Bernard Bolzano (1781–1848) is commonly thought to have attempted to develop a theory of size for infinite collections that follows the so-called part–whole principle, according to which the whole is always greater than any of its proper parts. In this paper, we develop a novel interpretation of Bolzano’s mature theory of the infinite and show that, contrary to mainstream interpretations, it is best understood as a theory of infinite sums. Our formal results show that Bolzano’s infinite sums (...) can be equipped with the rich and original structure of a non-commutative ordered ring, and that Bolzano’s views on the mathematical infinite are, after all, consistent. (shrink)

In §12 of his 1837 magnum opus, the Wissenschaftslehre, Bolzano remarks that “In the new logic textbooks one reads almost constantly that ‘in logic one must consider not the material of thought but the mere form of thought, for which reason logic deserves the title of a purely formal science’” (WL §12, 46).1 The sentence Bolzano quotes is his own summary of others’ philosophical views; he goes on to cite Jakob, Hoffbauer, Metz, and Krug as examples of thinkers (...) who held that logic abstracts from the matter of thought and considers only its form. Although Bolzano does not mention Kant by name here, Kant does of course hold that “pure general logic”, what Bolzano would consider logic in the traditional sense (the theory of propositions, representations, inferences, etc.), is formal. As Kant remarks in the Introduction to the 2nd edition of Kritik der reinen Vernunft , (pure general) logic is “justified in abstracting – is indeed obliged to abstract – from all objects of cognition and all of their differences; and in logic, therefore, the understanding has to do with nothing further than itself and its own form” (KrV, Bix).2. (shrink)

Bolzano hat seine Wahrscheinlichkeitslehre in 15 Punkten im § 14 des zweiten Teils seiner Religionswissenschaft sowie in 20 Punkten im § 161 des zweiten Bandes seiner Wissenschaftslehre niedergelegt. (Ich verweise auf die Religionswissenschaft mit 'RW II', auf die Wissenschaftslehre mit 'WL II'.) In der RW II (vgl. p. 37) ist seine Wahrscheinlichkeitslehre eingebettet in seine Ausführungen "Über die Natur der historischen Erkenntniß, besonders in Hinsicht auf Wunder", und die Lehrsätze, die er dort zusammenstellt, dienen dem ausdrücklichen Zweck, mit mathematischem (...) Rüstzeug Lehrmeinungen entgegentreten zu können, gemäß denen Wundererzählungen keine Glaubwürdigkeit zukommen könne. In der WL II (vgl. p. 171) führt Bolzano im großen und ganzen dieselben Lehrsätze an wie in der RW II, entwickelt nun aber die Wahrscheinlichkeitslehre innerhalb seiner Lehre von den Sätzen an sich. Dabei orientiert er sich zwar durchaus an den Lehrsätzen in den damaligen "Schriften über die Wahrscheinlichkeitsrechnung" (vg. WL II, p. 190), korrigiert aber dort, wo es ihm nötig erscheint (vgl. WL II, pp. 187–191), und leistet so im Grunde eine Reformulierung des elementaren Teils der Wahrscheinlichkeitslehre seiner Zeit innerhalb seiner logischen Theorie von den Sätzen an sich. — Ich bezwecke hier keine historische Studie über Bolzanos Wahrscheinlichkeitslehre, obwohl es von Interesse sein mag, herauszuschälen, worin Bolzano mit welchen Wahrscheinlichkeitstheoretikern seiner Zeit übereinstimmt, und worin nicht, insbesondere welche Schwächen von Bolzanos Wahrscheinlichkeitslehre Schwächen aller damaligen Wahrscheinlichkeitslehren waren. Eine wichtige systematische Studie über Bolzanos Wahrscheinlichkeitslehre bestünde — wie von Berg (1962, pp. 148-149) ansatzweise begonnen — in einer exakten Rekonstruktion seiner Wahrscheinlichkeitslehre innerhalb eines konsistenten logischen Systems der Sätze an sich. Ich werde im folgenden etwas bei weitem Bescheideneres, doch möglicherweise durchaus Fruchtbares versuchen, nämlich die Lehrsätze von Bolzanos Wahrscheinlichkeitslehre in die Sprache einer heutigen Wahrscheinlichkeitstheorie zu übersetzen und die übersetzten Lehrsätze dort herzuleiten, soweit dies möglich ist. Man könnte dann in einem zweiten Schritt, der hier nicht mehr unternommen wird, untersuchen, inwieweit jene Thesen, die den Herleitungstest überstanden haben, jenen Zweck erfüllen, den Bolzano ihnen ursprünglich zugedacht hat: als mathematisches Rüstzeug für seine Argumentationen gegen die Auffassung zu dienen, Wundererzählungen könnten nicht glaubwürdig sein. (shrink)

