by Raul Corazzon - e-mail: rc[at]ontology.co

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For an overview see the Index of the Pages or the Alphabetical Index of the Philosophers: A-F - G-O - P-Z; you can also download the page as or see the Table of Contemporary Ontologists (click on the image to see the PDF file)

Change of Address: The site www.formalontology.it is now at www.ontology.co

Selected Bibliography on Bernard Bolzano's Contributions to Logic and Ontology. First Part: A - G

Second Part: H - Z

Index of the Section: "The Rediscovery of Ontology in Contemporary Thought"

• Table of Formal and Descriptivists Ontologists (PDF - from Bernard Bolzano to present time)

• Ontologists of the 19th and 20th Centuries (a selection of critical judgments about some of the greatest philosophers of the recent past)

• Living Ontologists (a list of authors with an interest in ontology, with synthetic bibliographies)

Bernard Bolzano's Contributions to Logic and Ontology

Index of the Section: "Theory of Ontology"

MAIN PHILOSOPHICAL PUBLICATIONS IN GERMAN

Bolzano's Gesamtausgabe - (Collected Works - 82 volumes already published of 146).

The most important philosophical works are:

1. Wissenschaftslehre: Versuch einer ausführlichen und grösstetheils neuen Darstellung der Logik, mit steter Rücksicht auf deren bisherige Bearbeiter. Sulzbach: 1837.
   Herausgegeben von mehren seiner Freunde. Mit einer Vorrede von Dr. J. Cr. Heinroth.
   Vol. I XVI+571 [3], vol. II VIII+568+[2], vol. III VIII+575 and vol. IV XX+683 pages; the work is composed of five book and 718 paragraphs.
   Critical edition edited by Jan Berg: Bolzano's Gesamtausgabe - Voll. 11-14 (1985-2000).
   
   
2. Grundlegung der Logik. Ausgewahlte Paragraphen aus der Wissenschaftslehre, Band I und II. Hamburg: F. Meiner 1963.
   Mit erganzenden Textzusammenfassungen, einer Einleitung und Registern herausgeben von Friedrich Kambartel
   
   
3. Athanasia; oder, Gründe für die Unssterblichkeit der Seele. Sulzbach: 1827.
   Second edition 1838; reprinted Frankfurt/Main, Minerva, 1970.
   Contains in the first part Bolzano's metaphysics of simple substances and accidents.
   
   
4. Was ist Philosophie? Edited by Fesl M.J. Wien: 1859.
   An introduction to philosophy.
   
   
5. Paradoxien des Unendlichen. Edited by Príhonský Frantisek. Lipsia: 1851.
   On the theory of infinite manifolds.
   
   
6. Robert Zimmermanns Philosophische Propädeutik und die Vorlagen aus der Wissenschaftslehre Bernard Bolzanos: eine Dokumentation zur Geschichte des denkens und der Erziehung in der Domaumonarchie. Wien: Verlag der Osterreichischen Akademie der Wissenschaft 1975.
   Eingeleitet und herausgegeben von Eduard Winter.
   Zimmermann's Philosophische Propädeutik (1852) is divided into two parts, the first on Empirische Psychologie and the second on Formale Logik, that incorporated long sections of Bolzano's Wissenschaftslehre, and many passages almost word for word.

ENGLISH TRANSLATIONS

Two anthologies from Wissenschaftslehre (the content is different, so the books are complementary):

1. Paradoxes of the infinite. London: Routledge & Kegan Paul 1950.
   Translated from the German of the posthumous edition by Fr. Prihonský and furnished with a historical introduction by Donald A. Steele.
   
   
2. Theory of science, attempt at a detailed and in the main novel exposition of logic with constant attention to earlier authors. Berkeley: University of California Press 1972.
   Edited and translated by Rolf George.
   The Index lists the complete contents of the first three books of the Wissenschaftslehre.
   Cited above as: George 1972
   
   
3. Theory of science. Dordrecht: Reidel 1973.
   Edited, with an introduction, by Jan Berg. Translated from the German by Burnham Terrell.
   Part A. Selections from the Wissenschaftslehre pp. 35-367; Part B. Excerpts from Bolzano's correspondence pp. 371-383; Bibliography pp. 385-389.
   Cited above as: Berg 1973.
   
   
4. Contributions to a better-grounded presentation of mathematics (1810). In From Kant to Hilbert: a Source Book in the Foundations of Mathematics. Vol. I. Edited by Ewald William. Oxford: Clarendon Press 1996. pp. 174-224
   
   
5. On the mathematical method and correspondence with Exner. Amsterdam: Rodopi 2004.
   Translated by Paul Rusnock and Rolf George.
   
   
6. The mathematical works of Bernard Bolzano. Edited by Russ Steve. Oxford: Oxford University Press 2004.
   
   
7. Selected writings on ethics and politics. Amsterdam: Rodopi 2007.
   Translated by Paul Rusnock and Rolf Georg.

Rolf George and Paul Rusnock are working to a complete English translation of the Wissenschaftslehre.

STUDIES ON BERNARD BOLZANO'S LOGIC AND ONTOLOGY (A - G)

A complete bibliography up to 1999 will be available in:

• Bernard Bolzano - Gesamtausgabe. Einleitungsbände. Band 2, 3 - Bolzano Gesamtbibliographie 1804-1999 - Edited by Jan Berg and Edgar Morscher - ca. 450 pages - Stuttgart, Frommann-Holzboog (2010, not yet published).

An introductory work to Bolzano's thought is now available in English: Edgar Morscher - Bernard Bolzano's Life and Work - Sankt Augustin, Academia Verlag, 2008.

1. Bolzano als Logiker. Bolzano-Symposion am 17 und 18 Dezember 1973. Wien: Verlag der Österreichische Akademie der Wissenschaften 1974.
   Anlässlich des 125. Todestages Bernard Bolzanos (18 Dezember 1848)
   
   
2. Impact of Bolzano's epoch on development of Science - Conference papers Prague 1981. Prague: Ustav ceskoslovenských a svetových dejin CSAV 1982.
   Proceedings of a conference held in Prague 1981 as a part of the Bernard Bolzano bicentenary celebrations
   
   
3. Bolzano Studien. Philosophia Naturalis 24, 351-499 1987.
   
   
   
4. Bolzano's Wissenschaftslehre 1837-1987. International Workshop. Firenze: Leo S. Olschki 1992.
   Firenze, 16-19 September 1987
   
   
5. Bolzano and analytic philosophy. Grazer Philosophische Studien 53, 1-266 1997.
   
   Edited by Wolfgang Künne, Mark Siebel, Mark Textor.
   Proceedings of the International Symposium held in Hamburg 3rd-t5th January 1997.
   
   
6. Bolzano und die österreichische Geistesgeschichte. Edited by Ganthaler Heinrich von and Neumaier Otto. Sankt Augustin: Academia Verlag 1997.
   
   
7. Bernard Bolzano. Revue d'Histoire des Sciences 52[3-4], 339-506 1999.
   
   "Numéro spécial consacré à la mathématique et à la logique chez Bolzano, rassemblant les contributions suivantes: 1) Introduction; 2) Les conceptions rationalistes en arithmétique de Frege et Bolzano; 3) La théorie de la représentation chez Bolzano; 4) la critique des preuves indirectes chez Bolzano; 5) La philosophie des mathématiques: les réponses de Bolzano à Kant et Lagrange; 6) Bolzano et Cournot à propos de l'explication mathématique; 7) Réalisme mathématique, réalisme logique chez Bolzano; 8) Forme, variation et déductibilité dans la logique de Bolzano."
   
   
8. Bernard Bolzano. Études Philosophiques 4 2000.
   
   Special Issue edited by Jocelyn Benoist
   
   
9. Bernard Bolzanos geistiges Erbe für das 21. Jahrundert. Edited by Morscher Edgar. Sankt Augustin: Academia Verlag 2000.
   Beiträge zum Bolzano-Symposium der Osterreichischen Forschungsgemeinschaft im Dezember 1998 in Wien
   
   
10. Bernard Bolzanos Bibliothek. Edited by Berg Jan and Morscher Edgar. Sankt Augustin: Academia Verlag 2002.
    Two volumes.
    Im Auftrag der Österreichischen Forschungsgemeinschaft bearbeitet von Peter Michael Schenkel
    
    
11. Bernard Bolzano. Philosophie de la logique et théorie de la connaissance. Philosophiques 30 2003.
    
    Sous la direction de Sandra Lapointe
    
    
12. Bernard Bolzanos Leistungen in Logik, Mathematik und Physik. Edited by Morscher Edgar. Sankt Augustin: Academia Verlag 2003.
    Contributions to the Bolzano-Symposium of the Österreichischen Forschungsgemeinschaft (Wien, October 2002).
    
