Theory of Science, written by Bernard Bolzano

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  • 1 Carl von Ossietzky Universität Oldenburg stefania.centrone@uni-oldenburg.de

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Translated by Paul Rusnock and Rolf George. Oxford: Oxford University Press, 12014, clxxxvi, 1851 pp.; set isbn 978-0-19-968438-0; vol. 1 isbn 978-0-19-968439-7; vol. 2 isbn 978-0-19-968440-3; vol. 3 isbn 978-0-19-968441-0; vol. 4 isbn 978-0-19-968442-7.

The full German title of Bolzano’s Wissenschaftslehre 1 is: Dr. B. Bolzanos Wissenschaftslehre. Versuch einer ausführlichen und Grösstentheils neuen Darstellung der Logik mit steter Rücksicht auf deren bisherige Bearbeiter (Dr. B. Bolzano’s Theory of Science. Attempt at a Detailed and in the main Novel Exposition of Logic with Constant Attention to Earlier Authors). As Volker Peckhaus rightly stresses in his own review of the present translation for the Zentralblatt Mathematik, this is “an excellent scholarly English translation.”2 It is the fruit of an enormous amount of work and it is and will remain, for years to come, the standard translation of Bolzano’s Wissenschaftslehre.

The Wissenschaftslehre was first published in 1837 by Seidel in Sulzbach (Bavaria). There followed in 1882 an edition by Wilhelm von Braumüller of all of Bolzano’s works published earlier by Seidel.3 The first two volumes were, then, reprinted in 1914, and another corrected printing of all four volumes was made in 1929–31. The present translation is almost entirely based on the critical edition of the wl in the Bernard Bolzano-Gesamtausgabe.4 The Authors have added references, when needed, and notes, when clarification seemed to be in order. The pagination of the first edition of the wl (1837) is indicated in the margins like in the bga. This is a gift for the secondary literature on Bolzano as it allows citations to refer both to the original pagination and to the now standard translation.

There are two English translations of selected parts of the Theory of Science, one by Rolf George (1972) and the other one by Jan Berg (1973).5 George translates altogether more of Bolzano’s masterpiece than Berg. He follows a hint given by Bolzano himself (in a letter to Romang from May 1, 18476) as his criterion for selection, where Bolzano provides guidelines for reading the wl. All sections marked by Bolzano with an asterisk are included in George’s translation. Bolzano himself has not given a reason for the asterisks, but it is quite natural to assume that he has thus marked the most important sections. The 1972 edition also includes many historical notes, especially those dealing with Kant and the Kantians.

The 1973 edition by Berg translates selected texts from the wl and is based on the Manuscript 75 B 459, which is located in the Manuscript Department of the University Library in Prague. This is one of Bolzano’s own copies of his masterpiece and contains a number of corrections made by Bolzano himself. Like the 1972 translation, the 1973 one aims at giving a compact view of Bolzano’s most important ideas in logic, semantics, epistemology and the methodology of science. Also of interest for Bolzano research is the translation of a number of letters to F. Exner, M. J. Fesl, J. P. Romang, R. Zimmermann, F. Přionský and J. E. Seidel. The Editor’s introduction contains many clarifications that will be taken up again by J. Berg in his specific Introductions (in German) to the odd volumes of the Wissenschaftslehre (1985+) in the bga.

Given the partial natures of the 1972 and the 1973 translations, it is very welcome for Bolzano research to have, at last, a complete translation of the Theory of Science at its disposal.

The present translation is preceded by a General Introduction by Paul Rusnock and Rolf George, which turns out to be quite close to George’s introduction to his previous translation (1972).7 Each of the four volumes has an additional specific introduction that goes into the main points of the volume.

