The Adventure Of Reason by Paolo Mancosu
Interplay between Philosophy of Mathematics and Mathematical Logic, 1900–1940
A historical and philosophical study of the two-way exchange between mathematical logic and the philosophy of mathematics from 1900 to 1940, it shows how technical developments in axiomatization, categoricity, completeness, truth, and the decision problem both shaped and were shaped by debates among logicism, formalism, and intuitionism. Through detailed case studies and archival sources, it reconstructs shifting views on rigor, meaning, and proof, and explains how the emergence of metalogic—culminating in landmark results such as incompleteness and semantic theories of truth—transformed the foundations and practice of mathematics in the early twentieth century.
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