Mr. Gabriele Baratelli
Department of Philosophy
University of Turin
Torino, via Sant'Ottavio 20
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Jacob Klein and the Translation of Natural Language into Symbolic Language in Modern Mathematics

Jacob Klein’s account on the origin of modern conceptuality investigates the ontological transformation that occurred during the modern era of the concepts assimilated from Greek mathematical and philosophical thought. The neglected transformation of the Greek concept of number into the formalized modern one is taken as the exemplary one. At the core of this analysis, there is the conviction that the constitution of the symbolic language of algebra is not merely a technical aspect in the process, but its essential mark and the key to examining it. Following this path, we argue that Klein’s general project can be better understood by stressing the detachment of formal language from natural language and reading the transformation aforementioned in terms of a specific kind of translation of the former into the latter. This move allows in turn the highlighting of the overall critical character of Klein’s plan, consisting in the exposition of the covered over conceptual shift at the origin of modern conceptuality and of its paradoxical premises.