General Introduction. The General Introduction provides an overview of Bolzano’s life and work. Bolzano’s interest in the “purely speculative” part of mathematics, “that part of it which is at the same time philosophy” (xvii), is recalled as well as his debate with Kant (loc. cit.), his activity as professor of the newly instituted chair of the science of religion at the Charles Ferdinand University in Prague between 1805 and 1819 (loc. cit.), his role within the so called “Bohemian Enlightenment,” and his difficulties with the Authorities during the time of the Restoration (xviii–xx). The authors dwell on Bolzano’s utilitarian ethics as well as on Bolzano’s main project of, to say it with early Bolzano,8 “seeking out the grounds on which our judgments rest” (xvii),9 a project that will become, in Theory of Science, that of seeking out the grounds on which truths in themselves rest.10 The authors remark how a significant part of Bolzano’s time after his forced withdrawal from teaching and from any kind of public activity was spent carrying out the project of writing a Logic (xxi). The Logic in question is precisely the Theory of Science which, in Bolzano’s formulation, is the “collection of all rules which we must follow, if we want to do a competent piece of work, when we divide the total domain of truths into individual sciences, and present them in their respective treatises” (wl 7; 9). Logic in Bolzano’s sense includes both the theory of scientific method (xxi) and logic in the proper sense, that is, a discipline closer to what is taught in contemporary logic textbooks (xxv). Bolzano calls this logic in the proper sense “Theory of Elements” (loc. cit.). The latter occupies part of volume one and the whole of volume two of the Theory of Science. It is preceded by a Theory of Fundamentals, which consists of a refutation of skepticism, and in which Bolzano proves both that there is at least one truth in itself (xxv; wl 145–146; 107–108) and that there are several, even infinitely many truths (xxv; wl 146–147; 108–110). This is followed by a Theory of Knowledge that has as its proper object the relation of having as matter, which holds between mental acts and/or states and their abstract logical contents (xxv). The Theory of Knowledge and a Theory of Discovery (the heading “Theory of Discovery” echoes Leibniz’ “ars inveniendi”) make up the third volume of Bolzano’s Theory of Science, while volume four is dedicated to the theory of science proper, that is, to the theory of scientific method (loc. cit.).

The General Introduction also stresses the value of Bolzano’s mathematical work and its influence on mathematicians who, like Weierstraß, Cantor and Dedekind, were engaged in the so-called movement to establish rigor in analysis (xxiii). The authors rightly stress the influence of Bolzano’s logical and philosophical work within the Austrian-Polish tradition, that is, on the students of Franz Brentano in Vienna (Husserl, Meinong, …), and on the Lviv-Warsaw school (Twardowski, Tarski, …). They also recall how Husserl’s anti-psychologism can be largely traced back to Bolzano (not just to Frege, as is sometimes maintained in the secondary literature on Husserl11). Finally, they stress how the history of Bolzano’s reception radically changed when around the forties of the last century a group of scholars, including E. Winter, J. Berg, F. Kambartel, J. Loužil, and B. van Rootselaar, began working on the critical edition bga.

Introduction to Volume One. Volume One contains the Theory of Fundamentals and the first part of Theory of Elements, which deals with Bolzano’s ideas in themselves. The authors hint between the lines at Bolzano’s conception of each single science as the totality of all truths that are germane to a certain homogeneous kind (Gattung) of objects as well as his conception of the theory of science as the theory of scientific methodologies (xxx; xxxvii: “[…] [f]or his focus was on sciences understood as collections of true propositions […]”). They observe, further on, that Bolzano, “as is his custom, discusses the view of other philosophers on the subject” (loc. cit.) and put in evidence Bolzano’s criticism “of some important Kantian theses, in particular the claims that logic is a purely formal science, and that its subject is the laws of thought” (loc. cit.). Very useful for the reader is the authors’ indication of all paragraphs of the Wissenschaftslehre in which the first issue (ideas in themselves) is pursued. Regarding the second claim, the authors present Bolzano’s refusal of logical psychologism (xxxi–xxxiii) in a way that turns out to be very useful for the research on Edmund Husserl. Indeed, the secondary literature on Husserl is beginning to see Bolzano as a forerunner of the father of phenomenology,12 in that Husserl’s refusal in his Prolegomena to Pure Logic 13 of both the conception of logic as a normative science (on which logical laws are prescriptive laws of thought) and as a natural science (on which logical laws are descriptive laws of thought), stands on Bolzano’s shoulders. Similarly, the authors present Bolzano’s refutation of logical psychologism in a way that immediately suggests comparison with Frege’s wording in Der Gedanke. For instance, they write: “The most natural narrowing […] would be to say that logic describes the way we should think in order to arrive at the truth. At this point, however, the reference to thought becomes superfluous. We are better off, Bolzano claims, looking upon logic as simply studying the laws of truth” (xxxii). This is evocative of many places in Frege, for instance, “[…] der Logik [weise ich] die Aufgabe zu, die Gesetze des Wahrseins zu finden […]”.14 In addition, the authors point out Bolzano’s eminently non-epistemic conception of truth (xxxiii–xxxiv); his distinction between the scope of “there is” (coinciding with that of the existential quantifier) and that of “it exists” (applying to spatio-temporally located objects); his account of different kinds of existence (xxxiii–xxxiv), his conception of the content (xl–xli) and the extension (xl) of an idea in itself; his conception of conceptual analysis (xli); his rejection of the canon of reciprocity, i.e. of the traditional view that there is an inverse correspondence between content and extension of an idea in itself (xli–xliii); and his distinction between intuitions and concepts (xliii ff.). Now and again one finds hints that condense into one line a whole branch of the history of philosophy, as in the following: “Many of the authors Bolzano read thought of the relation between ideas and their objects as fundamental. Often, this relation was thought to be primarily one of resemblance, ideas being copies of the things outside the mind” (xxxviii). The reader is almost certainly led to think of Descartes, in particular, his Third Meditation, where he classifies ideas depending on their alleged origin: some ideas seem to be already in us (innate ideas), some seem to come from the outside (ideae adventitiae) and some, finally, seem to be made by us. Descartes here refutes two reasons for believing that the ideae adventitiae really do come from the outside: their independence from human will (“[…] non a mea vo-luntate […] pendere, saepe enim vel invite obversantur15) and the naturalness of our drive to take them as coming from the outside (“Cum hic dico me ita doctum esse a natura, intelligo tantum spontaneo quodam impetus me ferri as hoc credendum, non lumine aliquot naturali mohi ostendi esse verum16). The authors discuss Locke as a representative of the resemblance theory and depict Bolzano’s view on this as well (xxxviii ff.).