This article examines Bolzano’s aesthetic cognitivism. It argues that, while reminiscent of German rationalist aesthetics and hence potentially appearing rigid and outdated, Bolzano’s version of cognitivism is, in fact, highly innovative and more flexible than the cognitivism championed by the rationalists. He imports from the rationalists the idea that aesthetic appreciation and creation are rule-governed, yet does not construe rule-following and engaging in free aesthetic activities as mutually exclusive. Furthermore, thanks to his nuanced treatment of the interaction between (...) aesthetic values and other types of values, Bolzano’s aesthetic cognitivism presents a fresh alternative to contemporary versions of aesthetic cognitivism. (shrink)

Bolzano was the first to establish an explicit distinction between the deductive methods that allow us to recognise the certainty of a given truth and those that provide its objective ground. His conception of the relation between what we, in this paper, call "subjective consequence", i.e., the relation from epistemic reason to consequence and "objective consequence", i.e., grounding however allows for an interpretation according to which Bolzano advocates an "explicativist" conception of proof: proofs par excellence are those that (...) reflect the objective order of grounding. In this paper, we expose the problems involved by such a conception and argue in favour of a more rigorous demarcation between the ontological and the epistemological concern in the elaboration of a theory of demonstration. (shrink)

The paper discusses some changes in Bolzano's definition of mathematics attested in several quotations from the Beyträge, Wissenschaftslehre and Grössenlehre: is mathematics a theory of forms or a theory of quantities? Several issues that are maintained throughout Bolzano's works are distinguished from others that were accepted in the Beyträge and abandoned in the Grössenlehre. Changes are interpreted as a consequence of the new logical theory of truth introduced in the Wissenschaftslehre, but also as a consequence of the overcome (...) of Kant's terminology, and of the radicalization of Bolzano's anti‐Kantianism. Bolzano's evolution is understood as a coherent move, once the criticism expressed in the Beyträge on the notion of quantity is compared with a different and larger notion of quantity that Bolzano developed already in 1816. This discussion is enriched by the discovery that two unknown texts mentioned by Bolzano in the Beyträge can be identified with works by von Spaun and Vieth respectively. Bolzano's evolution is interpreted as a radicalization of the criticism of the Kantian definition of mathematics and as an effect of Bolzano's unaltered interest in the Leibnizian notion of mathesis universalis. As a conclusion, the author claims that Bolzano never abandoned his original idea of considering mathematics as a scientia universalis, i.e. as the science of quantities in general, and suggests that the question of ideal elements in mathematics, apart from being a main reason for the development of a new logical theory, can also be considered as a main reason for developing a different definition of quantity. (shrink)

This paper is aimed at understanding one central aspect of Bolzano's views on deductive knowledge: what it means for a proposition and for a term to be known a priori. I argue that, for Bolzano, a priori knowledge is knowledge by virtue of meaning and that Bolzano has substantial views about meaning and what it is to know the latter. In particular, Bolzano believes that meaning is determined by implicit definition, i.e. the fundamental propositions in a (...) deductive system. I go into some detail in presenting and discussing Bolzano's views on grounding, a priori knowledge and implicit definition. I explain why other aspects of Bolzano's theory and, in particular, his peculiar understanding of analyticity and the related notion of Ableitbarkeit might, as it has invariably in the past, mislead one to believe that Bolzano lacks a significant account oï a priori knowledge. Throughout the paper, I point out to the ways in which, in this respect, Bolzano's antagonistic relationship to Kant directly shaped his own views. (shrink)

One of Bolzano’s objections to Kant’s way of drawing the analytic-synthetic distinction is that it only applies to judgments within a narrow range of syntactic forms, namely, universal affirmative judgments. According to Bolzano, Kant cannot account for judgments of other syntactic forms that, intuitively, are analytic. A recent paper by Ian Proops also attributes to Kant the view that analytic judgments beyond a limited range of syntactic forms are impossible. I argue that, correctly understood, Kant’s conception of analyticity (...) allows for analytic judgments of a wider range of syntactic forms. (shrink)

This thesis presents a Bolzano whose genius resulted not from his freedom from powerful philosophical influences, but precisely from his response to the powerful philosophical influences of his day. Chief amongst these were the voices engaged in debate about the nature of science. It was precisely Bolzano's commanding synthesis of the views of those advocating progress through mathematical physics with the views of those advocating a classical model of a science as the study of causes that set the (...) stage for the development of Austrian and analytic philosophy in subsequent centuries. (shrink)

Bolzano propôs uma teoria da verdade que se diferencia das restantes por defender que as proposições são objetivas (não são juízos nem frases) e, consequentemente, que também as proposições verdadeiras (e as falsas) são objetivas (não constituem a correspondência entre um juízo/uma frase e um facto objetivo nem uma qualquer relação entre juízos/frases). Para além disso, considero que propõe uma teoria metafísica da correspondência (à qual não adiro), de acordo com a qual a verdade consiste na correspondência entre uma (...) proposição objetiva e um facto. (shrink)

I review Stefan Roski's "Bolzano's Conception of Grounding".

