Selected Bibliography on Bernard Bolzano's Contributions to Logic and Ontology. Third Part: N - Z
STUDIES ON BERNARD BOLZANO'S LOGIC AND ONTOLOGY
- Neeman Ursula. "Analytic and Synthetic Propositions in Kant and Bolzano." Ratio 12 (1970): 1-25.
"Whereas Kant regards the structure of being and knowing as identical, Bolzano interprets the Kantian true synthetic propositions as true propositions, in which the predicate is a characteristic of the subject and not a component of the notion of the subject (characteristic =df. a property of the object, which falls under the concept; component =df. ingredient of the concept). These propositions are analytic in a wider sense, because they render possible an analysis of an object, whereas the logico-analytic propositions render possible only an analysis of their concept. Therefore Bolzano also distinguishes between deductibility (ordo cognoscendi) and ground-consequence relation (ordo essendi) and grounds the latter on the principle of simplicity. A discovery of an objective connection in mathematics is only possible by a strict determination of the basic concepts and by axiomatization, because in opposition to Kant, Bolzano thinks mathematical laws to be discoveries and not creations of the human mind."
- ———. Bernard Bolzanos Lehre Von Anschauung Und Begriff in Ihrer Bedeutung Für Erkenntnistheoretische Und Pädagogische Probleme. München: F. Schöningh, 1972.
- ———. "Der Begriff Der Möglichkeit Bei Bernard Bolzano." Philosophia Naturalis 17 (1978): 70-89.
- ———. "Zeichen in Sprache Und Denken Nach Ockham, Lambert Und Bolzano." Zeitschrift für Semiotik, no. 23 (2001).
"According to B. Bolzano, signs are real objects or processes which are grasped not as something in themselves but in reference to other objects. The meanings of verbal signs are shared by the users of a language as their uniform semantical basis. It is a realm of ideas and sentences, in other words, what is known as the intension of verbal signs. Extension, the reference to extra-mental objects, is possible only on the basis of intensions. These considerations are used to clarify Bolzano's use of the expressions "meaning" and "reference". The emphasis on the intensional aspect leads to epistemological problems which are discussed with reference to the theories of signs suggested by W. of Ockham, J. H. Lambert, and G. W. Leibniz. Central in this discussion is the question whether what is signified by verbal signs is a copy of the extra-mental world of objects or whether the sign's function consists in a reference to the extra-mental world without being similar to it."
- Otte Michael. "The Analytic/Synthetic Distinction in Kant and Bolzano." In Relatively and Philosophically Earnest. Festschrift in Honor of Paul Ernest's 65 Birthday, edited by Sriraman, Bharath and Goodchild, Simon. 39-56. Missoula: Information Age Publishing, 2009.
- Palágyi Melchior. Kant Und Bolzano. Eine Kritische Parallele. Halle: Verlag von Max Niemeyer, 1902.
Italian translation: Kant e Bolzano. Un confronto critico - Edited by Luca Guidetti - Ferrara, Spazio Libri Editori 1993
- Preti Giulio. "I Fondamenti Della Logica Formale Pura Nella "Wissenschaftslehre" Di B. Bolzano E Nelle "Logische Unturschungen" Di E. Husserl." Sophia II-IV (1935): 187-194-361-376.
Reprinted in: Giuli Preti - Saggi filosofici - Vol. I - Firenze, La Nuova Italia 1976 p. 11-31
- Prihonsky Franz. Neuer Anti-Kant Und Atomenlehre Des Seligen Bolzano. Sankt Augustin: Academia Verlag, 2003.
New edtion of two works originally published in 1850 (Neuer Anti-Kant oder Prüfung der Kritik der reinen Vernunft nach den in Bolzano's Wissenschaftslehre niedergelegten Begriffen) and 1857 (Atomenlehre des seligen Bolzano).
- ———. Bolzano Contre Kant. Le Nouvel Anti-Kant. Paris: Vrin, 2006.
Introduit, traduit et annoté par Sandra Lapointe.
- Proust Joëlle. "Bolzano's Analytic Revisited." Monist.An International Quarterly Journal of General Philosophical Inquiry (1981): 214-230.
"This article offers a new interpretation of what Bolzano had in mind with the concept of 'analytic proposition'. In Bolzano's terms, an analytic proposition is a proposition in which there is at least one constituent that can be arbitrarily changed without altering the truth value of the original proposition. The author shows that a proper understanding of this criterion cannot be reached if one ignores the text in which a full account of the extensional properties of the variable constituent is provided by Bolzano. The completed criterion fits more sharply the Bolzanian epistemology, and is free from the inconsistencies inherent to the so-called 'Quinean' interpretation of Bolzano's analytic."
- ———. Questions of Form. Logic and the Analytic Proposition from Kant to Carnap. Minneapolis: University of Minnesota Press, 1989.
Translated by Anastasios Albert Brenner from the original French: Questions de forme. Logique et proposition analytique de Kant à Carnap - Paris, Fayard, 1986.
See the Third Chapter: Bolzano's Renovation of Analiticity, pp. 49-108.
- ———. "Bolzano's Theory of Representation." Revue d'Histoire des Sciences 52, no. 3-4 (1999): 363-383.
"Bolzano's theory of representation is one of the most radically intensionalist approaches to representation. It is based on the following three claims A. A representation is essentially independent of thought and of linguistic expression ; B. A representation is structured ; C. Such a structure is independent of the objects represented. These claims are both tools and constraints relative to Bolzano's substantive goals. Bolzano ultimately aimed to carry out a deep transformation of mathematical and scientific practice, thanks to a more accurate conception of logic and of the role of logic in scientific exposition. I examine tome of the consequences of Bolzano's claims in regard to his conception of mathematical treatises."
- Raspa Venanzio. "Su Ciò Che Non Esiste. Da Bolzano a Meinong: Un Excursus Nella Filosofia Austriaca." Studi Urbinati B 67 (1995): 115-201.
- Roberts Mark. "The Bearer of Truth and Falsity." Southwest Philosophy Review 10 (1994): 59-67.