    
13. Philosophie im Geiste Bolzanos. Edited by Hieke Alexander and Neumaier Otto. Sankt Augustin: Academia Verlag 2003.
    Anlässlich des 222. Geburtstages von Bernard Bolzano - Edgar Morscher gewidmet
    
    
14. Bar-Hillel Yehoshua, "Bolzano's definition of analytic propositions," Methodos: 32-55 (1950).
    Published also in Theoria 16, 1950, pp. 91-117.
    Reprinted in: Aspects of language. Essays and lectures on philosophy of language, linguistic philosophy and methodology of linguistics - Jerusalem - The Magnes Press - The Hebrew University, 1970 pp. 3-28.
    
    "In view of recent discussions on the nature of analytic truth, it should be rather interesting to inquire into the treatment which this subject received by the most outstanding logician of the first half of the 19th century, the Austrian philosopher, theologician, and: physicist Bernard Bolzano.
    Our investigation will turn upon section 148 of Bolzano's four volumed masterwork Wissenschaftslehre (1837). Only occasionally shall we need to refer to other parts of this work. This section, headed "Analytic or Synthetic Propositions", comprises pages 83-89 of the second volume and is divided into three subsections of less than two pages altogether, followed by four annotations, filling the next five pages. I dwell so long upon these bibliographical particulars only to bring into full light the wealth of systematic and historic material contained in these few pages.
    1. Pre-History.
    Bolzano's aim, in 148, was to define a concept which could serve as an adequate explication for what is now commonly termed 'logical truth'. Though this aim is nowhere explicitly stated, there can be no doubt about it, just as Kant before him and many logicians after him doubtless aimed at the same target when they proposed their respective definitions.
    Bolzano devotes the greater part of his fourth annotation the discussion of many such attempts made by his predecessors and contemporaries. He mentions Aristotle, Locke, Crusius (the German logician of the first half of the 18th century who was probably the first to use the terms 'analytic' and 'synthetic' in their Kantian senses), Kant and many other minor philosophers. He easily succeeds in proving the inadequateness of Kant's two definitions for analytic', the one given in his Logik and equating, in effect, Analytic (1) with Identical, the other much better known in the introduction to the Critique of Pure Reason, where he proposes to call propositions 'analytic', whose predicate-concept is contained (perhaps in a hidden manner) in the subject-notion. Bolzano points out (p. 87) the vagueness of the term 'contained' and argues that, according to a quite natural interpretation of this term, the proposition « The father of Alexander, King of Macedonia, was King of Macedonia » ought to be analytic, a consequence which Kant certainly did not intend to be drawn.
    But to even more refined versions of Kant's definition, given by some of his followers, replacing the vague 'contained' by more concise terms, such as those making use of 'essential characteristics', Bolzano objects that only one type of proposition conforms to them, namely 'A (which is B) is B'. But should not, continues Bolzano, also propositions of the type 'Every object is either B or non-B' be counted among the analytic propositions ?
    Having thus convinced himself of the inadequateness of all prior approaches, he started to attack the subject along a new and highly original line."
    
    
15. Bar-Hillel Yehoshua, "Bolzano's propositional logic," Archiv für Mathematische Logik und Grundlagenforschung I: 65-98 (1952).
    Reprinted in: Aspects of language. Essays and lectures on philosophy of language, linguistic philosophy and methodology of linguistics - Jerusalem - The Magnes Press - The Hebrew University, 1970. pp. 33-68
    "Bar-Hillel's papers are two of the most important studies on Bolzano's logic" Jan Berg.
    
    
16. Behboud Ali, "Remarks on Bolzano's collections," Grazer Philosophische Studien 53: 109-115 (1997).
    
    
17. Benmakhlouf Ali, "La proto-sémantique de Bolzano," Études Philosophiques 4: 489-504 (2000).
    "Ce texte vise à mettre en évidence une proto-sémantique à l'oeuvre dans la Wissenschaftslehre de Bolzano. Cette proto-sémantique est caractérisée par les possibles substitutions entre constituants conceptuels, qui suspendent la question relative aux propriétés d'un concept pour mettre en évidence le contenu conceptuel. Le "conceptualisme" de Bolzano met ainsi fin au discrédit de la logique: les logiciens peuvent maintenant prendre le vrai non seulement comme but mais aussi comme objet d'étude. Cela leur permettra à l'instar de Frege de construire un noyau sémantique dur, mais cela leur permet déjà avec Bolzano d'explorer le domaine de l'objectivité non réelle, en un mot de reprendre en un sens plus abstrait, moins qualifié ontologiquement, les leçons des Premiers analytiques d'Aristote."
    
    
18. Benoist Jocelyn, "De Kant à Bolzano: Husserl et l'analyticité," Revue de Métaphysique et de Morale: 217-238 (1997).
    
    
19. Benoist Jocelyn. Phénomenologie, sémantique, ontologie. Husserl et la tradition logique autrichienne. Paris: Presses Universitaires de France 1997.
    See particularly the Chapter 2: L'héritage de Bolzano: l'analytique formel - pp. 59-81
    
    
20. Benoist Jocelyn, "Bolzano, Husserl et l'idée de grammaire," Études Philosophiques: 521-534 (1999).
    "Mesurant l'ampleur de la dette qui lie l'auteur des Recherches logiques au philosophe pragois, l'Auteur se propose de rapprocher le projet d'édification d'une grammaire pure logique, chez Husserl, de ce qui constitue l'une de ses sources majeures, à savoir la méréologie des représentations chez Bolzano. Examinant le passage de la composition des représentations à la composition des significations, l'Auteur évalue leur connexité syntaxique et définit la limite du compositionnalisme face aux fondements d'une grammaire."
    
    
21. Benoist Jocelyn. L'a priori conceptuel. Bolzano, Husserl, Schlick. Paris: Vrin 1999.
    
    
22. Benoist Jocelyn, "Husserl entre Brentano et Bolzano: jugement et proposition," Manuscrito 23: 11-39 (2000).
    "ll est bien connu que, dans la Cinquième Recherche Logique, Husserl critique la théorie brentanienne du jugement. Son problème est de définir le "porteur" de vérité auquel le jugement donne une valeur de vérité. Un tel projet le conduit très près du propositionalisme bolzanien. Alors la théorie phénoménologique de jugement apparaît comme une sorte de compromis entre la psychologie brentanienne de l'acte et une point de vue purement sémantique hérité de Bolzano. La question demeure de savoir si une telle conciliation est possible sans un tournant transcendantal."
    
    
23. Benoist Jocelyn, "Pourquoi il n'y a pas d'ontologie formelle chez Bolzano," Études Philosophiques 4: 505-518 (2000).
    "Souvent aujourd'hui on présente Bolzano comme ayant jeté les bases d'une "ontologie formelle". On lui impute une théorie du "quelque chose en général" qui serait ontologique. Il est vrai que sa théorie combinatoire des représentations en soi permet de rendre compte de la constitution de "quelques choses" de différents degrés, sur un mode récursif. Pourtant, on pourra douter de ce que le réalisme strict qui est celui de Bolzano, et qui s'applique même aux représentations en soi, laisse réellement un espace pour ce qui pourrait être appelé à proprement parler des "objets formels"."
    
    
24. Benoist Jocelyn. Représentations sans objet. Aux origines de la phénomenologie et de la philosophie analytique. Paris: Presses Universitaires de France 2001.
    See particularly chapter 1: Bolzano et le paradoxe des objets inexistants pp. 17-41
    
    
25. Benoist Jocelyn. Bolzano et l'idée de Wissenschaftslehre. In Les philosophes et la science. Edited by Wagner Pierre. Paris: Gallimard 2002. pp. 659-678
    
    
26. Benoist Jocelyn. Entre acte et sens: recherches sur la théorie phénoménologique de la signification. Paris: Vrin 2002.
    Première partie: L'univers du sens: Bolzano pp. 33-86
    
    
27. Benoist Jocelyn. Husserl and Bolzano. In Phenomenology world-wide: foundations, expanding dynamisms, life-engagements. A guide for research and study. Edited by Tymieniecka Anna-Teresa. Dodrecht: Kluwer 2002. pp. 98-100
    
    
28. Benoist Jocelyn, "La réécriture par Bolzano de l' Esthétique transcendantale ," Revue de Métaphysique et de Morale: 299-315 (2002).
    "L' Elementarlehre de la Wissenschaftslehre de Bolzano peut être lue comme une sorte de réécriture de l' Elementarlehre de la Critique de la raison pure. Bien sûr, on pourrait avoir l'impression que toute Esthétique Transcendantale fait ici défaut. Des déterminations qui sont supposées intuitives chez Kant sont réinterprétées par Bolzano comme purement conceptuelles. Pourtant, en fait, développant sa propre Esthétique Transcendantale du point de vue d'une sémantique objective, Bolzano invente une nouvelle sorte d'a priori pour la sensibilité - précisément un a priori purement conceptuel."
    