This paper surveys Bolzano's Beyträge zu einer begründeteren Darstellung der Mathematik (Contributions to a better-grounded presentation of mathematics) on the 200th anniversary of its publication. The first and only published issue presents a definition of mathematics, a classification of its subdisciplines, and an essay on mathematical method, or logic. Though underdeveloped in some areas (including,somewhat surprisingly, in logic), it is nonetheless a radically innovative work, where Bolzano presents a remarkably modern account of axiomatics and the epistemology of the (...) formal sciences. We also discuss the second, unfinished and unpublished issue, where Bolzano develops his views on universal mathematics. Here we find the beginnings of his theory of collections, for him the most fundamental of the mathematical disciplines. Though not exactly the same as the later Cantorian set theory, Bolzano's theory of collections was used in very similar ways in mathematics, notably in analysis. In retrospect, Bolzano's debut in philosophy was a remarkably successful one, though its fruits would only become generally known much later. (shrink)

There are quite a few studies on late Bolzano’s notion of a collection (Inbegriff). We try to broaden the perspective by introducing the forerunner of collections in Bolzano’s early writings, namely the entities referred to by expressions with the technical term ‘et’. Special emphasis is laid on the question whether these entities are set-theoretical or mereological plenties. Moreover, similarities and differences to Bolzano’s mature conception are pointed out.

Our standard model-theoretic definition of logical consequence is originally based on Alfred Tarski’s (1936) semantic definition, which, in turn, is based on Rudolf Carnap’s (1934) similar definition. In recent literature, Tarski’s definition is described as a conceptual analysis of the intuitive ‘everyday’ concept of consequence or as an explication of it, but the use of these terms is loose and largely unaccounted for. I argue that the definition is not an analysis but an explication, in the Carnapian sense: the replacement (...) of the inexact everyday concept with an exact one. Some everyday intuitions were thus brought into a precise form, others were ignored and forgotten. How exactly did the concept of logical consequence change in this process? I suggest that we could find some of the forgotten intuitions in Bernard Bolzano’s (1837) definition of ‘deducibility’, which is traditionally viewed as the main precursor of Tarski’s definition from a time before formalized languages. It turns out that Bolzano’s definition is subject to just the kind of natural features—paradoxicality of everyday language, Platonism about propositions, and dependence on the external world—that Tarski sought to tame by constructing an artificial concept for the special needs of mathematical logic. (shrink)

Jusqu'à maintenant, il semble qu'on n'ait pas établi de lien entre le rejet par Bolzano de la notation quantificationnelle des propositions universelles de la logique traditionnelle et l'articulation inédite de sa notion de validité universelle. C'est ce que je veux faire ici. En particulier, dans la mesure où l'analyticité est un cas spécial de la validité universelle, j'ai l'intention de défendre l'idée qui veut que la notion bolzanienne d'analyticité cherche à résoudre des problèmes qui sont intrinsèquement liés à la (...) théorie traditionnelle de la quantification universelle tels qu'ils surviennent, notamment avec le traitement kantien de l'analyticité. It seems that the connection between Bolzano's rejection of the traditional quantificational notation for universal propositions and the articulation of his notion of universal validity has remained, until today, perfectly unnoticed. In this paper, I will show that there is such a connection. Particularly, since analyticity is a special case of universal validity, my intention is to show that the problems to which Bolzano's perfectly original account of analyticity seeks to find an answer are intrinsically related to the traditional conception of universal quantification as it arises in the context of Kant's treatment of analyticity. (shrink)

This paper takes the form of a series of sketches of 19th century Austrian political and intellectual history, allied with a number of more general reflections designed to contribute to our understanding of some of the peculiar characteristics of Austrian thought, particularly Austrian philosophy and economics, in the period in question.

Brentanians defend the view that there are distinct types of object, but that this does not entail the admission of different modes of being. The most general distinction among objects is the one between realia, which are causally efficacious, and irrealia, which are causally inert. As for being, which is equated with existence, it is understood in terms of “correct acknowledgeability.” This view was defended for some time by Brentano himself and then by his student Anton Marty. Their position is (...) opposed to Bolzanian, Husserlian, and Meinongian ontologies, in which a distinction in the (higher) types of object implies a distinction in their mode of being. These Austro-German discussions anticipate much of the contemporary debate between Quineans, who accept only differences in objects, and neo-Meinongians or other ontological pluralists, who accept different modes of being. My paper first presents the Brentanian view in detail and then evaluates its philosophical significance. (shrink)

La philosophie analytique est, dit-on, an-historique, anti-historique même. Elle s’est souvent présentée comme marquant une rupture avec le passé. L’attitude inspirant la question rhétorique que pose Wittgenstein dans les Carnets, « Was geht mich die Geschichte an ? », est répandue. Les multiples liens entre la réalité historique et l’anthropologie philosophique qui ont fasciné les philosophes depuis Hegel jusqu’à Dilthey, Heidegger, Adorno et Habermas – l’évolution historique, les dimensions historiques de l’éthique, de la politique, l’histoire de l’individu et les deux (...) philosophèmes qu’elle englobe : la Vie et la Mort – y sont singulièrement absents, absents tout court (pas dans le sens parisien du mot). (shrink)

