Husserl: Science, Logic, and Mathematics

[Heidegger’s account of the rise of mathematical natural science in confrontation with Husserl’s conception of mathematisation in “Krisis”].

The carer of the person with dementia is enjoined to maintain respect, and to reinforce this a bill of rights has been established . Of course, talk of rights does not guarantee respectful behaviour. In this paper it is argued that the discovery that the sufferer continues to be a person, with a unique lifeworld, can assist the carer to conform willingly to the demand that they act respectfully.The current research project makes central the idiographic description of the individual case.

Name der Zeitschrift: Zeitschrift für Religionswissenschaft Jahrgang: 24 Heft: 2 Seiten: 213-220.

Hermann Weyl, one of the twentieth century's greatest mathematicians, was unusual in possessing acute literary and philosophical sensibilities—sensibilities to which he gave full expression in his writings. In this paper I use quotations from these writings to provide a sketch of Weyl's philosophical orientation, following which I attempt to elucidate his views on the mathematical continuum, bringing out the central role he assigned to intuition.

"Diversos conceptos de la lógica y su relación con la subjetividad" Este ensayo considera el segundo volumen de las Investigaciones Lógicas: los Prolegómena acerca de la Lógica pura. La importancia de esta obra husserliana radica, por un lado en revelar los intentos titubeantes del autor por acercar la lógica a la psicologí­a descriptiva en el contexto del debate del psicologismo lógico, y por otro, en resaltar el papel de la Lógica -en todas sus configuraciones, esto es, no sólo para la (...) Lógica pura sino también para la Lógica normativa y la Tecnologí­a lógica- como teorí­a de la ciencia. "Diverse concepts of the logic and their relationship with í­he subjectivity." This essay considers the second volume of the Logical Investigations: the Prolegomena about the pure Logic. The importance of this husserlian work resides, on revealing the author's intents to bring near the logic to the descriptive psychology in the context of the debate of the logical psycologism, and in standing out the paper of the Logical -for all its configuraciones and not only pure Logic but also for the normative Logic and the logical Technology - as theory of the science. (shrink)

Phenomenological psychology has typically avoided the "importation" of such concepts as social class from sociology.Within the epoche, such terminology is bracketed on the grounds that it brings with it excess theoretical baggage and threatens the return to experience in itself. Yet, in uncovering the lifeworld of university students who—in what in Britain is still predominantly a preserve of the privileged—come from relatively economically disadvantaged homes, "class" or some cognate concept is found to be necessary to capture the range of modes (...) of alienation and disjunction experienced. Following Casey's discussion of the way in which Bourdieu's notion of habitus relates to Merleau-Ponty's description of the interpenetration of the natural and the cultural in the lived body, social class is shown to bring together students' accounts of their multi-faceted sense that "University is not for the likes of us"—encompassing issues of identity, sociality, and spatio-temporal dislocation. (shrink)

It is well known that Husserl, together with Plato and Leibniz, counted among Gödel’s favorite philosophers and was, in fact, an important source and reference point for the elaboration of Gödel’s own philosophical thought. Among the scholars who emphasized this connection we find, as Richard Tieszen reminds us, Gian-Carlo Rota, George Kreisel, Charles Parsons, Heinz Pagels and, especially, Hao Wang. Right at the beginning of After Gödel we read: “The logician who conducted and recorded the most extensive philosophical discussions with (...) Kurt Gödel during Gödel’s later years was Hao Wang” .This book takes Wang’s report about Gödel’s philosophical interests seriously and paves the way “to go beyond the contributions of Plato, Leibniz and Husserl, based on Gödel’s philosophical and technical writings, his comments to Hao Wang, and various items from the Gödel Nachlass” . Tieszen proposes a “type of Gödelian platonic rationalism” about mathematic and logic that makes no pretenc .. (shrink)

