Our Gemara on amud beis notes a dispute between Shamai and Hillel regarding the status of debt recorded in a valid note signed by witnesses. Shamai holds that a debt recorded in a bill of debt that is awaiting collection is as though it was already collected to the extent that the creditor is considered to be in possession of the debt. Hillel holds it is still considered uncollected.  

This has significance in relation to a situation where there is doubt about ownership of inherited property of the debtor, such as if there was a cave in, and a son and father die, but we are unsure who died first.  The creditor of the son, claims that the debtor’s father died first. Thus the son inherited part of his father’s estate and now the creditor may seize some of the property to pay off his lien.  However, the son’s brothers claim that the son died first, thus inheriting nothing, and leaving the creditor with no assets.  According to Shammai, since the debt is already as if it was collected, the creditor has an equal chazakah (presumptive status), and can claim just as easily that the father died first, and divides the asset in question with the inheritors. 

It is one of the great mysteries of Shas to try to understand the disputes between Shammai and Hillel thematically.  One cannot avoid the impression that Shammai is generally more strict and Hillel more lenient, but it cannot be as simple as that. Rav Moshe Amiel in Derashos El Ami (Chayim Uzemanim, Shonim 2) uses the debate about contracts in our Gemara as a window to understand Shammai and Hillel’s disputes according to an overall theme.  While I can see how it fits into a number of their debates, others do not fit as well, however it is a worthy attempt and one step closer to unraveling the truth behind this mystery.

Looking at this situation, we see that Shammai values the potential over the actual, while Hillel values the actual.  Thus, according to Shammai, the debt is already considered in the hands of the creditor.  Rav Amiel also relates it to the classic argument between Shammai and Hillel regarding the order of lighting the chanuka lights (Shabbos 21b). Shammai famously holds we light starting with eight lights counting downward to one. Of course as we are all familiar, Hillel holds we light starting with one light moving up to eight. Rav Amiel maintains this is the same idea as the contract. Shammai holds the miracle was already in place to occur from day one, so we start with eight lights. While Hillel follows the actual order of occurrence.

A few other disputes between Shammai and Hillel also follow this theme. For example, the dispute in Mishna Chaggigah (1:1) regarding the age that a minor becomes obligated in aliya leregel. According to Beis Shammai, any child who is able to ride on his father’s shoulders and ascend from Jerusalem to the Temple Mount must make the pilgrimage. According to Beis Hillel, any child who is unable to hold his father’s hand and ascend on foot from Jerusalem to the Temple Mount is not obligated.  

In contrast, the criteria for an adult’s obligation for Aliya leregel is if he is able to walk, hence the Mishna tells us that a person who is crippled is not obligated in the pilgrimage.  Shammai, who follows the potential, needs only for the child to be in a state that he will grow up and be able to walk; he does not need to be able to walk right now. (For practical reasons, he still needs to be old enough to manage being carried on his father’s shoulders.). Beis Hillel holds that the child must be able to walk himself, because potential ability is not enough.  

As another example, the Mishna Rosh Hashanah (1:1) records a dispute between Beis Shammai and Beis Hillel regarding the New Year for Trees. According to Beis Shammai, it is the first of the month of Shevat.  According to Beis Hillel it is the 15th of the month.  One can imagine that the House of Shammai looks at the beginning of the month as, literally, ripe with potential even if the buds have not yet shown, while the House of Hillel requires that the buds start to show, which happens mid-month.

Finally, there is a tradition from the Arizal that in Messianic times the halakha will be in accordance with the House of Shammai. (Arvei Nachal, Rosh Hashanah 2:66, and Kedushas Levi Likkutim 36.). According to the idea we have been discussing, it makes sense that in a utopian ideal future world, everything will be judged on its potential, because at that point, the potential merges with the actual.