The book departs from the question: what are colors? The four current competing theories hold that they are either

  1. in the mind, projected upon reality (projectivism),
  2. confused concepts that do not straightforwardly correlate to anything in reality (eliminativism),
  3. immediate qualities of worldly objects (naive externalism), or
  4. dispositions to cause the respective perceptions (dispositionalism).

These theories seem to be radically different for they contradict each other ontologically. Under the surface, however, they are not radically different for they share the same root. I show that these four theories have been discussed since the time of Galileo, when philosophers widely agreed on a distinction that has been known since Locke as the distinction between “primary” and “secondary” qualities. In spite of claiming that experiences or ideas of secondary qualities must be produced by configurations and movements of particles constituted of primary qualities, philosophers such as Descartes and Locke also claim that the connection between primary qualities and ideas of secondary qualities is inconceivable. The combination of the two claims I call the “paradox of the primary-secondary quality distinction.”

While Descartes and Locke recognize the paradox, the philosophical disputes around the distinction usually ignore it and instead circle around the four different types of explanations of secondary qualities in terms of primary qualities described above with respect to colors. These contradict each other ontologically, but nevertheless they share a common origin: the view that the world is mathematical in itself.
book of nature
Edmund Husserl claims in the Crisis of the European Sciences that this conception entails a misunderstanding and sets out to explain the confusion in the genesis of the mathematical concept of the world; a genesis he calls the “mathematization of nature.” In my exegesis of the Crisis and earlier works, I analyze four different steps in the mathematization:

  1. generalization,
  2. idealization,
  3. formalization, and
  4. symbolization

The first three build upon each other, while the fourth is applied to any of the other, allowing for confusion. Ultimately, the combination of these steps leads to, in Husserl’s assessment, a confusion of “true being” with “a method.” Husserl thinks that true being is experienced in the lifeworld, and that it can only be substructed, but never replaced with mathematizations. Contrary to what is often thought, Husserl’s concept of the lifeworld is not simply a belated response to Heidegger, but Husserl’s ultimate expression of his lifelong study of the relation of mathematics and experience. The result of the forgetting of original experience is, according to Husserl, the “crisis of the European sciences.” The recovery of the experience that is the origin of the mathematization is for Husserl thus not only a way to avoid the philosophical misunderstanding of science, but also an answer to a profound crisis of meaning.

Husserl’s genealogy of mathematization allows for a neat explanation for why the paradox seems unavoidable. Ideas of secondary qualities are not directly mathematizable, and therefore it seems that they must be produced by primary qualities. Yet, the connection between them is inconceivable because mathematizations are compared to something radically different, namely experiential qualities. Whether we agree with Husserl’s own account of lifeworldly experience and crisis or not: his genealogy of the development of the paradox reveals the need to reconsider the role of experience in the scientific concept of the world.
The Paradox of the Primary-Secondary Quality Distinction and Husserl’s Genealogy of the Mathematization of Nature (click to download pdf. Updated on 6/13/2014. The update includes a number of minor corrections such as spelling mistakes and clarifications. You can download the electronically published original here.)

How to cite in the notes and bibliography system of the Chicago Manual of Style, 16th edition (adjust accordingly for other styles)
Durt, Christoph. “The Paradox of the Primary-Secondary Quality Distinction and Husserl’s Genealogy of the Mathematization of Nature.” eScholarship University of California, 2012.