Al-Ghayb, A Formal Mathematical Definition of the Unseen

Abstract

The Qur'anic concept of al-ghayb (the Unseen) is central to Islamic theology, but scholarship usually treats it through exegetical, theological, mystical, or anthropological analysis. This paper develops a formal, time-indexed model separating actual discovery from accessibility in principle. Let Omega be a stipulated domain of states of affairs within created reality. The class A contains states accessible to independent creaturely inquiry, while M(t) contains those actually established by epoch t. The relative Unseen comprises states in A not yet established. The class G contains states inaccessible by independent creaturely inquiry. The total Unseen combines these classes. The main result shows that the historical residue is not automatically identical to G because it also includes accessible states that inquiry never establishes. The two coincide only if eventual inquiry is complete over A. Divine disclosure is represented separately rather than treated as independent inquiry. Cases from electromagnetic radiation and gravitational-wave astronomy illustrate only that absence from the historical record at one time does not entail non-existence. The model neither proves that G is non-empty, identifies a member of G, nor treats scientific unobservables as evidence for theological claims.