    
29. Benoist Jocelyn, "Propriété et détermination: sémantique et ontologie chez Bernard Bolzano," Philosophiques 30: 137-148 (2003).
    "The author tries to define the realm of the "metaphysical" in Bolzano's work. He shows how the metaphysics of reality (Wirklichkeit), with both its ingredients: substances and proprieties (Beschaffenheiten), has to be contrasted with the doctrine of the semantic realm (the realm of representations and propositions in themselves). The latter do not belong to ontology, and it is impossible to find something like a "formal ontology" dealing with them in Bolzano's work, viz. a doctrine describing them as "beings". The author deals, from this point of view, with the important distinction made by Bolzano, between proprieties (Beschaffenheiten), that have to be taken in an ontological sense, and determinations (Bestimmungen), that, though related to objects and even beings, do not make sense independently from the existence of some discourse on those objects, and are not ontological entities properly speaking. Thus, the author attempts to highlight the complexity of the relations between the semantic and the ontological level in Bolzano's work: both have to be distinguished accurately, and however remain correlated in a complex way."
    
    
30. Benthem Johan van. Lessons from Bolzano. Stanford: Center for the Study of Language and Information, Leland Stanford Junior University 1984.
    "Bernard Bolzano's contributions to logic, largely unnoticed in the 19th century, have been receiving ever more attention from modern logicians (cf. Scholz, 1937; Berg, 1962; Corcoran, 1975). As a result, it has already become something of a commonplace to credit Bolzano with the discovery of the notion of logical consequence in the semantic sense. Now, this particular attribution, whether justified or not, would at best establish a historical link between modern logical concerns and Bolzano's work. The purpose of the present note, however, is to bring out three important aspects of that work that are still of contemporary systematic interest. No detailed textual study of Bolzano is needed to substantiate our suggestions. We shall refer to well-documented 'public' aspects of the 'Wissenschaftslehre' (Bolzano, 1837), pointing out their more general logical significance." p. 1
    
    
31. Benthem Johan van, "The variety of consequence, according to Bolzano," Studia Logica 44 (4): 389-403 (1985).
    "Contemporary historians of logic tend to credit Bernard Bolzano with the invention of the semantic notion of consequence, a full century before Tarski. Nevertheless, Bolzano's work played no significant role in the genesis of modern logical semantics. The purpose of this paper is to point out three highly original, and still quite revelant themes in Bolzano's work, being a systematic study of possible types of inference, of consistency, as well as their meta-theory. There are certain analogies with Tarski's concerns here, although the main thrust seems to be different, both philosophically and technically. thus, if only obliquely, we also provide some additional historical perspective on Tarski's achievement."
    
    
32. Benthem Johan van. Is there still logic in Bolzano's key? In Bernard Bolzanos Leistungen in Logik, Mathematik und Physik. Edited by Morscher Edgar. Sankt Augustin: Academia Verlag 2003. pp. 11-34
    "Bolzano is widely seen as the philosopher of abstract propositions, far removed from psychological blemishes. Nevertheless, many themes in this paper suggest links with the actual reasoning performed by non-Platonic humans like us. We saw this with attention to diverse styles of task-dependent reasoning, with degrees of logicality for the expressions of natural language that we actually use, with inferences transferring information across discourse situations, with global architecture of reasoning styles, or with mixtures of such neatly compartmentalized logical activities as semantic evaluation and proof. When we take all this seriously, it becomes hard not to go one step further, and do something which Frege has forbidden - but probably also Bolzano: take the psychological facts seriously. All the above topics border on cognitive science and the experimental study of human reasoning, and the eventual agenda of modem logic will also have to come to better terms with that than the by now pretty stale slogan of 'anti-psychologism'.
    Conclusions.
    We have surveyed some aspects of Bolzano's logic from a modern standpoint, stressing in particular his different styles of consequence, the essential ternary nature of consequence when language is taken into account, and the mixed notion of consequence in a model. In all three cases we included some new technical observations to show that the issues are still alive. But the more general thrust is this.
    Bolzano's work remains interesting for logic today, both in its general sweep, and in some of its details. Partly, it is attractive precisely because it is so non-mainstream, and hence valuable for modern agenda discussions. Its themes crossing logic and philosophy of science reflect current rapprochements, while its thrust also seems to fit with some themes from AI. Classical mathematical logic has had an Austrian icon in Kurt Gödel: modem logic might consider at least having a Czech-Austrian patron saint."
    
    
33. Berg Jan. Bolzano's logic. Stockholm: Almqvist & Wiksell 1962.
    With an extended bibliography: pp. 179-207; the most complete study on the subject.
    
    
34. Berg Jan. Bolzano's notion of proposition. In Ost und West in der Geschichte des Denkens und der kulturellen Beziehungen. Festschrift für Eduard Winter zum 70. Geburtstag. Mit einem Geleitwort von A.P. Juskevic. Edited by Steinitz W. Berlin: Akademie-Verlag 1966. pp. 519-526
    
    
35. Berg Jan. Bolzano als Logiker. In Bernard Bolzano. Ein Denker und Erzieher im österreichischen Vormärz. [Von] Eduard Winter in Verbindung mit Paul Funk und Jan Berg. Edited by Winter Eduard, Funk Paul, and Berg Jan. Graz, Wien, Köln: Böhlaus in Kommission 1967. pp. 95-120
    
    
36. Berg Jan. Bolzano's theory of an ideal language. In Contemporary philosophy in Scandinavia. Edited by Paul Anthony, Olson Raymond, and Wright Georg Henrik von. Baltimore, London: The John Hopkins Press 1972. pp. 405-415
    "In his logical inquiries Bolzano employed a partly formalized language embracing an ordinary language extended by constants, variables, and certain technical expressions. In the second volume of the Wissenschaftslehre he investigated the relations of this semiformalized philosophical language to colloquial language (WL, sections 127-46, 169 84). He believed that all sentences of colloquial language were 'reducible' to sentences of certain canonical forms expressed in the philosophical language. These canonical sentences were said to mirror their corresponding propositions in the sharpest way.
    Had Bolzano's theory of reduction been completely developed it might have resulted in the construction of an ideal language for philosophical analysis. In this ideal language, however, sentences of canonical form would not play quite the same role as the atomic sentence forms on the basis of which more complex forms are built up in modern quantification theory. It seems, on the contrary, that Bolzano intended even the most complicated sentences to have canonical forms or to be reducible to sentences having such form.
    This paper attempts a reconstruction of an extensional Bolzanian ideal language on the level of elementary logic. After some preliminary explanations of fundamental notions in Bolzano's logic, the main points of his theory of reduction of sentences are described. Two principles that determine the construction of an elementary Bolzanian ideal language emerge from the exposition. We then move toward building such a language and begin by modifying the standard representation of elementary logic, replacing the universal and existential quantifiers by Hilbert's e-operator. By further modifications of both the syntax and the underlying semantics, a logical language satisfying the two principles is obtained." pp. 405-406.
    
    
37. Berg Jan. Was ist ein Satz ans sich nach Bolzano? In Bolzano als Logiker: Bolzano-Symposion. Wien: Verlag der Österreichische Akademie der Wissenschaften 1974. pp. 21-30
    
