Qinnim: Chapter 2, Mishnayot 1-3
El’azar Hisma states: Qinnim and Niddah, these are the essence of the laws; calculations of the seasons and geometry, the desserts to wisdom. Abot 3:18.
Qinnim departs from the typical direct language of mishnayot, so frequently bending to concision, almost to the point of abruptness. Our tractate, frequently cited as the most difficult in the entire mishnaic corpus, utilizes the distinct and elaborate language of complex mathematical logic. Qinnim, according to tradition, was said to be authored by R Joshua.
Certain sections of Niddah similarly read like increasingly complex and knotty hypothetical puzzles. The authority named in these sections is none other than the same tanna, R Joshua.
Problems of logic, including its application in astrological calculations and gematria, were philosophical constructs, not of traditional Jewish thought, but of contemporary philosophers of Greek thought. R Joshua was known for his openness to the logic puzzles of the Alexandrine Greeks, as well as maintaining continuing dialogue with philosophers of Greek thought.
In his statement, R El’azar Hisma, a student of R Joshua, seeks to defend his teacher’s work. All these subject matters utilize a uniform methodology, traditionally employed in Greek thought. One might think the utilization of this foreign methodology adversely affects the spiritual appraisal of these texts.
For R El’azar, methodology matters less than the substance. Despite the use of Greek logic puzzles, Qinnim and Niddah are still classified, as other areas of study of holy law, as “essentials.” Astrological calculations and gematria, subjects from which we may glean some academic pleasure, these qualify as mere aftercourses of wisdom.