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In the Philosophy of Mathematics & Physics, Weyl writes:

The coordinate system is, as it were, the residue of the annhilation of the ego.

What does he mean by this?

  • That arithmetization of continuum annihilates the creation by the Kantian ego of the "true" intuitive one in the second act of intuitionism. – Conifold Feb 13 '18 at 21:15
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We can see the long discussion of continuum into:

Hermann Weyl, The Continuum: A Critical Examination of the Foundations of Analysis (German ed., 1917), page 88-94.

In a nutshell, Weyl asserts that it is impossible to furnish the continuum as presented to intuition with an exact mathematical formulation.

His philosophival analisys is influenced by Husserl and phenomenolog and is focused on the continuum of immediately given phenomenal time:

[page 88] In order better to understand the relation between an intuitively given continuum and the concept of number (the above example having revealed the discrepancy between the two), let us stick to time as the most fundamental continuum. And in order to remain entirely within the domain of the immediately given, let us adhere to phenomenal time (rather than to objective time), i.e., to that constant form of my experiences of consciousness by virtue of which they appear to me to flow by successively.

[page 90] Now, I think that everything we are demanding here is obvious nonsense: to these questions, the intuition of time provides no answer. So the theoretical clarification of the essence of time's continuous flow is not forthcoming. The category of the natural numbers can supply the foundation of a mathematical discipline. But perhaps the continuum cannot, since it fails to satisfy the requirements mentioned in Chapter 1, §1: as basic a notion as that of the point in the continuum lacks the required support in intuition. It is to the credit of Bergson's philosophy to have pointed out forcefully this deep division between the world of mathematical concepts and the immediately experienced continuity of phenomenal time ("la durée").

[page 91] The view of a flow consisting of points and, therefore, also dissolving into points turns out to be false. Precisely what eludes us is the nature of the continuity, the flowing from point to point; in other words, the secret of how the continually enduring present can continually slip away into the receding past.

[page 94] Exact time- or space-points are not the ultimate, underlying, atomic elements of the duration or extension given to us in experience. On the contrary, only reason, which thoroughly penetrates what is experientially given, is able to grasp those exact ideas.

The exhibition of a single point is impossible. Further, points are not individuals and, hence, cannot be characterized by their properties. (Whereas the "continuum" of the real numbers consists of genuine individuals, that of the time- or space-points is homogeneous.) Therefore, points and sets of points can be defined only relative to (i.e., as functions of) a coordinate system, never absolutely. (The coordinate system is the unavoidable residue of the eradication of the ego in that geometrico-physical world which reason sifts from the given using "objectivity" as its standard-a final scanty token in this objective sphere that existence is only given and can only be given as the intentional content of the processes of consciousness of a pure, sense-giving ego.)


Very useful are also: Hermann Weyl's *Das Kontinuum as well as: John Bell, Hermann Weyl: Mathematician-Philosopher and John Bell, Hermann Weyl on intuition and the continuum.

  • Nice answer. I also was struck by Weyl's remark when I came across it. I grasped it at the time but am a bit vague now. I think it's to do with objectifying the co-ordinate system and overlaying it on experience, thus objectifying experience.or de-personalising it. . . – PeterJ Feb 13 '18 at 12:57

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