    
38. Berg Jan. Bolzano's contribution to logic and philosophy of mathematics. In Logic Colloquium '76. Edited by Gandy Robin O. and Hyland John Martin. Amsterdam: North-Holland 1977. pp. 147-171
    "The WL [Wissenschaftslehre] was intended merely as a prelude to Bolzano's work on mathematics. His main ambition was to recreate the whole body of contemporary mathematics in accordance with the vision of an abstract hierarchy of true propositions. For Bolzano this task implied the creation of entirely new foundations for certain branches of mathematics, as may be seen from his highly interesting efforts directed toward basing geometry on topological concepts.
    In carrying out this program, most of the means of expression of modern quantification theory were in essence available to Bolzano.
    He came very close to modern notions of satisfaction, logical truth, consistency and logical consequence. On the other hand, the formal deductive machinery of quantification theory is practically non-existent in Bolzano's works. This syntactic machinery appears only in Frege, who created the first strictly logistical system at the end of the 19th century. Bolzano's lack of interest in developing particular logical calculi most probably stems from his aspects of logic and mathematics and of science in general.
    The notion of calculus in the modern logistical sense was first clearly considered by Leibniz. His basic dream was of an effectively decidable, interpreted calculus embracing all "eternal" truth. Bolzano was justifiably critical of this overambitious program and presented instead his own theory of the Abfolge structure of nonlinguistic propositions, thereby taking his stand away from that line of development in logic which leads to modern syntactic concept formation. A reason for Bolzano's general lack of interest in questions of logical syntax was no doubt his profoundly intensional, non-linguistic approach to logic.
    Bolzano's central thesis, that there are abstract objects which differ from both mental occurrences and all kinds of linguistic expressions, has been advocated by later philosophers of the German-speaking countries, inter alia by Lotze, Brentano in his earlier period, Meinong and Frege. Lotze and Frege never refer to Bolzano's work, though, and the others protested their independence of Bolzano. Husserl admits that he received vital influences from Bolzano, but his notions of "ideal" objects derive from Lotze's and not from Bolzano's logic.
    Among the great Western philosophers Bolzano is perhaps the least influential. In epistemology, logic and mathematics his most fervent disciples were not able to propagate his ideas with sufficient vigor.
    His keen criticism of German idealistic philosophy and his important discoveries in logic: semantics and mathematical philosophy silently died away.
    A contributing cause of Bolzano's lack of influence on the development of the philosophical disciplines was, of course, the fact that most of his works were, for political reasons, published anonymously in editions not easily accessible. Furthermore, an immense number of unpublished manuscripts in a partly almost indecipherable handwriting is to be found in archives in Prague and Vienna. Several unfruitful attempts have been made in the last 150 years to bring out more or less complete editions of Bolzano's works. It is to be hoped that the latest venture launched in Stuttgart, West Germany, will prove more successful."
    
    
39. Berg Jan, "A requirement for the logical basis of scientific theories implied by Bolzano's logic of variation," Acta Historiae Rerum Naturalium nec non Technicarum 12: 415-425 (1982).
    Bernardo Bolzano (1781-1848) - Bicentenary. Impact of Bolzano's epoch on development of Science - Conference papers, Prague 7-13 September 1981
    
    
40. Berg Jan. B. Bolzano: Die Überwindung des Skeptizismus. In Grundprobleme der grossen Philosophen. Philosophie der Neuzeit III. Edited by Speck Josef. Göttingen: 1983. pp. 46-97
    
    
41. Berg Jan. A logic of terms with an existence operator. In Logic and abstraction: essays dedicated to Per Lindström on his fifthieth birthday. Edited by Furberg Mats, Wetterström Thomas, and Aberg Claes. Göteborg: 1986. pp. 71-94
    
    
42. Berg Jan, "Bolzano and situation semantics: variation on a theme of variation," Philosophia Naturalis 24: 373-377 (1987).
    "Some characteristic features of situation semantics can be represented in Bolzano's logic. Since the primitive notion of confirmation of a sentence in a model by a situation is a partial function, we must distinguish between the assertion that not-a is true in a model M and the assertion that a is not true in M. There is a similar distinction in Bolzano's semantics. Furthermore, a consequence relation stronger than that of logical consequence is typical of situation semantics. Bolzano's logic of variation entails an analogous notion stronger than his logical derivability."
    
    
43. Berg Jan, "Bolzano on induction," Philosophia Naturalis 24: 442-446 (1987).
    "Bolzano combined the fundamental notions of his theory of probability and his proof theory to achieve a logical analysis of the principles of induction. The relation between the conclusion and the premisses of an inference of incomplete induction or analogy is an interior probability relation in Bolzano's sense. The principles of induction endow the relation between the premisses and the conclusion with the character of a relation between ground and consequence. From Bolzano's subsumption of the rule of incomplete induction under the syllogistic rule of barbara, it follows that this relation is a special case of Bolzanian derivability."
    
    
44. Berg Jan and Morscher Edgar, "Bolzanos Biographie in tabellarischer Übersicht," Philosophia Naturalis 24: 353-372 (1987).
    
    
45. Berg Jan, "Is Russell's antinomy derivable in Bolzano's logic?," Philosophia Naturalis: 406-413 (1987).
    "The possibility of a consistent reconstruction of Bolzano's logic avoiding Russell's antinomy is investigated. A bolzanian collection ("Inbegriff") is a composite object consisting of at least two abstracts or concrete parts. A set in Bolzano's sense is a collection which contains no parts of its own parts and is invariant under their permutation. such a set cannot be a member of itself, and the collection of all entities which are not members of themselves is not a set. Furthermore, under a reasonable interpretation the collection of all collections which are not parts of themselves is not a part of anything."
    
    
46. Berg Jan. Zur logischen und mathematischen Ontologie. Goseologie und Resultatismus in der Analyse der Grundlagen der Bolzanoschen Zahlenlehre. In Rechnung mit dem Unendlichen. Edited by Spalt Detlef D. Basel: 1990. pp. 123-155
    
    
47. Berg Jan and Morscher Edgar. Bolzano-Forschung 1989-1991. Sankt Augustin: Academia Verlag 1992.
    
    
48. Berg Jan. Ontology without ultrafilters and possible worlds. An examination of Bolzano's ontology.Sankt Augustin - Academia Verlag 1992.
    Very important, but also very technical
    
    
49. Berg Jan. The connection between Bolzano's logic of variation and his theory of probability. In Bolzano's Wissenschaftslehre 1837-1987. International Workshop. Firenze: Leo S. Olschki 1992. pp. 107-120
    
    
50. Berg Jan. The ontological foundations of Bolzano's philosophy of mathematics. In Logic and philosophy of science in Uppsala. Edited by Prawitz Dag and Westerstähl Dag. Dordrecht: Kluwer 1994. pp. 265-271
    
    
51. Berg Jan, "Bolzano, the prescient Encyclopedist," Grazer Philosophische Studien 53: 13-32 (1997).
    "In his Wissenschaftslehre Bernard Bolzano tried to lay down a logically satisfactory foundation of mathematics and theory of probability. Thereby he became aware of the distinction between the actual thoughts and judgments of human beings, their linguistic expressions and the abstract propositions (Sätze an sich) and their components ( Vorstellungen an sich). This ontological distinction is fundamental in Bolzano's thinking paired with a universal world view in the sense that philosophy, mathematics, physics and metaphysics should be build upon the same logical foundations. Bolzano's enterprise is sketched in the light of examples from his logical semantics, proof theory, number theory, theory of truth and his variation logic."
    
    
52. Berg Jan. Kant über analytische und synthetische Urteile mit Berûcksichtigung der Lehren Bolzanos. In Bernard Bolzanos geistige Erbe für das 21. Jahrhundert. Edited by Morscher Edgar. Sankt Augustin: Academia Verlag 1999. pp. 97-128
    
    
53. Berg Jan. Naturphilosophie, Physik und Mathematik bei Bolzano. In Bernard Bolzanos geistige Erbe für das 21. Jahrhundert. Edited by Morscher Edgar. Sankt Augustin: Academia Verlag 1999. pp. 257-265
    
    
54. Berg Jan and Morscher Edgar. Bolzano-Forschung 1992-1996. Sankt Augustin: Academia Verlag 2000.
    
    
55. Berg Jan, "From Bolzano's point of view," Monist.An International Quarterly Journal of General Philosophical Inquiry 83 (1): 47-67 (2000).
    "In the Wissenschaftslehre (1837) Bolzano laid down a logical foundation of mathematics and the theory of probability. By means of the technique of variation of non-logical components in propositions he defined universal validity, logical derivability, and inductive probability. Characteristic features of situation semantics can be represented in the logic of variation. In his proof theory he stated counterparts of Gentzen's cut rule and Hauptsatz.
    In mathematical manuscripts he defined natural numbers as properties of bijective sets and real numbers as infinite sequences of rational numbers and accomplished a pioneering specification of infinitesimals. Infinite sets were identified as sets bijective to a proper subset of themselves. In a topological foundation of geometry he defined the notions of a closed, a simple closed, and a connected curve by means of spherical neighborhoods and stated a special case of Jordan's curve theorem. He also defined a notion of continuum and formulated steps toward a recursive definition of spaces with a homogeneous dimension number."
    
