This book offers an historically-informed critical assessment of Dummett's account of abstract objects, examining in detail some of the Fregean presuppositions whilst also engaging with recent work on the problem of abstract entities.

Der soziotechnische Wandel bringt neue Phänomene des Zufalls hervor, die sich den üblichen Strategien des Umgangs mit Risiken und Unsicherheit entziehen. Diese Akzidenzphänomene sind prinzipiell unvorhersehbar und in ihrer komplexen Effektgesamtheit jenseits von Kalkulation und Antizipation. Eine allgemeine Verzukünftigung unseres Weltbezuges mit spezifischen weitreichenden Problemen ist die Folge und lässt klassische Agenturen des Risikomanagements und der Unsicherheitsbewältigung an ihre Leistungsgrenzen stoßen. Bruno Gransche zeigt, dass Philosophie und Zukunftsforschung gemeinsam großes Potenzial aufweisen, hier zu helfen.

Austrian economics starts out from the thesis that the objects of economic science differ from those of the natural sciences because of the centrality of the economic agent. This allows a certain a priori or essentialistic aspect to economic science of a sort which parallels the a priori dimension of psychology defended by Brentano and his student Edmund Husserl. We outline these parallels, and show how the theory of a priori dependence relations outlined in Husserl’s Logical Investigations can throw light (...) on the Austrian account of entrepreneurship. (shrink)

Kotarbiński is one of the leading figures in the Lvov-Warsaw school of Polish philosophy. We summarize the development of Kotarbiński’s thought from his early nominalism and ‘pansomatistic reism’ to the later doctrine of ‘temporal phases’. We show that the surface clarity and simplicity of Kotarbiński’s writings mask a number of profound philosophical difficulties, connected above all with the problem of giving an adequate account of the truth of contingent (tensed) predications. The paper will examine in particular the attempts to resolve (...) these difficulties on the part of Leśniewski. It will continue with an account of the relations of Kotarbińskian reism to the ontology of things or entia realia defended by the later Brentano. Kotarbiński’s identification of Brentano as a precursor of reism is, it will be suggested, at least questionable, and the paper will conclude with a more careful attempt to situate the Brentanian and Kotarbińskian ontologies within the spectrum of competing ontological views. (shrink)

Tadeusz Kotarbinski is one of towering figures in contemporary Polish philosophy. He was a great thinker, a great teacher, a great organizer of philosophical and scientific life, and, last but not least, a great moral authority. He died at the age of 96 on October 3, 1981. Kotarbinski was active in almost all branches of philosophy. He made many significant contributions to logic, semantics, ontology, epistemology, history of philosophy, and ethics. He created a new field, namely praxiology. Thus, using an (...) ancient distinction, he contributed to theoretical as well as practical philoso~hy. Kotarbinski regarded praxiology as his major philosophical "child". Doubtless, praxiology belongs to practical philosophy. This collection, howewer, is mainly devoted to Kotarbinski' s theoretical philosophy. Reism - Kotarbinski' s fundamental idea of ontology and semantics - is the central topic of most papers included here; even Pszczolowski' s essay on praxiology considers its ontological basis.,Only two papers, namely that of Zarnecka-Bialy and that of Wolenski, are not linked with reism. However, both fall under the general label "Kotarbinski: logic, semantics and ontology". The collection partly consists of earlier published papers. (shrink)

In the final book of Logical Investigations from 1901, Husserl develops a theory of knowledge based on the intentional structure of consciousness. While there is some textual evidence that Husserl considered this to entail a critique of Kantian philosophy, he did not elaborate substantially on this. This paper reconstructs the covert critique of Kant’s theory of knowledge which LI contains. With respect to Kant, I discuss three core aspects of his theory of knowledge which, as Husserl’s reflections on Kant indicate, (...) Husserl was familiar with. These are the cooperation of two faculties for the justification of beliefs; the concept of a priori structures of knowledge Kant operated with; and the delivered transcendental proof of these structures. Regarding Logical Investigations, I first briefly outline the intentional structure of consciousness as presented in the fifth book and then turn to the theory of knowledge in the sixth book. I then clarify, partially on the basis of manuscripts and lecture notes, the covert critique of the three core aspects of Kant’s theory which the sixth book contains. (shrink)

