Gemara

Mishnah: One may not sharpen a knife on Yom Tov. One may rub it against another knife.

Gemara - Rav Huna: It is forbidden only with a sharpener of stone, but a wooden sharpener is permitted.

Version #1 - Shmuel: It is forbidden only to sharpen against a stone, but one may rub it against a stone to remove grease.

Inference: One may sharpen using a wooden sharpener.

Version #2 - Shmuel: A wooden sharpener is permitted only to remove grease, but not to sharpen against it.

Inference: One may not even remove grease using a stone sharpener.

Version #3 - Shmuel: The Mishnah forbids sharpening against a sharpener, but one may rub it against a sharpener to remove grease.

Inference: One may rub it against another knife to sharpen it!

Version #4 - Shmuel: The Mishnah permits scraping it against another knife to remove grease, but not to sharpen it.

Inference: One may not rub it against a sharpener even to remove grease!

Rav Chisda: Our Tana forbids sharpening. It is unlike R. Yehudah:

Beraisa: The only difference between Shabbos and Yom Tov is preparation of food;

R. Yehudah permits Machshirim.

Rava (to Rav Chisda): I heard in your name that the Halachah follows R. Yehudah.

Rav Chisda: May it be His will that such great teachings be said in my name!

Rav Nechemyah brei d'Rav Yosef: I saw Rava rub a knife against the mouth of a barrel. I asked if this was to sharpen it or to remove grease. He said that it was to remove grease. I could tell that really, it was to sharpen it. He holds that the Halachah follows R. Yehudah who permits sharpening, but Ein Morin Ken (we do not publicly expound this).

Abaye saw Rabah do so against a millstone. The same dialogue ensued, and Abaye drew the same conclusion.

Question: May one show a knife to a Chacham on Yom Tov? (It was enacted that before Shechitah one must show the knife to the local Chacham.)

Answer #1 (Mar bar Rav Bizna): It is permitted.

Answer #2 (Rabanan): It is forbidden.

Answer #3 (Rav Yosef): A Chacham may inspect for himself.

Rav Yosef: If a knife dulled (but was not dented), one may sharpen it on Yom Tov. This is only if it cuts when pressed hard. If not, it is forbidden.

Rav Chisda or Rav Yosef: R. Yehudah and Chachamim argue about fixing a dented knife

Rishonim

Rif and Rosh (3:10): It was taught in the name of Rav Chisda that the Halachah follows R. Yehudah. Rav Nechemyah and Abaye saw Rava and Rabah rub knives against the mouth of a barrel and a millstone. They said that this was to remove grease, but really, it was to sharpen. They hold that the Halachah follows R. Yehudah, but Ein Morin Ken.

Rif: If a knife dulled, one may sharpen it on Yom Tov, but only against the mouth of a barrel or a millstone. This is only if it cuts when pressed hard. If not, it is forbidden. R. Yehudah and Chachamim argue about fixing a dented knife.

Rosh (ibid.): The Rif permits sharpening only against the mouth of a barrel or a millstone. We do not publicly expound that one may sharpen it against a sharpener, but really it is permitted, for the Halachah follows R. Yehudah. The Rif did not bring the versions of Shmuel because the Halachah follows R. Yehudah, unlike our Mishnah. He brings the episode in which Rava rubbed a knife against the mouth of a barrel to teach that the Halachah follows R. Yehudah. He did not bring it to teach that we do not publicly expound this. Surely, one may expound that it is permitted against a wooden sharpener. Even Chachamim permit this according to one version! Since this is a mid'Rabanan matter we are lenient to expound like this version, and also to allow sharpening one knife against another and to rub it against a sharpener to remove grease.

Ba'al ha'Ma'or: R. Yehudah permits sharpening even with a stone sharpener. The Rif did not say so, for Ein Morin Ken. One may sharpen a knife that dulled. Rashi explains that even though it was dull before Yom Tov, perhaps he did not realize the need to sharpen it. However, if it was dented he needed to fix it before Yom Tov, so it is forbidden on Yom Tov. If it is too dull to cut even with pressure it is forbidden, for it is too much exertion to sharpen it. It seems to me that in this case it is not a Keli, and R. Yehudah agrees that one may not make a Keli (Mishnah, 32a).

Ran (DH Masnisin): The Mishnah forbids sharpening even with a wood sharpener.

Ran (DH Omar): Even R. Yehudah forbids sharpening with a stone sharpener, for this makes a Keli. Even though he permits proper Melachos for Machshirin, we are not more lenient than for Ochel Nefesh. Regarding Ochel Nefesh we do not permit Melachos normally done at once for a long time, be this mid'Oraisa or mid'Rabanan. This is why Rabah did not use a sharpener, even though he holds like R. Yehudah. This is not a solid proof. Perhaps he did not use a sharpener because Ein Morin that the Halachah follows R. Yehudah. Chachamim forbid a sharpener even to remove grease! Nevertheless, we do not seek leniencies, i.e. to use a stone sharpener, without a source. The reason one may not show a knife to a Chacham on Yom Tov is lest he sharpen it with a sharpener.

Rambam (4:9): One may not sharpen a knife against its usual (stone) sharpener, but one may sharpen it on wood, earthenware or a rock. We do not publicly expound this, lest people come to sharpen it against a sharpener. This is if it cuts when pressed hard, or if it was dented. If it cannot cut at all one may not sharpen it even against wood, lest he sharpen it with a sharpener.

Kesef Mishneh: The Rosh explains that the Rif rules like R. Yehudah, but Ein Morin Ken. The Ran says that the Rambam agrees. The Ran also says that a Stam sharpener is of stone; a wood sharpener is just like a barrel top. Rabah and Rava did not admit that they intended to sharpen, because Ein Morin like R. Yehudah.

Magid Mishnah: The Rif and Rambam rule unlike R. Yehudah. The Sugya (28b) is like Chachamim, and also several Stam Mishnayos.

Question: If so, why may one sharpen a knife on a barrel top or millstone?

Answer (Kesef Mishneh, for the Magid Mishnah): Chachamim agree about this, for it is a Melachah only with the sharpening stone. Also, the knife could cut as it was. We can say this for the Rambam, but the Rif surely holds like R. Yehudah, for he brings Rav Chisda who says so!

Poskim

Shulchan Aruch (OC 509:2): One may not sharpen a knife against its usual (stone) sharpener, but one may sharpen it on wood, earthenware or a rock. We do not publicly expound this, lest people come to sharpen it against a sharpener.

Beis Yosef (DH ul'Inyan): We rely on the Ran's Perush of the Rif, for then the Rambam follows his Rebbi; the Halachah follows them.

Beis Yosef (DH Nifgema): Rashi explains that the knife became dull before Yom Tov. The Ran explains that it became dull on Yom Tov. The Rambam did not distinguish when it became dull.

Shulchan Aruch (ibid.): This is if it cuts with difficulty, or if it was dented. If it cannot cut at all one may not sharpen it even against wood, lest he sharpen it with a sharpener.

Gra (DH ba'Meh): Even regarding Ochel Nefesh we forbid things done at once for a long time. All the more so Machshirin are forbidden in such a case. One makes a Keli to last for a long time.

Kaf ha'Chayim (15): Some say that if it was dented before Yom Tov, one may not even sharpen it on wood. Others permit.

Kaf ha'Chayim (23): We do not protest against butchers who sharpen knives against iron when flaying and removing Chelev. The knife cuts anyway; this merely makes it cut better. Ein Morin Ken, but we need not protest. Perhaps we infer from the Shulchan Aruch's words 'This is if it cuts with difficulty...'