CfP: Algebra as Philosophical Demonstration: Systems of Science around 1800

In what way can “A = A” provide students or readers an insight into the fundamental tenets of a philosophical system of science? Around 1800, answering this question seems almost redundant. The use of algebra (mainly through further algebraic elaborations and complications of the Aristotelian identity principle A = A) in the explication of problems and systematic foundations greatly intensifies. Curiously, this practice is not merely found among doctrinal allies who could be expected to share the same methodology, but also among avowed enemies. This shows a remarkably intense commitment to the importance of algebra, as i) a notational system that can capture systematic complexity, as ii) an aspirational form of philosophical presentation and, most of all, as iii) a way of explicating systematic complexity in a form that is easily comprehensible. 

In the 20th century, the use of algebra (among other mathematical approaches) to render philosophical problems accessible became controversial due to the so-called “science wars”. These concerns were by no means new. Many earlier twentieth century philosophers were inspired by various features of mathematics in presenting their philosophical systems (Tonelli 1959). In 1759, several rationalist philosophers complained of ‘misuse of mathematical concepts’ stating that this was ‘only acceptable if these [concepts] remain within their proper boundaries.’ (Mendelssohn 1759). Despite these calls for respecting the boundaries of mathematics, many other eighteenth century philosophers envied the self-evidentiality of mathematics and sought to emulate this feature in order to circumvent difficult prose, technical terminology and the problem of structuring philosophical texts. Algebra represents a particularly interesting avenue for achieving a self-evident philosophical system of science because it does not depend on empirical cognition that might be put into question, unlike geometry (depending on spatiality), infinity (depending on number), etc. One way of comparing the discussions around 1800 with those in the twentieth century is to point out that the didactical use of mathematics in philosophy is often motivated by the fact that it can make use of common principles established in the early education in mathematics for children. 

A return to the experiments with algebra around 1800 will provide insight into this and other reasons why the early formulations of a philosophy of science required algebraic examples for didactic and demonstrative purposes and, consequently, answer why algebra remained a preferred mode of exposition well into the twentieth century, both on the analytic and continental side of academic philosophy. Unlike many later examples, this period is perfect for such an examination because i) it occurs at a foundational time, the emergence of systematic exposition of systems in the philosophy of science during the Enlightenment, and ii) there is genuine and extensive discussion of its effectiveness among multiple adherents of this strategy.   

Organization Tom Giesbers (Open Universiteit).

Funded by the E. W. Beth Foundation and the Descartes Institute, Utrecht University.

 Confirmed speakers

  • Paul Ziche (Utrecht University)
  • Helmut Pulte (Ruhr-University Bochum)
  • Volker Peckhaus (Paderborn University)
  • Filip Moons (Utrecht University)
  • Theodor Berwe (Fernuniversität Hagen)

 We are looking for contributions on the following topics:

  • The role of algebra in philosophy in the eighteenth and nineteenth centuries.
  • The application of algebra in philosophical demonstration and teaching.
  • Didactical assessment of algebraic demonstration in philosophy.
  • Reassessments of the science wars from the perspective of the use of algebra in philosophy.

Please send an abstract of a maximum of 500 words to Tom Giesbers before March 25th.