Introduction to Volume Two. Volume two of the Theory of Science contains two main parts, devoted, respectively, to propositions (§§121–222) and inferences (§§223–268). The authors’ Introduction focuses on the most important issues, that is, on Bolzano’s logic of variation and his concepts of Ableitbarkeit and Abfolge. They proceed from Bolzano’s claim that it is difficult to trace a demarcation line between logical and non-logical ideas and recall, among others, Bolzano’s conception of existential statements as second-order statements, as we would say nowadays after Frege. For instance, “Some men are virtuous,” is saying of the concept expressed by the predicate “(…) is virtuous” that it is not empty, that it has objectuality, in Bolzano’s terminology (xxi–xxii). “There is no round square”, or “The concept of a round square lacks objectuality,” is saying of the concept expressed by the predicate “(…) is a round square” that it is empty (xxiii).

The authors recognise two different kinds of negation in Bolzano (xxiv). Perhaps it is even possible to recognise three different kinds.17 “In one 18 kind”, as the authors rightly stress, “negation attaches to the predicate, as in the proposition ‘Caius is unwise’ or ‘Caius has lack-of-wisdom’.” In the second 19 kind, the scope of the negation is the entire proposition, i.e., ‘Not (Caius has wisdom)’ or, more distinctly in Bolzano’s estimation, ‘The proposition “Caius has wisdom” has lack-of-truth’ (loc. cit.). A third kind of negation is discussed in § 89 of the Theory of Science, entitled Affirmative and Negative Ideas (wl i 416–426; 298–306). This time negation attaches to the subject-idea. In this context, Bolzano distinguishes purely negative ideas (like not-blue, not-red, nothing) and partially negative ideas (of the form ‘an A, which is not B’ and ‘something, which is not B’). Perhaps the Authors have not included this kind of negation as one of the negation forms considered by Bolzano, since Bolzano rejects the claim that purely negative ideas may ever act as subjects in true propositions (wl ii 45; 31) and explicitly says that partially negative ideas can be rephrased as “an A, which does not have B-ity” and “something, which does not have B-ity,” thus reading them as ‘an A, which has lack-of-B’ and ‘something, which has lack-of-B’, respectively, that is, as negations of the second kind.

Further on the authors go into Bolzano’s distinction between purely conceptual and intuitional propositions as well as into Bolzano’s conception of modalities (xxx–xxvii). They dwell on his logic of variation (xvii ff.) and discuss within this context Bolzano’s notions of general and relative validity/invalidity, analyticity (xvix ff.), and logical analyticity (xxxi ff.). They also consider some important relations among propositions that come to light, when one considers certain ideas they contain as variable and then asks in what relation the propositions obtained by variation stand to truth or falsity; in particular, the authors go into details about the relations of compatibility (Verträglichkeit) (xxx) and derivability (Ableitbarkeit) (xxxiv ff.).20

Introduction to Volume Three. Volume Three of the Theory of Science contains two of the five main parts of the work, Book Three, devoted to the Theory of Knowledge and Book Four, on the Art of Discovery. The authors discuss these parts separately.

Book Three: Theory of Knowledge. The basic notion in Bolzano’s Theory of Knowledge is having matter (Stoff) or content (Inhalt) that occurs between nominal as well as propositional mental acts or states, on the one side, and ideas in themselves as well as propositions in themselves, on the other side. Bolzano calls non-propositional mental acts or states “subjective ideas,” while he calls propositional ones “judgments” (xiii). The authors rightly stress that Bolzano’s Theory of Knowledge does not take account of non-thetical propositional mental acts, the ones Alexius Meinong later called “assumptions” (xiv),21 and they show how Bolzano discusses and avoids certain classical mistakes, such as, for instance, “the view that knowledge consists in the similarity or resemblance between our ideas and their objects” (xvi).