The paper is devoted to phenomenological ideas in conceptions of modern philosophy of mathematics. Views of Husserl, Weyl, Becker andGödel will be discussed and analysed. The aim of the paper is to show the influence of phenomenological ideas on the philosophical conceptions concerning mathematics. We shall start by indicating the attachment of Edmund Husserl to mathematics and by presenting the main points of his philosophy of mathematics. Next, works of two philosophers who attempted to apply Husserl’s phenomenological ideas to the (...) philosophy of mathematics, namely Hermann Weyl and Oskar Becker, will be briefly discussed. Lastly, the connections between Husserl’s ideas and the philosophy of mathematics of Kurt Gödel will be studied. (shrink)

The paper gives a historically informed reconstruction of Frege's view of statements of number. The reconstruction supports Frege's claim that a statement can be 'about a concept' although it does not contain a singular term referring to the concept. Hence, Frege's philosophy of number is not subject to the problems Frege sees for singular reference to concepts.

The issues surrounding the Caesar problem are assumed to be inert as far as ongoing mathematics is concerned. This paper aims to correct this impression by spelling out the ways that, in their historical context, Frege's remarks would have had considerable resonance with work that other mathematicians such as Riemann and Dedekind were doing. The search for presentation‐independent characterizations of objects and global definitions was seen as bound up with fundamental methodological questions in complex analysis and number theory.

In the present paper, we discuss Husserl's deep account of the notions of ?calculation? and of arithmetical ?operation? which is found in the final chapter of the Philosophy of Arithmetic, arguing that Husserl is as far as we know the first scholar to reflect seriously on and to investigate the problem of circumscribing the totality of computable numerical operations. We pursue two complementary goals, namely: (i) to provide a formal reconstruction of Husserl's intuitions, and (ii) to demonstrate on the basis (...) of our reconstruction that the class of operations that Husserl has in mind turns out to be extensionally equivalent to the one that, in contemporary logic, is known as the class of partial recursive functions. (shrink)

This article develops a critical investigation of the epistemological core of Hilbert's foundational project, the so-called the finitary attitude. The investigation proceeds by distinguishing different senses of 'number' and 'finitude' that have been used in the philosophical arguments. The usual notion of modern pure mathematics, i.e. the sense of number which is implicit in the notion of an arbitrary finite sequence and iteration is one sense of number and finitude. Another sense, of older origin, is connected with practices of counting (...) concrete things, and a third sense is linked up with the immediate intuitive experience of multitudes of concrete things. Hilbert's fìnitism is examined with respect to these differences, and it will be shown that there is a tendency to conflate the different senses of number and fìnitude, a tendency which has been a source of problems in the discussion of the foundations of mathematics and in the philosophy of logic and language. (shrink)

Husserl’s Idea of Phenomenology is his first systematic attempt to show how phenomenology differs from natural science and in particular psychology. He does this by the phenomenological reduction. One of his achievements is to show that the formal structures of intentionality are more akin to logic than to psychology. I claim that Husserl’s argument can be made more intuitive if we consider phenomenology to be the study of truth rather than knowledge, and if we see the reduction as primarily a (...) modification in our vocabulary and discourse and not as simply a change in attitude. I briefly compare Husserl’s concept of philosophy with those of Plato and Kant. (shrink)

The discussions which follow rest on a distinction, first expounded by Husserl, between formal logic and formal ontology. The former concerns itself with (formal) meaning-structures; the latter with formal structures amongst objects and their parts. The paper attempts to show how, when formal ontological considerations are brought into play, contemporary extensionalist theories of part and whole, and above all the mereology of Leniewski, can be generalised to embrace not only relations between concrete objects and object-pieces, but also relations between what (...) we shall call dependent parts or moments. A two-dimensional formal language is canvassed for the resultant ontological theory, a language which owes more to the tradition of Euler, Boole and Venn than to the quantifier-centred languages which have predominated amongst analytic philosophers since the time of Frege and Russell. Analytic philosophical arguments against moments, and against the entire project of a formal ontology, are considered and rejected. The paper concludes with a brief account of some applications of the theory presented. (shrink)