"Until Bolzano nearly all philosophers believed that truth and falsity are predicated of judgments of beliefs. Bolzano and other philosophers after him argue that propositions are the bearers of truth and falsity and that propositions have a timeless ideal existence: a position which seems to discredit completely their view that propositions are the bearers of truth and falsity. Yet, several arguments can be offered which show that propositions are the bearers of truth and falsity without introducing as a premise the timeless existence of propositions."
- Rojszczak Artur. From the Act of Judging to the Sentence: The Problem of Truth Bearers from Bolzano to Tarski. Dordrecht: Springer, 2005.
Edited by Jan Wolenski
- Rollinger Robin D. "Austrian Theories of Judgment: Bolzano, Brentano, Meinong, and Husserl." In Phenomenology and Analysis. Essays on Central European Philosophy, edited by Chrudzimski, Arkadiusz and Huemer, Wolfgang. 257-284. Frankfurt: Ontos Verlag, 2004.
Reprinted in: R. D. Rollinger, Austrian Phenomenology. Brentano, Husserl, Meinong, and Others on Mind and Object, Frankfurt, Ontos Verlag, 2009, pp. 233-262.
- Rootselaar Bob van. "Axiomatics in Bolzanos Logico-Mathematical Research." In Bolzano's Wissenschaftslehre 1837-1987. International Workshop. 221-230. Florence: Leo S. Olschki, 1992.
- Runggaldier Edmund. "Die "Einfachheit" Der Substanz Bei Bolzano." In Philosophie Im Geiste Bolzanos, edited by Hieke, Alexander and Neumaier, Otto. 69-86. Sankt Augustin: Academia Verlag, 2003.
- Rusnock Paul. "Bolzano and the Traditions of Analysis." Grazer Philosophische Studien 53 (1997): 61-85.
"Russell, in his History of Western Philosophy, wrote that modern analytical philosophy had its origins in the construction of modern functional analysis by Weierstrass and others. As it turns out, Bolzano, in the first four decades of the nineteenth century, had already made important contributions 'to the creation of "Weierstrassian" analysis, some of which were well known to Weierstrass and his circle. In addition, his mathematical research was guided by a methodology which articulated many of the central principles of modern philosophical analysis. That Russell was able to discover philosophical content within mathematical analysis was thus not surprising, for it had been carefully put there in the first place. Bolzano can and should, accordingly, be viewed as a founder of modern analytical philosophy, and not necessarily as an uninfluential one. This paper considers his work in mathematical and philosophical analysis against some of the relevant historical background."
- ———. "Philosophy of Mathematics: Bolzano's Responses to Kant and Lagrange." Revue d'Histoire des Sciences 52, no. 3-4 (1999): 399-428.
- ———. Bolzano's Philosophy and the Emergence of Modern Mathematics. Studien in Österreichischen Philosophie. Amsterdam: Rodopi, 2000.
- ———. "Qu'est-Ce Que La Représentation? Bolzano Et La Philosophie Autrichienne." Philosophiques 30 (2003): 67-81.
"Largely ignored in Germany during the nineteenth century, Bolzano was certainly better known in Austria, in particular among Brentano's students, who enthusiastically studied his Theory of Science. In this respect it makes sense to speak of Bolzano as belonging to a tradition of Austrian philosophy. Yet an examination of the reception of Bolzano's ideas among Brentano's students indicates that he was not always well understood. This article discusses a particular case, Twardowski's reaction to Bolzano's theory of representation."
- ———. "La Théorie Des Intuitions Chez Bolzano." In Aux Origines De La Phénoménologie. Husserl Et Le Contexte Des Recherches Logiques, edited by Fisette, Denis and Lapointe, Sandra. 111-123. Paris: Vrin, 2003.
- Rusnock Paul, and George Rolf. "Bolzano as Logician." In The Rise of Modern Logic: From Leibniz to Frege, edited by Gabbay, Dov and Woods, Jean. 177-205. Amsterdam: North-Holland, 2004.
Handbook of the History of Logic. Vol. 3.
"Bernard Bolzano (1781-1848) stands out with Frege as one of the great logicians of the nineteenth century. His approach to logic, set out in the Theory of Science [WL] of 1837, marks a fundamental reorientation of the subject on many fronts,
one which is as radical as any in the history of the field. In sharp contrast to many of his contemporaries, Bolzano insisted upon a rigorous separation of logic from psychology. It should be possible, he thought, to characterize propositions, ideas, inferences, and the axiomatic organization of sciences without reference to a thinking subject. Consistently pursuing this approach to logic and methodology, Bolzano developed important accounts of formal semantics and formal axiomatics.
A talented mathematician, Bolzano developed his logic in conjunction with his mathematical research. Among the first to work on the foundations of mathematics in the modern sense of the term, he made a number of key discoveries in analysis, topology, and set theory, and had a significant influence on the development of mathematics in the nineteenth century. In logic, Bolzano is best remembered for his variation logic (section 4.2 below), a surprisingly subtle and rigorous development of formal semantics. In this article, we discuss Bolzano's logic along with some of his work in the foundations of mathematics which has some bearing on logic." p. 177
- Rusnock Paul, and Burke Mark. "Etchemendy and Bolzano on Logical Consequence." History and Philosophy of Logic 31 (2010): 3-29.
"In a series of publications beginning in the 1980s, John Etchemendy has argued that the standard semantical account of logical consequence, due in its essentials to Alfred Tarski, is fundamentally mistaken. He argues that, while Tarski's definition requires us to classify the terms of a language as logical or non-logical, no such division is guaranteed to deliver the correct extension of our pre-theoretical or intuitive consequence relation. In addition, and perhaps more importantly, Tarski's account is claimed to be incapable of explaining an essential modal/epistemological feature of consequence, namely, its necessity and apriority.
