The Turing Completeness of Law

January 2024.

Alec Thompson

In Bettina Heiderhoff; Ilaria Quierolo (eds) 'EU and Private International Law: Trending Topics in Contracts, Successions, and Civil Liability’ (2023) Editoriale Scientifica (Naples/Napoli), pp. 347-375.

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A popular question is whether the law can be replaced with a digital system capable of carrying out all legal functions. Rarely, however, do we ask the opposite: can we use a legal system to run a computer program? The purpose of this paper is to answer the second question by investigating the Turing completeness of law. It uses modern English law as a test case and constructs a Universal Turing machine (UTM) entirely out of English private law. It does so using the property rights in a piece of moveable property over time as the ‘tape’ of the UTM, the persons the rights are vested in as the machine’s alphabet, and contract law to provide the machine instructions. Several interesting implications emerge from this thought-experiment.