    
56. Berg Jan. Bolzano's heuristics. In Bernard Bolzanos Leistungen in Logik, Mathematik und Physik. Edited by Morscher Edgar. Sankt Augustin: Academia Verlag 2003. pp. 35-56
    "In the fourth part of the Wissenschaftslehre [WL], contained in the third volume of the original 1837 edition, Bolzano treats heuristics or the "art of discovery", i.e., the "rules to be observed in the search for new truths" ( 9. Note 3; cf. also 15.2). The first main section of Bolzano's heuristics embraces the general rules of this discipline ( 325 -348).
    Logic in Bolzano's sense is a theory of science the objects of which are the different sciences and their linguistic representations ( 15). According to Bolzano a science is a set of true propositions (Sätze an sich) worthy of representation in a textbook. Logic or the theory of science is a set of rules which are necessary and sufficient for a representation to satisfy certain criteria concerning scientific textbooks ( 1). In view of this very broad conception of logic it is fairly obvious that heuristics is an integrant part thereof."
    
    This paper was already presented in 1991 at the International Bolzano Symposium in Salzburg, but has never been published since.
    
    
57. Berg Jan. The importance of being Bolzano. In Bernard Bolzanos Leistungen in Logik, Mathematik und Physik. Edited by Morscher Edgar. Sankt Augustin: Academia Verlag 2003. pp. 153-166
    "1. Logical consequence
    Ever since Aristotle philosophers have occupied themselves with the question whether a given statement follows from another statement. The first published precision of this notion in modern times was undertaken by the Polish logician Alfred Tarski in 1936. Accordingly, a closed formula F is a logical consequence of a set of formulas F if and only if F is true under every interpretation of the nonlogical constants under which all elements of F are true. Logical constants are inter alia connectives of sentential logic (expressed by words like "not", "and", "or", "if - then") and quantifiers of predicate logic (such as "for all" and "there is"); hence, the interpretation of these constants is determined.
    But who conceived this notion of logical consequence (mutatis mutandis) already a hundred years earlier?'
    Right: The Bohemian philosopher, ontologist, logician, mathematician and theologian Bernard Bolzano!
    Upon substitution of abstract nonlinguistic propositions for closed formulas and variants of propositions for interpretations, we get precisely a special case of Tarski's notion of logical consequence. (A variant of a proposition P is a proposition identical with P up to at least one nonlogical component.) Incidentally, at the university of Warsaw Tarski was a student of Łukasiewicz's who lectured inter alia on Bolzano's logic.
    Just like Bolzano Tarski admitted being unable to exactly distinguish between logical and nonlogical constants. Not until thirty years later did he formulate a necessary condition for the property of being a logical constant. Furthermore, if all constants of the formal language in question were regarded as logical, the notion of material implication, would emerge. Even this weakest of all notions of consequence was introduced by Bolzano and is playing an important role in some of his deduction rules.
    Tarski presupposed a fixed domain as a realm of reference for the interpretations. Even Bolzano did not conceive of a combined quantification over domains and components of propositions. (By introducing a predicate for domains and letting the quantifiers refer to this predicate, however, one can represent all theorems of the model theory developed later on.)
    Nowadays we know, of course, that Tarski's notion of logical consequence is unsuitable if the set-theoretic language is enlarged by a generalized existence quantifier expressing that there is an absolutely infinite class C (in the sense that C does not include exactly K elements for any cardinal number K). This esoteric fact of modern set theory cannot, however, diminish our appreciation of Bolzano's achievement.
    2. Analytic propositions
    A fundamental distinction in Kant's Critique of Pure Reason is that between analytic and synthetic judgements. In modern logical semantics analyticity is often considered a relation between a sentence S, a set of definitions, and a language L. For instance, one can say that S in L is analytic with respect to D if S is a logical consequence of D in L which embraces S and the elements of D.
    But who formulated an analogous explication of analyticity within the system of abstract propositions already in the 1830s?
    Right: Bernard Bolzano!
    (...)
    6. Situation semantics
    In modern so-called situation semantics, established at the beginning of the 1980s by the American logician and linguist Jon Barwise, a notion of consequence is introduced which is stronger than that of Tarski. In situation semantics certain set-theoretic structures are considered models and a situation is a partial submodel thereof. The primitive notion is the confirmation of a sentence in a model by a situation. For example, a sentence of the form of "A or not A" is a logical consequence of any sentence in the sense of Tarski but not a strong consequence of it.
    But who discovered this notion of strong consequence even a hundred years earlier?
    Right: Bernard Bolzano!
    In his logic Bolzano considered not only the variants with respect to the sequence of all nonlogical components of propositions but also the variants with respect to all subsequences. By that counterparts of main laws of situation semantics turn into theorems of Bolzano's logic.
    (...)
    17. Estimation
    Thus some outstanding achievements of Bolzano's on the fields of logic, semantics, and mathematics have been delineated. The fact that the connection of most of these achievements with modern research remained unknown until the 1960s is due to the circumstance that the study of Bolzano's work took a new turn then and that eventually editions of the often hardly legible manuscripts of the literary remains could be published in the Collected Works of Bernard Bolzano.
    Moreover, particularly in Bolzano's logical semantics there are many original ideas which have no precise affinity with modern theories. In addition to that he accomplished extensive investigations into concepts of epistemology, philosophy of nature, physics, metaphysics, ethics, and theology."
    
    
58. Bergmann Hugo. Das philosophisches Werk Bernard Bolzano mit Benutzung ungedruckter Quellen kritisch untersucht. Halle: Max Niemeyer 1909.
    With an Appendix: Bolzanos Beiträge zur philosophischen Grundlegung der Mathematik.
    Reprinted Hildesheim, Georg Olms 1970
    
    
59. Bergmann Hugo, "Bolzano und Brentano," Archiv für Geschichte der Philosophie 48: 306-311 (1966).
    
    
60. Berka Karel. The ideal of mathematization in B. Bolzano. In Nature mathematized. Historical and philosophical case studies in classical modern natural philosophy. Edited by Shea William R. Reidel: Kluwer 1983. pp. 291-298
    
    
61. Berka Karel. Natural deduction in Bolzano's Wissenschaftslehre. In Intensional logic, history of philosophy and methodology: to Imre Ruzsa on the occasion of his 65th Birthday. Edited by Bodnàr István M., Maté András, and László Pólos. Budapest: Department of Symbolic Logic, Eotvos University 1988. pp. 203-212
    
    
62. Berka Karel. Bolzanos Lehre vom natürlichen Schliessen. In Bolzano's Wissenschaftslehre 1837-1987. International Workshop. Firenze: Leo S. Olschki 1992. pp. 141-161
    
    
63. Berka Karel, "Bernard Bolzano. A historian of logic," History of Science and Technology 31: 121-130 (1998).
    
    
64. Betti Arianna. De Veritate: another chapter. The Bolzano-Lesniewski connection. In The Lvov-Warsaw School and contemporary philosophy. Edited by Kijania-Placek Katarzyna and Wolenski Jan. Dordrecht: Kluwer 1998. pp. 115-137
    
    
65. Betti Arianna. Sempiternal truth. The Bolzano-Twardowski-Lesniewski axis. In The Lvov-Warsaw School. The new generation. Edited by Jadacki Jacek Jusliuz and Pasniczek Jacek. Amsterdam: Rodopi 2006. pp. 371-399
    
    
66. Beyer Christian. Von Bolzano zu Husserl. Eine Untersuchung über den Ursprung der phänomenologischen Bedeutungslehre. Dordrecht: Kluwer 1996.
    
    
67. Beyer Christian, "Logik, Semantik und Ontologie: neuere Literatur zu Bolzano," Philosophische Rundschau 48: 231-262 (2001).
    "This is a quite detailed critical review of four more recent books on Bolzano, dealing in particular with his logic, mereology, metaphysics, semantics and epistemology. The books reviewed include three studies by young German philosophers, notably Frank Krickel (Teil und Inbegriff. Bernard Bolzano's Mereologie / Part and Collection. Bernard Bolzano's Mereology), Mark Siebel (Der Begriff der Ableitbarkeit bei Bolzano / The Concept of Derivability in Bolzano) and Markus Textor (Bolzanos Propositionalismus / Bolzano's Propositionalism). The fourth book is a collection of English-speaking papers on Bolzano and Analytic Philosophy, edited by Wolfgang Künne, Mark Siebel and Markus Textor. It is argued that Bolzano's system is of more than just historical interest to analytic philosophers."
    
    
68. Beyer Christian. Bolzano and Husserl on singular existential statements. In Phenomenology and analysis. Essays on Central European philosophy. Edited by Chrudzimski Arkadiusz and Huemer Wolfgang. Frankfurt: Ontos Verlag 2004. pp. 69-88
    "Which form does the propositional content take that is judged when a given speaker sincerely utters a sentence in order to assert a singular existential statement? Two thought-provoking answers to this question have been proposed by Bernard Bolzano and, when commenting upon Bolzano's proposal, by Edmund Husserl. In Section 1 of this paper the author clarifies what he means by "singular existential statements". In Section 2 Bolzano's proposed analysis is sketched. In Section 3 the author exposes the earlier Husserl's conception of "logical reflection" and draws upon it to explain why Husserl, around 1900, subscribed to Bolzano's proposal. Following this, he reconstructs and considers in detail the later Husserl's discussion of that proposal and Husserl's own mature theory of singular existential statements as manifested in a 1917/18 lecture series, both of which shed light upon a conception that is of central importance for Husserlian phenomenology: the conception of "noematic sense" (Section 4)."
    