This book is a survey of the most important developments in Austrian philosophy in its classical period from the 1870s to the Anschluss in 1938. Thus it is intended as a contribution to the history of philosophy. But I hope that it will be seen also as a contribution to philosophy in its own right as an attempt to philosophize in the spirit of those, above all Roderick Chisholm, Rudolf Haller, Kevin Mulligan and Peter Simons, who have done so much (...) to demonstrate the continued fertility of the ideas and methods of the Austrian philosophers in our own day. For some time now, historians of philosophy have been gradually coming to terms with the idea that post-Kantian philosophy in the German-speaking world ought properly to be divided into two distinct traditions which we might refer to as the German and Austrian traditions, respectively. The main line of the first consists in a list of personages beginning with Kant, Fichte, Hegel and Schelling and ending with Heidegger, Adorno and Bloch. The main line of the second may be picked out similarly by means of a list beginning with Bolzano, Mach and Meinong, and ending with Wittgenstein, Neurath and Popper. As should be clear, it is the Austrian tradition that has contributed most to the contemporary mainstream of philosophical thinking in the Anglo-Saxon world. For while there are of course German thinkers who have made crucial contributions to the development of exact or analytic philosophy, such thinkers were outsiders when seen from the perspective of native German philosophical culture, and in fact a number of them found their philosophical home precisely in Vienna. When, in contrast, we examine the influence of the Austrian line, we encounter a whole series of familiar and unfamiliar links to the characteristic concerns of more recent philosophy of the analytic sort. As Michael Dummett points out in his Origins of Analytic Philosophy, the newly fashionable habit of referring to analytic philosophy as "Anglo-American" is in this light a "grave historical distortion". If, he says, we take into account the historical context in which analytic philosophy developed, then such philosophy "could at least as well be called "Anglo-Austrian" (1988, p. 7). Much valuable scholarly work has been done on the thinking of Husserl and Wittgenstein, Mach and the Vienna Circle. The central axis of Austrian philosophy, however, which as I hope to show in what follows is constituted by the work of Brentano and his school, is still rather poorly understood. Work on Meinong or Twardowski by contemporary philosophers still standardly rests upon simplified and often confused renderings of a few favoured theses taken out of context. Little attention is paid to original sources, and little effort is devoted to establishing what the problems were by which the Austrian philosophers in general were exercised -- in spite of the fact that many of these same problems have once more become important as a result of the contemporary burgeoning of interest on the part of philosophers in problems in the field of cognitive science. (shrink)

It is well known that the discussion concerning the relations between content and object is a central theme in Brentano’s school after the decisive essay by Twardowski in 1894. However, less known is the fact that this discussion also takes place outside the aforementioned school and that the distinction between content and object is already present before 1893 amongst other authors.

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)

After describing the philosophical background of Kerry’s work, an account is given of the way Kerry proposed to supplement Bolzano’s conception of logic with a psychological account of the mental acts underlying mathematical judgements.In his writings Kerry criticized Frege’s work and Kerry’s views were then attacked by Frege.The following two issues were central to this controversy: the relation between the content of a concept and the object of a concept; the logical roles of the definite article.Not only did Frege in (...) 1892 offer an unconvincing solution to Kerry’s puzzle concerning “the concept horse” but he also overlooked the many criticisms levelled by Kerry against the notion of an extension on which his own definition of number was based. (shrink)

When Benno Kerry died at the age of 30 he was already well‐known for his competent and thoroughgoing philosophical criticism of Cantor’s set theory and Frege’s early philosophy of mathematics.Before his death he was working on a theory of limits which was an elaboration of his Habilitationsschrift of 1884 and of which only a first part was published posthumously.This paper gives a survey of Kerry’s basic biographical data, and a first description of his Habilitationsschrift which had been missing for a (...) long time but was found by chance in the Nachlass of the German philosopher Leonard Nelson. (shrink)

In early analytic philosophy, one of the most central questions concerned the status of arithmetical objects. Frege argued against the popular conception that we arrive at natural numbers with a psychological process of abstraction. Instead, he wanted to show that arithmetical truths can be derived from the truths of logic, thus eliminating all psychological components. Meanwhile, Dedekind and Peano developed axiomatic systems of arithmetic. The differences between the logicist and axiomatic approaches turned out to be philosophical as well as mathematical. (...) In this paper, I will argue that Dedekind’s approach can be seen as a precursor to modern structuralism and as such, it enjoys many advantages over Frege’s logicism. I also show that from a modern perspective, Frege’s criticism of abstraction and psychologism is one-sided and fails against the psychological processes that modern research suggests to be at the heart of numerical cognition. The approach here is twofold. First, through historical analysis, I will try to build a clear image of what Frege’s and Dedekind’s views on arithmetic were. Then, I will consider those views from the perspective of modern philosophy of mathematics, and in particular, the empirical study of arithmetical cognition. I aim to show that there is nothing to suggest that the axiomatic Dedekind approach could not provide a perfectly adequate basis for philosophy of arithmetic. (shrink)

Traces the development of recursive functions from their origins in the late nineteenth century to the mid-1930s, with particular emphasis on the work and influence of Kurt Gödel.

