Paul mentions the living sacrifices without explanation, as if the readers would be familiar with the concept. Similar early rabbinic vocabulary suggests that Paul is referring to sacrifices which were given to the Temple but which were inappropriate for offering, because they were female instead of male or for other technical reasons. They could not be un-offered so, although they were sacrifices, they were kept alive as Temple property till they became blemished, and any profit from them was for the Lord.
First-century Jewish cult practice is difficult to study because the main sources are the Old Testament which is too old and the rabbinic corpus which (on the whole) is too recent. The few references in contemporary sources like Josephus and Philo are often useful but they do not provide a comprehensive picture, and can do no more than confirm or question a few details in the two major sources.
Rabbinic traditions are difficult to use for studying first-century Judaism because the earliest written versions date from long after the Temple was destroyed, and although many early rabbis are cited, it is difficult to determine when these attributions are accurate. In recent decades the dating of some rabbinic material has become more certain, largely through the painstaking work of Neusner and his colleagues. The general consensus is that halakhic traditions (that is, traditions concerned with the practice of the Law) are usually reliable with regard to the date of attributions, and that some anonymous halakhic traditions can be dated with reference to the datable ones, but for all other rabbinic traditions it is still very difficult to have confidence in dating.
-  Hermann L. Strack’s Einleitung in Talmud und Midrasch (München, 1887), ET Introduction to the Talmud and Midrash was revised (or more properly, rewritten) by Günter Stemberger (Oscar Beck: München, 1982) ET by Markus N. A. Bockmuehl (London: T & T Clark, 1991; Minneapolis: Augsburg Fortress 1992, 1996), 63-65. ↩