This volume aims to establish the starting point for the development, evaluation and appraisal of the phenomenology of mathematics.

Historians of philosophy commonly regard as antipodal Bertrand Russell and Edmund Husserl, the founding fathers of analytic philosophy and phenomenology. This paper, however, establishes that during a formative phase in both of their careers Russell and Husserl shared a range of seminal ideas. In particular, the essay adduces clear cases of family resemblance between Husserl’s and Russell’s philosophy during their middle period, which spanned the years 1905 through 1918. The paper thus challenges the received view of Husserl’s relation to early (...) analytic philosophy and this by pursuing two strategies of exposition. One involves comparing Husserl with Russell, and not, as has been the usual practice, with Frege. The other, which follows the first, foregrounds Husserl’s thinking vis-à-vis Russell’s from 1905 onward, a move that constitutes a break with what has become the standard approach of emphasising the relatedness of Husserl of the Logical Investigations (1900/1) to analytic philosophy. Moreover, this approach discloses two chief grounds of relatedness between the middle Husserl and the middle Russell. One is their shared interest in exploring philosophical “fundamentals”. The second consists of common elements shared by their epistemologies and philosophies of mind. (shrink)

I argue that Husserl’s transcendental account of the role of the lived body in sense-making is a precursor to Alva Noë’s recent work on the enactive, embodied mind, specifically his notion of “sensorimotor knowledge” as a form of embodied sense-making that avoids representationalism and intellectualism. Derrida’s deconstructive account of meaning—developed largely through a critique of Husserl—relies on the claim that meaning is structured through the complication of the “interiority” of consciousness by an “outside,” and thus might be thought to lend (...) itself to theories of mind such as Noë’s that emphasize the ways in which sense-making occurs outside the head. But while Derrida’s notion of “contamination” rightly points to an indeterminateness of meaning in an outside, extended, concrete lived world, he ultimately reduces meaning to a structure of signification. This casts indeterminateness in terms of absence, ignoring the presence of non-linguistic phenomena of embodied sense-making central to both the contemporary enactivist program and to the later Husserl, who is able to account for the indeterminateness of meaning in lived experience through his distinction between sense and more exact linguistic meaning. Husserl’s transcendental theory of meaning also allows for a substantive contribution to sense-making from the side of the perceived object—an aspect missing from Noë’s account. Thus, in contrast to Derrida and to Noë, Husserl accounts for sense-making in terms of both the lived body and the lived world. (shrink)

I reconstruct the notion of significance [_Sinnhaftigkeit_] in the later Husserl, with attention to his conceptions of judgment and transcendental logic. My analysis is motivated by the idea that an account of significance can help to connect analytic, Anglo-American conceptions of meaning as a precise, law-governed phenomenon investigated via linguistic analysis and Continental European conceptions of meaning in a broader “existential” sense. I argue that Husserl’s later work points to a transcendental-logical conception of a founding level of _significance_ [_Sinnhaftigkeit_] prior (...) to language, and that this conception meets characteristically analytic demands for precision and governance by logical constraints. At the same time, since it is based in descriptions of perceptual intentionality at the level of essential possibility, it leaves room for an account of meaning as a partially undetermined phenomenon of lived experience, and not just of our language and concepts, and thereby meets the characteristically Continental demand to take at face value meaning’s vagueness and indeterminacy in everyday human life. (shrink)

The question of the psychologism of the theory of number developed by Husserl in his Philosophy of Arithmetic has long been debated, but it cannot be considered fully resolved. In this paper, I address the issue from a new point of view. My claim is that in the Philosophy of Arithmetic, Husserl made, albeit indirectly, a series of arguments that are worth reconstructing and clarifying since they are useful in shedding some light on the psychologism issue. More specifically, I maintain (...) that the clarification of these arguments, along with other arguments that Husserl presented against alternative theories of number as well as with some contemporary distinctions concerning the notion of ontological dependence, allows us to determine that Husserl’s theory of number is psychologistic in a minimal and precise sense: it entails a generic ontological dependence of numbers upon the mind. (shrink)

Au terme des Prolégomènes, Husserl formule son idée de la logique pure en la structurant sur deux niveaux: l'un, supérieur, de la logique formelle fondé transcendantalement et d'un point de vue épistémologique par l'autre, inférieur, d'une morphologie des catégories. Seul le second de ces deux niveaux est traité dans les Recherches logiques, tandis que les travaux théoriques en logique formelle menés par Husserl à la même époque en paraissent plutôt indépendants. Cet article est consacré à ces travaux tels que recueillis (...) dans les appendices VI-X du volume 12 des Husserliana. Mettant en évidence la théorie de la signification qui les sous-tend par le biais d'une analyse de la question dite de l'extension des systèmes d'axiomes et de sa résolution au moyen d'une notion de complétude, son objectif est d'expliciter les modalités de l'intégration de la logique formelle dans l'idée husserlienne de la logique pure au tournant du xx siècle.When formulating his idea of pure logic in the Prole.. (shrink)

Edmund Husserl was one of the very first to experience the direct impact of challenging problems in set theory and his phenomenology first began to take shape while he was struggling to solve such problems. Here I study three difficulties associated with Frege's use of sets that Husserl explicitly addressed: reference to non-existent, impossible, imaginary objects; the introduction of extensions; and 'Russell's paradox'.I do so within the context of Husserl's struggle to overcome the shortcomings of set theory and to develop (...) his own theory of manifolds. I define certain issues involved and discuss how Husserl's theory of manifolds might confront them. In so doing I hope to help bring Husserl's theories about sets and manifolds out of the realm of abstract theorizing and prompt further exploration of uncharted philosophical territory rich in philosophical implications. (shrink)

The recent move to naturalize phenomenology through a mathematical protocol is a significant advance in consciousness research. It enables a new and fruitful level of dialogue between the cognitive sciences and phenomenology of such a nuanced kind that it also prompts advancement in our phenomenological analyses. But precisely what is going on at this point of ‘dialogue’ between phenomenological descriptions and mathematical algorithms, the latter of which are based on dynamical systems theory? It will be shown that what is happening (...) is something more than a mere ‘passing of the baton’ from phenomenology to mathematics. For this sophisticated naturalization to prove a worthy endeavour it must produce more than just correlation, it must prove some form of interrelation to the extent that phenomenology is deterministic. But such interrelational and deterministic requirements are the start of a slippery slope, and it will be argued that this slope only loses more friction once a further demand of formal and precise descriptions is made of phenomenology. Such deterministic and formally precise demands misconstrue phenomenology’s ideal goal of a unification of genuine/originary reason and truth. Not a deductive and definitive discipline, phenomenology is rather from the outset descriptive and critical. Phenomenology’s descriptive beginnings will thus be employed as an essential barrier to the naturalization of phenomenology. (shrink)

In this talk I present the main results from Anta (2021), namely, that the theoretical division between Boltzmannian and Gibbsian statistical mechanics should be understood as a separation in the epistemic capabilities of this physical discipline. In particular, while from the Boltzmannian framework one can generate powerful explanations of thermal processes by appealing to their microdynamics, from the Gibbsian framework one can predict observable values in a computationally effective way. Finally, I argue that this statistical mechanical schism contradicts the Hempelian (...) (1958) thesis that the predictive power of a scientific theory is directly proportional to its explanatory potential, and vice versa. (shrink)