Embora algumas posições filosóficas de Gödel sejam bem conhecidas, como o platonismo, a sua teoria do conhecimento é, em comparação, menos divulgada. A partir do «Problema da Evidência» de Hilbert-Bernays, I, pg. 20 seq., apresento a seguir os traços essenciais da posição de Gödel sobre a caracterização epistemológica da evidência finitista, com especial relevo para a história dos conceitos utilizados.

The concept of depth is central to Merleau-Ponty’s phenomenology and informed not only his philosophy of perception but also his thinking about psychology, art and politics. This article traces the ways the notion of depth appears in Merleau-Ponty’s thinking in these fields, contrasting it with Husserl’s own phenomenological investigations. The article starts with a comparison of the function of perception in Husserl’s phenomenology and then proceeds with an analysis of how the issue of depth reappears in Merleau-Ponty’s phenomenology of perception, (...) phenomenology of art and political philosophy. I argue that while Husserl’s approach to phenomenology led him to analyses of aesthetics stemming from works of art as random examples, and to non-participation in politics, Merleau-Ponty’s phenomenology leads to the opposite approach, inviting concrete criticism in art and active participation in politics. It is argued that Merleau-Ponty’s approach is more philosophically consistent. The choice of particular works of art, and the particular political engagements, can retrospectively clarify the transcendental phenomenological investigations themselves. (shrink)

On the basis of Martin-Löf’s meaning explanations for his type theory a detailed justification is offered of the rule of identity elimination. Brief discussions are thereafter offered of how the univalence axiom fares with respect to these meaning explanations and of some recent work on identity in type theory by Ladyman and Presnell.

We offer an interpretation of the words and works of Richard Dedekind and the David Hilbert of around 1900 on which they are held to entertain diverging views on the structure of a deductive science. Firstly, it is argued that Dedekind sees the beginnings of a science in concepts, whereas Hilbert sees such beginnings in axioms. Secondly, it is argued that for Dedekind, the primitive terms of a science are substantive terms whose sense is to be conveyed by elucidation, whereas (...) Hilbert dismisses elucidation and consequently treats the primitives as schematic. (shrink)

There are two principles which bear the name Frege''sprinciple: the principle of compositionality, and the contextprinciple. The aim of this contribution is to investigate whether thisis justified: did Frege accept both principles at the same time, did hehold the one principle but not the other, or did he, at some moment,change his opinion? The conclusion is as follows. There is a developmentin Frege''s position. In the period of Grundlagen he followed to a strict form of contextuality. He repeatedcontextuality in later (...) writings, but became less strict. From 1914 on,pushed by the needs of research, he comes close to compositionality. Buthe could never make the final step toward compositionality forprincipled reasons, therefore he always would reject compositionality. (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)

Among the correspondence between Husserl and Brentano kept at the Houghton Library of Harvard University there is a letter from Husserl to Brentano from 29 XII 1889, whose contents were completely unknown until now. The letter is of some significance, both historically as well as systematically for Husserl’s early development, painting a vivid picture of his relation and indebtedness to his teacher Franz Brentano. As in his letter to Stumpf from February 1890, Husserl describes the issues he had encountered during (...) the elaboration of his habilitation work into the Philosophy of Arithmetic, but also announces that he has finally found "clarity" regarding the arithmetica universalis. (shrink)

The article introduces and discusses an unpublished manuscript by Edmund Husserl, conserved at the Husserl-Archives Leuven with signature K I 26, pp. 73a–73b. The article is followed by the text of the manuscript in German and in an English translation. The manuscript, titled “The Transition through the Impossible” ( Der Durchgang durch das Unmögliche ), was part of the material Husserl used for his 1901 Doppelvortrag in Göttingen. In the manuscript, the impossible is characterized as the “sphere of objectlessness” ( (...) Sphäre der Gegenstandslosigkeit ) and Husserl addresses the question whether and when it is warranted to perform a transition through the impossible to obtain valid results for the sphere of objectivity. (shrink)