Bernard Bolzano (1781-1848) is widely recognized as having anticipated Tarski's definition in his Wissenschaftslehre (or Theory of Science) of 1837. Because of the similarities between his account and Tarski's, Etchemendy's arguments have also been extended to cover Bolzano. The purpose of this article is to consider Bolzano's theory in the light of these criticisms. We argue that, due to important differences between Bolzano's and Tarski's theories, Etchemendy's objections do not apply immediately to Bolzano's account of consequence. Moreover, Bolzano's writings contain the elements of a detailed philosophical response to Etchemendy."
- Rusnock Paul. "Remarks on Bolzano's Conception of Necessary Truth." British Journal for the History of Philosophy 20 (2012): 817-837.
"This essay presents a new interpretation of Bolzano's account of necessary truth as set out in §182 of the Theory of Science. According to this interpretation, Bolzano's conception is closely related to that of Leibniz, with some important differences. In the first place, Bolzano's conception of necessary truth embraces not only what Leibniz called metaphysical or brute necessities but also moral necessities (truths grounded in God's choice of the best among all metaphysical possibilities). Second, in marked contrast to Leibniz, Bolzano maintains that there is still plenty of room for contingency even on this broader conception of necessity."
- Schaar Maria van der. "Bolzano on Judgement and Error." In The Logica Yearbook 2006, edited by Tomala, O and Honzi, R., 211-221. Prague: Filosofia, 2007.
- Schmit Roger. "Über Bolzanos Begriff Der Auslegung." Grazer Philosophische Studien 47 (1994): 1-29.
- Schmutz Jacob. "Quand Le Langage a-T-Il Cessé D'être Mental? Remarques Sur Les Sources Scolastiques De Bolzano." In Le Langage Mental Du Moyen Âge À L'âge Classique, edited by Biard, Joël. 307-337. Paris: Vrin, 2009.
- Schnieder Benjamin. Substanz Und Adhärenz. Bolzanos Ontologie Des Wirklichen. Sankt Augustin: Academia Verlag, 2002.
- ———. "Bolzano Sur La Structure Des Propositions Et Le Rôle Sémantique Des Propriétés." Philosophiques 30 (2003): 83-103.
Bernard Bolzano developed a highly elaborate and comprising account of propositions as structured entities composed of concepts. One of his main contentions was that all propositions share a common structure: "A - has - (the property) b". The main part of my paper is a discussion of the role which properties play for this thesis and thus in Bolzano's semantics.
Where properties feature as semantic values in standard semantic theories they are (at least in general) conceived of as shareable entities, in other words, as universals. I show that (contrary to a commonly agreed doctrine in the literature) it is particularised properties which Bolzano thought to be the entities standing under the predicate-ideas of propositions. With this idea, a rather
uncommon semantic arises : a proposition of the form [A - has - (the property) b] will be true iff one of the particularised properties standing under the predicate-idea [b] inheres in the subject of the proposition, i.e. in the entity denoted by the subject-idea."
- ———. "Mere Possibilities: A Bolzanian Approach to Non-Actual Objects." Journal of the History of Philosophy 45 (2007): 525-550.
"The paper is a detailed reconstruction of Bernard Bolzano's account of merely possible objects, which is a part of his ontology that has been widely ignored in the literature so far. According to Bolzano, there are some objects which are merely possible. While they are neither denizens of space and time nor members of the causal order, they could have been so. Thus, on Bolzano's view there are, for example, merely possible persons, i.e., objects which are neither actual nor persons but which could have been both. In course of the development of Bolzano's views, they are contrasted with the better known theory of his compatriot Alexius Meinong, and it is shown that they have a modern counterpart in the accounts of merely possible objects that were developed by Bernard Linsky and Ed Zalta, and by Timothy Williamson."
- ———. "Bolzanos Zwei Substanzbegriffe. Anmerkungen Zu Krauses Bolzano-Interpretation." Zeitschrift für Philosophische Forschung 62 (2008): 97-108.
- ———. "Bolzanos Erklärung Des Zeitbegriffs." Archiv für Geschichte der Philosophie 91 (2009): 42-69.
"Bernard Bolzano repeatedly tried to provide an analysis of the concept of time. This paper develops a detailed reconstruction of Bolzano's analysis. Thereby it clarifies the logical form of the analysis and thus discovers its principal problem: While the analysis may well incorporate an important insight on our conception of time, it cannot succeed as an analysis."
- Scholz Heinrich. "Die Wissenschaftslehre Bolzano's. Eine Jahrhundert-Betrachtung." Abhandlungen der Fries'schen Schule 6 (1937): 399-472.
Reprinted in: H. Scholz, Mathesis universalis. Abhandlungen zur Philosophie als strenger Wissenschaft, (eds. H. Hermes, F. Kambartel & J. Ritter), Basel, Benno Schwabe, 1961, pp. 219-267.
- Schubring Gert. "Bernard Bolzano. Not as Unknown to His Contemporaries as Is Commonly Believed?". Historia Mathematica (1993): 45-53.
- Schuffenhauer Werner. Bernard Bolzano 1781-1848. Studien Und Quellen. Berlin: Akademie Verlag, 1981.
- Sebestik Jan. "Bolzano Et Brentano. Deux Sources Autrichiennes Du Cercle De Vienne." Fundamenta Scientiae 5 (1984): 219-235.
- ———. "Premiers Paradoxes Bolzaniens De L'infini Avec Un Texte Inèdit De B. Bolzano." Archives de Philosophie 50 (1987): 403-411.
"This paper presents an unpublished note by Bolzano, which surveys the various difficulties linked to the notion of infinity. This note, written in 1813-1814, is an excerpt from his mathematical diaries, "Miscellanea mathematica". Raising the question whether one may deduce the equivalence of two sets from the existence of a bijective correlation between them ends in a blind alley: from every possible answer, absurd consequences follow."
- ———. "The Archaeology of the Tractatus: Bolzano and Wittgenstein." In Wittgenstein, Eine Neubewertung. Akten Des 14. Intemationalen Wittgenstein-Symposiums, edited by Haller, Rudolf and Brandl, Johannes L., 112-118. Wien: Hölder-Pichler-Tempsky, 1990.
