Masechet Kilayim opens with prohibition of kilei zerayim -- planting a mixture of seeds. The Mishnah lists pairs of vegetables that, despite having different names, are not considered kilayim, and other pairs that are. We shall try to understand the parameters the define two different vegetables as being kilayim.
R' Yonatan in the Yerushalmi (1:5) explains that when determining whether two species are kilayim, we sometimes look at the similarity in the vegetable or fruit, whereas in other cases we look at the leaves of the plant. The Gemara explains that lefet (turnip) and tznon (radish) are not kilayim since the vegetables have a similar appearance. Likewise, lefet and nafos are not kilayim since their leaves are similar (as learnt in the earlier Mishnah (1:3)). The Gemara then asks that the Mishnah (1:5) ruled that tznon and nafos are kilayim despite having both similar vegetables and leaves. The Gemara explains that the reason why they are kilayim is because their tastes are very different. We shall try to understand these three criteria: appearance of vegetable, leaf, and taste.
The Rambam (Hilchot Kilayim 3:5-6) cites the similarity in vegetable or leaf as grounds for permitting planting two different species together. The Rambam explains that this is because the issue with kilayim is appearance. Similarity of either vegetable or leaf is therefore sufficient unless the tastes of the two vegetables are very different. It is important to understand that according to the Rambam, similarity in vegetable or leaf, either of them, is grounds to be lenient.
The Rash (1:5, s.v Yerushalmi) however understand the importance of these qualities differently. He understands that differences in any of these attributes is reason to consider the two species as kilayim. That being the case we need to reread the Yerushalmi. In other words, when the Gemara continued with the example of lefet and tznon, and of lefet and nafos, these were examples where one of the characteristics was different and reason to define them as kilayim.
The difficulty with this explanation is that, as cited above, the earlier Mishnah (1:3) ruled that lefet and nafos were not kilayim. The Derech Emunah cites the Ri Kurkos who explains that the Gemara was discussing the lefet and nafos whereas the Mishnah was discussing the lefet and nafotz. (Note that the text of the Mishnah we have reads nafotz, whereas the text of the Mishnah in the Yerushalmi reads nafos.) The Rash therefore must have understood that nafos and nafotz are two different vegetables.
The Chazon Ish (3:4) however does not differentiate between nafos and nafotz and explains that the Rash reads the Yerushalmi as follows. Lefet and tzon are indeed considered two species due to their difference of appearance. Yet lefet and nafos are not kilayim, not because their leaves are similar, but because they are the same.
An important difference to stress between the readings of the Rambam and Rash is whether lefet and tzon are considered kilayim. Indeed, we find the Rambam rules that they are not, because they have a similar appearance, whereas the Raavad disagrees.
It would seem then that the Raavad had the same reading of the Yerushalmi as the Rash. The Chazon Ish (3:5) raises this possibility. The difficulty however is that the Raavad only argues about whether lefet and tzon are kilayim, but does not argue with the rest of the Rambam's understanding of the role of the similarities. In other words, when the Rambam rules that similarities in either the appearance of fruit or leaf is ground for leniency, the Raavad does not argue or present the position of the Rash that they are grounds for stringency.
The Chazon Ish (3:4) therefore suggests that perhaps the Raavad understands the flow of the Yerushalmi as follows. The Yerushalmi was explaining the statement, that "we sometimes go by the leaves". Indeed, like the Rambam explained, similarity in leaves alone would be grounds enough for leniency. The question is, how similar? The Gemara continues by describing where the line is drawn by way of example. For lefet and tznon, the similarity is not enough. Consequently, since the vegetables are also different, they are considered kilayim. For lefet and nafos however, the leaves are similar enough to be lenient.
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