Eruvin 5 The unfenced courtyard and a mathematics teaser

We have learnt that although מדאורייתא (biblically,) an area enclosed on three sides is generally considered a רשות היחיד (private domain) as far as the laws of carrying on shabbos are concerned, there is a rabbinical requirement to mark or enclose the fourth side in some way.
It is important to note that the biblical rule could have both stringencies and leniencies associated, a subject I hope to discuss in a later post.
The leniency is that at least on a biblical level, one is permitted to carry within this area, or from this area to an adjacent private domain, without restriction.  The stringency is that if one carries from this area to a public domain, one would be liable for biblical level shabbos desecration, with all its ramifications.
The rabbinic requirement to enclose or mark the fourth side limits one’s ability to carry within that area or from that area to the adjacent רשות היחיד  without doing so, but probably does not affect the biblical prohibition against carrying from it to the רשות  הרבים.   
Until now, we have focused on a מבוי, or narrow street, which requires only a לחי (pole) or קורה (beam) to mark the fourth side.
What happens with an unfenced private front-yard or garden, either belonging to the owners of one house, or shared by various houses?
Does this also need to be enclosed, and if so, is the solution that works for a מבוי also sufficient for such an area?
On the one hand, this area is less public than a מבוי and more similar to a private domain by its nature, so perhaps Chazal didn’t see the same need to make it more distinguishable from the public domain.
On the other hand, it still shares an open fourth side to the public domain, or at least to a כרמלית ( open area not busy enough to be a public domain, but treated by Chazal with the stringencies of both public and private domains.)
On this daf, we see that there are strict rules defining the מבוי  that may be permitted by just a לחי  or קורה . Otherwise, it is considered a חצר (courtyard) and is actually treated more stringently!
1.       Its width needs to be narrower than its length, the width being the dimension only enclosed on one side, as opposed to the length which is the dimension enclosed on both sides.
2.       It needs to have houses and courtyards open to it. The Gemara (Shabbos 130b and Rashi) understands the later to mean at least two courtyards that each have two houses open to them.
As such, it seems clear that both a shared courtyard and a private one certainly do not meet the later criteria, and might sometimes not meet the former one either.
It seems to follow from here that at least the shared courtyard would definitely be treated stricter than the מבוי, and with the argument in favor of leniency for a less public area to be treated more leniently disregarded, in the absence of precedent to  the contrary , it seems that this would also be the case with a private front-yard or garden.
What precisely is required in order to be able to carry in such an area will hopefully be the topic of a later post as the sugyos develops.

There is a מחלוקת (dispute) on this daf between Rav Yosef and his student, Abaya regarding the minimum length of a מבוי.
Rav Yoseif holds that 4 טפחים (handbreadths) are sufficient, whereas Abaya requires 4 אמות (arm-lengths.)
Abaya attempts to prove his point from the above rule that we learnt- in order to be considered aמבוי  as far as the more lenient requirement for a לחי  or קורה, there have to be at least 2 courtyards that open to it.
As the minimum width of a פתח  (opening) is 4 טפחים  (the maximum being 10 אמות,) it is impossible for a courtyard to share one with a מבוי  that itself is only 4 טפחים long, without the entire length being open and thus disqualified .
The opening can also not be along the width that is already closed, as the width may not be wider than the length!
Rav Yoseif counters that one opening could still be possible on each side, if it is in the corner between the length and the width.
Rashi explains that this could be made of a 3 טפחים  gap along the length PLUS a 1 טפח  opening along the adjacent wall of the width, making the minimum 4 טפחים in total.
Tosfos , as well as other Rishonim make the rather strong observation that Rashi is not being precise, as the true entrance would then be marked by the diagonal between the enclosed part of the length and the enclosed part of the width, which mathematically (by pythagorus) will be the root of 10, still below the minimum width of 4 טפחים  !
Is Tosfos accusing Rashi of being unaware of basic mathematics such as the theorem of Pythagoras? Absolutely impossible, as there are various sugyos which mention this, approximating the root of 2 with 7 over 5 (See sukkah 8a for example)
It is also very simple for any mathematical layman to measure such a diagonal and see that the diagonal is much closer to 3 than 4.
As such, it seems clear that Tosfos understood that Rashi was aware of this discrepancy but deliberately chose to ignore it and be happy with an approximate minimum with  slightly more than 3 in place of 4, something that seems rather odd.
We have seen elsewhere that the Tosfos have pointed out that Chazal themselves were not always precise with their measurements (see Eruvin 13b for example) , but this was a question of rounding to the nearest integer, not rounding down more than a  half  and resulting in a major leniency.
It thus seems more likely that Rashi did not measure the entrance from the diagonal, but from the imaginary wall that would exist in the corner if the 3 plus 1 handbreadths were closed.
This would be a rather substantial מחלוקת  with a huge נפקא מינה (practical ramification) regarding the status of the area in-between this imaginary boundary and the diagonal as well as whether a bent opening like this is valid.
It is also clearly not the way Tosfos understood Rashi!
וצריך עיון גדול

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 2 Introduction, Technical measurements and clean language.

I was discussing my daf posts with my friend and colleague, Rabbi Matthew Liebenberg of Claremont Shul, Cape-Town, and he tried to warn me that keeping up the pace and variety of posts will be much more challenging when we get to Eruvin, which is known as a particularly complicated and technical masechta.

Though I could not deny that I share a degree of concern, I replied that Eruvin is actually one of my “favorite” tractates, assuming it is possible or appropriate to say such a thing. In addition to being filled with fascinating and extremely practical rules essential to understanding the practicalities of Eruv building, something almost all of us need to know, it also contains many general ideas and topics that apply to all of Torah holistically.