Husserl’s early picture of explanation in the sciences has never been completely provided. This lack represents an oversight, which we here redress. In contrast to currently accepted interpretations, we demonstrate that Husserl does not adhere to the much maligned deductive-nomological (DN) model of scientific explanation. Instead, via a close reading of early Husserlian texts, we reveal that he presents a unificationist account of scientific explanation. By doing so, we disclose that Husserl’s philosophy of scientific explanation is no mere anachronism. It (...) is, instead, tenable and relevant. We discuss how Husserl and other contemporary thinkers draw theoretical inspiration from the same source—namely, Bernard Bolzano. Husserl’s theory of scientific explanation shares a common language and discusses the same themes as, for example, Phillip Kitcher and Kit Fine. To advance our novel reading, we discuss Husserl’s investigations of grounding, inter-lawful explanation, intra-mathematical explanation, and scientific unification. (shrink)

Per Husserl, come per Bolzano, la logica e una dottrina della sdenza. Husserl prende pero piu sul serio l'idea che le teorie scientifiche siano costituite dagli atti mentali di soggetti conoscenti. Quella che segue e un' esposizione della concezione husserliana della logica e della scienza, fondata appunto sugli atti; essa approdera a una delineazione dell'idea husserliana di «ontologia formale».

Thinking of problems of aesthetics has a long and strong tradition in Austrian Philosophy. It starts with Bernard Bolzano (1781-1848); it is famously represented by the critic and musicologist Eduard Hanslick (1825-1904); and it is continued within the school of Alexius Meinong (1853-1920), in particular by Christian von Ehrenfels (1859-1932) and Stephan Witasek (1870-1915). Nowadays the aesthetic writings of Bolzano, Ehrenfels, and Witasek are hardly known, particularly not in the Anglo-Saxon world. Austrian aesthetics is surely less known than (...) Austrian contributions to other philosophical disciplines, like ontology, epistemology or philosophy of science. One of the aims of this paper is to show that this is both regrettable and unjustified for the following reasons: Austrian aestheticians have dealt with a number of problems (mainly concerning the foundations of aesthetics) that are salient until today; in terms of subtlety and depth as well as exactness and originality, in general, they easily stand comparison with today's analytic aesthetics; and many of there views and arguments are still worthy of consideration. In this paper, the focus is on a number of hardly known Austrian contributions to aesthetics. These contributions concern the following, partly interrelated, central problems of philosophical aesthetics: i. The problem of the definition of beauty (What is beauty? What does it mean to say of an object that it is beautiful?) ii. The problem of the ontological status of works of art (What kinds of objects are works of art?) iii. The problem of the objectivity of aesthetic values (Do we claim objective validity for aesthetic value judgements, and if so, is this claim justified?) The answers of Bolzano, Meinong, Witasek and Ehrenfels to these questions will be considered. (shrink)

This study is about an aspect of the reception of Herbatianism in Austria which has not been thoroughly investigated so far. It pertains to a controversy opposing Robert Zimmermann and Franz Brentano in the context of discussions which took place in the Philosophical Society of the University of Vienna. This study looks more specifically at three important episodes involving the Philosophical Society, first, the controversy over Herbartianism, second that over the evaluation of Schelling’s philosophy, and finally the reception of (...) class='Hi'>Bolzano in Austria. I will first describe the circumstances that led Zimmermann to get involved in the Philosophical Society and the source of his controversy with Brentano and his followers. I will then comment Zimmermann’s address as chairman of the Philosophical Society and Brentano’s reaction to Zimmermann’s remarks on Schelling and the historical period to which he belongs. I will complete my analysis of Brentano’s reaction with a summary of his evaluation of Herbart’s philosophical program to which Zimmermann adhered. The last part focuses on Zimmermann’s decisive role in the reception of Bolzano in Vienna in connection with the Bolzano Commission established by the Philosophical Society. I will conclude with brief remarks on Zimmermann’s legacy in Vienna. (shrink)

This article draws on several crucial and unpublished manuscripts from the Scholem Archive in exploration of Gershom Scholem's youthful statements on mathematics and its relation to extra-mathematical facts and, more broadly, to a concept of history that would prove to be consequential for Walter Benjamin's own thinking on "messianism" and a "futuristic politics." In context of critiquing the German Youth Movement's subsumption of active life to the nationalistic conditions of the "earth" during the First World War, Scholem turns to mathematics (...) for a genuine and self-consistent theory of action. In the concept of actual infinity (in Cantor and Bolzano) he finds an explanation of how mathematics relates to "the physical" without reducing the former to an "image" of the latter, and without relying on the concept of geometric intuition. This explanation, insofar as it relies on the notion of actual infinity, provides Scholem with a conception of mathematics (and the history of mathematics) that reconciles freedom and necessity—remarks on which he outlines in his diaries and communicates to Benjamin in early March 1916. (shrink)