- ———. Logique Et Sémantique Chez Bernard Bolzano. Paris: Vrin, 1992.
"The work of J. Šebestík contains besides various technical components a chronology, primary and secondary bibliographies [pp. 481-504], a German-French terminological dictionary, a notation list and indexes, a foreword, an introduction and a conclusion: four principal parts subdivided into fourteen chapters in all. Part I (pp. 33 - 112), primarily devoted to Bolzano's mathematical papers published from 1804 till 1817, analyses his geometrical ideas, among others his views on the theory of parallels and topology, and topics connected with the arithmetization of analysis. Part II (pp. 115 - 293) deals in four chapters with Bolzano's logic and philosophy of logic as elaborated in the first two volumes of his Wissenschaftslehre; the fifth chapter of this part discusses very briefly Bolzano's philosophy of science proper expounded extensively in the fourth volume of the Wissenschaftlehre. Part III (pp. 297 - 431) concerned with Bolzano's mathematical system, presents his doctrines of sets, magnitudes and numbers, the construction of real numbers and the theory of real functions, together with some related topics of his Grössenlehre. Part IV (pp. 435 - 474) handles the subject-matter of infinity systematically developed in Bolzano's posthumously published Paradoxien des Unendlichen (1851)." Karel Berka
- ———. "The Construction of Bolzano's Logical System." In Bolzano's Wissenschaftslehre 1837-1987. International Workshop. 163-177. Firenze: Leo S. Olschki, 1992.
"Several reconstructions of Bolzano's logical system have been proposed until now, some of them at the present workshop. They exploit systematically different aspects of Bolzano's logic and interpret it in terms of different XXth century systems. Such an approach has its own rights, as the full force of Bolzano's logic can be measured only by the standards of our contemporary logic. This is precisely the mark of great authors: each important discovery in their field brings to the light some hitherto unnoticed aspects of their work. That such reinterpretations are possible in the case of Bolzano, that his system can be represented in a quite different conceptual frame and translated into modern symbolic notation simply shows how rich and far reaching are his theories. Another argument favours this approach: a XXth century logician can read Bolzano and other logicians of the past only against the background of modern theories. It is in this way that the body of scientific knowledge is continuously being transmitted: by adapting and translating incessantly old theories into the present language. Moreover, the very meaning of past theories can often be understood only in the light of our systems. Already Husserl noticed that he would not have been able to grasp the significance of Bolzano's logic if he had not previously studied the most advanced contemporary logical theories - which in his case mainly meant the logic of Schroder!
Nevertheless, this modernizing approach does not yield full justice to Bolzano. Even if some of his doctrines are definitively obsolete, they have their function in the construction of his system. Like his mathematics, his philosophy and his theology, Bolzano's logic was conceived in a specific historical context and its complete understanding requires a close attention to the logical and philosophical theories of his time. This is why a complementary approach seems necessary, namely a historical analysis which would trace the links between his system and the logical doctrines of his contemporaries as well as with great logical theories of the past.
My intention is to explain the formation and the structure of his logical system whose core is propositional logic. Bolzano's system of extensional relations between propositions represents one of the decisive innovations in the history of logic. It has no historical antecedents. It is nevertheless connected with logical theories of the late XVIIIth and early XIXth century and my paper tries to elucidate the genesis of Bolzano's system against this historical background. This approach will not only show the originality of Bolzano's achievement in full light, but also give a perhaps unexpected insight into the structure of his logical system.
In my reconstruction, I intend to remain within Bolzano's logic, using only conceptual tools which he himself has designed. Therefore, I shall neither attempt to translate his definitions into some XXth century notation, nor confront his logic with our systems. One of the advantages of this approach is to give a presentation of Bolzano's logic which is as simple as possible and has no recourse either to symbolic language (except for elementary set-theoretical notational devices) or to sophisticated semantic framework. Those who have tried to explain Bolzano's logical theories to non-specialists or even to students of modern logic may test the advantage of such an approach." (pp.163-164).
- ———. "Twardowski Entre Bolzano Et Husserl: La Théorie De La Représentation." Cahiers de la Philosophie Ancienne et du Langage de l'Université de Paris XII 1 (1994): 61-85.
- ———. "Etudes Bolzaniennes." Revue de Métaphysique et de Morale, no. 3 (1996): 437-448.
- ———. "Bolzano, Exner and the Origins of Analytical Philosophy." Grazer Philosophische Studien 53 (1997): 33-59.
"Analytical philosophy begins with the first mathematical and philosophical works of Bolzano published between 1804 and 1817. There, Bolzano set out a project for the global reform of mathematics by means of the axiomatic method. Having completed the Wissenschaftslehre, Bolzano wrote a summary of his logic for the Grossenlehre, which he sent to Exner in 1833. The correspondence between Bolzano and Exner covered some of the main subjects treated by analytical philosophy: the status of abstract objects (propositions and objective ideas), intuitions, objectless ideas, the concept of object and many others. While Bolzano argued in favor of abstract entities independent of mind and of language, Exner considered them as abstractions obtained from the subjective judgments and representations. During the XIXth century, Bolzano's philosophy spread over Bohemia and Austria through manuscripts and through the first edition of Zimmermann's textbook of philosophy. The most important Brenta-n ians, Kerry, Twardowski, Meinong and Husserl, discussed his doctrines which may also have influenced Wittgenstein and the Polish school."
- ———. "Forme, Variation Et Déductibilité Dans La Logique De Bolzano." Revue d'Histoire des Sciences 52 (1999): 479-505.
"Bolzano's main innovations in logic result from his introduction and systematic use of the method of variation, which corresponds to the substitutional method in contemporary logic. The application of this method yields the fundamental logical concepts of validity, analyticity and deducibility. I also put forward a tentative list of Bolzano's logical concepts. I compare deducibility with Tarski's notion of logical consequence. This comparison allows specific features of Bolzano's logic to be brought out -- above all, his ontology of logic. Although Bolzano also worked with propositional forms, the true objects of his logic were propositions-in-themselves and ideas-in-themselves."
