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May one kill an insect on Shabbas

תָּנוּ רַבָּנַן: הַצָּד חֲגָבִין, גַּזִּין, צְרָעִין וְיַתּוּשִׁין בְּשַׁבָּת — חַיָּיב, דִּבְרֵי רַבִּי מֵאִיר. וַחֲכָמִים אוֹמְרִים: כׇּל שֶׁבְּמִינוֹ נִיצּוֹד — חַיָּיב, וְכֹל שֶׁאֵין בְּמִינוֹ נִיצּוֹד — פָּטוּר.

The Sages taught in a baraita: One who traps locusts, cicadas, hornets, or mosquitoes on Shabbat is liable. This is the statement of Rabbi Meir. And the Rabbis say: Not every insect is the same in this matter. If one traps any insect whose species is typically trapped for personal use, he is liable, and if one traps any insect whose species is typically not trapped for personal use, he is exempt.

From here we clearly learn that anything that is not normal trapped for personal use one is not liable

what’s the reason for במינו ניצוד and ניצוד ?

Something that is normally trapped compared to some that is unlikely to be trapped

וְעַל עַקְרָב שֶׁלֹּא תִּישָּׁךְ. אָמַר רַבִּי יְהוֹשֻׁעַ בֶּן לֵוִי: כׇּל הַמַּזִּיקִין נֶהֱרָגִין בְּשַׁבָּת. מֵתִיב רַב יוֹסֵף: חֲמִשָּׁה נֶהֱרָגִין בְּשַׁבָּת, וְאֵלּוּ הֵן: זְבוּב שֶׁבְּאֶרֶץ מִצְרַיִם, וְצִירְעָה שֶׁבְּנִינְוֵה, וְעַקְרָב שֶׁבְּחַדְיָיב, וְנָחָשׁ שֶׁבְּאֶרֶץ יִשְׂרָאֵל, וְכֶלֶב שׁוֹטֶה בְּכׇל מָקוֹם.

And we also learned in the mishna that one may cover a scorpion with a bowl on Shabbat so that it will not bite. Rabbi Yehoshua ben Levi said: All harmful creatures are killed on Shabbat. Rav Yosef raised an objection to this from the following baraita: Five creatures may be killed even on Shabbat, and they are: The poisonous fly that is in the land of Egypt, and the hornet that is in Ninveh, and the scorpion that is in Ḥadyab, and the snake that is in Eretz Yisrael, and a mad dog in any place.

why only these specific 5 animal?

- this were seen as the most dangerous animals around then

whats the difference between a normal fly and Egyptian fly?

- it’s clear that it must be a poisonous fly

- Tur says these are also known to be damaged

(ג) כל שבמינו ניצוד חייב עליו אין במינו ניצוד פטור אבל אסור הלכך זבובים אע"פ שאין במינו ניצוד אסור לצודן:

הגה ולכן יש ליזהר שלא לסגור תיבה קטנה או לסתום כלים שזבובים בו בשבת דהוי פסיק רישיה שיצודו שם [בעל התרומה ומרדכי ס"פ כירה ואגור]

(3) 3. One is liable for trapping a species that is usually hunted, and it is Rabbinically forbidden to trap species that are not usually hunted. Therefore it is forbidden to trap flies even though they are a species that are not hunted.

RAMA: Accordingly one must be careful not to shut a small box or close a Keili with flies inside on Shabbos, because it is a Pesik Reisha that they will be trapped within [Ba'al HaTerumah; Mordechai].

a pesik reisha (Lit. cutting off the head) is an action that ordinarily would be permitted but which will definitely cause as an unintended side effect an action that would be forbidden].

Therefore forbidden to do

(כא) אֶחָד שְׁמֹנָה שְׁרָצִים הָאֲמוּרִין בַּתּוֹרָה וְאֶחָד שְׁאָר שְׁקָצִים וּרְמָשִׂים שֶׁיֵּשׁ לְמִינָן צִידָה הַצָּד אֶחָד מִכֻּלָּן בֵּין לְצֹרֶךְ בֵּין שֶׁלֹּא לְצֹרֶךְ אוֹ לְשַׂחֵק בָּהֶן חַיָּב הוֹאִיל וְנִתְכַּוֵּן לָצוּד וְצָד.

(21) It is the same, whether with the eight swarming animals mentioned in the Torah or with the other repugnant creatures and creeping things the species of which is trapped – one who traps from one of them is liable, as he intended to trap and he trapped.

We learn from here whether [this is done] for a need or not for a need or to play with them – as [one is even] liable for forbidden work that is not needed for itself. One who traps a sleeping or blind [creature] is liable.

אורח חיים שטז ג,ד

הילכך זבובים אף על פי שאין במינן ניצוד אסור לצודן לכן כתב בעל התרומה שאסור לנעול בשבת התיבה שיש בה זבובים אלא יתן סכין או שום דבר בין הכיסוי לתיבה בענין שיוכלו לצאת משם.

ונראה לי שאין צריך לדקדק בזה שאין הזבובים ניצודין בתיבה שאם בא לפתוח התיבה וליטלם יברחו

We do not want to catch the bugs. However we want to stop the bug from escaping. Therefore one is allowed to put a partial cover to make it more difficult for the bug to escape.

You do not need to do this previous statement. Why?

the fly won’t be caught. If you trap the fly in a box it’s not really trapped. If you try to catch the fly and opened the lid, they will just all fly away.

Have to do the act with a shinoy (a lid of a water bottle with a pen in between the lid and the bottle)

As long as you do not have the intention to trap it is okay to close the door

- even if you had intentions to close the box for flies it’s okay as there is no chance one could catch it

- the bee hive is small so they are confined to a small space therefore Asur if you have intention to trap

(ד) פורסין מחצלת על גבי הכוורת [מקום שמתכנסים בו הדבורים לעשות דבש] ובלבד שלא יכוין לצוד וגם הוא בענין שאינו מוכרח שיהיו ניצודים כי היכי דלא להוי פסיק רישיה:

(4) 4. It is permitted to spread a mat over a beehive provided that one does not intend to trap and the circumstance is such that it is not certain that they will be trapped, thereby not being a Pesik Reisha (it’s obviously going to happen)

It’s all about ones intention not about the act

שמירת שבת כהלכתה;

אבל מותר לדרוס עליהם דרך הילוכו, אפילו אם מתכון לקטילתם, אבל עליו לעשות באופן שלא יבואו אחרים לידי טעות ויחשבו שמותר לקטול חרקים גם כאשר אין חשש להינזק מהם.

ואם מזיקים כאלה רודפים אחרי האדם ואם אפשר לצודם, מותר אף להורגם.

If it is not possible to catch them, one may tread on them in the course of walking, even if they have the intention.
However, one must not kill them in such a way that others will recognise that this is ones intention

When insect is pursuing one and it is not possible to catch them, one may kill it in the normal way.

If you have to kill the bug then do it in a way others won’t think it’s permissible whenever .

Daily Halacha by Rabbi Eli Mansour.

Hence, Halacha would forbid spraying insect repellent in a manner that would invariably cause an insect to die. One may spray insect repellent only if he does so in the air – as opposed to directly on an insect – and he opens at least one window in the room to allow the insect to escape. The Chazon Ish (Rabbi Avraham Yeshaya Karelitz, Lithuania-Israel, 1879-1954) ruled more stringently, allowing one to spray under these conditions only if there is an ill patient in the home for whom the insects cause discomfort. Most other authorities allow spraying into the air even if nobody in the home is ill, provided, as mentioned, that one leaves a window open, and the insects are causing discomfort to those in the room. (See Yabia Omer, Helek 3, O"H siman 20.)