The authors briefly go into Bolzano’s metaphysics, that is, the theory of what is real and appropriately make a comparison with Leibniz’ metaphysics. Like Leibniz, Bolzano thought that substances and their qualities (which he calls “adherences”) are what is real. Both for Leibniz and for Bolzano, “substances are simple and indestructible by natural means” (xiii). However, “Bolzano disagreed with Leibniz on some important points maintaining that substances are in space and time (each one occupying a distinct point at any given instant), and really (not merely ideally) interact” (xii–xiv).

Further on the authors focus on Bolzano’s characterization of knowledge (Kenntnis or Erkenntnis), ignorance and error. Bolzano characterizes knowledge, in a broader sense, as true judgment, and in a strong sense (Wissen), as “confidence in a truth that we ourselves perceive to be unshakable” (xxvi). Ignorance he characterizes as a lack of awareness of a truth, and error as being committed to a false proposition (xxii). The authors also recall how Bolzano “embarks on an inquiry into the origin of error” (xxiii ff.).

Book Four: The Art of Discovery. Given Bolzano’s definition of the Theory of Science as the totality of “the rules according to which we must proceed [(i)] in the business of dividing the entire realm of truth into single sciences and [(ii)] in the exposition thereof in special textbooks,” Book Four examines the “way in which one should proceed in order to discover truth” (wl iii, 293; 197), but only with respect to the above mentioned goals [(i)] and [(ii)]. “Thus not all the rules which must be observed if one wishes to be successful in the search for truth” are considered by Bolzano, “but rather only those that relate to the way we conduct our thinking, and are in addition generally applicable” (loc. cit.), that is, they do not serve to discover one single truth, “but rather many truths belonging to diverse fields of human knowledge” (loc. cit. wl iii, 294; 197).

Introduction to Volume Four. Volume Four of the Theory of Science is devoted to the Theory of Science Proper, that is, “to the presentation of the general rules governing the determination of the domains of individual sciences as well as the elaboration of these sciences in treatises”.22 It contains, in addition to this, “reflections on general methodological topics such as definitions, principles, proofs, and classifications” (xxiii).

Reading the authors’ Introduction one might get the impression that, while early Bolzano’s investigations focused on the conditions a well-grounded presentation of mathematics should comply with, late Bolzano trusts in good old human understanding to answer these questions from a practical standpoint (xxiii ff.). Indeed, the authors stress that, contrary to expectations, Bolzano’s approach is pragmatic in character: “Sciences exist to serve human needs, and their limits are determined by these needs” (xxiv) and they claim that, on the basis of the Theory of Elements, one might have expected Bolzano “to work out an account of sciences in themselves, independent of any reference to human beings, their minds, or needs” (xxiii–xxiv). Thus presented, the authors’ approach turns out to be somewhat misleading, for someone who is not familiar with Bolzano could be led to believe that Bolzano’s principal interest is not really that of rigorous scientific exposition. The authors write, for instance, “[Bolzano] explicitly rejects the views that the boundaries of sciences should be fixed by the kind of objects they deal with, by their sources of knowledge, or by dependence on a particular principle” (xviii). As far as the first view is concerned (the boundaries of sciences should be fixed by the kind of objects they deal with), the authors refer to § 393 of the wl. However, § 393 presents an account of science that is just the same as that presented in § 1, which can be viewed as a deepening of early Bolzano’s conception. He writes (wl iv, 6–7; 3 my emphasis):

I already stated in §1 that by a science in the proper, objective [!] sense I mean nothing other than a collection of all the truths of a certain kind, which are of such a nature that the part of these truths that are noteworthy and known to us is worth writing down in a special book […] According to this definition, I presuppose: (a) that sciences can only contain truths. […] I also count as belonging to a science only (b) truths of a special kind, the various kinds of truths serving to distinguish different sciences. Just how these kinds are to be determined I leave undecided in the concept. It might be the object the truths concern [!!!] or some other attribute (Beschaffenheit) of these truths. But I do always count the entire collection of truths with the stipulated attribute (Beschaffenheit) as belonging to the content of the science, regardless of whether they are known to us or noteworthy. I only require of each science (c) that it be a collection of truths among which there are at least some that are humanly attainable and noteworthy enough to merit presentation in a special book as indicated above. Thus it must not merely be possible but also useful to collect such truths in a book, to order them appropriately, and if need be, to add others to them, so that they appear quite comprehensible and convincing to the reader.

Bolzano is merely saying, in my opinion, that the homogeneity that characterises some truths as belonging to one science can be given not only by the kind of objects about which the science says something, but also by a certain common quality, for instance, as in the case of normative sciences, by the fact that the laws of normative sciences tell us what ought-to-be the case, though perhaps, under actual circumstances, it neither is nor can be. Moreover, talk of an a priori objective nexus that gives sciences their unity makes sense only insofar as theoretical sciences are concerned and may refer to normative and practical sciences only in a derivative way, that is, insofar as these are grounded in theoretical sciences. Bolzano, of course, has to cope also with a number of practical issues connected with the factual presentation of the sciences. However, the core of Bolzano’s argument is still that the task of each single science is to make manifest the objective relation of dependency among its own truths.