- ———. "Bolzanos Paradoxien Des Unendlichen." In Bernard Bolzanos Geistige Erbe Für Das 21. Jahrhundert, edited by Morscher, Edgar. 231-256. Sankt Augustin: Academia Verlag, 1999.
- ———. "La Dispute De Bolzano Avec Kant. Fragment D'un Dialogue Sur La Connaissance Mathématique." Philosophiques 30 (2003): 47-66.
"In this dialogue, two opposed conceptions, which dominate the philosophy of mathematics till today, are confronted. Kant's account of mathematics is based upon the activity of constructing mathematical objects in pure intuition (time and space). In yielding objects for mathematics, our intuition contributes in an essential way to the formulation of mathematical truths. Against Kant, Bolzano argues that intuition has place neither in arithmetic nor in geometry and that mathematical existence consists in the possibility of the defined objects, i.e., in non-contradiction. For Bolzano, the central idea of mathematics is that of rigorous proof."
- ———. "Husserl Reader of Bolzano." In Husserl's Logical Investigations Reconsidered, edited by Fisette, Denis. Dordrecht: Kluwer, 2003.
"The incredible soundness of Husserl's judgment in the matter of logic is unique among his contemporaries - only Frege's insight is on par with it, if not superior. This is due to the lesson of Bolzano whose logic is the truth itself. Husserl adapted his logical system so that it became the logical basis of phenomenology. He adopted Bolzano's main ideas: the extension of logic to the theory of science, the theory of ideal meanings, the distinction between mental act, linguistic expression, meaning and denoted object, the concept of analyticity. Independently of Bolzano and consonant with later mathematical theories, Husserl developed his formal analytics along two lines, apophantic and formal ontology.
Bolzano, however, had articulated the domain of conceptual truths in the same manner: he constructed his logical system as a theory of meaning and his mathematics as a theory of object in general or Etwas überhaupt. Both set theory and mereology have their origin here. By his theory of science, Bolzano gave a new impetus to philosophy and logic. For the first time in modern thought, such questions as the nature of logical objects, the problems of meaning and reference, the relation between logic and language became central issues of philosophy."
- Sedmak Clemens. "Die Bedeutung "Wichtiger Sätze" Für Die Philosophie." In Philosophie Im Geiste Bolzanos, edited by Hieke, Alexander and Neumaier, Otto. 127-142. Sankt Augustin: Academia Verlag, 2003.
- Segura Luis Felipe. La Prehistoria Del Logicismo. México: Plaza y Valdés, 2001.
- Seron Denis. "La Controverse Sur La Négation De Bolzano À Windelband." Philosophie 90 (2006): 58-78.
"L'auteur s'attache au problème de la négation, qui a traversé la philosophie germanique du XIXème et de la première moitié du XXème siècle, et se définit par un ensemble de questions fondamentales: l'affirmation et la négation sont-elles co-originaires, ou l'une se laisse-t-elle dériver de l'autre? la négation est-elle assimilable à l'acte de nier ou appartient-elle au contenu sémantique idéal visé par cet acte? si la négation est un acte de rejet, que rejette-t-elle? s'identifie-t-elle à une diairesis, et implique-t-elle une synthesis entre contenus de représentation? L'auteur retrace l'histoire de ce problème qui, ancrée dans la Logique de Lotze et la Doctrine de la science de Bolzano, conduit à Husserl et Frege."
- Siebel Mark. Der Begriff Der Ableitbarkeit Bei Bolzano. Sankt Augustin: Academia Verlag, 1996.
"In his Wissenschaftslehre (1837, § 155), Bolzano defined a consequence relation, titled "Ableitbarkeit": a proposition P is derivable from a proposition Q with respect to certain variable ideas iff varying these ideas leads to a true variant of P, whenever the corresponding variant of Q is true. In the first part, I introduce the relevant fundamental concepts, the method of variation and the characteristics of derivability. In the second part, I examine how far Bolzano anticipated Russell's propositional functions, Tarski's definition of logical consequence and relevance logic. The result is that there are many more differences than unusually claimed."
- ———. "Variation, Derivability and Necessity." Grazer Philosophische Studien 53 (1997): 117-137.
"In Bolzano's view, a proposition is necessarily true iff it is derivable from true propositions that include no intuition (Anschauung). This analysis is historically important because it displays close similarities to Quine's and Kripke's ideas. Its systematic significance, however, is reduced by the fact that derivability is defined with recourse to the method of variation, which we are allowed to apply even to propositions containing none of the respective variables. This liberality leads to the result that, according to Bolzano's analysis, every truth is necessarily true. Even by introducing his condition of relevance (shared variables), Bolzano cannot avoid that some propositions come out as necessarily true which are merely contingently true."
- ———. "Bolzanos Ableitbarkeit Und Tarskis Logische Folgerung." In Analyomen 2. Proceedings of the Second Conference "Perspectives in Analytical Philosophy". 148-156. Berlin: Walter de Gruyter, 1997.
Vol. I: Logic, Epistemology, Philosophy of science.
"It is a commonplace that Bolzano ("Wissenschaftslehre", 1837, § 155) anticipated Tarski's definition of logical consequence. This is true only in a limited sense: one can extract a definition from Bolzano's "Wissenschaftslehre" resembling Tarski's insofar as the corresponding relation is neither symmetrical nor asymmetrical, but transitive and defined by recourse to variation of nonlogical elements. But there remain important differences concerning inconsistent premises and logically true conclusions. Moreover, unlike Tarski, Bolzano treats synonymous expressions alike, with the result that "All "drakes" are birds" is a logical consequence of "All Male Ducks" are ducks" and "All ducks are birds"."
- ———. "Bolzano Über Erkenntnistheorie." In Bernard Bolzanos Geistige Erbe Für Das 21. Jahrhundert, edited by Morscher, Edgar. 59-95. Sankt Augustin: Academia Verlag, 1999.
- ———. "Bolzano Über Ableitbakeit." In Bernard Bolzanos Geistige Erbe Für Das 21. Jahrhundert, edited by Morscher, Edgar. 147-178. Sankt Augustin: Academia Verlag, 1999.
