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The Berlin Group and the Philosophy of Logical Empiricism pp 205–228Cite as

Dubislav and Bolzano

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Part of the book series: Boston Studies in the Philosophy and History of Science ((BSPS,volume 273))

Abstract

This chapter deals with Dubislav’s reconstruction of Bolzano’s Kant criticism and his discussion of analyticity and analytic declarative statements (Sätze) which is central to Kant and Bolzano. Dubislav’s views are discussed, namely that Bolzano anticipated modern mathematical logic, his examination of Bolzano’s propositional functions, as well as the implications of other Bolzanian notions, such as derivability and probability. Bolzano’s contributions are reconstructed and situated in the contemporary discussion by Bolzano’s commentators. In regard to Dubislav’s (Erkenntnis 1:408–409, 1931a) account of definition, his interpretation of Bolzano and Bolzano’s replies concerning definition are reconstructed and evaluated. Dubislav brought Bolzano to the attention of the Berlin Group. The aim of this chapter is to reconstruct and evaluate their respective contributions to logic and philosophy for the current discussion in this volume.

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Notes

  1. 1.

    Bolzano writes: “Kant penetrated this distinction the deepest and it is to him that the author of this book owes his correct view on this issue. […] It suffices to grasp this distinction appropriately, on order to understand that there are attributes (Beschaffenheiten) which belong to an object and necessarily belong to it according to the concept we form of that object, without being presented as components of this concept.” (1837, § 65.8, cf. also § 148, my translation—A. K.).

  2. 2.

    Pace Y. Bar-Hillel (1950, 97), who notes Dubislav’s (1926) “return to Bolzano’s proposal” to accept analytically false as well as analytically true statements. Bar Hillel writes “[i]t is well known that a term corresponding to Bolzano’s ’analytically false’ lacked in Kant’s terminology, that therefore Kant’s classification of propositions into analytic and synthetic ones was by no means exhaustive.” While Kant’s classification may not be exhaustive, this is not because he did not accept analytically false statements but rather because he lacked Bolzano’s innovative notion of statements with a variable component (Bar-Hillel 1950, 97).

  3. 3.

    Quine, in “Two Dogmas of Empiricism”, has similar objections against the Kantian notion of analytic judgments (Quine 1951, 21). Cf. Edgar Morscher (2003).

    N.B. Kant could rebut (ii) because, in addition, he accepts judgments as analytic if they rest on the principle of contradiction. He gives the following examples of analytic geometrical principles: “a = a”, “the whole is equal to itself”, “(a + b) > a, i.e., the whole is greater than its part” (Kant 1789, B 16). But discussing the relevance of Bolzano- Přihonský’s Kant-criticism goes beyond the scope of this chapter. Let it suffice to say with Dubislav that via Kant, Bolzano worked his way into crucial problems of philosophy and discovered solutions which anticipate views in modern logic and philosophy.

  4. 4.

    See on this Jan Berg (Berg 1999, 122–124).

  5. 5.

    “[Logically analytic statements] differ from [analytic statements in the wider sense] in that for an assessment of the analytic nature of the former, only logical knowledge is necessary because the concepts which form the invariable part of those statements all belong to logic. The assessment of the truth and falsity of propositions of the former, however, require a wholly different kind of knowledge, since concepts alien to logic intrude. This distinction is admittedly unstable, for the domain of concepts belonging to logic is not that sharply delimited so that some controversy is inevitable.” (1837, § 148.3, my translation—A. K.). Bolzano’s distinction between analytic statements and logically analytic statements is famously discussed by Bar-Hillel (1950), Berg (1999), and Künne (2008).

  6. 6.

    “But suppose a statement contains just a single presentation which could be arbitrarily varied without disturbing the truth or falsity of the statement; i.e. if all statements obtainable from it by arbitrarily substituting this presentation by others, are either all be true or all false, provided only they have objectuality (Gegenständlichkeit). This property of the statement is already sufficiently remarkable to differentiate it from all those statements for which this is not the case. Hence I allow myself to call statements of this kind analytic, borrowing an expression from Kant.” (1837, § 148.1, my translation—A. K.).

  7. 7.

    Bolzano holds that if a proposition is true, it expresses the sense of a certain combination of words. Omnipotence can be predicated of God if and only if the subject “God” actually has this property, otherwise the proposition is false and has no sense (1837, § 28).