In the following I will consider and discuss some terminological choices by the authors.

(i) “Vorstellung”; “an sich”. The authors translate Bolzano’s “Vorstellung” as “idea”, Bolzano’s “an sich” as “in itself” and rightly warn against any misinterpretation of Bolzano’s “an sich” in a Kantian sense, since the connotation of unknowability is not at all present in Bolzano’s “an sich”. I believe that the chosen translation is a good one, as it accounts for Bolzano’s Platonism, that is, for his fundamental assumption that there is a realm of abstract logical objects, like objective ideas and propositions, that are the contents of our mental acts or states and/or linguistic utterances. It is through them, indeed, that the intersubjectivity of the cognitive situation becomes comprehensible. By prefixing the term “subjective” or “objective”, respectively, the choice of the term “idea” allows to distinguish at once between subjective ideas, which are events that occur at a certain time and need a bearer, and objective ideas, which are abstract logical objects, instead.

(ii) “Beschaffenheit”. The authors translate this as “attribute” and justify their choice as follows: “What is required for most occurrences of this word is a generic term covering both properties (Eigenschaften) and relations (Verhältnisse)” (xxvii). I am not sure that “attribute” is a good choice. I would have preferred to stay closer to Bolzano’s wording and translate “Beschaffenheit” as “quality”. “Attribute” has, among others, a Spinozian flavor: “Per attributum intelligo id, quod intellectus de substantia percipit, tamquam ejusdem essentiam constituens” (Ethics, Part i, Def. 4). When defining “attribute” this way, Spinoza is trying, among other things, to save Descartes’ notion of attribute. Now, according to Descartes, the principal attribute of the body is that of being extended, while the principal attribute of the mind is that of being a thinking thing, but no secondary quality is an attribute in this sense. However, according to Bolzano, anything that is had (quodcumque habetur) is a quality.

At this point I take the opportunity to say a few words on a controversial issue in the secondary literature on Bolzano, namely, whether Bolzano admits vacuous qualities in his system. The controversy is depicted very well in Casari 2016, 233–239. If we take seriously the equivalence between being a quality and being had by something, we have as a consequence that there are no vacuous qualities. In wl i 379–380; 272–273, Bolzano explicitly addresses the definability problem for the notions of quality and having. In this context, he writes: “The word ‘have’ is […] commonly used in two senses, a wider and a narrower one. According to the first we can say of any [quality] which is found in an object that the object has it […]. In the second case we mean by it a mere possessing […] of a certain object. […]. I shall use the word ‘have’ always only in the first and wider sense, hence for [qualities] alone. Thus, I can say, whatever is had (quodcumque habetur) must be a quality [was immer gehabt werde (quodcumque habetur) müsse eine Beschaffenheit sein]. If I am asked what parts I take these intimately related concepts to have, I must admit that I am uncertain about their parts and about the exact relation between them. It seems to me that one of them is absolutely simple, and the other is composed of it and a few other parts. Perhaps it is the concept of having that is simple and the concept of a [quality] is always something that is had [… so zwar, dass eine Beschaffenheit immer nur dasjenige was gehabt wird sey]. But it could also be the concept of a [quality] that is simple, and the concept of having could contain it as a part. I am not certain what the answer is, but the former alternative seems more likely.” In the passage just quoted, Bolzano does not doubt that whatever is had is a quality, he questions whether adding to this principle its converse [eine Beschaffenheit [ist] immer nur dasjenige was gehabt wird], provides a definition of quality. In any case, if we take seriously the equivalence between being a quality and belonging to something, it follows that there are no vacuous qualities in Bolzano’s universe.

