Download `Spaces` in Mathematics, Physics, Subjectivity, and Historiography

Abstract, Norman Sieroka (ETH), 1/2
An Exemplary Case for an Integrated Historiography of Philosophy and
Science: Weyl, Medicus, and the Concepts of Surrounding
The aim of this paper is to sketch an approach for integrating the historiography of science and of
philosophy in a systematic way. Although the details of this approach are tailor-made for a certain
historical period and specific context, it might be viewed as an exemplary case for integrated
approaches on science and philosophy also in other historical contexts.
The present approach makes central use of the concept of surrounding and has been elaborated for a
systematical and historically detailed assessment of the interaction between the eminent
mathematician Hermann Weyl and the philosopher and Fichte scholar Fritz Medicus in Zurich
around 1920. As their published and unpublished work, correspondences, and further archived
material shows, they both stood in close intellectual contact and scientific exchange: they quote
each other in their publications, took extensive notes and commented on each others drafts and
publications, attended each others lectures, met regularly to read the main works of Fichte, etc.
In his writings on the philosophy of mathematics and physics Weyl often develops rather intriguing
positions. It is especially the work of Fichte and Husserl which influenced and shaped his position.
From a present day perspective these philosophers seem to be rather strange allies for a
mathematician and philosopher of science. However, if considering the historical documents on
Weyl's “constructive intellectual interference” with Medicus (and his undergraduate days in
Göttingen, where he attended lectures by Husserl) these references appear rather straightforward
and also make plausible the otherwise rather unconventional details of Weyl's Fichte reception. In
turn, something similar is true of Medicus's philosophical work. Hence, I suggest that the close
historical study of this academic constellation (surrounding, environment) between Weyl and
Medicus allows for a systematic reconstruction of their positions.
The particular historiographical method I suggest for investigating such a historically concrete
intersubjective environment is (a slightly revised version of) Konstellationsforschung. This method
has recently been introduced by Henrich, Mulsow and others and focuses on the close investigation
of historical documents in order to reconstruct the “space of thought” (Denkraum) of a constellation
(surrounding) of people. Besides, this method was originally developed to comprehend the
beginnings of German idealism in Jena around 1800; i.e. in a context which, like the present one,
involved many considerations and assumptions related to the philosophy of Fichte.
Moreover, the concept of surroundings also played a crucial role in the various topics discussed by
Weyl and Medicus and arguably led them to structurally analogous approaches in the philosophy of
mathematics and physics and in the theory of subjectivity. Let me briefly hint at some of the issues
involved here:
In his philosophical writings of around 1920 Weyl aimed to show that the then prominent debate
between intuitionism and formalism can be understood as a debate about whether truth is related to
some sort of disclosure or creation; a debate which, at least for Weyl, was related to an innerphilosophical dispute between Husserl’s phenomenology and Fichte’s “doctrine of knowledge”
(Wissenschaftslehre). In the same context, the treatment of the topological analysis of the continuum
led Weyl to a discussion of the concept of surroundings. (In English the technical mathematical
term here is “neighbourhood”. However, here as well as in the following cases the German term for
surrounding/neighbourhood/environment is always “Umgebung”.)
Abstract, Norman Sieroka (ETH), 2/2
Around the same time and in reaction to certain inconsistencies and tensions between field physics
and atomic (later quantum) physics, Weyl developed an agency theory of matter. Here his
considerations on continuity and discreteness transferred from the mathematical to the natural
realm. Weyl now understood matter to be something which causes effects in space-time without
being a part of space-time itself. The alleged “inside of matter” is, for him, not an object for
science—the only things which exist in this realm are the spatiotemporal neighbourhoods
(“surroundings”). And, like in the case of mathematical neighbourhoods, Weyl referred to Fichte to
motivate his view.
Next, in Medicus' writings on the theory of subjectivity the tension between continuity and
discreteness (re-)appears as a tension between a community and an individual. According to
Medicus the concept of a human individual is a limiting idea, constituted by means of overlapping
communities (in the sense of personal environments or surroundings). His approach is strongly
influenced by Fichte's early accounts on (inter-)subjectivity and developed during the time of his
close intellectual interaction with Weyl. Accordingly, it is hardly a coincidence that Medicus's
concept of a person is structurally analogous to Weyl's concept of a point in mathematics as being
constituted by means of neighborhoods and as being a limiting idea. Moreover, Medicus's concept
of (inter-)subjectivity and personal surroundings links back directly to the methodology of
Konstellationsforschung.
To sum up: Weyl's and Medicus's approaches within these very different philosophical and scientific
areas show striking similarities. They all refer to certain concepts of (mathematical, spatiotemporal,
intersubjective) surroundings to enable a satisfying treatment of a certain tension between
continuity and discreteness. Points, matter, humans are all constituted by their surroundings.
Furthermore, the concept of personal surroundings also forms a constitutive part of the
historiographical assessment of the philosophical positions and debates involved. Thus, by focusing
on the personal environment of Weyl and Medicus a particular unity of content and method is
reached; an integration of historical and systematic thinking which is congenial to what Medicus
and Weyl themselves demanded in their philosophical writings. Arguably, this specific kind of
nearness between the historical material and the way in which it is approached is also crucial for
making the issues and debates encountered in the historical surrounding contractible and relevant
for our current expressions of similar concerns and debates.
My claim is not that the look at surroundings is the universal remedy for the historiography of
science and of philosophy. Other protagonists, times, disciplines, and debates might likely suggest
focusing on other concepts and methods. However, what I suggest is that there might be
combinations between content and method which produce a certain nearness to the historical
material and which might make us see former philosophical problems as being variations of our
current ones.