Intuition and Conceptual Construction in Weyl’s Analysis of the Problem of Space

Abstract

Hermann Weyl adopted the Kantian definition of space as a form of intuition and referred to Edmund Husserl's phenomenological approach for the philosophical characterization of space in the introduction to Raum-Zeit-Materie (1918) and other writings from the same period (1918-1923). At the same time, Weyl emphasized that subjective factors are completely excluded from the mathematical construction of physical reality in Albert Einstein's general theory of relativity, with the sole exception of the setting of a coordinate system, which for Weyl is what remains of the original perspective of the self in becoming aware of one's own intuitions. This paper reconsiders Weyl's philosophical position as a possible response to the earlier debate on the relation between intuition and conceptual construction in the foundation of geometry, key figures of which, besides Husserl, included Hermann von Helmholtz, Felix Klein, and Moritz Schlick.

Weyl’s Raum-Zeit-Materie and the Philosophy of Science

“…It has brought us much nearer to grasping the plan that underlies all physical happening (welche dem physischen Weltgeschehen innewohnt). 3 [21 v] At that time, these words could sound prophetic. We now know that relativity disclosed to us objects that we could not even imagine 100 years ago, such as black holes.…”

“…It is in the composite idea of motion that these three fundamental conceptions enter 2 For a mature view on this topic, see [24]. 3 The notion of physical happening is of fundamental relevance here. In 1918-1920 Weyl follows very closely the lines of Husserl's Ideen zu einer reinen Phänomenologie und phänomenologischen Philosophie [11], and I suggest that he gives a meaning to this expression that is very similar, albeit not identical to Husserl's.…”

“…This time, however, I would like to emphasize the reference that Weyl makes here to "the working of the mathematical intellect". The mathematical intellect, as we shall see, embodies the metaphor of a specific perspective that through symbolic construction (see [3,6,7,12,13] leads to the objective understanding of the world. We can say that gauge theory illustrates the power of this mathematical intellect thanks to symmetry that dictates the form of interactions.…”