    
69. Bouveresse Jacques, "Sur les représentations sans objet," Études Philosophiques 4: 519-534 (2000).
    "L'auteur réinscrit l'oeuvre de Bolzano dans le contexte de l'histoire de la philosophie autrichienne. Il montre comment le fameux problème des "représentations sans objet", dont l'école de Brentano s'est tant occupée. trouve sa source dans l'oeuvre du philosophe tchèque. Il compare le traitement bolzanien du problème et les traitements variés essayés dans l'école de Brentano. En définitive, il met en lumière l'originalité de la position wittgensteinienne sur cette question: comme Bolzano (mais contre Brentano), Wittgenstein rejette une interprétation psychologique du problème; mais il refuse aussi (comme Brentano) l'objectivisme sémantique de Bolzano."
    
    
70. Brisart Robert, "Husserl et Bolzano: le lien sémantique," Recherches Husserliennes 18: 3-29 (2002).
    
    
71. Bucci Paolo, "Bernard Bolzano e la logica kantiana," Rivista di Filosofia 80: 241-260 (1989).
    
    
72. Bucci Paolo, "Logica e organizzazione del sapere nella dottrina della scienza di Bernard Bolzano," Rivista di Filosofia 85: 241-259 (1994).
    
    
73. Bucci Paolo, "La teoria bolzaniana delle spazio e del tempo," Rivista di Filosofia 86: 217-237 (1995).
    
    
74. Bucci Paolo. Husserl e Bolzano. Alle origini della fenomenologia. Milano: Edizioni Unicopli 2000.
    
    
75. Bussotti Paolo, "Il problema dei fondamenti della matematica negli scritti giovanili di Bernard Bolzano," Epistemologia 21: 225-243 (1998).
    "The main aim of this article is to provide a conceptual summary of the theory of Bernhard Bolzano related to the foundations of mathematics preceding his two great encyclopedic works: the "Grossenlehre" and the "Wissenschaftslehre" (both completed in 1837, even if the former was not published while Bolzano was still alive)."
    
    
76. Cantù Paola. Bolzano et les propositions en soi: une théorie objective des vérités. In Propositions et états de choses. Entre être et sens. Edited by Benoist Jocelyn. Paris: Vrin 2006. pp. 51-66
    
    
77. Casari Ettore, "L'universo logico bolzaniano," Rivista di Filosofia 76: 339-366 (1985).
    
    
78. Casari Ettore. Remarks on Bolzano's modalities. In Atti del Convegno Internazionale di Storia della Logica: le teorie della modalità. Edited by Corsi Giovanna, Mangione Corrado, and Mugnai Massimo. Bologna: CLUEB 1989. pp. 319-322
    
    
79. Casari Ettore, "Una fonte dimenticata? La teoria bolzaniana del significato," Rivista di Filosofia 80: 319-349 (1990).
    
    
80. Casari Ettore. An interpretation of some ontological and semantical notions in Bolzano's logic. In Bolzano's Wissenschaftslehre 1837-1987. International Workshop. Firenze: Leo S. Olschki 1992. pp. 55-105
    
    
81. Casari Ettore. Sull'origine dell'"oggettivo" in Bolzano. In Logica e teologia. Studi in onore di Vittorio Sainati. Edited by Fabris Adriano, Fioravanti Gianfranco, and Moriconi Enrico. Pisa: ETS 1997. pp. 93-115
    
    
82. Castrillo Pilar, "La teoría lógica de Franz Bolzano: una reacción contra el subjetivismo kantiano," Éndoxa.Series filosóficas 18: 417-443 (2004).
    "Objectivism may be taken as a landmark of Austrian philosophy. This tradition begins with Bernard Bolzano. Contrary to the Kantian picture of the working of the human mind as imposing its own structure on nature, Bolzano stresses the objectivity of our grasping the truth, thus liberating cognition from the subjective constraints. To know something means always to know propositions as such. Bolzano's theory states that there are propositions in themselves which are the bearers of truth values and of logical relations."
    
    
83. Cavaillès Jean, "La théorie de la science selon Bolzano," Deucalion I: 195-202 (1946).
    Reprinted in: J. Cavaillés - Sur la logique et la théorie de la science - Paris 1947
    
    
84. Cellucci Carlo. Bolzano and multiple-conclusion logic. In Bolzano's Wissenschaftslehre 1837-1987. International Workshop. Firenze: Leo S. Olschki 1992. pp. 179-189
    
    
85. Chattopadhyaya D.P. Bolzano and Frege: a note on ontology. In Logic. ontology and action. Edited by Banerjee K.K. Atlantic Highlands: The Humenities Press 1979. pp. 214-242
    
    
86. Chihara Charles, "Frege's and Bolzano's rationalist conceptions of arithmetic," Revue d'Histoire des Sciences 52 (3-4): 343-361 (1999).
    
    
87. Chisholm Roderick. Bolzano on the simplicity of the soul. In Traditionen und Perspektiven der analytischen Philosophie. Edited by Gombocz Wolfgang, Rute Heiner, and Sauer Werner. Vienna: Hölder-Pichler-Tempsky 1989. pp.
    
    
88. Chisholm Roderick, "Bernard Bolzano's philosophy of mind," Philosophical Topics 19: 207-216 (1991).
    "According to Bolzano, the best way to find out what thinking as such requires is to reflect upon our own acts of thought. Such acts can be performed only by substances and the acts themselves do not logically require any multiplicity of parts. But thinkers may be corporeal in the sense of "having" bodies. The only thinker who does not have a body is God. Corporeal thinkers may be rational or non-rational. The so-called lower animals are non-rational. Such entities, unlike rational beings, cannot be called "minds". These conclusions are developed in detail in Bolzano's "Athanasia: Or Grounds for the Immortality of the Soul"."
    
    
89. Coffa J.Alberto, "Kant, Bolzano and the emergence of logicism," Journal of Philosophy 74: 679-689 (1982).
    "Logicism is presented as an ingredient in a tradition designed to show that Kant's pure intuition plays no role in the foundation of "a priori" knowledge. Kant had argued for the necessity of the pure intuition from two assumptions: the claim that there is synthetic "a priori" knowledge and "the principle of synthetic judgments", (i.e., the thesis that synthetic judgments must be grounded on intuition). Bolzano was the first one to note that this principle is false and to propose that mathematics be constructed from concepts alone, thus excluding the representations that Kant associated with human sensibility."
    
    
90. Coffa J.Alberto. The semantic tradition fro Kant to Carnap. Cambridge: Cambridge University Press 1991.
    See the Second Chapter: Bolzano and the birth of semantics pp. 22-40
    
    
91. Cohen Jonathan L. Bolzano's theory of induction. In Impact of Bolzano's epoch on development of Science - Conference papers Prague 1981. Prague: Ustav ceskoslovenských a svetových dejin CSAV 1982. pp. 443-457
    
    
92. Corcoran John, "Meanings of implication," Diálogos 9: 59-76 (1975).
    Reprinted in: R. I. G. Hughes (ed.) - A philosophical companion to First-order Logic - pp. 85-100.
    
    "In philosophical and mathematical discourse as well as in ordinary scholarly contexts the term 'implies' is used in several clear senses, many of which have already been noticed and explicated. The first five sections of this article codify and interrelate the most widely recognized meanings. Section 6 discusses a further significant and common use. Section 7 discusses and interrelates Tarski's notion of logical consequence, the "model-theoretic" notion of logical consequence, and Bolzano's two grounding relations. The eighth section employs the use-mention distinction to separate the three common grammatical categories of 'implies'. Section 8 also shows that criteria based on use-mention are not reliable indications of intended usage of 'implies'. The ninth and last section relates the above to the counterfactual and gives reasons for not expecting to find 'implies' used to express counterfactuals. A summary is provided.
    