The dominant theory of judgment in 1870 was one or other variety of combination theory: the act of judgment is an act of combining concepts or ideas in the mind of the judging subject. In the decades to follow a succession of alternative theories arose to address defects in the combination theory, starting with Bolzano’s theory of propositions in themselves, Brentano’s theory of judgment as affirmation or denial of existence, theories distinguishing judgment act from judgment content advanced by Brentano’s (...) students Twardowski, Husserl and Meinong, and finally, Adolf Reinach’s addition of a linguistic dimension to the Brentano-Husserlian theory of judgment – an account of judgments as ways of doing things with words in what Reinach called ‘social acts’. (shrink)

Bolzano fut le premier philosophe à établir une distinction explicite entre les procédés déductifs qui nous permettent de parvenir à la certitude d’une vérité et ceux qui fournissent son fondement objectif. La conception que Bolzano se fait du rapport entre ce que nous appelons ici, d’une part, « conséquence subjective », à savoir la relation de raison à conséquence épistémique et, d’autre part, la « conséquence objective », c’est-à-dire la fondation , suggère toutefois que Bolzano défendait une (...) conception « explicativiste » de la preuve : les preuves par excellence sont celles qui reflètent l’ordre de la fondation objective. Dans cet article nous faisons état des problèmes liés à une telle conception et argumentons en faveur d’une démarcation plus stricte entre la préoccupation ontologique et la préoccupation épistémologique dans l’élaboration d’une théorie de la preuve.Bolzano was the first to establish an explicit distinction between the deductive methods that allow us to recognise the certainty of a given truth and those that provide its objective ground. His conception of the relation between what we, in this paper, call “subjective consequence”, i.e. the relation from epistemic reason to consequence and “objective consequence”, i.e. grounding however suggests that Bolzano advocated an “explicativist” conception of proof : proofs par excellence are those that reflect the objective order of grounding. In this paper, we expose the problems involved by such a conception and argue in favour of a more rigorous demarcation between the ontological and the epistemological concern in the elaboration of a theory of proof. (shrink)

Prior to Kripke’s seminal work on the semantics of modal logic, McKinsey offered an alternative interpretation of the necessity operator, inspired by the Bolzano–Tarski notion of logical truth. According to this interpretation, ‘it is necessary that A’ is true just in case every sentence with the same logical form as A is true. In our paper, we investigate this interpretation of the modal operator, resolving some technical questions, and relating it to the logical interpretation of modality and some views (...) in modal metaphysics. In particular, we present an hitherto unpublished solution to problems 41 and 42 from Friedman’s 102 problems, which uses a different method of proof from the solution presented in the paper of Tadeusz Prucnal. (shrink)

This study examines the place of the Philosophical Society of the University of Vienna (1888-1938) in the evolution of the history of philosophy in Austria up to the establishment of the Vienna Circle in 1929. I will examine three aspects of the relationship between the Austrian members of the Vienna Circle and the Philosophical Society which has been emphasized by several historians of the Vienna Circle: the first aspect concerns the theory of a first Vienna Circle formed mainly by H. (...) Hahn, P. Frank and O. Neurath; the second aspect is the contention that the missing link between the Vienna Circle and the Bolzano tradition in Austria is Alois Höfler, a student of Brentano and Meinong; I will finally examine the link they established between the annexation of the Philosophical Society to the Kant-Gesellschaft in 1927 and the founding of the Vienna Circle in 1929. I will argue that this institution played a key role in the history of philosophy in Austria and is partly responsible for the formation of the Vienna Circle. (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)

The dominant theory of judgment in 1870 was one or other variety of combination theory: the act of judgment is an act of combining concepts or ideas in the mind of the judging subject. In the decades to follow a succession of alternative theories arose to address defects in the combination theory, starting with Bolzano’s theory of propositions in themselves, Brentano’s theory of judgment as affirmation or denial of existence, theories distinguishing judgment act from judgment content advanced by Brentano’s (...) students Twardowski, Husserl and Meinong, and finally, Adolf Reinach’s addition of a linguistic dimension to the Brentano-Husserlian theory of judgment – an account of judgments as ways of doing things with words in what Reinach called ‘social acts’. (shrink)

In this paper I argue for an association between impurity and explanatory power in contemporary mathematics. This proposal is defended against the ancient and influential idea that purity and explanation go hand-in-hand (Aristotle, Bolzano) and recent suggestions that purity/impurity ascriptions and explanatory power are more or less distinct (Section 1). This is done by analyzing a central and deep result of additive number theory, Szemerédi’s theorem, and various of its proofs (Section 2). In particular, I focus upon the radically (...) impure (ergodic) proof due to Furstenberg (Section 3). Furstenberg’s ergodic proof is striking because it utilizes intuitively foreign and infinitary resources to prove a finitary combinatorial result and does so in a perspicuous fashion. I claim that Furstenberg’s proof is explanatory in light of its clear expression of a crucial structural result, which provides the “reason why” Szemerédi’s theorem is true. This is, however, rather surprising: how can such intuitively different conceptual resources “get a grip on” the theorem to be proved? I account for this phenomenon by articulating a new construal of the content of a mathematical statement, which I call structural content (Section 4). I argue that the availability of structural content saves intuitive epistemic distinctions made in mathematical practice and simultaneously explicates the intervention of surprising and explanatorily rich conceptual resources. Structural content also disarms general arguments for thinking that impurity and explanatory power might come apart. Finally, I sketch a proposal that, once structural content is in hand, impure resources lead to explanatory proofs via suitably understood varieties of simplification and unification (Section 5). (shrink)