This essay is a contribution to the historical phenomenology of science, taking as its point of departure Husserl’s later philosophy of science and Jacob Klein’s seminal work on the emergence of the symbolic conception of number in European mathematics during the late sixteenth and seventeenth centuries. Sinceneither Husserl nor Klein applied their ideas to actual theories of modern mathematical physics, this essay attempts to do so through a case study of the conceptof “spacetime.” In §1, I sketch Klein’s account of (...) the emergence of the symbolic conception of number, beginning with Vieta in the late sixteenth century. In §2,through a series of historical illustrations, I show how the principal impediment to assimilating the new symbolic algebra to mathematical physics, namely, thedimensionless character of symbolic number, is overcome via the translation of the traditional language of ratio and proportion into the symbolic language of equations. In §§3–4, I critically examine the concept of “Minkowski spacetime,” specifically, the purported analogy between the Pythagorean distance formula and the Minkowski “spacetime interval.” Finally, in §5, I address the question of whether the concept of Minkowski spacetime is, as generally assumed, indispensable to Einstein’s general theory of relativity. (shrink)

In this paper I study the variants of the notion of completeness Husserl pre-sented in “Ideen I” and two lectures he gave in Göttingen in 1901. Introduced primarily in connection with the problem of imaginary numbers, this notion found eventually a place in the answer Husserl provided for the philosophically more im-portant problem of the logico-epistemological foundation of formal knowledge in sci-ence. I also try to explain why Husserl said that there was an evident correlation between his and Hilbert’s notion (...) of completeness introduced in connection with the axiomatisation of geometry and the theory of real numbers when, as many commen-tators have already observed, these two notions are independent. I show in this paper that if a system of axioms is complete in Husserl’s sense, then its formal domain, the manifold of formal objects it determines, does not admit any extension. This is precisely the idea behind Hilbert’s notion of completeness in question. Therefore, the correlation Husserl noted indeed exists. But, in order to see it, we must consider the formal domain determined by a formal theory, not its models. (shrink)

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)

Cette these divisee en trois parties, comporte deux caracteristiques essentielles: ; Elle comporte une teneure mathematique: des progres accomplis entre 1870 et 1914 par les mathematiciens au sein des savoirs que sont l'analyse infinitesimale, l'algebre, la geometrie etc. ont conferre une place sui generis a l'algebre. Sa redefinition va integrer des objets quelconques et non plus seulement les simples techniques du calcul litteral. Aussi certains mathematiciens observerent un desinteret pour ces calculs au profit d'une reflexion theorique autour du mot d'ordre (...) de Dirichlet de "substituer les idees au calcul" . L'enjeu consistait a donner un fondement sur au concept de nombre. ; Historiquement, c'est entre 1891 et 1906 que Frege et Husserl ont entretenu un echange epistolaire sur la question. Pour Husserl, eleve de Brentano, ce fondement est a trouver dans le sujet connaissant, pole constitutif de tous les ordres du savoir. Sa Philosophie de l'Arithmetique en donne les contours. Critique et oppose a cette base psychologiste, Frege va presenter son approche qui privilegie la logique. Dans les Fondements de l'arithmetique , Frege estime que l'arithmetique entiere peut etre reduite aux lois de logique generale. Cette reduction de l'arithmetique a la logique donna naissance a la tradition logiciste qui fut mortellement ebranlee par le paradoxe de Russell et inaugura la crise des fondements de type ensembliste. ;Aux alentours de 1894, Husserl abandonna le psychologisme. Faut-il y voir l'influence de Frege? Cette question est debatue dans la 2e partie de la these par Mohanty et Dummett. Ils ne s'entendent ni sur la date de l'abandon par Husserl du psychologisme ni sur l'influence que Frege aurait pu exercer sur lui. ;La troisieme partie est un recours a Wittgenstein. Elle porte sur ce qu'on peut percevoir comme esquisse d'une solution qui passe par le renoncement de la philosophie a fonder les objets mathematiques qui ne sont que des conventions, brisant ainsi 2000 ans de domination platoniste. D'aucuns taxent la position de Wittgenstein de strict finitisme. Si cela s'averait juste, n'y-a-t-il pas la un lien possible entre Wittgenstein et le constructivisme de Kronecker? (shrink)