  8. 8.

    If Bolzano was little known at his time, the main reason was political rather than scientific: a Roman Catholic priest and professor of theology, Bolzano was removed from his post at the German University of Prague in 1820, after nearly being excommunicated for criticizing the official theological manual. The mathematical discoveries of the young Bolzano, such as the 1917 theorem that, given any bounded sequence (a n ) of real numbers, there exists a convergent sub-sequence (a n j ) which was later called the “Bolzano–Weierstraß theorem”, remained unnoticed until it was independently re-discovered by Weierstraß 50 years later. Dubislav (1931d, 344, 1931e) briefly mentions Bolzano’s contributions to mathematics. Bolzano’s logical and philosophical teachings were, however, propagated in the Danube Monarchy by his students R. Zimmermann and F. Přihonský and influenced philosophers such as Husserl and Meinong.

  9. 9.

    “The expression ‘mathematical logic’ is not free of ambiguities, but if its component ‘mathematical’ is not to be devoid of any literal value, then we cannot assent to Dubislav when he calls Bolzano “a forerunner of mathematical logic”. There seem to be among German logicians a certainly understandable tendency to praise Bolzano beyond his certainly great merits. Even if he did not anticipate either semantics or mathematics, he did investigate topics far beyond his own time and created foundations for many disciplines of actual value.” (1952, 337–338).

  10. 10.

    See on this Kasabova (2006).

  11. 11.

    Bar Hillel (1950, 1952), Corcoran (1993), Etchemendy (1999), Künne (2006, 2008), Dubislav (1931c), Siebel (1996, 1999, 2002), and Tatzel (2002).

  12. 12.

    “Mit der Aufdeckung von derartigen Variable enthaltenden Urteilsformen hat nun Bolzano eine der tiefsten Entdeckungen auf dem Gebiete der elementaren Logik gemacht. Man nennt diese Gebilde, die Bolzano selbst als Sätze mit veränderlichen Vorstellungen bezeichnet hat, Satzfunktionen. Es sind also Gebilde so beschaffen, daß, wenn man die in ihnen enthaltenden Variablen nach einer Substitutionsvorschrift durch Werte derselben ersetzt, Sätze im üblichen Sinne des Wortes resultieren. Man kann also anschaulich derartige Satzfunktionen mit L. Couturat als Gießformen für Sätze bezeichnen.”

  13. 13.

    Unfortunately Dubislav gives no reference for Louis Couturat. In 1905 Couturat published Les Principes des Mathematiques: avec un appendice sur la philosophie des mathématiques de Kant, L’Algèbre de la logique, Les définitions mathématiques and Définitions et démonstrations mathématiques. The last two works are cited in the bibliographie of Die Definition (1931a), as well as the German translation of Les principes des mathématiques (1908). It is likely that Dubislav refers to Couturat (1905) when citing the expression “Gießformen”.

  14. 14.

    “Eine Aussagefunktion charakterisiert er folgendermaßen, wobei wir die heute übliche Terminologie benutzen : eine Aussagefunktion ist ein Gebilde, welches ein oder mehrere Leerstellen dergestalt enthält, daß, wenn man die Leerstelle nach Maßgabe einer Einsatzungsvorschrift ausfüllt, eine Aussage resultiert”.

  15. 15.

    “Begriffe im Sinne der Logik sind lediglich Zeichen besonderer Art. Und zwar Zeichen in Gestalt von Aussage- oder, wie man sie auch genannt hat, Satzfunktionen einer Variablen. Unter einer derartigen Aussagefunktion […] versteht man […] eine Gießform für Aussagen [....] Eine Aussagefunktion einer Variablen resultiert, wenn man sich innerhalb einer Aussage ein Zeichen durch eine Variable […] ersetzt denkt”.

  16. 16.

    “Vorstellung […] welche sich willkürlich abändern läßt” (1837, § 148.1)

  17. 17.

    “Wenn man die Erläuterungen, die Bolzano für das, was er unter einer Vorstellung an sich verstanden wissen wollte, ihres mystischen Charakters entkleidet, dann ist festzustellen, daß eine Aussagefunktion einer Variablen im obigen Sinne gerade diejenigen Beschaffenheiten besitzt, die Bolzano seinen Vorstellungen an sich zuschrieb.”

