concerning which there was disagreement. This is followed by knowledge of the evidence for those rulings from the Quran and Sunnah.

As for “inheritance calculation,” it consists of determining the base numbers of inheritance calculations and adjusting them to yield whole-number shares, calculating successive inheritances before an estate has been divided, and distributing estates. This second branch consists entirely of rational knowledge accessible through reason, like other calculations concerning transactions and the other kinds of calculation people need.

They have also discussed, in this connection, the calculation of unknowns, known as algebra. This is an ancient science, but the first person known to have applied it to bequests, circular calculations, and similar matters was Muhammad ibn Mūsā al-Khwārizmī. Some people relate that ʿAlī ibn Abī Tālib discussed it and learned it from a Jew. This is a fabrication falsely attributed to ʿAlī.

The term “circular dependence” is used for three kinds. The first is “circular dependence in existence,” discussed in rational arguments: this cannot exist until that exists, and that cannot exist until this exists. Some speculative thinkers used to hold that it is impossible. The correct view, as al-Āmidī and others explain, is that it comprises two kinds: “circular dependence involving priority” and “simultaneous interdependence.”

The former is impossible. It is the kind discussed in connection with causes, agents, producers of effects, and similar matters. For example, one may say that each of two things cannot bring the other into existence, because this would entail circular dependence: this would have to precede that, and that would have to precede this.

“Simultaneous interdependence,” however, is possible. It is the interdependence of a condition and what is conditional upon it, or of two mutually correlative things. For example, fatherhood exists only together with sonship, and sonship exists only together with fatherhood.