Erst in Husserls und Heideggers Spätzeit rückt die kritische Besinnung auf das gegenwärtige, durch die Herrschaft der naturwissenschaftlich-technischen Rationalität geprägte Zeitalter ins Zentrum ihres Denkens. Der eigentliche Ursprung dieser Besinnung liegt aber in dem phänomenologischen Denkweg, den beide Philosophen von früh an beschritten haben. Nur weil sie der Urmaxime der Phänomenologie Zu den Sachen selbst! verpflichtet waren, konnte ihnen eine Wissenschaftsanalyse gelingen, durch die sich die wissenschaftliche Erkenntnis als ein abgeleitetes Verhalten des Menschen gegenüber den Dingen herausstellt, das auf ein (...) ursprüngliche Weise der Welterfahrung zurückweist. Wenn die so angesetzte Zeitkritik bei beiden Denkern erst spät in den Vordergrund tritt, so nicht, weil sie sich vom ursprünglichen Ansatz der Phänomenologie abgekehrt hätten, sondern umgekehrt deswegen, weil sie erst allmählich zur vollen Entfaltung der in diesem Ansatz liegenden Möglichkeiten vordrangen. Allein hierdurch konnten sie die Geschichte entdecken und sich das Rüstzeug erarbeiten, um den geschichtlichen Hintergrund der modernen Wissenschaft in die Grundlagen ihrer Betrachtung einzubeziehen. Die phänomenologische Wissenschaftskritik wird so zu einer Ortsbestimmung der Gegenwart. Diese Zusammenhänge rechtfertigen einen Vergleich von Husserls und Heideggers Denken in ihrer Spätzeit. Er zeigt, daß die Positionen, von denen aus die beiden Philosophen Perspektiven für einen Ausweg aus der gegenwärtigen Situation entwerfen, entgegengesetzte Grundeinstellungen zur technisch-wissenschaftlichen Weltauffassung repräsentieren. (shrink)

This article locates Weyl''s philosophy of mathematics and its relationship to his philosophy of science within the epistemological and ontological framework of Husserl''s phenomenology as expressed in the Logical Investigations and Ideas. This interpretation permits a unified reading of Weyl''s scattered philosophical comments in The Continuum and Space-Time-Matter. But the article also indicates that Weyl employed Poincaré''s predicativist concerns to modify Husserl''s semantics and trim Husserl''s ontology. Using Poincaré''s razor to shave Husserl''s beard leads to limitations on the least upper (...) bound theorem in the foundations of analysis and Dirichlet''s principle in the foundations of physics. Finally, the article opens the possibility of reading Weyl as a systematic thinker, that he follows Husserl''s so-called transcendental turn in the Ideas. This permits an even more unified reading of Weyl''s scattered philosophical comments. (shrink)

This article locates Weyl's philosophy of mathematics and its relationship to his philosophy of science within the epistemological and ontological framework of Husserl's phenomenology as expressed in the "Logical Investigations" and "Ideas". This interpretation permits a unified reading of Weyl's scattered philosophical comments in "The Continuum" and "Space-Time-Matter". But the article also indicates that Weyl employed Poincaré's predicativist concerns to modify Husserl's semantics and trim Husserl's ontology. Using Poincaré's razor to shave Husserl's beard leads to limitations on the least upper (...) bound theorem in the foundations of analysis and Dirichlet's principle in the foundations of physics. Finally, the article opens the possibility of reading Weyl as a systematic thinker, that he follows Husserl's so-called transcendental turn in the "Ideas". This permits an even more unified reading of Weyl's scattered philosophical comments. (shrink)

The work addresses the problem of the relationship between science and philosophy in the work of Hermann Weyl. The author begins by discussing Weylls Gottingen tradition. Contrary to standard accounts of this tradition, Edmund Husserl and Georg Cantor are included. The influence of this tradition on Weyl is then illustrated by an examination of Weyl's early philosophy of mathematics. Here Weyl attempts to use Husserl's early phenomenology to amalgamate the thought of Felix Klein, David Hilbert and Cantor. Weyl's "phenomenological period," (...) in which he wrote The Continuum and Space-Time-Matter, is then discussed in detail. The work reveals that for Weyl, philosophy and science, guided by the same telos to construct an objective picture of the world, are involved in a dialectic in which each serves as a corrective and limitation of the other. (shrink)

