Binary Logic as Legal Algorithm: Computational Evidence of Systematic Decision-Making in Ottoman Sheikh al-Islam Fatwas

Bridging computational linguistics, machine learning, and Islamic legal studies, this interdisciplinary investigation examines the algorithmic structure underlying Ottoman Sheikh al-Islam fatwa reasoning. Analysis of 9,913 fatwas from authoritative collections—including Fetâvâ-yı Feyziye, Fetâvâ-yı Ebüssuûd Efendi, and Behcetü'l-Fetâvâ—establishes that nearly 87% of rulings follow binary prohibition/permission logic. This binary architecture exhibits notably low entropy (1.599 bits), falling 66% below maximum possible entropy, which suggests highly structured decision patterns characteristic of the centralized Sheikh al-Islam authority. Machine learning models achieved considerable predictive accuracy (87.6% with XGBoost), with simple linguistic markers ("olmaz"/"olur") emerging as the strongest predictors. Among binary cases, prohibitions (4,410) and permissions (4,199) appear balanced, challenging assumptions about Islamic law's supposedly restrictive nature. Financial matters pointed to even higher binary classification rates than non-financial cases (88% versus 84%), likely reflecting commercial law's demand for clear guidance. Such systematic patterns, developed centuries before digital computing, suggest that algorithmic legal reasoning may represent an ancient practice rather than a modern innovation. These results carry implications for contemporary debates around legal automation and the appropriate role of Artificial Intelligence (AI) in religious jurisprudence, while documenting how pre-modern institutions achieved systematization through human rather than technological means.