  18. 18.

    “Physische Wirklichkeit kann man ihr nicht gut zuschreiben, man kann ihr nicht im Walde begegnen […]. Da man sie auch nicht gut als Vorstellung aussprechen kann, so muß man ihr, wenn überhaupt, eine ideale Existenz zuschreiben, womit man also vom Regen in die Traufe gekommen ist, oder […] den Teufel mit Beelzebub ausgetrieben hat.”

  19. 19.

    “Bolzano erkannte nämlich, daß es zwei Arten von Ableitsbeziehungen gibt. Erstens solche, zu deren Feststellung man lediglich logischer Kenntnisse bedarf, und zweitens solche, zu deren Feststellung außerlogische Kenntnisse herangezogen werden müssen.” Apparently Bar-Hillel (1952) did not read this part of Dubislav’s reconstruction of Bolzano because he claims that Bolzano “does not distinguish, strangely enough, between material and formal derivability, but he does so, for instance, with respect to a closely related concept, that of consequence (Abfolge).” (Bar-Hillel 1952, 86). Pace Bar-Hillel, Bolzano’s logical derivability is close to the modern notion of consequence, whereas Abfolge is grounding (or ground-consequence).

  20. 20.

    “Ein sehr merkwürdiges Verhältnis, vermöge dessen sich einige derselben zu andern als Gründe zu ihren Folgen verhalten.” Bolzano 1837, § 162; § 221.note: “der Begriff einer solchen Anordnung unter den Wahrheiten, vermöge deren sich aus der geringsten Anzahl einfacher Vordersätze die möglich größte Anzahl der übrigen Wahrheiten als bloßer Schlußsätze ableiten lasse”.

  21. 21.

    1810, Beyträge II, § 2; 1837, § 401.

  22. 22.

    Twice Dubislav (1930a, 409, 1931d, 343), Dubislav cites the following passage in the Wissenschaftslehre (1837, § 161.1): “Let us consider certain presentations i, j … in a single proposition A or in several propositions A,B,C,D, … as variable, and in the latter case suppose that propositions A,B,C,D are in a relation of compatibility in regard to these presentations. Then it will often be particularly important to know the relation of the collection of cases in which propositions A,B,C,D … all become true, stands to the collection of those cases in which an additional proposition M becomes true, and whether we should also take M to be true or not. For if the latter collection comes to half of the former, we can hold M to be true merely on account of the truth of propositions A,B,C,D … and if this is not the case, then we cannot. So I permit myself to call this relation between said collections the relative validity of proposition M in regard to propositions A,B,C,D, or the probability proposition M attains from the presuppositions A,B,C,D.” (my translation—A. K.).

  23. 23.

    In a reply to Grelling (1932) and Dubislav (1932, 203), concedes having tacitly accepted Pascal’s characterization of definition that, he now admits, is too narrow because it does not allow for inductive definitions in which newly introduced signs are not eliminable.

  24. 24.

    Bolzano gives an account of stipulative definition in part 4 of the Theory of Science and it is reconstructed in Kasabova (2006).

  25. 25.

    Bolzano famously claims that all statements in natural language are expressible by a uniform structure: “that the following holds of all propositions in general. The concept of having […] the concept signified by the word has occurs in all propositions. Besides this one component two others occur […] in all propositions connected with each other by a has as indicated in the expression A has b. One of these components, namely the one indicated by A, stands as if it were to present the object dealt with in the proposition and the other, b, as if it were to present the attribute (Beschaffenheit) the proposition ascribes to that object. Therefore I permit myself to call […] A the supporting or subject-presentation; […] and b the assertive part (Aussagetheil) or predicate presentation.” (1837, § 127, my translation—A. K.). Cf. on this Textor (1997).

  26. 26.

    “Wie kann aber Bolzano, dass ist zu fragen, seine These begründen, daß die genannte Beschaffenheitsvorstellung b den fraglichen Gegenständen vermöge des bloßen Begriffes zukommt, unter dem wir sie aufzufassen pflegen? Er ist genötigt, sich zu diesem Zwecke auf seine Lehre von den Wahrheiten an sich und Vorstellungen an sich zu beziehen […], zu ermitteln, daß derartige Aussagen nicht nur relativ zu einem als wahr unterstellten System von Grundvoraussetzungen gelten, sondern schlechthin. Damit wird aber sein Begründungsversuch für uns hinfällig.”