In this paper I highlight two opposing models of the notion of divine revelation: the propositional and the radical. The propositional understanding of revelation was central to theology and philosophy until the 19th century. Since then, a number of other models of revelation have emerged. I define as radical the understanding of revelation which emphasizes two features of revelation: (1) God’s existence is per se revelatory; (2) God’s revelation is per se self-revelation. I propose too an assessment of the notion (...) of propositional revelation as presented by Richard Swinburne. And I offer detailed analyses of two representatives of the early understanding of divine revelation as self-revelation: the views of Bernard Bolzano and Anton Günther. Bolzano, the renowned mathematician, was also a philosopher of religion; and Günther, one of the most ingenious writers in Austrian philosophy, was not only a theologian but also a philosopher comparable to the important figures of 19th-century Ge. (shrink)

John Corcoran ’s “Meanings of Implication” outlines and discusses 12 distinct uses of the term “implies” while also commenting on the ways in which these different notions of implication might be confused or conflated. Readers may take special note of Corcoran ’s analysis of Russell’s truth-functional account of “implication” and its historical function as logical consequence, as well as Corcoran ’s discussion of Bolzano’s previously obscure and rarely mentioned notion of “relative implication.”.

The dominant theory of judgment in 1870 was one or other variety of combination theory: the act of judgment is an act of combining concepts or ideas in the mind of the judging subject. In the decades to follow a succession of alternative theories arose to address defects in the combination theory, starting with Bolzano’s theory of propositions in themselves, Brentano’s theory of judgment as affirmation or denial of existence, theories distinguishing judgment act from judgment content advanced by Brentano’s (...) students Twardowski, Husserl and Meinong, and finally, Adolf Reinach’s addition of a linguistic dimension to the Brentano-Husserlian theory of judgment – an account of judgments as ways of doing things with words in what Reinach called ‘social acts’. (shrink)

On the one hand, Scheler's critique of Kant's concept of a priori benefits from Husserl to a large extent, and it complements and deepens Husserl's. On the other hand, Scheler also critiques Husserl's definition of a priori. Husserl's material a priori as ideal object primarily thanks to his so-called "Bolzano- turn". In this connection, Scheler grabs hold of the relation of Husserl to Bolzano from the very beginning. For Scheler, Husserl thinks in a "platonic" way, and still falls (...) in a new type of "Platonism", or rather, logical Platonism, although he correctly refuses the ordinary Platonism. In Scheler's view, Husserl's phenomenological reduction is "not purely" executed, and therefore his phenomenological experience is problematic, or more precisely, the relation between categorial intuition and sensuous intuition is problematic. The final aim of Scheler's critique of Husserl's phenomenological understanding of "objective a priori" is to win the primary position of categorial intuition and its content , ethical insight and its correlate , and ultimately of phenomenological ethics of material value.Einerseits nimmt Schelers Kritik an Kant bezüglich des Begriffs des Apriori die Einsichten Husserls in großem Umfang auf. Schelers Kritik an Kant ergänzt und vertieft die Husserlsche Kant-Kritik. Andererseits kritisiert er aber auch Husserls Bestimmung des Apriori. Vor allem verdankt sich das materiale Apriori als idealer Gegenstand bei Husserl der sogenannten “Bolzano’schen Wendung”. Von Anfang an kritisiert Scheler Husserl in diesem Punkt, indem er dem Verhältnis zwischen Bolzano und Husserl immer präziser nachging. Für Scheler unterliegt Husserl mit Recht keinem platten Platonismus. Aber dennoch verfahre Husserl immerhin “platonistisch”, er unterliege einem “Neoplatonismus”, bzw. einem logischen Platonismus. Weil die phänomenologische Reduktion bei Husserl nach Schelers Meinung “nicht reinlich” durchgeführt wird, ist die phänomenologische Erfahrung bei Husserl problematisch, genauer gesagt ist das Verhältnis zwischen der kategorialen Anschauung und der sinnlichen Anschauung problematisch. Der Endzweck von Schelers Kritik an der phänomenologischen Auffassung des gegenständlichen Apriori bei Husserl besteht darin, die primäre Stelle der kategorialen Anschauung und ihrer Gehalte , sowie der sittlichen Einsicht und ihrer Korrelate und zuletzt der phänomenologisch materialen Wertethik zu gewinnen.S jedne strane, Schelerova kritika Kantova pojma a priori u velikoj mjeri duguje Husserlu, te dopunjuje i produbljuje Husserlovu. S druge strane, Scheler kritizira i Husserlovu definiciju apriorija. Husserlov materijalni a priori kao idealni predmet prvenstveno proizlazi iz njegova takozvanog bolzanovskog obrata. Prema Scheleru, Husserl razmišlja na "platonski" način te upada u novi tip "platonizma" ili, točnije, logičkog platonizma, iako s pravom odbacuje obični platonizam. Scheler smatra da Husserlova fenomenološka redukcija nije izvedena "čisto" te da je stoga njegovo fenomenološko iskustvo proble- matično ili, točnije, problematičan je odnos između kategorijalnog zora i osjetilnog zora. Krajnji cilj Schelerove kritike Husserlova fenomenološkog shvaćanja "objektivnog a priori" jest zadobivanje primarne pozicije kategorijalnog zora i njegova sadržaja , etičkog uvida i njegova korelata te, na koncu, fenomenološke etike materijalne vrijednosti. (shrink)

