This article presents a case study of the influence of Muslim and Christian logicians on medieval Jewish law. The case in question is why it is a punishable offense for Jews to eat mammals that do not have either sign of purity—that is, neither have split hooves nor chew their cud—and the article examines the answers given by three medieval Jewish sages: Rashi, Maimonides, and Naḥmanides. The Written Law of the Torah explicitly allows the consumption of mammals, such as cattle, with both signs of purity. It also explicitly prohibits the eating of mammals, such as camels or pigs, with one sign but not the other. It does not, however, appear to explicitly prohibit the consumption of mammals, such as horses, with neither sign. Using a fortiori logic, Rashi derives a punishable prohibition against eating horses from the prohibition against eating camels and pigs. Maimonides ascribes this prohibition to the Oral Law of the Talmud. Naḥmanides, by contrast, attributes it directly to the Written Law without relying on either a fortiori logic or the Oral Law. This article argues that this solution was available to Naḥmanides because he adopted inclusive disjunction from Christian logicians, but it was not available to Maimonides because he adopted exclusive disjunction from Muslim logicians. The choice between inclusive and exclusive disjunction is shown to continue to be of importance in modern American law.