  27. 27.

    “It does not lie as a constituent in the concept of a triangle, but is only a consequence ensuing from this concept (nur eine aus diesem Begriffe sich ergebende Folgerung), that a triangle could be equilateral.” (1837 § 55.10c, my translation—A. K.).

  28. 28.

    “In this narrower meaning (Bedeutung) one takes the essence (Wesen) of a thing, also called the grounding essence (Grundwesen) to discern it better, as the collection of only those attributes ensuing from its mere concept, which cannot be objectively derived (herleiten) from any other concept of it (i.e. as consequences from their ground, § 198).” (1837, § 502, my translation—A. K.).

  29. 29.

    “In my view it is by no means necessary that a concept ensuing that the object corresponding to it is composed of so and so many parts, should be composed of just as many parts (such as the presentations of those particular parts)” (1837, § 65.7, my translation—A. K.).

  30. 30.

    A further reason for rejecting structural isomorphism are, as Bolzano points out, cases of complex objectless presentations such as [a regular 10-chiliagon (Zehntausendeck)], [round square], [blue yellow] or [golden mountain] which have no corresponding object, as well as objectual presentations comprising relative clauses, such as [a land without mountains] or [a book without copper] in which the attributive concept does not correspond to any property of objects falling under that concept but to properties the object is lacking (1837, §§ 63, 66, 70).

  31. 31.

    Pace Kneale and Kneale (1962, 364), “Bolzano seems to be in danger of confusing a whole of parts with a set of members.”

  32. 32.

    “wonach Umfang und Inhalt eines Begriffes sich zueinander reziprok verhalten sollen. Ferner wird mit dieser Begriffslehre die […] ebenfalls von Bolzano als unrichtig erwiesende Behauptung verbunden, daß die sogenannten Teilvorstellungen eines Begriffes immer zugleich auch Merkmale der unter den Begriff fallenden Gegenstände […] sein sollen. Daraus hat sich dann bei Verwechslung der beiden Sachverhalte “Von einem Begriffe umfaßt worden” und “Unter einen Begriff fallen” die verwirrende Terminologie entwickelt, die sogenannten Teilvorstellungen eines Begriffes Merkmale desselben zu nennen, weil unter der erwähnten Annahme die Teilvorstellungen eines Begriffes u. U. umfassen würden.”

  33. 33.

    Cf. on this Künne (2008, 212–215).

  34. 34.

    Roman Jakobson (1980) notes Bolzano’s distinction between the meaning (Bedeutung) of a sign as such and the sense (Sinn) that this sign acquires in the context of the present circumstance. Unlike Frege, Bolzano uses Bedeutung to denote the presentation of a sign, which is why ‘meaning’ is the appropriate translation. Cf. Kasabova (2006).

  35. 35.

    Jakobson (1980) points out Bolzano’s contribution to semiotics, although logicians and philosophers usually neglect this fact. Bolzano considered the theory of signs as belonging to methodology or the theory of science proper. Logic taken in a wide sense is a theory of science and the theory of science proper is the organon which regulates our acquisition of knowledge and includes a didactic theory of signs because Bolzano subscribes to the view that the correct understanding and use of words are based on a correct understanding of signs. See on this Kasabova (2006).

  36. 36.

    Jan Sebestik (1992, 139) notes that in Bolzano’s notion of explication paraphrastic elucidations or contextual definitions appear for the first time in the history of logic. Cf. Kasabova (2006, 13).

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  1. Department of Anthropology, New Bulgarian University, Sofia, Bulgaria

    Anita Kasabova

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  1. Universität Paderborn, Warburger Straße 100, Paderborn, 33098, Germany

    Nikolay Milkov

  2. Fak. Kulturwissenschaften, Abt. Philosophie, Universität Paderborn, Warburger Str. 100, Paderborn, 33098, Germany

    Volker Peckhaus

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Kasabova, A. (2013). Dubislav and Bolzano. In: Milkov, N., Peckhaus, V. (eds) The Berlin Group and the Philosophy of Logical Empiricism. Boston Studies in the Philosophy and History of Science, vol 273. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5485-0_10

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