(iii) Ableitbarkeit. I do not know whether the authors’ choice of translating “Ableitbarkeit” by “deducibility” is a good one. Nowadays this terminology is prone to cause a misunderstanding, since it has become customary, at least in current logic, to use this term in a purely syntactical sense. Indeed, “deducibility” has now a definite syntactical connotation, while, according to Bolzano, Ableitbarkeit is a (quasi) semantic relation. It obtains between two (sets of) propositions with respect to a certain series of ideas if and only if (i) the pre-mises are compatible with respect to that series of ideas and (ii) every series of ideas that makes all the premises true, when substituted for the chosen series, also makes all the conclusions true. It has been remarked repeatedly in recent studies,23 that this is a first characterization of a precursor of the model theoretic notion of logical consequence, which differs from the one given by Tarski in various respects. (a) Bolzano’s explanation of the notion of “following from certain premises through a correct inference” rests on the concept of ‘variation’ of ideas, whereas the model-theoretic version of Tarski’s definition of truth is concerned with non-interpreted languages and so, in order to define truth, or rather satisfaction, one has to put that language in correspondence with an “external” (set-theoretic) structure. (b) Bolzano also allows for varying only some extra-logical notions contained in a proposition: the concept of “following from certain premises” is then relativized to a certain set of ideas, while the basically Tarskian account of the concept of logical consequence given in current logic corresponds to a special case of the Bolzanian account, namely that in which all (and only) extra-logical ideas are varied. By admitting derivability not only with respect to all the extra-logical components (formal or logical Ableitbarkeit) but also with respect to just some of them, Bolzano can cope with material or enthymematic inferences.24

Thus, again, if Ableitbarkeit is a predecessor of Tarski’s logical consequence, it is a (quasi) semantic relation and not a syntactical one. Nevertheless, the rendering of “Ableitbarkeit” by “derivability” that I am pleading for here would also have a syntactical connotation, but, at least, it would stay closer to Bolzano’s wording.

Bernard Bolzano, Theory of Science, translated by Paul Rusnock and Rolf George, is a very important work. From an exegetical point of view, it presents careful readings of the more than 2000 pages of the Theory of Science. At the same time, it exhibits, through the thoroughly thought out translations of key words, a profound knowledge of Bolzano’s earlier and later texts, as well as of the relevant literature and the controversies arising within it. Its publication will help further tremendously our understanding of Bolzano’s thought.

Bibliography

  • Bolzano Bernard 1969+. Bernard Bolzano-Gesamtausgabe, ed. by Berg J. et al. Stuttgart-Bad Cannstatt: Frommann-Holzboog [Abbr.: bga].

  • Bolzano Bernard 1810. Beyträge zu einer begründeteren Darstellung der Mathematik. Erste Lieferung. Prague: Caspar Widtmann. Reprint: Darmstadt: Wissenschaftliche Buchgesellschaft 1974. English translation in: Russ 2004, 82137 [Abbr.: bm].

    • Search Google Scholar
    • Export Citation
  • Bolzano Bernard 1837. Wissenschaftslehre. Versuch einer ausführlichen und größtentheils neuen Darstellung der Logik mit steter Rücksicht auf deren bisherige Bearbeiter, Bd 1–4. Sulzbach: Seidel.

    • Search Google Scholar
    • Export Citation
  • Bolzano Bernard 1972. Theory of Science, ed. & transl. by George R. . Oxford: Blackwell.

  • Bolzano Bernard 1973. Theory of Science, ed. & transl. by Berg J. . Dordrecht: Reidel.

  • Casari Ettore 1984. “L’universo logico bolzaniano”. Rivista di Filosofia 76, 339366.

  • Casari Ettore 2016. Bolzano’s Logical System. Oxford: Oxford University Press.

  • Centrone Stefania 2010. Logic and Philosophy of Mathematics in the Early Husserl. Dordrecht: Springer.

  • Centrone Stefania 2017 . Essays on Husserl’s Logic and Philosophy of Mathematics. Berlin: Springer.

  • Descartes Rene 1897–1913. Oeuvres, ed. by Adam Charles E. and Tannery Paul , Paris: Léopold Cerf [Abbr.: at].

  • Descartes Rene 1641. Meditationes de prima Philosophia. In: at , vii, 1561.

  • Dreyfus Hubert (ed.) 1982. Husserl, Intentionality and Cognitive Science. Cambridge, Ma.: mit Press.

  • Føllesdal Dagfinn 1958. Husserl und Frege. Ein Beitrag zur Beleuchtung der Entstehung der phänomenologischen Philosophie. Oslo: Aschehoug. English translation, Husserl and Frege. In Haaparanta 1994, 3–47.

    • Search Google Scholar
    • Export Citation
  • Føllesdal Dagfinn 1982. “Husserl’s conversion from psychologism and the Vorstellung-meaning-reference distinction: Two separate issues”. In Dreyfus 1982, 5256.

    • Search Google Scholar
    • Export Citation
  • Frege Gottlob 1918–19. „Der Gedanke. Eine logische Untersuchung“. Beiträge zur Philosophie des deutschen Idealismus i, 5877.

  • George Rolf 1983. “Bolzano’s Consequence, Relevance and Enthymemes”. Journal of Philosophical Logic 12, 299318.

  • George Rolf 1983a. “A Postscript on Fallacies”. Journal of Philosophical Logic 12, 319325.

  • Haaparanta Leila (ed.) 1994. Mind, Reasoning and Mathematics. Essays on the Philosophical Views of Husserl and Frege. Dordrecht: Kluwer.

