Shabbat 42A

מותר.

is permitted, since one did not intend to perform that prohibited labor.

למימרא דשמואל כרבי שמעון סבירא ליה? והאמר שמואל: מכבין גחלת של מתכת ברשות הרבים בשביל שלא יזוקו בה רבים, אבל לא גחלת של עץ. ואי סלקא דעתך סבר לה כרבי שמעון ⁠— אפילו של עץ נמי!

The Talmud asks: Is that to say that Shmuel, who permits adding water even in an amount sufficient to harden a vessel, holds in accordance with the opinion of R' Shimon, who says that one may perform an action that inadvertently results in a prohibited labor? Didn’t Shmuel say: One may extinguish a piece of white-hot metal in a public area on Shabbat so that the masses will not be injured? That is because the piece of white-hot metal is not actual fire and extinguishing it is prohibited by rabbinic decree, not Torah law. The rabbis did not issue decrees in situations where there is concern for public safety. However, one may not extinguish a red-hot wood coal because extinguishing it is prohibited by Torah law. And if it would enter your mind that Shmuel holds in accordance with the opinion of R' Shimon, it should even be permitted to extinguish wood as well. When one extinguishes the coal, he intends neither to perform a prohibited labor nor to derive any benefit. He merely intends to prevent the coal from causing injury. Extinguishing the coal is a labor not necessary for its own sake. R' Shimon says that one who performs a labor not necessary for its own sake is exempt.

בדבר שאין מתכוין סבר לה כרבי שמעון, במלאכה שאינה צריכה לגופה סבר לה כרבי יהודה. אמר רבינא: הלכך קוץ ברשות הרבים מוליכו פחות פחות מארבע אמות, ובכרמלית אפילו טובא.

The Talmud responds: In the case of an unintentional act, Shmuel holds in accordance with the opinion of R' Shimon. In the case of labor not necessary for its own sake, he holds that he is liable, in accordance with the opinion of R' Yehuda. Ravina said: Therefore, a thorn in the public domain that is liable to cause injury, one may move it from there in increments, each less than 4 cubits, on Shabbat. Although the Torah prohibits carrying an object 4 cubits in the public domain on Shabbat, carrying less than 4 cubits is prohibited only by rabbinic law. From Shmuel’s statement, it is clear that the rabbis did not issue a decree in any case where there is a threat to the masses. And, therefore, if the thorn was in a karmelit, where the prohibition to carry is by rabbinic law, one is permitted to carry it even more than 4 cubits.