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DOI :10.26650/mecmua.2025.83.1.0006   IUP :10.26650/mecmua.2025.83.1.0006    Full Text (PDF)

Philosophical Foundations of Law’s Relationship with Mathematics: Is Law Having Mathematical Certainty?

Murat Bayram

 Mathematics is often given as an example of the precision and perfection of reasoning. The success achieved through the methods of mathematics has encouraged the use of mathematical techniques in various fields and among thinkers. In particular, the logical axioms, which are the indisputable truths about mathematical concepts, have been applied in the field of law with the success seen in the natural sciences. Logic has often served as a tool for law, helping it achieve its purpose. Lawyers use logical techniques to address deficiencies in legal practice. In this regard, logical techniques are considered to provide mathematical certainty in law. Positivists and natural law theorists approach mathematical certainty differently. While the positivist approach focuses on the purely axiomatic dimension of mathematics, the natural law perspective emphasizes the a priori domain. In this context, we discuss whether the synthetic a priori plane of mathematical propositions is valid for legal rules. By examining the historical development of logic and mathematics, this study explores their influence on the mathematical certainty of law and its relationship with legal concepts and the world of existence. This study also aims to evaluate the ontological domains of mathematics and law from a philosophical perspective. The main objectives of this study are to evaluate the ontological relationship between mathematics and law and to examine the extent to which mathematical precision can be applied in the field of law.

Keywords: Law, Logic, Mathematics, Certainty, Philosophy
DOI :10.26650/mecmua.2025.83.1.0006   IUP :10.26650/mecmua.2025.83.1.0006    Full Text (PDF)

Hukukun Matematikle İlişkisinin Felsefi Temelleri: Hukuk Matematiksel Kesinliğe Sahip Midir?

Murat Bayram

 Usa vurmanın kesinliğine ve kusursuzluğuna çoğu zaman matematik örnek verilir. Matematiğin yöntemleriyle elde edilen başarı, çeşitli alanlarda ve düşünürler arasında matematiksel tekniklerin kullanımını teşvik etmiştir. Özellikle matematiğin kavramlarıyla ilgili akıl yürütme süreçleri, doğa bilimlerinde şüphe duyulmayan mantıksal belitler aracılığıyla başarı sağlamış ve bu yöntem hukuk alanında da uygulanmıştır. Hukukta mantık, çoğu zaman bir araç olarak kullanılarak hukukun amacına ulaşmasına yardımcı olmuştur. Hukukçular, hukuki davalarda var olan eksiklikleri tamamlamak için mantıksal tekniklerden faydalanır. Bu bağlamda mantıksal tekniklerin hukukta matematiksel bir kesinlik sağladığı düşünülmektedir. Matematiksel kesinlik pozitivist ve doğal hukukçular tarafından farklı şekillerde ele alınır. Pozitivist yaklaşım, matematiğin salt aksiyomsal boyutuna odaklanırken, doğal hukukçu görüş apriori alana vurgu yapar. Bu çalışmada matematiksel önermelerin sahip olduğu sentetik apriori düzlemin hukuk kuralları için geçerli olup olmadığını tartışmayı amaçlıyoruz. Bu doğrultuda, mantık ve matematiğin tarihsel gelişiminden faydalanarak hukukun matematiksel kesinliği, matematik kavramları ve varlık dünyası ile ilişkisi ele alınacaktır. Matematiğin ve hukukun varlık alanlarının felsefi bir bakış açısıyla değerlendirilmesi, matematiksel kesinliğin hukuk alanında ne ölçüde uygulanabileceğinin incelenmesi, çalışmamızın temel amaçları arasında yer almaktadır. 

Keywords: Hukuk, Mantık, Matematik, Kesinlik, Felsefe

EXTENDED ABSTRACT


 In the name of legal certainty, the language of law has been approached from a mathematical and logical perspective. Most of us accept that law includes logic to some extent. However, the view that mathematical language resembles law has led to controversy. Some of these discussions attempted to reduce the law to a mathematical language by focusing on mathematical certainty. In this sense, reducing the legal language to a mathematical formula may achieve certainty. In other words, it aims to create definitions similar to those in mathematics for the general validity of legal concepts. At the same time, for this purpose, the present study attempts to identify the moral background of law with the apriori field of mathematics. Discussions on the other side focused on the conclusion that law derives from complex human relations, arguing that mathematical language is invalid in law. They argued that such reductions were invalid, claiming that the two domains were independent of each other. In fact, both discussions focused on the direct representation of law as a mathematical language. Law has neither purely mathematical precision nor a view that there is no mathematical objectivity. The focus should be on the similarity between law and mathematical language.