"The book before us is a sympathetic treatment of Bolzanofs concept of consequence and much of his logic. It is historically sensitive and reflects the more relaxed approach to alternative logic systems of the last few decades.
Siebel begins by exploring Bolzanofs well-known claim that logical relations hold between abstract entities, i.e. propositions and representations "in themselves" (p. 15-45). The resolute anti-psychologism implied here has long been recognized and acclaimed: according to Bolzano, pure logic is not concerned with judgments, mental manifestations, but with their contents. Less appreciated is the equally important point that the objects of logical inquiry, the relata of logical relations, are not linguistic entities. For example, synonymous expressions, like 'male goose' and 'gander', stand for the same abstract representation.
In a logic so conceived, problems of synonymy cannot be addressed. As Siebel points out, in Bolzanofs logic of variation (of which more presently) abstract representations are varied, not their linguistic expressions (p. 86)." (from the Review by Rolf George, Logical Analysis and History of Philosophy, 2, 1999, pp. 265-270).
- ———. "Bolzano's Concept of Consequence." Monist.An International Quarterly Journal of General Philosophical Inquiry 85 (2002): 580-599.
"In the second volume of his Wissenschaftslehre (2) from 1837, the Bohemian philosopher, theologian, and mathematician Bernard Bolzano (1781-1848) introduced his concept of consequence, named derivability (Ableitbarkeit), together with a variety of theorems and further considerations. Derivability is an implication relation between sentences in themselves (Sätze an sich), which are not meant to be linguistic symbols but the contents of declarative sentences as well as of certain mental episodes. When Schmidt utters the sentence 'Schnee ist weiss', and Jones judges that snow is white, the sentence in itself expressed by Schmidt is the same as the one to which Jones agrees in thought. This sentence in itself is an abstract entity: in some sense, it exists; but it is unreal insofar as it lacks a position in space and time, does not stand in causal relationships, and is independent
of the existence of thinking beings and languages.(3)"
(*) On the whole, this contribution is a summary of my book Der Begriff der Ableitbarkeit bei Bolzano (Siebel 1996).
(2) I refer to it by 'WL' plus number of volume, section, and page. It is partly translated by Rolf George: Theory of Science, Oxford 1972; but here translations are mine.
(3) Cf. WL I, § 19, pp. 77f.; § 22, p. 90; § 25, p. 112; § 28, p. 121; WL II, § 122, 4.
- ———. "La Notion Bolzanienne De Déductibilité." Philosophiques 30 (2003): 171-189.
"The article: (i) presents the concept of deducibility which Bolzano introduced in his Wissenschaftslehre, (ii) points out some of the characteristic features in virtue of which it differs from many modern conceptions of consequence, and (iii) examines the claims that it displays a strong similarity to Tarski's account and relevance."
- ———. "Bolzanos Urteilslehre." Archiv für Geschichte der Philosophie 86 (2004): 56-87.
"The article introduces Bolzano's theory of judgment, that is, his notions of a judgment, its content and its degree of confidence, the differentiation between mediate and immediate judgments and his account of inferences as judgments caused by judgments. A larger part is devoted to a passage in which Bolzano seems to claim that all of our inferences are valid. It is argued that what he says there is correct and does not rule out fallacies."
- Siitonen Arto. "Zu Bolzanos Kritik Der Kantischen Antinomien." Kriterion 21 (2007): 84-97.
- Simons Peter. "Bolzano, Tarski, and the Limits of Logic." Philosophia Naturalis (1987): 378-405.
Reprinted in: Peter Simons,Philosophy and logic in Central Europe from Bolzano to Tarski. Selected essays, Dordrecht, Kluwer 1992, pp. 13-40.
"Both Bolzano and Tarski doubted whether logic has a sharp boundary. This paper uses Bolzano's procedure of concept variation, together with Tarski's suggestion that those objects are logical which are invariant under all permutations of the domain, to define what it is to be a logical constant in a typed extensional language, and provide an answer to their doubts."
- ———. "Bolzano on Collections." Grazer Philosophische Studien 53 (1997): 87-108.
"Bolzano's theory of Collections (Inbegriffe) has usually been taken as a rudimentary set theory. More recently, Frank Krickel has claimed it is a mereology. I find both interpretations wanting. Bolzano's theory is, as I show, extremely broad in scope; it is in fact a general theory of collective entities, including the concrete wholes of mereology, classes-as-many, and many empirical collections. By extending Bolzano's ideas to embrace the three factors of kind, components and mode of combination, one may develop a coherent general account of collections. But it is most difficult to take Bolzano's view to fit modern set theory. So while Krickel's positive thesis is rejected, his negative thesis is confirmed."
- ———. "Bolzano, Brentano and Meinong: Three Austrian Realists." In German Philosophy since Kant, edited by O'Hear, Anthony. 109-136. Cambridge: Cambridge University Press, 1999.
"Bolzano's work will in due course be wholly accessible in print and should present relatively few problems of interpretation. I foresee a steadily growing reputation, but whether he comes to his just recognition will depend on attracting sufficiently many interested and talented commentators. The most promising centre of Bolzano studies is currently Hamburg, where a number of young enthusiasts have gathered around Wolfgang Künne.
Of the three philosophers I have mentioned, Bolzano is without doubt the most considerable. Meinong's theories are in the end unacceptably extreme and Brentano's work is often unclear in its implications, though both say things which are of much value to present-day discussions. On the other hand, whether one agrees with his semantic Platonism or not, Bolzano's views are up to the highest standards of contemporary discussion and in their clarity above much of it. His correspondence with Ferdinand Exner has been called the first text of modern analytical philosophy. Most work has to date concentrated on his logic and semantics, but his ethics, political philosophy, philosophy of religion and philosophy of mathematics all deserve greater exposure. The Complete Edition will serve as a definitive textual basis, but it is very expensive, and we badly need cheap study texts in English and German to complement it, and a good introduction to Bolzano in English. We also need to revise our histories of nineteenth-century philosophy to take adequate account of its greatest representative." p. 126
- ———. "Bolzano Über Wahrheit." In Bernard Bolzanos Geistige Erbe Für Das 21. Jahrhundert, edited by Morscher, Edgar. 13-28. Sankt Augustin: Academia Verlag, 1999.
