The Origin of the Logic of Symbolic Mathematics: Edmund Husserl and Jacob Klein

The Origin of the Logic of Symbolic Mathematics: Edmund Husserl and Jacob Klein

The Origin of the Logic of Symbolic Mathematics: Edmund Husserl and Jacob Klein

The Origin of the Logic of Symbolic Mathematics: Edmund Husserl and Jacob Klein

Synopsis

Burt C. Hopkins presents the first in-depth study of the work of Edmund Husserl and Jacob Klein on the philosophical foundations of the logic of modern symbolic mathematics. Accounts of the philosophical origins of formalized concepts--especially mathematical concepts and the process of mathematical abstraction that generates them--have been paramount to the development of phenomenology. Both Husserl and Klein independently concluded that it is impossible to separate the historical origin of the thought that generates the basic concepts of mathematics from their philosophical meanings. Hopkins explores how Husserl and Klein arrived at their conclusion and its philosophical implications for the modern project of formalizing all knowledge.

Excerpt

Jacob Klein’s foundational work on the roots of modernity could not have been more fortunate in its first comprehensive expositor and interpreter. Burt Hopkins lays out its argument, which is as intricate as it is bold, with discerning precision and sympathetic acuity. It is actuated by the judgment that he is explicating one of the philosophical masterpieces of the twentieth century (§ 208).

At the time I translated Greek Mathematical Thought and the Origin of Algebra some forty years ago, I had felt its force and appreciated its complexity sufficiently to achieve a passable rendering. But it was not until I read and reread the book which is before you that I began to apprehend Klein’s faithful originality. I mean his ingenious yet unforced use of sources. The translation has had a favorable publication history. The MIT Press first brought it out in 1968, and Dover reprinted it in 1992, effectively giving Klein’s work the status of a classic.

Nevertheless, though mentioned increasingly often in the scholarly literature on Plato, Descartes, and the philosophy of mathematics, it was not altogether well understood, as Hopkins’s detailed critical footnotes show. Not that the various treatments were grossly mistaken, but that the fine points— and in this undertaking the devil is in the details—had not been carefully enough considered. Moreover, the significant relation to Husserl’s work on arithmetic had not been worked out.

Hopkins, following up the “scholarly curiosity” of Klein’s silence about Husserl’s theories of intentionality and symbolic thinking, shows that Klein had indeed in some respects anticipated and corrected before the fact, as it were, Husserl’s analysis of the concept of number in particular and of the conceptual presuppositions of modern science in general. What Hopkins does is to set out in detail how Klein’s analysis undercuts Husserl’s basic assumption that modern mathematical thinking must be understood from the perspective of direct experience. Yet he also shows that Klein’s investigation is in fact a large-scale actualization of Husserl’s historical method (§ 28).

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