    SUMMARY AND CONCLUSION: In the first five sections we have distinguished twelve uses of the term 'implies'. At the outset we distinguished: implies 1 (truth-functional), implies2 (logical consequence) and implies3 (logical deducibility). Next we distinguished three elliptical or enthymematic varieties of implication: C-implies1, C-implies2 and C-implies3. In none of these six senses did "A implies B" presuppose the truth of A. Then we discussed the cases wherein "A implies B" is used to mean "The-fact-that-A implies B," which does presuppose the truth of A. We paraphrased the latter as "A is true and A implies 13" where 'implies' indicates any of the previous six senses of the term. Thus, at that point, twelve senses of implies were distinguished, six which do not presuppose the truth of the implying sentence and six which do. Of the six which do, three are enthymematic.
    In addition, the three original senses were carefully distinguished and interrelated, and possible causes of confusion were identified.
    Then, building on some off-hand observations of Russell, we related the truth-functional use of 'implies' to two further notions which have been used as explications of traditional logical consequence. We also brought in Bolzano's relative implication and his two grounding relations.
    We argued briefly that counterfactuals are not normally expressed using 'implies' and that the distinction between use and mention cannot be used as a test for distinguishing different meanings of 'implies'.
    Use of 'implies' as a transitive verb taking a human subject has been ignored."
    
    
93. Danek Jaromir. Weiterentwicklung der Leibnizschen Logik bei Bolzano. Meisenheim a Glan: A. Hain 1970.
    
    
94. Danek Jaromir, "La méthodologie de Bolzano," Dialogue 10: 504-516 (1971).
    "L'étude concerne la theorie des fondements, developpée dans la "Doctrine de la Science" de Bolzano, théorie très proche des points de départ de la méthode phénoménologique. L'oeuvre de Bolzano est une des sources de la logique, conçue comme theorie de la science; ses resultats ont contribué à la version sémantique des recherches logiques, ainsi qu'a la fondation de la théorie des modèles. notre temps évalue surtout le contenu ethique de l'oeuvre bolzanienne."
    
    
95. Danek Jaromir. Les projets de Leibniz et de Bolzano. Deux sources de la logique contemporaine. Quebec: Presse de l'Université de Laval 1975.
    
    
96. Dapunt Inge, "Zur Klarstellung einiger Lehren Bernard Bolzanos," Journal of the History of Philosophy 7: 63-73 (1969).
    "The purpose of this paper is to clarify some of Bolzano's ontological and semantic notions and theses. Especially the following topics in Bolzano are discussed here: division of all things; distinction between "there is" (es gibt) and "exist" (existiert, ist wirklich); difference between propositions (satze an sich) and ideas-in-themselves (vorstellungen an sich); difference between judgements (urteile) and actual ideas (subjektive vorstellungen); thesis that linguistic expressions of different structure can have the same sense. The paper is a discussion and correction of part 1 of Grossmann's "Frege's ontology" ("The Philosophical Review" LXX, 1961, p. 23-40) in which Bolzano's ideas are referred inexactly or even wrongly. "
    
    
97. Dapunt Inge, "Zur Frage der Existenzvoraussetzungen in der Logik," Notre Dame Journal of Formal Logic 11: 89-96 (1970).
    
    
98. Dähnhardt Simon. Wahrheit und Satz an sich: Zum Verhältnis des Logischen zum Psychischen und Sprachlichen in Bernard Bolzanos Wissenschaftslehre. Pfaffenweiler: Centaurus-Verlagsgesellschaft 1992.
    
    
99. De Jong Willem R., "Bernard Bolzano, analyticity and the Aristotelian model of science," Kant-Studien 91: 328-349 (2001).
    "This article intends to make clear that Bolzano's at first sight somewhat strange perception and use of the analytic-synthetic distinction should be understood in the framework of the so-called
    Aristotelian model of science. In contrast with the case of Frege and the logical positivists, logical truth is not central to Bolzano's approach to analyticity. It is shown that Bolzano, at least
    originally, hoped to argue that every analytic truth is based on or grounded in a synthetic truth. The difficulties however encountered to clarify the notion of scientific demonstration prevent him to work out this view in a systematic way."
    
    
100. Di Bella Stefano, "L' "Anti-Kant" di Franz Príhonsky e la critica bolzaniana alla teoria kantiana del giudizio," Rivista di Filosofia 97: 233-250 (2006).
     "Franz Príhonsky's "Neuer Anti-Kant" - a concise commentary to Kant's "Critique of Pure Reason", written by a follower of Bernard Bolzano - is an exemplary specimen of a critical approach to Kant from Bolzano's point of view. This paper focuses attention on the criticism of Kant's theory of judgement. In Bolzano's and Príhonsky's reflection, Kantian dichotomies - "a priori / a posteriori," and analytic/synthetic - play a seminal role; but their meaning is profoundly reshaped in a different conceptual framework. As a consequence, also their combination in the doctrine of synthetic "a priori" judgements - hence, the problem itself of the "Critique", and the solutions it receives - turns out to be seen in a quite different light."
     
     
101. Dörn Georg, "Zu Bolzanos Wahrscheinlichkeitslehre," Philosophia Naturalis 24: 423-441 (1987).
     
     
102. Drozdek Adam, "Logic and ontology in the thought of Bolzano," Logic and Logical Philosophy 5 (1997).
     "Logic and theology were two domains of great importance to Bolzano. His attempt to reconcile the demands of these two domains led Bolzano to very strong logical realism, or, objectivism, whereby theology could be put on a firm ground. The paper analyzes the problem of objective concepts, propositions, and truths, with an attempt to give an interpretation of these entities, to account for their puzzling ontological status in Bolzano's system."
     
     
103. Dubucs Jacques and Lapointe Sandra, "Preuves par excellence," Philosophiques 30: 219-234 (2003).
     "Bolzano was the first to establish an explicit distinction between the deductive methods that allow us to recognize 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 (Abfolge), 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 favor of a more rigorous demarcation between the ontological and the epistemological concern in the elaboration of a theory of proof."
     
     
104. Dubucs Jacques and Lapointe Sandra, "On Bolzano's alleged explicativism," Synthese.An International Journal for Epistemology, Methodology and Philosophy of Science 150: 229-246 (2006).
     "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 (Abfolge) 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."
     
     
105. Duhn Anita von. Bolzanos Kritik an Kants theoretischer Philosophie. In Bolzano-Forschung 1992-1998. Edited by Berg Jan and Morscher Edgar. Sankt Augustin: Academia Verlag 1999. pp. 169-180
     
     
106. Duhn Anita von. Theoretical laws and normative rules: Kant and Bolzano's views on logic. In Kant und die Berliner Aufklarung. Akten des 9. Internationalen Kant-Kongresses. Band V: Sektionen XV-XVIII. Edited by Gerhardt Volker, Horstmann Rolf-Peter, and Schumacher Ralph. Berlin: Walter de Gruyter 2001. pp. 3-12
     "Does logic instruct us how to think correctly? If so, what place does methodology have in logic? Is logic an instrument which provides rules for correct thinking or a system of proof for scientific theories, or is the doctrine of method merely an appendix to a doctrine of elements? The question whether logic is an organon is related to the question whether logical laws are theoretical truths or normative laws. Kant and Bolzano agree that logical laws basically provide us with truths, but that they can be apprehended as telling us how to think. (1) So a theoretical judgment that something is the case precedes the normative judgment that we may or should do something about it. Does it follow that Kant and Bolzano also agree on the question of whether logic is an organon which instructs us how to think? I will show that despite their divergent positions on logic, both authors claim that we apply normative rules because they are true." p. 3
     
     (1) Kant and Bolzano agree with Husserl and Frege, who thought that a normative act, such as demanding or permitting, presupposes a theoretical act, such as judging or believing and that every law that states what is can be apprehended that one ought to think in accordance with it. Cf. Frege (1893) Grundgesetze der Arithmetik, intro. XV; Husserl (1900) Prolegomena, 3, 13-14. I discuss this issue in "Is logic a theoretical or practical discipline? Kant and/or Bolzano", to appear in the Archiv für Geschichte der Philosophie. [vol. 84, no. 3 (2002) pp. 319-333]
     
     
107. Duhn Anita von, "Bolzano's account of justification," Vienna Circle Institute Yearbook 10: 21-33 (2002).
     "Bolzano claims that even self-evident propositions require proofs. I reconstruct his account of justification, designed to replace the criterion of intuitive self-evidence by providing a scientific base for the demonstrative sciences. Justification combines epistemological and logical aspects: it is both a mark distinguishing knowledge from opinion and a strict derivative proof excluding all relevant alternatives as well as alien intermediate concepts. I conclude that whilst Bolzano devised a procedure for grounding true propositions, he reintroduces an epistemological problem: how can we understand primitive truths without recurring to intuition and justify the applicability of logical rules without empirical verification?"
     
