UC Santa Cruz

Since the time of Galileo, philosophers widely agree 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." The philosophical disputes around the distinction usually ignore the paradox, and instead circle around different types of explanations of secondary qualities in terms of primary qualities: projectivism, eliminativism, physicalism, and dispositionalism. These contradict each other ontologically, but nevertheless they share a common origin: the view that the world is mathematical in itself.

Edmund Husserl claims in the Crisis 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." I analyze four different steps in the mathematization: generalization, idealization, formalization, and symbolization. The combination of these steps leads to, in Husserl's estimation, a confusion of "true being" with "a method." Husserl thinks that true being is experienced in the life-world, and that it can only be substructed, but never replaced with mathematizations. Contrary to what is often thought, Husserl's concept of the life-world 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 the mathematization allows for a neat explanation for why the paradox seems unavoidable. Ideas of secondary qualities are not directly mathematizeable, 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 life-worldly 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.