In fact, the fields of law and mathematics cross borders without syntheses and identification. Mathematics tries to analyse the infinite by reducing it to symbols. The ∞ symbol denotes infinite equals. This symbol simply helps us understand the concept of infinity, which we cannot fully comprehend. Law also symbolizes justice, equality, and the scales. The scale symbolizes these two concepts, which we can never reach completely. Of course, the holders of these scales may vary, and the realisation of these concepts may vary. Both approaches attempt to identify areas of uncertainty.

Our primary purpose here is to reveal the relationship between law, logic, and mathematics. Although mathematical methods are not used in law, law uses logical techniques. Although law does not use mathematical methods, law and mathematics can be observed within the same limits. Our aim here will be to dwell on the similarities between mathematical reasoning and legal reasoning rather than reducing law to a purely mathematical level. After the similarities between law and mathematical propositions, how important is the effect of mathematical reasoning on law? Does mathematical reasoning provide fairness to the law? Does it also provide objectivity? We will discuss the effect of logic on legal reasoning with questions like these. In fact, our aim in this study was not to create a purely mathematical law. In fact, it would be utopian to accept the foundations of law and mathematics as identical to undertake such a business. At the same time, efforts to construct a law using a purely mathematical language are one of the most dangerous ways. The effort to mathematize the law is only due to efforts to create a legal field and to realise  justice. In such a situation, ignoring the exceptions in law causes the language of the law to be unfairly constructed.

However, logic is effective in making correct inferences in law. Although mathematics does not explicitly source law, the function of logic in law is obvious. As a matter of fact, few lawyers would seriously defend the thesis that legal decision-making consists solely of applying the facts of a case to a rule to draw legal consequences. Considering the content of the rule and the decisions regarding the classification of events, the legal consequences of the case are handled logically.


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APA

Bayram, M. (2025). Philosophical Foundations of Law’s Relationship with Mathematics: Is Law Having Mathematical Certainty?. Istanbul Law Review, 83(1), 395-415. https://doi.org/10.26650/mecmua.2025.83.1.0006


AMA

Bayram M. Philosophical Foundations of Law’s Relationship with Mathematics: Is Law Having Mathematical Certainty?. Istanbul Law Review. 2025;83(1):395-415. https://doi.org/10.26650/mecmua.2025.83.1.0006


ABNT

Bayram, M. Philosophical Foundations of Law’s Relationship with Mathematics: Is Law Having Mathematical Certainty?. Istanbul Law Review, [Publisher Location], v. 83, n. 1, p. 395-415, 2025.


Chicago: Author-Date Style

Bayram, Murat,. 2025. “Philosophical Foundations of Law’s Relationship with Mathematics: Is Law Having Mathematical Certainty?.” Istanbul Law Review 83, no. 1: 395-415. https://doi.org/10.26650/mecmua.2025.83.1.0006


Chicago: Humanities Style

Bayram, Murat,. “Philosophical Foundations of Law’s Relationship with Mathematics: Is Law Having Mathematical Certainty?.” Istanbul Law Review 83, no. 1 (May. 2025): 395-415. https://doi.org/10.26650/mecmua.2025.83.1.0006


Harvard: Australian Style

Bayram, M 2025, 'Philosophical Foundations of Law’s Relationship with Mathematics: Is Law Having Mathematical Certainty?', Istanbul Law Review, vol. 83, no. 1, pp. 395-415, viewed 22 May. 2025, https://doi.org/10.26650/mecmua.2025.83.1.0006


Harvard: Author-Date Style

Bayram, M. (2025) ‘Philosophical Foundations of Law’s Relationship with Mathematics: Is Law Having Mathematical Certainty?’, Istanbul Law Review, 83(1), pp. 395-415. https://doi.org/10.26650/mecmua.2025.83.1.0006 (22 May. 2025).


MLA

Bayram, Murat,. “Philosophical Foundations of Law’s Relationship with Mathematics: Is Law Having Mathematical Certainty?.” Istanbul Law Review, vol. 83, no. 1, 2025, pp. 395-415. [Database Container], https://doi.org/10.26650/mecmua.2025.83.1.0006


Vancouver

Bayram M. Philosophical Foundations of Law’s Relationship with Mathematics: Is Law Having Mathematical Certainty?. Istanbul Law Review [Internet]. 22 May. 2025 [cited 22 May. 2025];83(1):395-415. Available from: https://doi.org/10.26650/mecmua.2025.83.1.0006 doi: 10.26650/mecmua.2025.83.1.0006


ISNAD

Bayram, Murat. “Philosophical Foundations of Law’s Relationship with Mathematics: Is Law Having Mathematical Certainty?”. Istanbul Law Review 83/1 (May. 2025): 395-415. https://doi.org/10.26650/mecmua.2025.83.1.0006



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Submitted15.05.2021
Accepted24.02.2025
Published Online06.05.2025

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