This combination of material typical of the Gemara can be found right here on the first daf as well.

The thrust of the first daf deals with the technical requirements for a quiet side-street or alley to be considered a private domain on Shabbos.

The typical neighborhood in the times of Chazal (as can still be seen in some older neighborhoods of Yerushalayim) consisted of a מבוי – a short and narrow side-street or alley which opened to the main public thoroughfare on 1 or 2 sides.

Various חצרות (courtyards) opened to this central מבוי and each courtyard had houses that opened to it.

מדאורייתא ( at a biblical level,) any area enclosed on 3 sides (the exact number of sides/partitions is subject to debate later) was considered a private domain, and carrying within it was permitted.

As such, as far as biblical law is concerned, it is permitted to carry from one house to another within the courtyard, from one courtyard to another within the common מבוי , or within the courtyards or מבוי , so long as the מבאי is only open on one side to the public domain.

If the מבוי is open on two sides to the public domain, it is more complex, as the מבוי itself could be considered part of it.

Our Mishna and sugya deals with a מבוי that is closed on 3 sides and only open on one side to the public domain.

We see later that there is a rabbinical requirement to symbolically mark or enclose such a מבוי with either a pole on one side, or a beam going from one side to the other (there is some debate about these precise requirements as well.)

Our Mishna focusses on the maximum height that this pole or beam may be, as well as the maximum width of the open side, and rules that if they are higher than 20 amos (arm-lengths/cubits) or wider than 10 amos respectively, they need to be lowered or narrowed.

Rabbi Yehuda disagrees and says there is no such requirement.

It is unclear from the Mishna whether Rabbi Yehuda holds that the fourth side can be of infinite height or width, or whether he too places a limit on this, but simply a higher or wider one, but it would seem that if the later is correct, one could have expected him to say what this limit is.

The Gemara notes that a similar maximum height is discussed regarding a Sukkah (Sukkah 2a,) but the language used there is different.

Whereas in our case, we are told that a מבוי that is too high needs to be lowered, regarding Sukkah, we are simply told that it is פסול (invalid.)

As in both cases, lowering it is both compulsory and effective, the difference in language needs to be explained, and the parallel sugya in sukkah asks the very same question and gives the very same answers.

Two answers are given :

  1. Seeing as the Sukkah is דאורייתא (biblical,) the Mishna uses the word “invalid.” As the pole or beam of aמבוי are only rabbinical requirements, the mishna simply tells us the תקנתיה (solution.)
  2. The later language is also appropriate in theory for the biblical requirement of Sukkah, but seeing as a Sukkah has multiple constraints, each requiring a different solution, the Mishna chooses one word that applies to all of them, for the sake of brevity. Rashi explains that this is based on the principle (Pesachim 3b) that one should always teach one’s students using concise language.

There are various approaches in the Rishonim as to how to understand the first answer.

Rashi seems to understand that when the Gemara contrasts the biblical Sukkah with the rabbinical מבוי , it is not referring to the actual requirement of dwelling in a Sukkah or putting a pole or beam on a מבוי, even though the distinction certainly applies to that as well, but to the maximum height of the Sukkah and the מבוי.

We derive the maximum height of a sukkah from a verse in the Torah: למען ידעו דורותיכם כי בסוכות הושבתי את בני ישראל (“So that your generations will know that I placed the Jewish people in sukkot” -Vayikra 23/43.)- the Sukkah has to be low enough for the roof to be noticed.

As such, this requirement predates the writing down of the mishna by far, and it is appropriate to say that it is already invalid.

In contrast, the requirement to mark a מבוי with a pole or a beam itself is only rabbinical and its maximum dimensions are also. Seeing as the Mishna is the first to teach us these maximum dimensions, it is not appropriate to label the מבוי as already invalid but only to tell us how to solve the issue from the beginning.

This explanation has various difficulties, but I shall not dwell on them in this post.

Tosfos understands the answer a little differently- Due to the strict biblical requirements of sukkah, we are concerned that using a softer language would make us think that the requirement to fix it up is only לכתחילה (in the first place,) but if one sat in the sukkah without making these corrections, one would fulfill the mitzva still בדיעבד (post-facto.)

As such, the harsher language is preferred.

In the case of Eruvin, seeing as the requirement is only rabbinical, we are less concerned that a person might make this error, and we choose to use the softer language, in keeping with the principle (Pesachim 3a) that it is always best to use לישנא מעליה (positive language ) where possible.

We see that there are 3 principles at work here, which sometimes need to be traded off against each other, and it is fascinating to note that both Rashi and Tosfos refer to the same sugya in Pesachim which discusses 2 of these principles and the trade-off between them, but for completely opposite purposes.

  1. Language needs to be נקיה (clean), and that doesn’t just mean avoiding foul language but specifically choosing לשון מעליא (positive language.)
  2. Language needs to be concise (probably to make it easier to comprehend and remember.)
  3. Language needs to be clear or strong enough to convey the historical timeline of the law (Rashi) or the stringency of the law (Tosfos)

According to the first answer in the Gemara, the third factor over-rides the first factor, and strength of message over-rides the need for positive language.

According to the second answer in the Gemara, either positive language still takes priority over strength of message, or the positive language given is still considered appropriate or strong enough to give over the importance of the message.

However, the second factor certainly takes priority over the first, and concise direct language is preferred over positive language, as is indeed the conclusion of the above-quoted sugya in Pesachim.

There is lots more to say about the requirements for language to be clean, concise, and strong enough and how they trade-off with each other, but we have certainly seen on this first daf how the Gemara is able to focus on the one hand on specific and technical rules relating to the subject at hand, and at the same time teach us multiple principles that could apply to every aspect of our lives!

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.