- ———. "Bolzano Sur Les Nombres." Philosophiques 30 (2003): 127-135.
"In this article, the author exposes Bolzano's theory of numbers. He shows, on the basis of a comparison with Frege, that Bolzano's conception not only meets all the requisites of such a theory but also exhibits original features, such as for instance the fact that it is grounded in a theory of "collections" (Inbegriffe), which impart it with undeniable philosophical interest. After indicating one problem relating to the Bolzanian notion of a Reihe, the author presents Bolzano's conception of natural numbers, reconstructs his theory of abstract numbers and expounds the connection between the latter and their application to concrete sets of things."
- Sinaceur Hourya. "Bolzano Est-Il Le Précurseur De Frege?". Archiv für Geschichte der Philosophie 57 (1975): 286-303.
- ———. "Réalisme Mathématique, Réalisme Logique Chez Bolzano." Revue d'Histoire des Sciences 52, no. 3-4 (1999): 457-478.
"The majority of Bolzano's scholars present his theory of propositions and representations in themselves -- a theory of objective sense -- as a paradigm example of his philosophical realism. Goal of this article is to show the difficulties encountered by too monolithic an interpretation of this realism. Bolzano's logical theory is in fact more nuanced than is generally appreciated. Surely, the propositions in themselves constitute an universe of objective significations with their own reality. But the propositions in themselves are not, strictly speaking, logical objects; they are matter, not object, of thought. As for Bolzano's mathematical realism, it is affected by a certain empirism, which is evident especially in his account of the natural numbers."
- Smart Harold R. "Bolzano's Logic." Philosophical Review 53 (1944): 513-533.
- Spalt Detlef D. "Bolzano's Zahlbegriffe. Bislang Ubersehene Marksteine Feudal-Absolutischer Mathematik." In Bolzano's Wissenschaftslehre 1837-1987. International Workshop. 27-54. Firenze: Leo S. Olschki, 1992.
- Stachel Peter. "Die Bedeutung Von Bolzanos Wissenschaftslehre Für Die Österreichische Philosophiegeschichte. Ein Baustein Zu Einer Geschichte Der Pluralistischen Tradition Österreichischer Philosophie." In Bolzano Und Die Österreichische Geistesgeschichte, edited by Ganthaler, Heinrich von and Neumaier, Otto. Sankt Augustin: Academia Verlag, 1997.
- ———. "Der Logische Realismus Bernard Bolzanos." In Geschichte Der Österreichischen Humanwissenschaften. Vol 6.1: Philosophie Und Religion: Erleben, Wissen, Erkennen, edited by Acham, Karl. 53-63. Wien: Passagen Verlag, 2004.
- Stelzner Werner. "Compatibility and Relevance: Bolzano and Orlov." Logic and Logical Philosophy 10 (2002): 137-171.
Ivan Orlov (1886 - not later 1936) is the author of "The Logic of Compatibility of Propositions", Matematicheskii Sbornik 35, 1928, pp. 263-86 (in Russian), "the first precisely elaborated modern system of relevance logic" p. 137.
"In Bernard Bolzano Orlov had a great predecessor in the attempt of deriving the concept of logical consequence, and indeed of relevant consequence, from the concept of compatibility of sentences. It is appropriate, therefore, to turn to Bolzano in order to check out parallels and divergences in the treatment and role of the compatibility of sentences in Bolzano's and Orlov's logical projects." p. 142.
- Strasser Kurt, ed. Die Bedeutung Bernard Bolzanos Für Die Gegenwart. Akten Des Internationalen Symposiums 30. Oktober-1. November 2001 in Prag. Praha: Filosofia, 2003.
- Sundholm Göran. "Ontologic Versus Epistemologic: Some Strands in the Development of Logic 1837-1957." In Logic and Philosophy of Science in Uppsala, edited by Prawitz, dag and Westerstähl, Dag. 373-384. Dodrecht: Kluwer, 1994.
- ———. "Maccoll on Judgement and Inference." Nordic Journal of Philosophical Logic 3, no. 1 (1998): 119-132.
- ———. "When, and Why, Did Frege Read Bolzano?". In Logica Yearbook 1999. 164-174. Praga: Filosofia Publishers, 1999.
- ———. "A Century of Inference: 1837-1936." In In the Scope of Logic, Methodology and Philosophy of Science. Vol. Ii, edited by Gardenfors, Peter, Wolenski, Jan and Kijania-Placek, Katarzyna. 565-580. Dordrecht: Kluwer, 2002.
- ———. "A Century of Judgement and Inference: 1837-1936. Some Strands in the Development of Logic." In The Development of Modern Logic, edited by Haaparanta, Leila. 263-318. New York: Oxford University Press, 2009.
- Süssbauer Alfons. "Propositionen Und Sachverhalte in Der Österreichischen Philosophie Von Bolzano Bis Popper." Philosophia Naturalis 24 (1987): 476-498.
"On the basis of a conceptual framework the theories on propositions and/or Sachverhalte of Bolzano, Husserl, Meinong, Wittgenstein, and Popper are discussed. But to commit oneself to propositions and/or Sachverhalte is not the whole show. So the attention is directed to the examination of different strategies of justifying the ontological commitment to propositions and/or Sachverhalte. As a result, normative and pragmatic aspects become important as to the problem of propositions and/or Sachverhalte. Finally some rudimentary requirements for a future theory of propositions and/or Sachverhalte are established."
- Tatzel Armin. "Bolzano's Theory of Ground and Consequence." Notre Dame Journal of Formal Logic 43 (2002): 1-25.
