Purpose – The purpose of this paper is to critique Gödel's and Tarski's axiomatic approach in their theorems of incompleteness of the arithmetical system. Design/methodology/approach – Mathematical theory of self‐referencing is contrasted and an original contribution made by an extension of the same theorem beyond Godel and Tarski, showing how the Islamic epistemology contributes to establishing new thought in mathematical logic with unity of the divine law. Findings – The paper finds that behind the critique of the axioms of provability and non‐provability, decidability and undecidability, lies the morally valid episteme of all socio‐scientific systems and that this is as true of social systems as it is of the hard‐core sciences. Research limitations/implications – The paper has the potential for extension to applications, which has not been included. Originality/value – The paper contributes to new and original thinking in the area of mathematical logic of self‐referencing theorem in the framework of unity of the divine law as the episteme of “everything”.
Kybernetes – Emerald Publishing
Published: Jan 1, 2009
Keywords: Islam; Epistemology; Formal logic; Mathematics; Systems theory; Cybernetics
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