One who leaves leaven in his domain during Passover, even though he does not eat it, violates two prohibitions. This is derived from the verses stating that leaven shall not be seen within all your borders and leaven shall not be found in your houses. The prohibition of leaven and the prohibition of the leavening agent from which it is made are considered one and the same. The Torah uses various terms and locations—referring once to "your houses" and once to "your borders," and once to "leavening agent" and once to "leaven." Through a verbal analogy, the Gemara teaches that all the expositions and laws mentioned in one context apply to the others as well. This means that the prohibition applies not only to one's house but to any place within one's domain, including hidden places or even leaven buried underground in a field. Wherever a person is in the world, if the leaven belongs to him, he violates a Biblical prohibition. Therefore, it is necessary to remove all leaven from our domain on the festival.
The Torah distinguishes between two types of leaven: the leavening agent and the leaven itself. The difference, as explained in the Gemara, is that the leavening agent is considered "hard leaven," while the leaven itself is "leaven fit for eating." The unique quality of the leavening agent is its ability to leaven other doughs. In ancient times, this was a piece of old, hardened dough that had become highly fermented and acidic, containing potent bacteria. A small piece would be added to a new batch of dough to make it rise. Even though this hardened starter is not fit for eating, the Torah commands us to remove it because of its leavening power. This distinction is the subject of a famous dispute in Masechet Beitzah between Beit Shammai and Beit Hillel.
In ha-Mishnah, Beit Shammai argue that the minimum measure for violating the prohibition is an olive-sized volume for a leavening agent, but a larger, date-sized volume for edible leaven. Beit Hillel, however, maintain that the measure for both is an olive-sized volume. Beit Shammai reason that since edible leaven is less potent than a concentrated leavening agent, the Torah must have intended a more lenient, larger measure for its removal. Beit Hillel counter that both terms are necessary because each has a unique stringency: the leavening agent is potent but inedible, while the leaven is edible but lacks leavening power. Therefore, the law follows Beit Hillel, and there is no distinction in the measure; for both types, leaving an olive-sized volume in one's home is a Biblical violation.
However, a distinction exists regarding the punishment of lashes. As the Rambam explains, a person does not receive Biblical lashes for the prohibitions of "not being seen" and "not being found" unless he actively performed an action, such as buying leaven during the festival or kneading it himself. If he simply owned the leaven before the festival and failed to remove it, he has indeed violated two prohibitions, but he does not receive Biblical lashes because it is a "prohibition without an action." Instead, he receives disciplinary lashes. This is a major principle: one only receives Biblical lashes for a violation involving a physical act. If the violation occurred through inaction, the punishment is different. The Tosefta supports this by comparing it to one who maintains forbidden mixtures in a vineyard. If a person sees forbidden plants growing in his vineyard and fails to uproot them despite a decree from the Beit Din, the vineyard becomes forbidden, but the owner does not receive lashes because he merely sat and did nothing. He would only be liable for lashes if he had actively sown the forbidden seeds.
While the Rambam attributes the lack of lashes to the absence of a physical action, Tosafot in Masechet Pesachim offer a different reasoning. They suggest that the prohibition of leaven is a "prohibition linked to a positive command." There is a general rule that if the Torah provides a positive commandment to rectify a violation, lashes are not administered. For example, a robber is not lashed for the prohibition against stealing because the Torah commands him to return the stolen object. Tosafot argue that since one is commanded to destroy leaven even during the festival itself, the positive command to remove it serves to rectify the prohibition. If a person finds leaven on a festival day, he must cover it with a vessel—as it is forbidden to handle because it is considered "set aside"—and then burn it as soon as the festival day ends. Because this positive obligation exists, it functions as a remedy for the prohibition.
This raises a question on the Rambam: why did he not use the reasoning of a "prohibition linked to a positive command"? Rabbi Akiva Eiger explains that there is a difference between a command that fixes a violation retroactively and one that merely prevents further violation. In the case of leaven, every moment it remains in one's house, the prohibition is being violated anew. The command to destroy it is intended to stop the ongoing violation from that point forward; it does not uproot the prohibition that was already violated in the previous hour. Therefore, it does not fit the classic definition of a prohibition linked to a positive command, and the Rambam instead relies on the principle that it is a prohibition without an action.
There is another dispute between the Ra'avad and the Rambam regarding the status of leaven that is no longer edible. The Ra'avad derives a principle from Masechet Pesachim regarding moldy bread. He argues that if a leavening agent is fit to leaven other doughs, one violates the prohibition even if the agent itself is moldy and unfit for human consumption. He even suggests that if a person hardens a piece of leavening agent to use as a chair, it must still be neutralized with clay because its leavening potential remains. The Ra'avad innovates a distinction: while edible leaven is no longer prohibited once it becomes unfit for a dog to eat, a leavening agent remains prohibited as long as it can still leaven other doughs.
The Rambam, however, does not accept this distinction, and his view is shared by the Ran, the Ramban, and the Rosh. They hold that once any form of leaven—including a leavening agent—becomes unfit for a dog to eat, the obligation to remove it ceases. When the Sages speak of being "unfit for a dog," they do not mean a pampered pet that might refuse even slightly stale meat, but a stray dog that has not eaten for three days. If such a dog would refuse the substance, it is no longer legally considered food or leaven, and it may be kept in the house. This is the majority opinion among the early authorities.
Regarding the use of such substances, the Rosh adds a stringency: if a person chooses to eat something that is unfit for a dog, he is "treating it as significant," thereby restoring its status as food. However, the Chazon Ish clarifies that this only applies when the substance is consumed on its own. If a tiny amount of inedible leaven is part of a larger mixture, and the person has no intention of consuming the leaven itself, the principle of "treating it as significant" does not apply. This is why one may use toothpaste, soap, or shampoo during the festival. Even if they contain leaven, they are unfit for a dog to eat, and the person using them has no intention of eating the leaven. Even if one accidentally swallows a bit of toothpaste, it is not considered "treating it as significant" because the leaven is a minor, secondary part of the mixture.
This principle also applies to chemical additives like citric acid. As explained in the work Yechaveh Da'at by Ha-Rav Maran, even if leaven was used in the production of citric acid, the processing involves drying and chemical changes that render the substance completely inedible during the manufacturing stages. Once it has reached the point of being unfit for a dog, it loses its legal status as leaven. Even if it is later incorporated into food, we rely on the reasoning of the Chazon Ish that since it is part of a mixture and not the primary focus of the consumer, it is not "treated as significant." Therefore, such products are permissible. Similarly, medications that are bitter and inedible may be taken by a sick person upon a doctor's instructions, as they are not being consumed in a conventional manner of enjoyment. Thus, according to the law, one may keep and use standard toiletries and necessary medications during the festival, as they have lost the legal status of leaven.