"The aim of the paper is to present and evaluate Bolzano's theory of grounding, that is, his theory of the concept expressed and the relation brought into play by 'because'. In the first part of the paper (Sections 1-4) the concept of grounding is distinguished from and related to three other concepts: the concept of an epistemic reason}, the concept of causality, and the concept of deducibility (i.e., logical consequence). In its second part (Sections 5-7) Bolzano's positive account of grounding is reconstructed in axiomatic form and critically discussed."
- ———. "La Théorie Bolzanienne Du Fondement Et De La Conséquence." Philosophiques 30 (2003): 191-217.
"The aim of the paper is to present and evaluate Bernard Bolzano's theory of grounding, i.e., his theory of the concept expressed and the relation brought into play by 'because'. In the first part the concept of grounding is distinguished from and related to three other concepts: the concept of an epistemic reason, the concept of causality and the concept of deducibility (i.e., logical consequence). In its second part Bolzano's positive account of grounding is reconstructed in axiomatic form and critically discussed."
- Textor Mark. Bolzanos Propositionalismus. Quellen Und Studien Zur Philosophie. Berlin: De Gruyter, 1996.
- ———. "Bolzano's Sententialism." Grazer Philosophische Studien 53 (1997): 181-202.
"Bolzano holds that every sentence can be paraphrased into a sentence of the form "A has b". Bolzano's arguments for this claim are reconstructed and discussed. Since they crucially rely on Bolzano's notion of paraphrase, this notion is investigated in detail. Bolzano has usually been taken to require that in a correct paraphrase the sentence to be paraphrased and the paraphrasing sentence express the same proposition. In view of Bolzano's texts and systematical considerations this interpretation is rejected: Bolzano only holds that the sentence to be paraphrased and the paraphrasing sentence must be equipollent ("gleichgeltend"). It is shown that even this modest view of paraphrase does not help Bolzano in sustaining his claim that all sentences have the form "A has b"."
- ———. "Bolzano Et Husserl Sur L'analyticité." Études Philosophiques (2000): 435-454.
"L'auteur expose la tentative faite par Bolzano de définir le concept de proposition en soi analytique à l'aide du concept de variation de représentation. Puis, il discute les difficultés qui résultent de ce modèle quant à la définition bolzanienne du concept étroit de vérité logiquement analytique ou de vérité logique. En conclusion, il compare la définition bolzanienne du concept de proposition en soi analytique et la définition husserlienne : celle-ci se découvre être une application de l'idée fondamentale de Bolzano - employer la variation de représentation pour définir les concepts logiques fondamentaux."
- ———. "Logically Analytic Propositions "a Posteriori"?". History of Philosophy Quarterly 18 (2001): 91-113.
- ———. "Caius-at-Noon or Bolzano on Tense and Persistence." History of Philosophy Quarterly 20 (2003): 81-102.
Translated in French as: Bolzano sur le temps et la persistence - Philosophiques, 30, 2003, pp. 105-125.
"How can we can truly say that a is tired in the morning, and not tired at noon? Bolzano holds that every proposition about a contingent thing contains an idea representing a time in its subject-part. In this paper I reconstruct and assess Bolzano's arguments for his view of propositions about contingent things, comparing them to those of his main opponent, the view according to which every proposition about a contingent thing contains a copula combined with an idea hat represents a time at which the object represented by the subject-part of the proposition has the property represented by the predicate-part (copula-modification view)."
- ———. "Bolzano on the Source of Necessity: A Reply to Rusnock." British Journal for the History of Philosophy (2013): (Forthcoming).
"According to Bolzano, an object has necessary being if, and only if, there is a conceptual truth that ascribes being to it. I (Textor, 1996, chapter 5) proposed that the notion of conceptual truth bears the explanatory weight in Bolzano's theory of necessity because, ultimately, the truth of such a proposition depends only on the nature of the concepts it contains. Rusnock (2012) argues against this interpretation and proposes, in turn, that for Bolzano necessity and contingency are tied to free choice. In this article I will provide conceptual and historical background for Bolzano's view of necessity and use it to motivate my interpretation as well as to rebut Rusnock's criticism."
- Thompson Paul B. "Bolzano's Deducibility and Tarski's Logical Consequence." History and Philosophy of Logic 2 (1981): 11-20.
- Voltaggio Franco. Bernard Bolzano E La Dottrina Della Scienza. Milano: Edizioni di Comunità, 1974.
Premessa 7; Introduzione 9; Parte prima: Logica come Dottirna della Scienza; 1. L'idea generale della logica 27; 2. La concezione generale della verità (Presupposti) 55; 3. La concezione generale della verità (Le verità in sé) 79; Parte seconda: L'Infinito come criterio di verità. 1. Dell'esistenza di un numero infinito di verità in sé 89; 2. Infinito e totalità 119; Parte terza: La critica della filosofia trascendentale. 1.Critica della prospettiva trascendentale kantiana 159; 2. Critica della dialettica hegeliana 209; 3. L'ontologia bolzaniana come fondamento della moderna teoria dell'intenzionalità 239; Postilla 263; Bibliografia 265-275.
- Winter Eduard. Bernard Bolzano. Ein Lebensbild. Stuttgart: Frommann-Holzboog, 1969.
First volume of the Gesamtausgabe.
- ———. Ausgewahlte Schriften Aus Dem Nachlass. Sankt Augustin: Academia Verlag, 1993.
"The volume contains essays selected from the posthumous works of Eduard Winter, especially concerning Bernard Bolzano and Franz Brentano. It includes a previously unpublished report by Johann Heinrich Loewe on Robert Zimmermann's "Philosophische Propaedeutik", one of the first textbooks in philosophy used in Austrian schools in the second half of the nineteenth century (first edition published in 1853). The volume is introduced by a short biography of Eduard Winter and a report on the Salzburg Bolzano- Winter- Archiv, both by Edgar Morscher."
- Wolenski Jan. "Bolzano Über Verneinende Existezaussagen." In Bernard Bolzanos Geistige Erbe Für Das 21. Jahrhundert, edited by Morscher, Edgar. 207-216. Sankt Augustin: Academia Verlag, 1999.