El propósito del presente estudio es afirmar la deuda de Husserl con la filosofía de Lotze durante el período de Halle. Mi interés se centra especialmente en el pensamiento del joven Husserl desde su llegada a Halle en 1886 hasta la publicación de su Hauptwerk en 1900-1901. Primero me remontaré a las fuentes del conocimiento de la filosofía de Lotze por parte de Husserl durante sus estudios con Brentano en Viena y después con Stumpf en Halle. Luego comentaré brevemente las (...) referencias de Husserl a Lotze en sus primeros trabajos y en sus manuscritos de investigación para el segundo volumen de su Filosofía de la aritmética. En la tercera sección, examino la influencia de Lotze en el giro antipsicologista de Husserl a mediados de la década de 1890. La cuarta sección es un comentario al manuscrito de Husserl titulado "Microcosmos", al cual se refiere explícitamente en sus Prolegómenos, y que planeaba publicar como anexo a sus Investigaciones lógicas. Esta obra contiene un análisis detallado del tercer volumen de la Lógica de Lotze de 1874. La última sección examina los argumentos de Husserl contra el psicologismo lógico en sus Prolegómenos, que yo expongo a través del prisma de la crítica de Stumpf al psicologismo en su artículo "Psicología y teoría del conocimiento". Sostengo que las primeras obras de Stumpf sobre este asunto hacen posible establecer una conexión entre la interpretación de Lotze de la teoría de las Ideas de Platón y el antipsicologismo de Husserl. Mi hipótesis es que los análisis de Stumpf representan el fondo de la crítica de Husserl al psicologismo lógico en sus Investigaciones lógicas. Concluiré este estudio mostrando que la posición de Husserl respecto de la filosofía de Lotze permanece básicamente la misma después de la publicación de sus Investigaciones lógicas, y que la principal crítica de Husserl a Lotze se refiere, en un último análisis, a la ausencia de una teoría de la intencionalidad en la filosofía de Lotze. (shrink)

ExcerptPrecisely a definition like Wittgenstein's, “The world is everything that is the case,” …is about the least interesting thing that can be said about the world … Hans Blumenberg1Thinking, for Hans Blumenberg, is everything but normal.As flippant as this may sound, the non-normality of thought is central to Blumenberg's work and in particular to the nexus of the lifeworld and his theory of nonconceptuality. Blumenberg's claim that, in his exact words, “not thinking is thoroughly normal”2 can be found in the (...) posthumously published study given the agonistic title Theory of the Lifeworld (2010, Theorie…. (shrink)

The dissertation considers the methodological and thematic correspondences in Isaac Newton's Principia and Albert Einstein's "On the Electrodynamics of Moving Bodies," from a Husserlian point of view. It proposes to recover from an analysis of their work an account of the operative method of Newton and Einstein, so as to determine the thematic foundations which make possible their scientific projects. These themata are then examined for their relevance to a Husserlian phenomenology of the intentional structure of scientific rationality. Towards this (...) end, the dissertation considers Husserl's Crisis of European Sciences and Transcendental Phenomenology, for its analysis of the problematic relationship between experience and formalization in science. The dissertation culminates in an analysis of Husserl's Formal and Transcendental Logic, wherein I translate Husserl's account of formal logic and formal mathematics into a viable account of the formal and experiential intentionality in the scientific method. The result of this study is a phenomenological account of science which explains the continuity between the concrete life-world and abstract, formal structures, such that the activity of the scientist is explained by means of intentional shifts. According to this new interpretation, the thematic convictions of the scientist provide operational justification for the scientific method, within the confines of the natural attitude, but are ultimately founded in the intentional structure of knowing, as articulated in Husserlian phenomenology. (shrink)