     
108. Dummett Michael. The origins of analytical philosophy. Cambridge: Harvard University Press 1994.
     
     
109. Dummett Michael, "Comments on Wolfgang Künne's paper," Grazer Philosophische Studien 53: 241-248 (1997).
     Comments on: Propositions in Bolzano and Frege
     
     
110. Etchemendy John. The concept of logical consequence. Cambridge: Harvard University Press 1990.
     
     
111. Fels Heinrich. Bernard Bolzano. Sein Leben und sein Werk. Leipzig: Felix Meiner 1929.
     
     
112. Føllesdal Dagfin, "Bolzano's legacy," Grazer Philosophische Studien 53: 1-11 (1997).
     Original German published as: Bolzanos bleibende Leistungen in: Arkadiusz Chrudzimski and Wolfgang Huemer (eds.) - Phenomenology and analysis. Essays on Central European philosophy - Frankfurt, Ontos Verlag, 2004 pp. 57-68.
     
     "Bernard Bolzano (1781-1848) was an original and independent thinker, who left a lasting legacy in several areas of philosophy. Four such areas are singled for special attention: political philosophy, ethics and theology, logics and semantics, and mathematics. In all these areas he was far ahead of his time. He had pioneering ideas in political philosophy and in ethics and philosophy of religion, and he argued for them in a brilliantly clear way. In logic and semantics he anticipated Frege, Carnap and Quine on important points, and he had intriguing, yet to be explored, ideas on intuition and other fundamental philosophical notions. In the foundations of mathematical analysis and the theory of infinite sets he anticipated Weierstrass and Cantor."
     
     
113. Føllesdal Dagfin. Bolzano, Frege and Husserl on reference and object. In Future pasts. The analytic tradition in twentieth century philosophy. Edited by Floyd Juliet and Shieh Sanford. Oxford: Oxford University Press 2001. pp. 67-80
     "Husserl's notion of the intentional object may be compared and contrasted with Bolzano's and Frege's views on the reference of linguistic expressions, especially since Bolzano was a main influence on the development of Husserl's views. Føllesdal responds to David Bell's criticisms of Føllesdal's earlier readings of Husserl on reference, directedness, and the notion of a determinable object x. He argues that Husserl's treatment of indexicals and reference is in some ways more insightful than the treatments of either Bolzano or Frege. To preempt the charge that Husserl's philosophy forwards a naïve, overly mentalistic model of the mind and its expressive capacities, Føllesdal mentions that Husserl developed a thought experiment nearly identical to the well-known Twin Earth scenario later framed by Hilary Putnam to criticize internalist, mentalistic theories of meaning. Føllesdal argues that Husserl was ahead of his time in trying to account for the semantics of indexical and demonstrative terms, partly under the influence of Brentano. This study shows that the opposition between so-called continental and so-called analytic philosophy is not historically as well-grounded as many have supposed."
     
     
114. Ganthaler Heinrich von and Simons Peter, "Bolzanos Kosmologischer Gottesbeweis," Philosophia Naturalis 24: 469-475 (1987).
     
     
115. Gensini Stefano. "De linguis in universum": on Leibniz's ideas on languages. Five essays. Munster: Nodus Publikationen 2000.
     
     
116. George Rolf, "Enthymematic consequence," American Philosophical Quarterly 9: 113-116 (1972).
     "Enthymematic validity, in contrast to logical validity, obtains when all substitutions on some (but not all) of an argument's extralogical constants which make the premises true also make the conclusion true. This condition is shown to be equivalent to the classical view for the domain of syllogisms, and for arguments which depend on the properties of relations. Enthymematic consequence turns out to be a special case of consequence as defined by Bolzano."
     
     
117. George Rolf, "Bolzano's consequence, relevance and enthymemes," Journal of Philosophical Logic 12: 299-318 (1983).
     
     
118. George Rolf, "Bolzano's concept of consequence," Journal of Philosophy 83: 558-564 (1986).
     "Bolzano consequence (or entailment) (BC) is a triadic relation of premises, conclusion(s) and "variands", i.e., items explicitly tagged for substitution. argument forms are sets generated by variation. The preferred construal captures all of Bolzano's theorems ("Wissenschaftslehre" 155). BC also gives a promising account of formal fallacies, of enthymemes and sheds light on the deductivism controversy. A subvariety of BC is "relevant": premises and conclusion share a variand."
     
     
119. George Rolf, "Bolzano on time," Philosophia Naturalis 24 (4): 452-468 (1987).
     "The paper reviews Bolzano's conception of the grammar of time determinations and of the structure of the time series. His definition that time is "that determination in a real thing which is the condition for correctly attibuting to it a given property" is examined, and his claim rejected that all properties of time can be deduced from it. Finally, there is an account of Bolzano's views on time consciousness, and the influence they had on Brentano and Husserl."
     
     
120. George Rolf. Concepts of consequence. In Bolzano's Wissenschaftslehre 1837-1987. International Workshop. Firenze: Leo S. Olschki 1992. pp.
     
     
121. George Rolf, "Bolzano's programme and abstract objects," Grazer Philosophische Studien 53: 167-180 (1997).
     "Most of the Bolzano literature is exegetical, neglecting, unfortunately, the great potential of his logic as the beginning of a Programme. Specifically, his unorthodox construal of the consequence relation as triadic, and his account of logical form are promising beginnings which even as they stand shed light on question of relevance, the ancient problems of enthymemes and others. Instead of developing these suggestions, Bolzano scholars have been occupied with elucidating the ontology of sentences in themselves, and related topics. I argue, and believe to be in agreement with Bolzano, that the nature of sentences is fully explained by the relations that hold between them, just as money has no nature or essence beyond the transactions it makes possible. It follows that the development of his logic would contribute at least as much to the understanding of sentences than any exegesis."
     
     
122. George Rolf, "Psychologism in logic: Bacon to Bolzano," Philosophy and Rethoric 30 (3): 213-242 (1997).
     "Various types of psychologisms are distinguished and historically discussed: reduction of logic to psychology in Beneke and others; replacement of (school) logic by an account of the actual workings of the mind in Locke, Hume; syllogistics as an adequate account of thought in Wolff; inadvertent psychologism is discussed in Kant and others. The end of psychologism in Bolzano's theory of propositions in themselves and their relations, etc."
     
     
123. George Rolf. Anschauungen bei Kant und Bolzano. In Bernard Bolzanos geistige Erbe für das 21. Jahrhundert. Edited by Morscher Edgar. Sankt Augustin: Academia Verlag 1999. pp. 129-144
     
     
124. George Rolf. Bolzano and the problem of psychologism. In Husserl's Logical investigations reconsidered. Edited by Fisette Denis. Dordrecht: Kluwer 2003. pp. 95-108
     "The Theory of Elements in the first two volumes of Bolzano's Wissenschaftslehre of 1837 "on which logic as a science must be built" (Husserl), is a historical first in avoiding all connection with psychological doctrine. It was then common to argue that specific "laws of thought" reflect what we can or cannot think. A brief account of the psychologism debate at the time of Husserl is
     followed by a survey of claims about psychology and logic in British Empiricism, Kant, Herbart and others. Then Bolzano's theory of "propositions in themselves" is discussed and justified."
     
     
125. George Rolf, "Intuitions," Philosophiques 30: 19-46 (2003).
     "Kant impressed on the philosophical public the distinctions between sensations, intuitions and concepts. Bolzano followed him in terminology, but not in substance. This essay deals with Bolzano's astute and detailed critique of Kant, and then outlines his own theory. His famous propositions "in themselves", allowed him to discuss, with precision, the concepts of logical consequence, equivalence, analyticity, etc., and to escape from common logical psychologism. Intuitions are an exception. They are introduced with heavy reliance on mental activity and are thought -- they are episodes representing our direct empirical awareness -- and they indeed Constitute the narrow door of Bolzano's philosophy of mind."
     
     
126. George Rolf. Intuitions: the theories of Kant and Bolzano. In Semantik und Ontologie. Beiträge zur philosophischen Forschung. Edited by Siebel Mark and Textor Mark. Frankfurt: Ontos Verlag 2004. pp. 319-354
     
     
127. Gieske Carsten Uwe, "Bolzano's notion of testifying," Grazer Philosophische Studien 53: 249-266 (1997).
     
     
128. Gieske Carsten Uwe, "Bolzano über den Sinn von Wahrheit," Zeitschrift für Philosophische Forschung 55: 556-570 (2001).
     
     
129. Granger Gaston-Gilles, "Le concept de continu chez Aristote et Bolzano," Études Philosophiques: 513-523 (1969).
     
     
130. Grossmann Reinhardt, "Frege's ontology," Philosophical Review 70: 23-40 (1961).
     Reprinted in: E. D. Klemke - Essays on Frege - Urbana, University of Illinois Press 1968, pp. 79-98.

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