In the treatise we wrote on “circularity” (dawr) we clarified that the term is used in three distinct senses:
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Cosmological circularity, cited in rational arguments with the phrase, “This cannot be until that is, and that cannot be until this is.” Some dialecticians—al-Rāzī among them—judge it impossible, yet the correct view, affirmed by al-Āmidī and others, is that it comes in two forms: antecedent (qabliy) and concomitant (maʿī). Antecedent circularity is impossible, whereas concomitant circularity is possible.
• Antecedent circularity is invoked in discussions of causes, agents, and the like; for example, the claim that each of two things is the agent that brings the other into being. This would mean that one precedes the other and the other precedes the one, each acting upon the other, so that a thing becomes the agent of its own agent and prior to what is prior to it. Al-Rāzī and others have posed objections to this; we have listed those objections and shown how to answer them in our works on proving the existence of the Creator.
• Concomitant circularity resembles the interdependence between a condition and that which is conditioned, or between two correlatives. Thus we say, “The attributes of the Lord are never found except together with His Essence, and His Essence is never found except together with His attributes”—and this is sound. In the same way, fatherhood cannot exist without sonship, nor sonship without fatherhood.
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The second sense called “circularity” is the juristic, declaratory variety that surfaces in the Sarījiyyah problem and similar cases. We have written separate treatises on this, explaining its true nature and demonstrating that it is invalid both rationally and according to the Sacred Law. In another work we examined whether anything of this sort actually occurs in the revealed law.
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The third sense is mathematical circularity, expressed by the statement, “This cannot be known until that is known.” It is this kind whose resolution is sought through the algebraic method of “restoration and reduction.”