In the first year of the twentieth century, in Gottingen, Husserl delivered two talks dealing with a problem that proved central in his philosophical development, that of imaginary elements in mathematics. In order to solve this problem Husserl introduced a logical notion, called “definiteness”, and variants of it, that are somehow related, he claimed, to Hilbert’s notions of completeness. Many different interpretations of what precisely Husserl meant by this notion, and its relations with Hilbert’s ones, have been proposed, but no (...) consensus has been reached. In this paper I approach this question afresh and thoroughly, taking into consideration not only the relevant texts and context, as others have also done before, but, more importantly, Husserl’s philosophy, his intuition-based epistemology in particular. Based on a system of clearly defined concepts that I here present, I reinforce an interpretation—definiteness as a form of syntactic completeness—that has, I believe, some advantages vis-à-vis alternative interpretations. It is in conformity with the available texts; it makes clear that Husserl’s notion of definiteness is indeed close to Hilbert’s notions of completeness; it solves the important problem of imaginaries for which it was created; and last, but not least, it fits naturally into Husserl’s system of concepts and ideas. (shrink)

In this paper I discuss the version of predicative analysis put forward by Hermann Weyl in "Das Kontinuum". I try to establish how much of the underlying motivation for Weyl's position may be due to his acceptance of a phenomenological philosophical perspective. More specifically, I analyze Weyl's philosophical ideas in connexion with the work of Husserl, in particular "Logische Untersuchungen" and "Ideen I". I believe that this interpretation of Weyl can clarify the views on mathematical existence and mathematical intuition which (...) are implicit in "Das Kontinuum". (shrink)

Husserl left many unpublished drafts explaining (or trying to) his views on spatial representation and geometry, such as, particularly, those collected in the second part of Studien zur Arithmetik und Geometrie (Hua XXI), but no completely articulate work on the subject. In this paper, I put forward an interpretation of what those views might have been. Husserl, I claim, distinguished among different conceptions of space, the space of perception (constituted from sensorial data by intentionally motivated psychic functions), that of physical (...) geometry (or idealized perceptual space), the space of the mathematical science of physical nature (in which science, not only raw perception has a word) and the abstract spaces of mathematics (free creations of the mathematical mind), each of them with its peculiar geometrical structure. Perceptual space is proto-Euclidean and the space of physical geometry Euclidean, but mathematical physics, Husserl allowed, may find it convenient to represent physical space with a non-Euclidean structure. Mathematical spaces, on their turn, can be endowed, he thinks, with any geometry mathematicians may find interesting. Many other related questions are addressed here, in particular those concerning the a priori or a posteriori character of the many geometric features of perceptual space (bearing in mind that there are at least two different notions of a priori in Husserl, which we may call the conceptual and the transcendental a priori). I conclude with an overview of Weyl’s ideas on the matter, since his philosophical conceptions are often traceable back to his former master, Husserl. (shrink)

In this paper, I carry out a comparative study of the philosophical views of Edmund Husserl and Hermann Weyl on issues such as mathematical existence and mathematical intuition, the validity of classical logic, the concept of logical definiteness, the nature of symbolic mathematics, the role of mathematics in empirical science, the relation of scientific theories with perception, space representation and the philosophy of geometry, and intentional constitution in general. My main goal is not simply to assess the extent of Husserl’s (...) influence on Weyl, although this is an ever present concern, but to clarify the views of one by contrasting them with those of the other. (shrink)

The notion of mathesis universalis appears in many of Edmund Husserl’s works, where it corresponds essentially to “a universal a priori ontology”. This paper has two purposes; one, largely exegetical, of clarifying how Husserl elaborates on Leibniz’ concept of mathesis universalis and associated notions like symbolic thinking and symbolic knowledge filtering them through the lesson of the so called “bohemian Leibniz”, Bernard Bolzano; another, more properly philosophical, of examining the role that the universal mathesis is allowed to play, and the (...) space it occupies in Husserl’s intuition-based epistemology. (shrink)

I carry out in this paper a philosophical analysis of the principle of excluded middle. This principle has been criticized, and sometimes rejected, on the charge that its validity depends on presuppositions that are not, some believe, universally obtainable; in particular, that any well-posed problem is solvable. My goal here is to show that, although excluded middle does indeed rest on certain presuppositions, they do not have the character of hypotheses that may or may not be true, or matters of (...) fact that may or may not be the case. These presuppositions have, I claim, a transcendental character. Hence, the acceptance of excluded middle does not necessarily require, as some have claimed, an allegiance to ontological realism or some sort of cognitive optimism, construed as factual theses concerning the ontological status of domains of objects and our capability of accessing them cognitively. (shrink)

In this paper I present and discuss Husserl’s concept of material a priori truth, particularly with respect to color-concepts, and show that Schlick’s criticism of Husserl’s notion is based on misunderstandings and misconceptions.

O objetivo do presente artigo é apresentar e confrontar os pressupostos de duas tradições interpretativas _Leviatã _de Thomas Hobbes. Pretendo demonstrar como, a partir dos pressupostos e dos critérios de interpretação de cada uma delas, teremos não apenas duas abordagens diversas, mas resultados e soluções distintas para problemas políticos e morais que o próprio Hobbes buscou solucionar com essa obra. Na primeira parte do artigo, apresentarei os aspectos inovadores da nova interpretação do _Leviatã_ em contraposição às interpretações tradicionais ou ortodoxas. (...) Na segunda parte, confrontarei essa abordagem com a abordagem tradicional sobre um problema específico, mas central na filosofia de Hobbes: o problema da desordem social. Apresentarei a tese tradicional segundo a qual a solução para o problema da desordem seria criar um poder capaz de impor sanções que não permitissem que o interesse racional egoísta atuasse de forma irrestrita. Em seguida, apresentarei a solução revisionista segundo a qual a solução seria produzir uma estável e apropriada reconfiguração dos diversos interesses morais e religiosos dos cidadãos através de um processo de educação contínua responsável pelo consenso social. (shrink)

O aparecimento do coronavírus fez ressurgir um antigo debate no âmbito da filosofia política: o debate entre liberdade e segurança. A maioria dos países atingidos precisou adotar medidas que restringiram a liberdade dos cidadãos para conter o avanço da doença. Esse artigo tem o objetivo de apresentar a posição do filósofo inglês, Thomas Hobbes exposta no _Leviatã_, para enfrentar esse problema. O texto está dividido em três partes. Em um primeiro momento, apresento a tese de Hobbes sobre a segurança e (...) contra a liberdade irrestrita para evitar o estado de natureza. Em um segundo momento, apresento a tese de Hobbes sobre a liberdade limitada no estado político. Por fim, apresento uma possível solução para conjugar liberdade e segurança a partir do conceito hobbesiano de razão pública. (shrink)