Humanities Studios: Pedagogy, Psychology, Philosophy

Grounds for the renewal and mathematisation of logic and their historical characterisation

Georgii Kulebyakin
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Abstract

The relevance of the study is conditioned by the necessity of a historico-philosophical understanding of the process of renewal and mathematisation of logic, which determined the formation of contemporary mathematical logic and substantially influenced the development of the philosophy of science, mathematics, and the analytic tradition. The aim of the article was to elucidate the philosophical grounds, arguments, and conceptual prerequisites that contributed to the reform of classical logic and the emergence of its mathematical forms in the second half of the nineteenth and the early twentieth centuries. The methodological basis of the study comprised the historical, analytical, comparative, and genealogical methods, which allow one to trace the evolution of conceptions of logic from the scholastic tradition to the modern forms of mathematical logic. The method of formalisation was also employed to analyse the distinctive features of propositional logic and predicate logics in the context of their differences. As a result of the study, it was established that the first grounds for the modernisation of logic were formed already within the scholastic tradition, in particular in the works of W. Ockham, where the necessity of refining and simplifying syllogistic rules was substantiated. It was shown that an important stage in the development of these ideas was constituted by the logical projects of G.W. Leibniz, who was among the first to advance a programme for the mathematisation of logic and the creation of a universal symbolic language of science. It was determined that a decisive role in the reform of logic was played by the investigations of G. Frege, who laid the foundations of logicism, carried out the axiomatisation of propositional logic, and created the foundations of the modern predicate calculus. It was established that the further development of these ideas in the works of B. Russell and A.N. Whitehead contributed to the consolidation of mathematical logic as an independent branch of knowledge and a universal instrument of scientific analysis. It was also established that important factors in the mathematisation of logic were the limitations of classical syllogistic and the necessity of overcoming the logical paradoxes that arose in the course of the development of mathematics. The practical value of the study lies in the possibility of using its results for the historico-philosophical analysis of logic, for teaching courses in logic, philosophy of science, and the history of analytic philosophy, as well as for further research into the genesis of mathematical logic

Keywords

positivism; logicism; cognition; syllogistic; predicate calculus; quantifier; judgement

Suggested citation
Kulebyakin, G. (2026). Grounds for the renewal and mathematisation of logic and their historical characterisation. Humanities Studios: Pedagogy, Psychology, Philosophy, 14(2), 176-193. https://doi.org/10.31548/hspedagog/2.2026.176
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