The twenty-seventh perek begins with the differences between various materials and their susceptibility to tumah. One difference mentioned is their minimum sizes for them to be susceptible to tumah midras – tumah that is transferred by, for example, a zav sitting or lying upon it. The determining factor is how large the material must be such that it becomes useful to sit on. The Mishnah taught that this varies with type of material in question.
What if the patch is made from a combination of materials? The Mishnah (27:3) explains:
If one made [a patch] two [tephachim] of cloth and one [tephach] of sacking… it is tahor.
The minimum measure of cloth is three-by-three tephachim and the minimum measure for sacking is four-by-four. The Mishnah teaches that if the minimum measure is completed with another material whose minimum measure is greater, then the patch is not susceptible to tumah.29 If however a patch was completed in the reverse way, for example sacking of three with an extra tephach of cloth, then it would be susceptible to tumah.30
Why do the different fabrics not combine? The Bartenura explains that “the less significant cannot complete the shiur (measure) of the more significant.” In other words, that which has a larger shiur (in the above example sacking) is considered less significant and cannot complete the smaller shiur. According to this understanding the problem is the “significance” of the fabric being used to complete the shiur. It is as if each of the fabrics have different, for want of a better word, potencies. The Tifferet Yisrael understands that if one and a third tephachim of sacking were added to the two tephachim of the cloth then the shiur would be complete. To explain, since three tephachim of cloth is equal to four tephachim of sacking, one and third tephachim of sacking should be enough to complete the missing tephach. Once the minimum measures were fixed by the Chachamim this “mathematical” system came into play.
The Mishnah Achrona explains differently. He understands that since it is not the way for one to complete a garment of a higher quality fabric with an inferior one, it is as if it is not attached. Accordingly, even if one added sacking of a tephach and a third, the patch would not be susceptible to tumah. One proof comes from the Rash who learns that when the Mishnah teaches that this composite patch is tahor it should not be taken literally. The reason is that we find that for a cloth to be susceptible to tumah that is transferred by contact, the minimum size is three finger-breadths. Consequently, using the above example, the Mishnah means that if a source of tumah touched the two tephachim sized cloth, even though the cloth would be tameh, the attached sacking would not. Consequently it is as if the sacking is not attached.
A difficulty faced is that the Tifferet Yisrael, cited as part of the first understanding, also brings the ruling of the Rash. If the sacking can complete the minimum measure of cloth if it is large enough, why is not considered attached when it cannot not? Perhaps that answer is found simply be asking the following question: is the detachment in the ruling of the Rash a cause or effect? According to the Mishnah Achrona since people do not combine material in this manner, they are by definition considered detached. According to the Tifferet Yisrael, the sacking is not by definition detached; given the right quantity it could complete the shiur. However since in the case of the Mishnah it does not, the effect is that for the purpose of tumah transferred by contact, it is considered detached.
This explains another question. The Mishnah Lemelech is initially unsure that if, within the patch, the cloth alone was larger than the minimum shiur and had the sacking attached is it now considered one garment or is the sacking still considered detached? The Mishnah Achrona believes that it is obviously detached and does not understand the doubt. Perhaps one could explain that the doubt is based on the question above: is the detachment the cause of effect?
29 The Mishnah Achrona explains that this is only if the patch was made unintentionally or by a minor. The reason is that we learnt (27:4) that if one intentionally crafted any fabric, then the minimum measure in all cases in one tephach by one tephach.
30 Ordinarily items that have different shiurim cannot combine. The Gemara (Sukkah 17b) explains since in some cases these materials share the same measure (see previous footnote) they can combine even in our case when they have different shiurim.
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