    • Search Google Scholar
    • Export Citation
  • Hill Claire Ortiz and Rosado Haddock, Guillermo E. (2000). Husserl or Frege? Meaning, Objectivity and Mathematics. Chicago and La Salle: Open Court.

    • Search Google Scholar
    • Export Citation
  • Husserl Edmund 1900–1901. Logische Untersuchungen. Bd i, Prolegomena zur reinen Logik. Halle: Max Niemeyer (21913); Bd ii, Untersuchungen zur Phänomenologie und Theorie der Erkenntnis. Halle: Max Niemeyer (21913–1921). English translation by Findlay J.N. , Logical Investigations, New York: Routledge 1970.

    • Search Google Scholar
    • Export Citation
  • Meinong Alexius 1902. Über Annahmen. In: mga , iv.

  • Meinong Alexius 1969–1978. Alexius-Meinong-Gesamtausgabe. Ed. by Haller Rudolf & Kindinger Rudolf , vols. 1–7. Graz: Akademische Druck- und Verlagsanstalt [Abbr.: mga].

    • Search Google Scholar
    • Export Citation
  • Paoli Francesco 1991. “Bolzano e le dimostrazioni matematiche”. Rivista di Filosofia 83, 221242.

  • Peckhaus Volker 2016. “Review of: B. Bolzano, Theory of science. 4 volume set.” Translated from the German and edited by Rusnock Paul and George Rolf , Zentralblatt Mathematik zbl 1315.01056.

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  • Rosado Haddock Guillermo E. 2017 . “Husserl and Riemann”. In Centrone 2017.

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  • Rusnock Paul 2000. Bolzano’s Philosophy and the Emergence of Modern Mathematics. Amsterdam: Rodopi.

  • Russ Steve (ed.) 2004. The Mathematical Works of Bernard Bolzano. Oxford: Oxford University Press.

  • Schmidt R. 1902. Deutsche Buchhändler, vol. 1. Berlin: Eberswalde.

  • Siebel Mark 1996. Der Begriff der Ableitbarkeit bei Bolzano . St. Augustin: Academia Verlag.

  • Spinoza Baruch 1667, Ethica. In: Baruch de Spinoza Opera , 4 vols., ed. by Gebhardt C. . Heidelberg: Carl Winters 1925.

1

Henceforth quoted as wl, followed by the pages of the German original (Sulzbach 1837) and of the present English translation, separated by a semicolon.

3

George & Rusnock, as well as George 1972, suggest that “Braumüller [could have] obtained the unsold signatures from Seidel and put his own wrappers on them” (xxv). “In any case, the 1882 edition of the Wissenschaftslehre is precisely like that of 1837” (loc. cit.). However, since Seidel and Braumüller had been running the bookstore publisher and later the publishing firm together till 1840, it is perhaps more natural to assume that Braumüller, having become the only owner of the enterprise in 1840, simply republished manuscripts he already had. Hereto cf. Schmidt 1902, 84–87.

4

Bolzano 1969+. Henceforth bga.

6

Published in Bolzano 1973, 379–381.

8

Beyträge zu einer begründeteren Darstellung der Mathematik. Henceforth quoted as bm followed by the pages of the German text and of the English translation, separated by a semicolon.

9

bm xi, 88.

10

Hereto see in particular wl §§ 162; 198–222.

11

To this issue cf. Føllesdal’s classic from 1958 (Føllesdal 1958, Engl. transl. Føllesdal 1994) and Føllesdal 1982, a reply to one of his critics. The philosophical systems of Frege and Husserl are compared in Haaparanta 1994 and Hill & Rosado Haddock 2000. To this issue also cf. Centrone 2010, 13–25 and Rosado Haddock 2017.

12

Cp. among others Centrone 2010, Ch. 2.

13

Husserl 1900 Chs. 2–10.

16

loc. cit.

17

Cp. Casari 2016, 52ff.

18

My emphasis.

19

My emphasis.

20

For reasons I explain below, I prefer to stay close to the German name of this relation.

22

wl iv, 3; 1. Cp. Authors’ Introduction to vol. 4, xxiii.

23

Cf. e.g. Berg, in: bga i, 12/1, 26; Casari 1985; Paoli 1991; Siebel 1996.

24

Cp. George 1983.

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  • Bolzano Bernard 1969+. Bernard Bolzano-Gesamtausgabe, ed. by Berg J. et al. Stuttgart-Bad Cannstatt: Frommann-Holzboog [Abbr.: bga].

  • Bolzano Bernard 1810. Beyträge zu einer begründeteren Darstellung der Mathematik. Erste Lieferung. Prague: Caspar Widtmann. Reprint: Darmstadt: Wissenschaftliche Buchgesellschaft 1974. English translation in: Russ 2004, 82137 [Abbr.: bm].

