There is a Torah-level violation to erase (mochek) writing or, according to many authorities, a picture or a figure.[1] When the erasure does not serve a positive purpose, such as enabling new writing, the violation is only Rabbinic.[2] One could argue that there is no Torah prohibition in your case, as the erasure’s result is actually “destructive” (mekalkel); the pleasant-looking forms are being destroyed, and a better surface is certainly not created. Whether or not this constitutes mekalkel, however, would be the subject of debate, because the disintegration provides the side benefit of providing desirable information about the wetness of the diaper.[3]
The main reason for leniency relates to who is doing the erasure and in what manner. Directly, it is the baby who erases by urinating, but he is almost always too young to require training in Shabbat prohibitions. Although one must not “feed” (i.e., directly facilitate) children to do prohibited matters, he may allow a situation in which a baby might choose to do a forbidden action.[4] Here the situation is even better, as the baby “violates” Shabbat without any knowledge of this consequence of his action, in which case it is not a fundamental Shabbat violation even for an adult.[5]
Thus, the question is whether the adult violates Shabbat by creating a situation (putting on the diaper) wherein a future event will set off a melacha (urination will cause the forms to deteriorate). When the direct cause of the erasure (urination) has yet to occur at the time of the adult’s action (diapering), we say that the adult acted through gerama (indirect action). Gerama only sets up a situation in which an external factor will activate the Shabbat-forbidden result at some later time. Violation of Shabbat through gerama is a very low-level violation of Shabbat, to the extent that it is permitted in certain cases of need.[6]
Is your case forbidden if there is no special need? In this case, there are often additional points of leniency. For parents who are interested only in using a quality diaper and not in the special wetness indicator (there is an “old way” to know when the diaper is soaked), the erasure is permitted as a davar she’eino mitkaven.[7] Although it is true that when the forbidden result is a definite outcome (p’sik reishei), the action is forbidden by Torah law,[8] when the result comes about through gerama, many important poskim permit p’sik reishei.[9] Some say that gerama is permitted in cases in which direct action is only Rabbinically forbidden, but others disagree; in any case, the leniency likely does not apply to every Rabbinic prohibition.[10] This discussion is probably not necessary, however, since the erasure is likely not a p’sik reishei. For a variety of reasons, including that the baby may soil the diaper with solids before the diaper is soaked through, such diapers do not always reach the point that the forms are erased.
When there are no meaningful figures or letters on the diaper, but just a line or dots, there is even more room for leniency, as erasing such nondescript things is not a (full) violation of mochek unless the erasure enables subsequent writing.[11] We find this distinction in such cases as cutting a cake with writing or clear figures vs. nondescript shapes.[12]
In summary, one may generally use diapers with disintegrating ink.[13] However, note that many of the reasons for leniency are based on the assumption that one does not have the intention when diapering to rely on the erasure to indicate when the diaper should be changed. This is a valid assumption when one did not intentionally buy diapers with this marginally useful feature. On the other hand, for one who values this function, use of such diapers on Shabbat may very well be forbidden and should be avoided.[14]