This volume contains an English translation of Edmund Husserl’s first major work, the Philosophie der Arithmetik, (Husserl 1891). As a translation of Husserliana XII (Husserl 1970), it also includes the first chapter of Husserl’s Habilitationsschrift (Über den Begriff der Zahl) (Husserl 1887) and various supplementary texts written between 1887 and 1901. This translation is the crowning achievement of Dallas Willard’s monumental research into Husserl’s early philosophy (Husserl 1984) and should be seen as a companion to volume V of the Husserliana: (...) Collected Works series (Husserl 1994b), which already contained selected translations from Hua XII. As Willard re- marks on the inner cover of the volume, it is “a window on a period of rich and illuminating philosophical activity”, to which I wholeheartedly agree. Willard’s two volumes of translations open this window on the beginnings of Husserl’s philosophy for the English-speaking world. This earliest period of Husserl’s philosophy has often been unjustly ignored and Willard provides the English reader with an excellent starting point. Husserl’s first steps into phenomenology and the philosophy of logic and mathematics contain many promising seeds that will flower later on, in the Logische Untersuchungen and beyond. (shrink)

Nadie puede negar que la figura de Edmund Husserl constituye la llave de acceso para el horizonte filosófico de nuestro tiempo, tanto en su versión continental como analítica. Pero ¿en qué medida un mismo planteamiento pudo dar suelo y sustento al despliegue de corrientes tan distintas? Aunque mucho se ha trabajado ya para desembrollar el renovado sentido que filosofía y ciencia adquieren en su propuesta, el camino que siguió para llegar a esas conclusiones todavía no goza de suficiente claridad. Por (...) ello, en este artículo nos hemos propuesto esclarecer algunos intersticios de la transformación de su pensamiento, tomando como hilo conductor las preocupaciones de juventud que, a la larga, desembocarán en la formulación de su contundente crítica al conocimiento. Para lograr nuestro objetivo daremos seguimiento al itinerario husserliano, comenzando por la Filosofía de la aritmética, para luego finalizar con su concepción de la filosofía como la más estricta de las ciencias. Nobody can deny that the figure of Edmund Husserl represents the key to the philosophical horizon of our time in both version, as continental as analytical one. But, how can the same approach give ground and support to the development of such diverse topics? Although much work has been done to explain the renewed sense that science and philosophy acquire inside their proposal, the way Husserl reached that conclusion is not sufficiently clear yet. That is why in this article we intend to clarify some aspects of his thought transformation, keeping it up whit his early concerns that will lead, inevitably, in his critique of knowledge. To achieve this, we will follow the husserlian itinerary from The philosophy of arithmetic to his conception of philosophy as the strictest science. (shrink)

The problem of ‘collective unity’ in the transcendental philosophies of Kant and Husserl is investigated on the basis of number’s exemplary ‘collective unity’. To this end, the investigation reconstructs the historical context of the conceptuality of the mathematics that informs Kant’s and Husserl’s accounts of manifold, intuition, and synthesis. On the basis of this reconstruction, the argument is advanced that the unity of number – not the unity of the ‘concept’ of number – is presupposed by each transcendental philosopher in (...) their accounts of the transcendental foundation of manifold, intuition, and synthesis. This presupposition is ultimately traced to Kant’s and Husserl’s responses to Hume’s philosophy of human understanding and the critical limits of what Kant calls the ‘qualitative’ unity of transcendental consciousness. These critical limits are exposed in both philosophers’ attempts to account for that ‘qualitative’ unity on the basis of the ‘quantitative’ unity of number. (shrink)

Dallas Willard’s contribution to phenomenology is presented in terms of his articles on, and translations into English of, Edmund Husserl’s early philosophical writings, which single-handedly prevented them from falling into oblivion, both literally and philosophically. Willard’s account of Husserl’s “negative critique” of formalized logic in those writings, and argument for its contemporary relevance, is presented and largely endorsed.

The view that mathematics deals with ideal objects to which we have epistemic access by a kind of perception has troubled many thinkers. Using ideas from Husserl’s phenomenology, I will take a different look at these matters. The upshot of this approach is that there are non-material objects and that they can be recognized in a process very closely related to sense perception. In fact, the perception of physical objects may be regarded as a special case of this more universal (...) way of recognizing objects of any kind. (shrink)

Erratum to: Axiomathes DOI 10.1007/s10516-014-9234-yIn the original publication of the article, some of the references were published incorrectly. Please find below the corrected version of these references.

