Gemara

103a - Question: This Tana of the Beraisa says that Chalitzah with a Kav (false foot) is Kosher. He holds that it is like a shoe. Who is the Tana?

Answer: It is R. Meir:

(Mishnah - R. Meir): A Kite'a (one who is missing a foot) may go out with a Kav.

R. Yosi forbids.

Shabbos 66a Question (Rava): What is the text of our Mishnah (does R. Meir permit or forbid), and what is the Halachah?

Answer #1 (Shmuel and Rav Huna): R. Meir forbids.

Rav Yosef: Since both say 'forbids', we will adopt this text.

Objection (Rabah bar Ula): Rav Chanan bar Rava was teaching Rav's son that R. Meir forbids and R. Yosi permits, and Rav gestured to him to switch the opinions!

(Rav Nachman bar Yitzchak): A Siman to remember the opinions is Samech - Samech (R. Yosi, who has a Samech in his name, is Oser (forbids. Oser also has a Samech)).

Shmuel and Rav Huna retracted.

63a (Mishnah): A man may not go out with a sword, bow, shield, club or spear. If he did, he is Chayav Chatas;

R. Eliezer says, these are ornaments for him.

Question: (If they are ornaments) they should be permitted, for Noy (beauty)!

Answer (Abaye): This is like a lamp in daylight (since it is useless, it is not Noy).

Beitzah 25b (Beraisa): A blind person may not go out (on Yom Tov) with a staff.

Yoma 78b - Question: May one go out on Yom Kipur wearing sandals made of rush (a kind of reed or bark)?

Answer: R. Yehoshua ben Levi did so (they are not considered shoes).

Question (Rami bar Chama): R. Meir and R. Yosi argue about whether or not a Kite'a may go out with a Kav in Reshus ha'Rabim on Shabbos. All forbid wearing it on Yom Kipur (even though R. Yosi does not consider it to be a shoe)!

Answer (Rava): All agree that it is a shoe. Regarding Shabbos, R. Yosi decrees not to wear it lest it fall off and he will carry it four Amos. R. Meir does not decree.

Rishonim

The Rif and Rosh (Shabbos 30a and 6:17) bring our text of the Mishnah (in which R. Meir permits) and say that the Halachah follows R. Yosi.

Rif, Rosh and Rambam (Beitzah 14a and 3:5 and Hilchos Yom Tov 5:3): A blind person may not go out with a staff.

Rambam (Hilchos Shabbos 19:15): A Kite'a may not go out with a Kav.

Rosh (ibid.): Even though a Kite'a may go out with a staff, that is because he cannot walk without it. It is like his shoe. A blind person's staff is merely to straighten his steps; it is a disgrace to Yom Tov.

Maharshal (3:14): It is forbidden only in Reshus ha'Rabim, or in Karmelis, which is like Reshus ha'Rabim.

Rosh: Rashi explains that the Kav is the form of a foot. A cavity is carved into it in which he puts the stump of his leg. It is known that a Kite'a cannot walk without staffs in his hands. We infer that a lame person may go outside on Shabbos with staffs even if they are not tied to his hands. Also in the Seifa, Rashi says that an amputee in a chair has boxes under his hands that he uses to propel himself. R. Tam permitted one whose ligaments constricted (and could not straighten his leg) to go out with staffs on Shabbos. It seems that this is only if he cannot walk without them. If an elder walks in his house without staffs and uses them outside to lean on, he may not go out with them on Shabbos.

Hagahos Ashri: R. Yosi forbids a Kav lest one come to carry it. This is why it is invalid for Chalitzah, just like a sandal too big to walk in. However, if it is covered with leather one may go out with it on Shabbos and it is valid for Chalitzah. It fits well around his foot, or he can insert his leg deeper and it fits more tightly. R. Yosi forbids. It seems that the same applies to a healthy person, for R. Nisim Ga'on holds that a Kite'a cannot do Chalitzah, so our Sugya must discuss a healthy person. Even according to R. Tam, who says that a Kite'a can do Chalitzah and our Sugya could discuss a Kite'a, the same applies to a healthy person. The Ri says that the Kite'a could walk using staffs if his Kav fell off. If not, there would be no need to decree lest it fall off and he carry it.

Poskim

Shulchan Aruch (OC 301:15): A Kite'a may not go out with his Kav. This is the form of a foot with a cavity carved into it, in which he puts the stump of his leg. It is not made for walking, for in any case he needs his staff. Rather, he does not want to look like one who is lacking a foot, rather, like one whose foot is broken. Since it is not needed for walking, it is forbidden.

Mishnah Berurah (56 and Sha'ar ha'Tziyon 59): Because it is not needed, we decree lest he carry it. This is unlike the opinion that because it is not needed, it is carrying.

Kaf ha'Chayim (87): The Levush permits if it is covered with leather. Then, it looks like a shoe. It is an ornament, not a load, and it is unlikely to fall off.

Shulchan Aruch (17): A lame person who cannot walk without a staff may go out with it even if it is tied to him. If he cannot walk without it and he takes it merely to support himself, it is forbidden.

Mishnah Berurah (63): Since he cannot walk without it, it is like his shoe. If he can walk without it, it is carrying.

Magen Avraham (27): Important people who walk with a stick may not go with them on Shabbos. We cannot consider it an ornament, for we do not find an ornament carried in the hand. Even R. Elazar (63a) only exempts from a Chatas. He does not permit. Tosfos (62a DH veha'Tanya) forbids carrying ornaments in the hand due to Mar'is ha'Ayin. The Yerushalmi says that R. Gamliel carried a key in his hand. It cannot truly mean in his hand, for then there could not be a decree lest he remove it to show it and come to carry it! Rather, it was inserted between his fingers. An important person may carry a stick where there is an Eruv, but a regular person should not, for it disgraces Shabbos.

Kaf ha'Chayim (104): Eliyahu Rabah (36) permits an important person even outside the Eruv. Machazik Berachah is hesitant even inside the Eruv. Perhaps it is not an ornament. Also, it seems absurd to permit only to certain people. Everyone considers himself to be important!

Taz (12): If he walks in a place where there is concern lest he fall, e.g. a steep path after rain fell or there is ice, he may go with a staff because he is afraid to go (without it).

Kaf ha'Chayim (105): Noda bi'Yehudah is unsure about a street where there is only a small amount of ice. Eliyahu Rabah permits this only where there is an Eruv, but we do not call one who relies on the Taz a 'Mechalel Shabbos.' The Radvaz is stringent even within an Eruv, for it is a weekday act.

Kaf ha'Chayim (102): If there is a nail at the bottom that makes a hole in the ground, this is a Pesik Reishei that he does not desire. This requires investigation whether it is permitted, so one should be stringent.

Rema: A sick person who recovered is like a lame person.

Shulchan Aruch (18): A blind person may not go out (on Shabbos) with a staff.

Mishnah Berurah (68 and Sha'ar ha'Tziyon 74): It is permitted inside the Eruv, like other things people need.

Kaf ha'Chayim (111): It is a load. Alternatively, perhaps one will carry it. The Radvaz (brought above in 105) would forbid even inside the Eruv.