Abstract
I discuss in this paper Husserl and Weyl’s views on the role of intuition and symbolization in empirical science and their reactions to purely symbolic extensions of mathematical representations of empirical reality. Although both accept that physical space as considered in mathematical physics, for instance, is an intentional construct out of perceptual space that eliminates subjective content of perceptual experience in favor of objective form, thus transforming space as perceived in an empty mathematical manifold, they differ as to the freedom allowed to mathematics to further elaborate this and other mathematical representatives of perceptual reality. Husserl puts serious restrictions to non-eliminable, non-denoting symbolic extensions of representing manifolds, which Weyl, in his more holistic approach, is willing to accept.
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Notes
- 1.
For the notion of material a priori see da Silva 2016.
- 2.
Provided, of course, pointing happens in a context where it is interpreted as denoting.
- 3.
“[…] this world does not exist in itself, but is merely encountered by us as an object in the correlative variance of subject and object. The world exists only as that met with by an ego, as an appearing to consciousness; the consciousness in this function does not belong to the world, but stands out against the being as the sphere of vision, of meaning, of image, or however else we may call it” (Weyl 1934, 83).
- 4.
For Weyl, objective reality, as an intentional object, relates to experience in a manner that (1) there cannot be incoherent experiences of reality and (2) there cannot be anything in reality that cannot in principle correspond to something in experience (see Weyl 1963, 121–24).
- 5.
“…this objective world, representable only in symbols…[my emphasis]” (Weyl 1963, 120).
- 6.
“The datum of consciousness is the starting-point at which we must place ourselves if we are to understand the absolute meaning as well as the right to the supposition of reality” (Weyl 1952, 5).
- 7.
“It cannot be denied that a theoretical desire, incomprehensible from the merely phenomenal point of view, is alive in us which urges toward totality. Mathematics shows that with particular clarity; but it also teaches us that that desire can be fulfilled on one condition only, namely, that we are satisfied with the symbol and renounce the mystical error of expecting the transcendent ever to fall within the lighted circle of our intuition” (Weyl 1963, 66).
- 8.
See Weyl 1963, 75–78.
- 9.
One can easily distinguish an hierarchy: (1) morphological, quality-filled perceptual space; (2) an abstract and idealized, properly mathematical physical space; and (3) an analytic surrogate of physical space, isomorphic to it and only remotely representing in ideal form the structure discernible in perceptual space.
- 10.
Husserl was quite aware of this possibility: “The solution of problems raised within a theoretical discipline, or one of its theories, can at times derive the most effective methodological help from recourse to the categorial type or (what is the same) to the form of the theory, and perhaps also by going over to a more comprehensive form or class of forms and to its laws” (Husserl 1900, §70).
- 11.
See Husserl 1936/1954.
- 12.
- 13.
See Weyl 1954, 200.
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da Silva, J.J. (2019). Husserl and Weyl on the Constitution of Space. In: Bernard, J., Lobo, C. (eds) Weyl and the Problem of Space. Studies in History and Philosophy of Science, vol 49. Springer, Cham. https://doi.org/10.1007/978-3-030-11527-2_14
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