Als zu Beginn des Jahrhunderts der Realismus wieder ernst genommen wurde, gab es viele Philosophen, die sich mit der Ontologie der Wahrheit befaßten. Unabhängig von der Bestimmung der Wahrheit als Korrespondenzbeziehung wollten sie herausfinden, inwieweit zur Erklärung der Wahrheit von Sätzen besondere Entitäten herangezogen werden müssen. Einige dieser Entitäten, so zum Beispiel Bolzanos ‘Sätze an sich’, Freges ‘Gedanken’ oder die ‘propositions’ von Russell und Moore, wurden als Träger der Eigenschaften Wahrheit und Falschheit aufgefaßt. Einige Philosophen jedoch, wie Russell, Wittgenstein im (...) ›Tractatus‹ und Husserl in den ›Logischen Untersuchungen‹, argumentierten, zusätzlich zu den Wahrheitsträgern bzw. an ihrer Stelle müßten Entitäten angenommen werden, auf Grund deren Sätze und/oder ‘Propositionen’ wahr sind. Solchen Entitäten gab man verschiedene Namen, insbesondere ‘fact’, ‘Tatsache’, ‘state of affairs’ und ‘Sachverhalt’. 1 Wir wollen einer Entscheidung über die Angebrachtheit dieser Ausdrücke nicht vorgreifen und daher zunächst eine neutralere Terminologie verwenden: Alle Entitäten, die für diese zweite Rolle in Frage kommen, wollen wir ‘Wahrmacher’ nennen. (shrink)

Husserl’s theory of manifolds was developed for the first time in a very short form in the Prolegomena to his Logical Investigations, §§ 69–70 (pp. 248–53), then repeatedly discussed in Ideas I, §§ 71–2 (pp. 148–53), in Formal and Transcendental Logic, §§ 51–4 (pp. 142–54), and finally in the Crisis, § 9 (pp. 20–60). Husserl never lost sight of it: it was his idée fixe. He discussed this theme over forty years, expressing the same, in principle, ideas on it in (...) different terms and versions. His discussions of it, however, were always cut short and inconclusive, so that he never developed his theory of manifolds in detail. Main claim in this essay is that Husserl’s theory of manifolds is twofold. It is (1) a theory of theories, advanced in the good German tradition of Wissenschaftslehre, launched first by Bernard Bolzano. The latter, in turn, is an offspring of the ancient tradition of mathesis universalis, explored in the modernity by Descartes and Leibniz. Further, (2) the theory of manifolds is also a formal theory of everything. Its objective is to provide a systematic account of how the things in the world (its parts) hang together in wholes of quite different kind. It is to be noted that Husserl explicitly speaks about (1) and only implicitly about (2). In this paper we shall also show that the theory of everything is intrinsically connected with the theory of theories. (shrink)

I discuss Prawitz’s claim that a non-reliabilist answer to the question “What is a proof?” compels us to reject the standard Bolzano-Tarski account of validity, andto account for the meaning of a sentence in broadly verificationist terms. I sketch what I take to be a possible way of resisting Prawitz’s claim---one that concedes the anti-reliabilist assumption from which Prawitz’s argument proceeds.

The aim of this paper is to show that the account of objective truth taken for granted by logicians at least since the publication in 1933 of Tarski’s “The Concept of Truth in Formalized Languages” arose out of a tradition of philosophical thinking initiated by Bolzano and Brentano. The paper shows more specifically that certain investigations of states of affairs and other objectual correlates of judging acts, investigations carried out by Austrian and Polish philosophers around the turn of the (...) century, formed part of the background of views that led to standard current accounts of the objectivity of truth. It thus lends support to speculations on the role of Brentano and his heirs in contemporary logical philosophy advanced by Jan Wolenski in his masterpiece of 1989 on the Logic and philosophy in the Lvov-Warsaw School. (shrink)

