On the basis of previous studies in relational biology and the phenomenological calculus, in my contribution I outline the mathematical foundations of biological perception generally, and visual perception specifically. In this approach, the premise is that objects in nature are not directly accessible, and that real manifestations are projections of these invariant objects. The morphology of observables is mathematically entailed by the duality of projections and projectors in a bilinear algebra that is the phenomenological calculus. The relationships between what is (...) not directly accessible (which can be defined as noumena) and phenomena may be explicated in terms of metabolism and repair, whence a geometric theory of the perceived, the visible in particular, may be formulated in the category-theoretic language of relational biology. (shrink)

Quite a few cognitive scientists are working toward a naturalization of phenomenology. Looking more closely at the relevant literature, however, the ‘naturalizing phenomenology’ proposals show the presence of different conceptions, assumptions, and formalisms, further differentiated by different philosophical and/or scientific concerns. This paper shows that the original Husserlian stance is deeper, clearer and more advanced than most supposed contemporary improvements. The recent achievements of experimental phenomenology show how to ‘naturalize’ phenomenology without destroying the guiding assumptions of phenomenology. The requirements grounding (...) the scientific explanation of subjective experience are discussed, such as the nature of the stimuli, their variables, and their manipulation by properly phenomenological methods. (shrink)

Since the end of the last century, there has been several ambitious attempts to naturalize Husserlian phenomenology by way of mathematization. To justify themselves in view of Husserl’s adamant antinaturalism, many of these attempts appeal to the new physico-mathematical tools that were unknown in Husserl’s time and thus allegedly make his position outdated. This paper critically addresses these mathematization proposals and aims to show that Husserl had, in fact, sufficiently good arguments that make his antinaturalistic position sound even today. The (...) starting point of the discussion presented in this paper is the mathematization project introduced by Jean-Michel Roy, Jean Petitot, Bernard Pachoud, and Francisco Varela in their introduction to the book Naturalizing Phenomenology. This proposal was followed by a number of critiques but also by several alternative naturalization attempts clearly inspired by Roy et al.’s ambitious project. The review of some of Husserl’s important arguments often overlooked or misinterpreted by both the naturalization advocates and their critics leads the author of the paper to the twofold conclusion which, on the one hand, explores the deeper reasons for the impossibility of a physical and mathematical treatment of phenomenology, on the other hand, clarifies the sense in which such treatments are possible, namely by way of restriction of the variety of experiential aspects that undergo naturalization and substitution of the aspects amenable to the direct mathematization for the directly unmathematizable ones. In the fourth section of this paper, the author attempts to demonstrate that, contrary to widespread belief, Husserl’s arguments are not obsolete by the standards of the contemporary physico-mathematical approaches employed in the mathematization of phenomenology and indeed stand the test of time. (shrink)