residents of the same domain.
This is of course a symbolic mechanism which does not in any way affect the actual ownership of the houses and shared courtyards, and serves merely as a reminder not to carry from a private domain to a public domain proper- something Chazal were concerned enough about to prohibit carrying from one private domain to another owned by different people in the absence of such an eruv.
This eruv can only be done before Shabbos, as doing it on Shabbos resembles מקח וממכר  (commercial activity.)
If one or more of the inhabitants did not participate in the eruv before shabbos, the eruv is essentially ineffective.
This is because although all those who participate in the eruv are considered as if they share each other’s houses as well as their share in the common courtyard, the courtyard is also owned by those who did not participate, and therefore subject to different ownership than the houses of the participants.
This means that no one can transfer items between their houses and the common courtyard or vice versa.
One solution available is the mechanism of בטול רשות , also referred to in the Mishna as נתינת רשות .
The relationship between these two phrases requires analysis in its own right-for one approach, see Rambam Pirush haMishnayos Eruvin 6/1, 6/3 and 6/4 who seems to understand that נתינת רשות sometimes refers to making the eruv and sometimes refers to בטול רשות.
Whereas the phrase בטול רשות  seems to indicate a one-way mechanism by which the owner removes himself from ownership, control, or some other connection to his share in the courtyard (or possibly also his house,) the phrase נתינת רשות seems to indicate a two-way mechanism similar to a gift where the owner “gives over” one of the above at least symbolically to the other inhabitants.
There is a debate between Beis Shamai and Beis Hillel as to whether this may be done on shabbos, and the Gemara explains that Beis Shamai view בטול  as a form of two-way transaction whereby the non-participants  give over their “authority” over the courtyard to the participants, effectively leaving the courtyard owned in its entirety by the participants and making the eruv effective.
Seeing as such transactions are forbidden on shabbos, it may not be performed on shabbos.
In contrast, Beis Hillel view this as simply  סלוק (removing oneself from authority), a one-way mechanism that achieves the goal of making the courtyard owned solely by the participants due to his share being irrelevant, rather than owned by them.
Such an arrangement is permitted on shabbos, and at first glance, it might appear to be a form of הפקר- declaring one’s property to be ownerless- once his share of the courtyard is ownerless, the others remain its sole owners and their eruv is valid/
However, there are limitations that apply to the rules of הפקר  that do not seem to apply here.
For example:
i.                    Hefker needs to be declared in front of three people )Nedarim 45a), yet one person can be מבטל רשות to 2 people, and there is no indication here that someone else needs to be present (Tosfos deals with this issue in Pesachim 4b)
ii.                  According to the view that one needs to be מבטל רשות to each one of the people who were included in the eruv, simply making one’s share הפקר is clearly not enough
iii.                Hefker removes all legal connection between oneself and the object, to the point that anyone else can perform a קנין  (transactional act) on it and acquire it. In addition, the person who declared it הפקר  would need to perform an official קנין  in order to reaquire it- doing so in one’s mind would not do the trick. In this case, there does not appear to be any ability on the part of those who benefit from this בטול to take legal ownership of the property, but the benefit is limited to symbolic permission to carry within the area “as if” they owned it. Furthermore, it does not seem that a legally valid קנין needs to be made by the original owner in order to cancel this בטול.
iv.                It is not at all clear that declaring something הפקר  on shabbos is permitted, as the Ramban points out (Pesachim 4a)- it could be included in the general prohibition of commerce.
The concept of בטול  can be found in various other areas of halacha, for example:
1.      בטול חמץ  – one is required to declare any chametz left in one’s possession before midday on erev pesach “nullified like the dust of the earth.”
According to Rashi (Pesachim 4b,) this seems to be a way of fulfilling the mitzva of תשביתו  (removing chametz from one’s possession) and Tosfos seem to understand that it is a form of הפקר that creates a situation where that mitzva is simply not relevant anymore
2.      בטול ע”ז – an item of idolatry may become permitted if it is nullified by the idol-worshipper- this can done by breaking part of it, possibly a sign of its lack of importance to the owner (see A.Z. 52b.)
Though all 3 usages of this phrase seem to share in common the idea that one is declaring or showing that the item is no longer of importance to him, there is no need to assume that the “lomdus” (logical mechanism) in all three is similar. It is very possible that בטול חמץ  is a real form of הפקר  which בטול עבודה זרה  is certainly not, and that בטול רשות  is something completely different.
After all the phrase בטול  is also used regarding  בטול תורה  (wasting time when Torah could have been studied,) בטול עשה and   (avoiding performing a positive mitzva,)  בטול and none of them have anything to do with הפקר or ownership.
More specifically, whereas בטול חמץ  and בטול עבודה זרה  seem to work on a biblical level to avoid the prohibitions of owning chametz on pesach or an item of idolatry, בטול רשות  is a rabbinical measure which might simply be meant to have a similar symbolic effect  to that of the eruv.
However, there are views in the Rishonim, principally that of the Ramban (Pesachim 4b,) who  seem (at least a first glance) to assume that all three work on a similar mechanism and thus attempt to leave הפקר  out of the discussion altogether.
Although a thorough analysis of the various views as to how these different instances of בטול  work is still required, it is clear that whatever explanation is offered will need to pass the test of the different rules Chazal prescribed for each of them, in the absence of some other “external” explanation for the rule in question. The topic is vast- I have barely scratched the surface of the many sugyas and mefarshim that relate to the topic.
These posts are intended to raise issues and stimulate further research and discussion on contemporary topics related to the daf. They are not intended as psak halacha.