In this work Husserl makes the distinction between expressions and indications that Derrida will later plant the bomb of Husserl's own Phenomenology of Internal Time Consciousness underneath it in order to undermine the dream for presence and inaugurate Deconstruction. Logic, as Husserl sees it, is concerned in the first place with meanings (propositions, concepts) and with associated meaning-instantiating acts. Most importantly, it is concerned with that sort of deductively closed collection of meanings which constitutes a scientific theory. For Husserl, as (...) for Bolzano, logic is a theory of science. Only where we have an appropriate unity and organization also on the side of the objects (states of affairs, properties) to which the relevant acts refer, however, will we have a scientific theory, so that the unity which is characteristic of the latter must involve both (1) an interconnection of truths (or of propositional meanings in general), and (2) an interconnection of the things to which these truths (and the associated cognitive acts) are directed. Where formal logic relates in the first place to meaning categories such as proposition, concept, subject and predicate, its sister discipline of formal ontology relates to object categories such as object and property, relation and relatum, manifold, part, whole, state of affairs, existence and so on. Logic in a broader sense therefore seeks to delimit the concepts which belong to the idea of a unity of theory in relation to both meanings and objects, and the truths of logic are all the necessary truths relating to those categories of constituents, on the side of both meanings and objects, from out of which science as such is necessarily constituted (including what we might think of as bridge-categories such as identity and truth which span the division between meanings and objects). The best way to deal with Husserl's theory of formal ontology, therefore, is to explicate both the connections between the formal and material, and those between the ontological and the logical. In introducing his distinction between formal and material ontology, Husserl asserts that the former is descriptive and involves analytic a priori judgements, and that the latter involves synthetic a priori judgements. In its most general sense formal ontology concerns itself with characterizing the simple 'something'. The sphere of material ontology in this sense are the laws of non-independence (2) which delimit the ontological regions. For the genetic interpretation, material ontology precedes formal ontology; for the descriptive interpretation it is the other way round (1913, art. 10). Here emerges 'the fundamental distinction between formal and material ontology': namely, the distinction between analytic a priori and synthetic a priori (Introduction to Formale und transzendentale Logik, 1929). (shrink)

This paper is about the topic of psychologism in the work of Kazimierz Twardowski and my aim is to revisit this important issue in light of recent publications from, and on Twardowski’s works. I will first examine the genesis of psychologism in the young Twardowski’s work; secondly, I will examine Twardowski’s picture theory of meaning and Husserl’s criticism in Logical Investigations; the third part is about Twardowski’s recognition and criticism of his psychologism in his lectures on the psychology of thinking; (...) the fourth and fifth parts provide an overview of Twardowski’s paper “Actions and Products” while the sixth part addresses the psychologism issue in the last part of this paper through the delineation of psychology and the humanities. I shall conclude this study with a brief assessment of Twardowski’s solution to psychologism. (shrink)

Recent discussions of phenomenal consciousness have taken increased interest in the existence and scope of non-sensory types of phenomenology, notably so-called cognitive phenomenology. These discussions have been largely restricted, however, to the question of the existence of such a phenomenology. Little attention has been given to the character of cognitive phenomenology: what in fact is it like to engage in conscious cognitive activity? This paper offers an approach to this question. Focusing on the prototypical cognitive activity of making a judgment (...) that p, it proposes a characterization in terms of a Ramsey sentence comprised of twenty-three phenomenological platitudes about what it is like to make a judgment. (shrink)

As Kevin Mulligan, more than anyone else, has demonstrated, there is a distinction within the philosophy of the German-speaking world between two principal currents: of idealism / transcendentalism, characteristic of Northern Germany; and of realism / objectivism, characteristic of Austria and the South. We explore some of the implications of this distinction with reference to the influence of Austrian (and German) philosophy on philosophical developments in Hungary, focusing on the work of Ákos von Pauler, and especially on Pauler’s reading of (...) Wittgenstein’s Tractatus. (shrink)

In this book, for the first time, authors try to introduce the concept of linguistic variables as a continuum of linguistic terms/elements/words in par or similar to a real continuum. For instance, we have the linguistic variable, say the heights of people, then we place the heights in the linguistic continuum [shortest, tallest] unlike the real continuum (–∞, ∞) where both –∞ or +∞ is only a non-included symbols of the real continuum, but in case of the linguistic continuum we (...) generally include the ends or to be more mathematical say it is a closed interval, where shortest denotes the shortest height of a person, maybe the born infant who is very short from usual and the tallest will denote the tallest one usually very tall; however this linguistic continuum [shortest, tallest] in the real continuum will be the closed interval say [1 foot, 8 feet] or [1, 8] the measurement in terms of feet. So, the real interval is a subinterval with which we have associated the real continuum in terms of qualifying unit feet and inches in this case. (shrink)

The term ‘Continental philosophy’ designates not philosophy on the continent of Europe as a whole, but rather a selective slice of Franco-German philosophy. Through a critical analysis of the arguments advanced by Otto Neurath, the paper addresses the issue of why Austrian philosophers in particular are not counted in the pantheon of Continental philosophers. Austrian philosophy is marked by the predominance of philosophical analysis and of the philosophy of science. The paper concludes that it is not Austria which is the (...) special case when seen against the background of contemporary mainstream philosophy, but rather Germany and France. (shrink)