This paper discusses Jean van Heijenoort’s (1967) and Jaakko and Merrill B. Hintikka’s (1986, 1997) distinction between logic as auniversal language and logic as a calculus, and its applicability to Edmund Husserl’s phenomenology. Although it is argued that Husserl’s phenomenology shares characteristics with both sides, his view of logic is closer to the model-theoretical, logic-as-calculus view. However, Husserl’s philosophy as transcendental philosophy is closer to the universalist view. This paper suggests that Husserl’s position shows that holding a model-theoretical view of (...) logic does not necessarily imply a calculus view about the relations between language and the world. The situation calls for reflection about the distinction: It will be suggested that the applicability of the van Heijenoort and the Hintikkas distinction either has to be restricted to a particular philosopher’s views about logic, in which case no implications about his or her more general philosophical views should be inferred from it; or the distinction turns into a question of whether our human predicament is inescapable or whether it is possible, presumably by means of model theory, to obtain neutral answers to philosophical questions. Thus the distinction ultimately turns into a question about the correct method for doing philosophy. (shrink)

The paper discusses Husserl’s notion of definiteness as presented in his Göttingen Mathematical Society Double Lecture of 1901 as a defense of two, in many cases incompatible, ideals, namely full characterizability of the domain, i.e., categoricity, and its syntactic completeness. These two ideals are manifest already in Husserl’s discussion of pure logic in the Prolegomena: The full characterizability is related to Husserl’s attempt to capture the interconnection of things, whereas syntactic completeness relates to the interconnection of truths. In the Prolegomena (...) Husserl argues that an ideally complete theory gives an independent norm for objectivity for logic and experiential sciences, hence the notion is central to his argument against psychologism. In the Double Lecture the former is captured by non-extendibility, that is, categoricity of the domain, from which, so Husserl assumes, syntactic completeness is thought to follow. In the so-called ‘mathematical manifolds’ the expressions of the theory are equations that are reducible to equations between elements of the theory. With such an equational reduction structure individual elements of the domain are given criteria of identity and hence they are fully determined. (shrink)

RESUMEN La fenomenología de Husserl está inmersa en un entramado de regresiones y revisiones conceptuales que dificultan la identificación de una estructura sistémica. Los conceptos característicos de la fenomenología carecen de univocidad y no son propios de algunas obras de Husserl. Philosophie der Arithmetik ilustra el problema referido. ¿Puede inscribirse esta obra dentro de la categoría de texto fenomenológico? ¿Es posible hablar de una fenomenología de la matemática en Husserl? y ¿qué sentido tendría esto? Los objetivos del presente ensayo son: (...) primero, analizar la dificultad que tiene Philosophie der Arithmetik para responder a las inquietudes de la filosofía de las matemáticas, y segundo, proponer la posibilidad de una fenomenología de la matemática condicionada a la clarificación conceptual y al estudio crítico de la influencia de la tradición analítica sobre la filosofía de las matemáticas. ABSTRACT Husserl's phenomenology is immersed in a network of regressions and conceptual revisions that hinder the identification of a systemic structure. The characteristic concepts of phenomenology fall short of uniqueness and are not appropriate for some of Husserl's works. Philosophie der Arithmetik illustrates the aforementioned problem. Can this work be classified under the category of phenomenological texts? Is it possible to talk about a phenomenology of mathematic in Husserl? And what would be the point of this? The objectives of the present essay are: first, to analyze the difficulty that Philosophie der Arithmetik has responding to the concerns of the philosophy of mathematics, and second, to propose the possibility of a phenomenology of mathematics, conditioned to conceptual clarification and critical study of the influence of the analytical tradition on the philosophy of mathematics. (shrink)

The title is meant to emphasize the immense loss of status I take logic to have undergone in recent decades, and to suggest something about its causes. The loss is most obvious in the context of higher education, where almost no post-secondary institutions now have effectual general requirements in standard formal logic, as that was easily understood thirty or more years ago. Courses in so-called 'critical thinking' are, with rare and noble exceptions, only a further illustration of the point, for (...) many of them, if not most, say nothing at all about logical form and formal logic, and proceed as if thought and discourse could be critically understood and appraised in total ignorance of their formal aspects. (shrink)