The Mishnah (2:5) teaches that if one partially cuts vegetables for cooking, then the pieces are no longer considered connected for the laws of tumah. In other words, if tumah touches one of the pieces, the others remain tahor. The Tifferet Yisrael explains that since it understood that during cooking, the pieces will soften and separate from one another, the fact that they are still connected is not significant.
The Mishnah however continues that if the food was partially cut for display purposes, then the pieces are considered connected. For example, partially cut fruit that is placed on the table, where the guest will break off the piece they wish to eat. The Mishnah continues that the food that one begins to eat from, is no longer considered connected. We shall try to understand this law.
The Bartenura explains that the Mishnah means that only the piece that was taken is no longer considered connected. The remaining pieces in the food remain connected. He adds that one might have thought that removing one piece reveals that all the other pieces will now also be separated and all the pieces should no longer be connected. The Mishnah therefore teaches that this is not the case.
The assumption that is rejected in the Bartenura's explanation is the conclusion in the Tifferet Yisrael's. He explains that once one of piece is remove, all the pieces are considered separated even though they are physically attached. When the Mishnah teaches that the fruit that one begins to eat is no longer considered connected, it is to the exclusion of other fruits on display.
The Rash brings both these understands when explaining the Mishnah, and continues by citing the Tosefta that appears to match the Bartenura explanation above (see Chasdei David 2:7)
The Rambam (Tumat Ochlin 6:7) writes that if one cuts vegetables for display, they are considered connected "even if one began to pull it apart". The Raavad argues however that the Rambam's ruling does not appear to match the language of our Mishnah. Instead the Mishnah ruled that "if one began to pull it apart, the food one started is no longer connected." The Chasdei David understands that the Rambam and Raavad are each adopted these two opposing positions. The Raavad's issues is that if the Mishnah was only referring to the separated piece, then it should have said the "piece" that was removed and not the "food". Furthermore, the most important novelty, that the remaining pieces are still considered connected, is not explicitly stated and only implied.
How do we understand this debate? Is there something behind the disagreement in the understanding of our Mishnah?
In the introduction we cited the Tifferet Yisrael's explanation, why partially cut vegetables for cooking are no longer considered connected. We explained that this because, since they are going to soften and separate as part of cooking, the owner does not care much that they are connected now. Matters change when they are being partially cut for display prior to eating. The person wants them to be connected for its presentation. According to this understanding it follows that once a particular fruit begins to be pulled apart, then it is as good as dismantled. The law appears to hinge on the owner perception of the physical join.
The other side however may disagree with the original assumption. In other words, whether the pieces are considered connected may not be related to the wishes of the owner. Instead, determining whether they are connected depends on whether the connection is strong enough in a given context. When the vegetables were partially cut for cooking, since they are going to come apart, that physical join is not considered substantial. For partially cut vegetables put on display, even if a piece has been pulled away, the remain pieces are substantially connected and therefore connected for tumah also.
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