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  • Bolzano Bernard 1837. Wissenschaftslehre. Versuch einer ausführlichen und größtentheils neuen Darstellung der Logik mit steter Rücksicht auf deren bisherige Bearbeiter, Bd 1–4. Sulzbach: Seidel.

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  • Bolzano Bernard 1972. Theory of Science, ed. & transl. by George R. . Oxford: Blackwell.

  • Bolzano Bernard 1973. Theory of Science, ed. & transl. by Berg J. . Dordrecht: Reidel.

  • Casari Ettore 1984. “L’universo logico bolzaniano”. Rivista di Filosofia 76, 339366.

  • Casari Ettore 2016. Bolzano’s Logical System. Oxford: Oxford University Press.

  • Centrone Stefania 2010. Logic and Philosophy of Mathematics in the Early Husserl. Dordrecht: Springer.

  • Centrone Stefania 2017 . Essays on Husserl’s Logic and Philosophy of Mathematics. Berlin: Springer.

  • Descartes Rene 1897–1913. Oeuvres, ed. by Adam Charles E. and Tannery Paul , Paris: Léopold Cerf [Abbr.: at].

  • Descartes Rene 1641. Meditationes de prima Philosophia. In: at , vii, 1561.

  • Dreyfus Hubert (ed.) 1982. Husserl, Intentionality and Cognitive Science. Cambridge, Ma.: mit Press.

  • Føllesdal Dagfinn 1958. Husserl und Frege. Ein Beitrag zur Beleuchtung der Entstehung der phänomenologischen Philosophie. Oslo: Aschehoug. English translation, Husserl and Frege. In Haaparanta 1994, 3–47.

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  • Føllesdal Dagfinn 1982. “Husserl’s conversion from psychologism and the Vorstellung-meaning-reference distinction: Two separate issues”. In Dreyfus 1982, 5256.

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    • Export Citation
  • Frege Gottlob 1918–19. „Der Gedanke. Eine logische Untersuchung“. Beiträge zur Philosophie des deutschen Idealismus i, 5877.

  • George Rolf 1983. “Bolzano’s Consequence, Relevance and Enthymemes”. Journal of Philosophical Logic 12, 299318.

  • George Rolf 1983a. “A Postscript on Fallacies”. Journal of Philosophical Logic 12, 319325.

  • Haaparanta Leila (ed.) 1994. Mind, Reasoning and Mathematics. Essays on the Philosophical Views of Husserl and Frege. Dordrecht: Kluwer.

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  • Hill Claire Ortiz and Rosado Haddock, Guillermo E. (2000). Husserl or Frege? Meaning, Objectivity and Mathematics. Chicago and La Salle: Open Court.

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  • Husserl Edmund 1900–1901. Logische Untersuchungen. Bd i, Prolegomena zur reinen Logik. Halle: Max Niemeyer (21913); Bd ii, Untersuchungen zur Phänomenologie und Theorie der Erkenntnis. Halle: Max Niemeyer (21913–1921). English translation by Findlay J.N. , Logical Investigations, New York: Routledge 1970.

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  • Meinong Alexius 1902. Über Annahmen. In: mga , iv.

  • Meinong Alexius 1969–1978. Alexius-Meinong-Gesamtausgabe. Ed. by Haller Rudolf & Kindinger Rudolf , vols. 1–7. Graz: Akademische Druck- und Verlagsanstalt [Abbr.: mga].

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  • Paoli Francesco 1991. “Bolzano e le dimostrazioni matematiche”. Rivista di Filosofia 83, 221242.

  • Peckhaus Volker 2016. “Review of: B. Bolzano, Theory of science. 4 volume set.” Translated from the German and edited by Rusnock Paul and George Rolf , Zentralblatt Mathematik zbl 1315.01056.

    • Search Google Scholar
    • Export Citation
  • Rosado Haddock Guillermo E. 2017 . “Husserl and Riemann”. In Centrone 2017.

    • Export Citation
  • Rusnock Paul 2000. Bolzano’s Philosophy and the Emergence of Modern Mathematics. Amsterdam: Rodopi.

  • Russ Steve (ed.) 2004. The Mathematical Works of Bernard Bolzano. Oxford: Oxford University Press.

  • Schmidt R. 1902. Deutsche Buchhändler, vol. 1. Berlin: Eberswalde.

  • Siebel Mark 1996. Der Begriff der Ableitbarkeit bei Bolzano . St. Augustin: Academia Verlag.

  • Spinoza Baruch 1667, Ethica. In: Baruch de Spinoza Opera , 4 vols., ed. by Gebhardt C. . Heidelberg: Carl Winters 1925.

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