Husserl is well known for his critique of the “mathematizing tendencies” of modern science, and is particularly emphatic that mathematics and phenomenology are distinct and in some sense incompatible. But Husserl himself uses mathematical methods in phenomenology. In the first half of the paper I give a detailed analysis of this tension, showing how those Husserlian doctrines which seem to speak against application of mathematics to phenomenology do not in fact do so. In the second half of the paper I (...) focus on a particular example of Husserl’s “mathematized phenomenology”: his use of concepts from what is today called dynamical systems theory. (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appeal to the new physico-mathematical tools that were unknown in Husserl’s time and thus allegedly make his position outdated.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)

The paper addresses the main questions to be dealt with by any semantic theory which is committed to provide an explanation of how meaning is possible. On one side the paper argues that the resources provided by the development of mathematical logic, theoretical computer science, cognitive psychology, and general linguistics in the 20th Century, however indispensable to investigate the structure of language, rely on the existence of end products in the morphogenesis of meaning. On the other, the paper argues that (...) philosophy of language, which, either in the analytic or the structuralist or the hermeneutical tradition, made little use of such resources (when they are not simply rejected). Left the main question unanswered. Though phenomenology intended to focus on the constitutive process, it ended up mostly with philology. Cognitive semantics paved the way to focus on patterns of bodily interaction within the natural environment out of which basic schemes emerge and are metaphorically “lifted” to any universe of discourse. The explanatory commitment is thus endorsed through two hypotheses: (1) these schemes, of topological and kinaesthetic structure, determine the range of forms of atomic sentences of any natural language, and (2) the category-theoretic notion of universality allows for a proper analysis of how such schemes are “lifted”. (shrink)

Brouwer and Weyl recognized that the intuitive continuum requires a mathematical analysis of a kind that set theory is not able to provide. As an alternative, Brouwer introduced choice sequences. We first describe the features of the intuitive continuum that prompted this development, focusing in particular on the flow of internal time as described in Husserl's phenomenology. Then we look at choice sequences and their logic. Finally, we investigate the differences between Brouwer and Weyl, and argue that Weyl's conception of (...) choice sequences is defective on several counts. (shrink)

Gödel has argued that we can cultivate the intuition or perception of abstractconcepts in mathematics and logic. Gödel's ideas about the intuition of conceptsare not incidental to his later philosophical thinking but are related to many otherthemes in his work, and especially to his reflections on the incompleteness theorems.I describe how some of Gödel's claims about the intuition of abstract concepts are related to other themes in his philosophy of mathematics. In most of this paper, however,I focus on a central (...) question that has been raised in the literature on Gödel: what kind of account could be given of the intuition of abstract concepts? I sketch an answer to this question that uses some ideas of a philosopher to whom Gödel also turned in this connection: Edmund Husserl. The answer depends on how we understand the conscious directedness toward objects and the meaning of the term abstract in the context of a theory of the intentionality of cognition. (shrink)