Not all truths are on a par. The realm of truths is structured: some propositions are only true because others are. The relation that endows the realm of truths with this structure is often called grounding. Grounding has achieved much attention in 21st century metaphysics, but the topic is arguably as old as philosophy itself. -/- This becomes apparent when investigating the works of the 19th-century philosopher Bernard Bolzano, who developed what is perhaps the first comprehensive theory of grounding, (...) drawing on a rich tradition that goes back to Aristotle’s Posterior Analytics. Roski’s book provides, for the first time, a comprehensive study of Bolzano’s theory of grounding in its entirety, paying more attention than previous studies to the interaction between grounding and the consequence-relation of deducibility. -/- . (shrink)

Contents: Acknowledgements. Conventions. Preface. Biographical sketch. 1 Introduction. 2 The Contributions. 3 Early work in analysis. 4 The Theory of Science . 5. Later mathematical studies. A On Kantian Intuitions. B The Bolzano-Cauchy Theorem.

"Provides translations of Bolzano's most important work on grounding, including previously untranslated material"--.

In the course of the last few decades, Bolzano has emerged as an important player in accounts of the history of philosophy. This should be no surprise. Few authors stand at a more central junction in the development of modern thought. Bolzano's contributions to logic and the theory of knowledge alone straddle three of the most important philosophical traditions of the 19th and 20th centuries: the Kantian school, the early phenomenological movement and what has come to be known (...) as analytical philosophy. This paper identifies three Bolzanian theoretical innovations that warrant his inclusion in the analytical tradition: the commitment to ‘logical realism’, the adoption of a substitutional procedure for the purpose of defining logical properties and a new theory of a priori cognition that presents itself as an alternative to Kant's. All three innovations concur to deliver what counts as the most important development of logic and its philosophy between Aristotle and Frege. In the final part of the paper, I defend Bolzano against a common objection and explain that these theoretical innovations are also supported by views on syntax, which though marginal are both workable and philosophically interesting. (shrink)

The aim of the paper is to present and evaluate Bolzano's theory of grounding, that is, his theory of the concept expressed and the relation brought into play by 'because'. In the first part of the paper (Sections 1-4) the concept of grounding is distinguished from and related to three other concepts: the concept of an epistemic reason}, the concept of causality, and the concept of deducibility (i.e., logical consequence). In its second part (Sections 5-7) Bolzano's positive account (...) of grounding is reconstructed in axiomatic form and critically discussed. (shrink)

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

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

It is sometimes mentioned that Bernard Bolzano’s work on grounding anticipates many insights of the current debate on metaphysical grounding. The present paper discusses a certain part of Bolzano’s theory of grounding that has thus far not been discussed in the literature. This part does not so much anticipate what are nowadays common assumptions about grounding, but rather goes beyond them. Central to the discussion will be a thesis of Bolzano’s by which he tries to establish a (...) connection between grounding and unification. The paper spells out this thesis in detail and discusses the assumptions on which it rests. Next to this mainly historical aim, the paper also presents reasons why philosophers who are not interested in the historical Bolzano should find the thesis interesting by relating it to a certain view on unification and explanation that has been put forward by Kim. A final part of the paper provides a critical evaluation of the thesis against the background of current accounts of grounding. (shrink)

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Bernard Bolzano criticised Kant's philosophy so vehemently that his pupil Franz Prihonsky called him "Anti-Kant". One of his criticisms concerns Kant's cosmological antinomies. The context of this critique is the problem of limits of knowledge. Kant wanted to prove that there are such boundaries, and to show where these are located. In this paper we will schematize Kant's antinomies and summarize Bolzano's criticism, which is distributed over his and his student's work. At the beginning we will work out (...) the theoretical differences between Kant's and Bolzano's philosophy to see what roles these play in the construction of the antinomies. (shrink)

Die Reden des Studentenpfarrers Bolzano -- Von den Grausamkeiten der Christen an den Juden -- Über den Mut -- Über den Selbstmord -- Über das Verhältnis der beiden Volksstä̕mme in Böhmen -- Über Lug und Trug -- Die Edition der Reden in der Bolzano-Gesamtasugabe : Korrekturen, Konjekturen und Annotationen -- Anhang: Sprachliche Eigentümlichkeiten der Schriften Bolzanos und ihrer Editionen im 19. Jahrhundert.

Here I revisit Bolzano's criticisms of Kant on the nature of logic. I argue that while Bolzano is correct in taking Kant to conceive of the traditional logic as a science of the activity of thinking rather than the content of thought, he is wrong to charge Kant with a failure to identify and examine this content itself within logic as such. This neglects Kant's own insistence that traditional logic does not exhaust logic as such, since it must (...) be supplemented by a transcendental logic that will in fact study nothing other than thought's content. Once this feature of Kant's views is brought to light, a much deeper accord emerges between the two thinkers than has hitherto been appreciated, on both the nature of the content that is at issue in logic and the sense of logic's generality and formality. (shrink)

This paper sets forth Bolzano’s little-known 1843 account of beauty. Bolzano accepted the thesis that beauty is what rewards contemplation with pleasure. The originality of his proposal lies in his claim that the source of this pleasure is a special kind of cognitive process, namely, the formation of an adequate concept of the object’s attributes through the successful exercise of the observer’s proficiency at obscure and confused cognition. To appreciate this proposal we must understand how Bolzano explicated (...) a number of concepts in his Wissenschaftslehre. I argue that Bolzano was ahead of his time and anticipated some of the results of recent empirical psychological research on the relations between beauty, affect, and processing fluency. Bolzano’s remarks on ugliness and on relations between pure and mixed beauty are also of contemporary interest. The upshot is that Bolzano’s account of beauty is neither as derivative nor ‘dark’ as some of his commentators have claimed. (shrink)

Bolzano incorporated Kant's distinction between intuitions and concepts into the doctrine of propositions by distinguishing between conceptual (Begriffssätze an sich) and intuitive propositions (Anschauungssätze an sich). An intuitive proposition contains at least one objective intuition, that is, a simple idea that represents exactly one object; a conceptual proposition contains no objective intuition. After Bolzano, philosophers dispensed with the distinction between conceptual and intuitive propositions. So why did Bolzano attach philosophical importance to it? I will argue that, ultimately, (...) the value of the distinction lies in the fact that conceptual and intuitive truths have different objective grounds: if a conceptual truth is grounded at all, its ground is a conceptual truth. The difference in grounds between conceptual and intuitive truths motivates Bolzano's criticism of Kant's view that intuition plays the fundamental role in mathematics, a conceptual science by Bolzano's lights. (shrink)

Bolzano's theory of collections (Inbegriffe) has usually been taken as a rudimentary set theory. More recently, Frank Krickel has claimed it is a mereology. I find both interpretations wanting. Bolzano's theory is, as I show, extremely broad in scope; it is in fact a general theory of collective entities, including the concrete wholes of mereology, classes-as-many, and many empirical collections. By extending Bolzano's ideas to embrace the three factors of kind, components and mode of combination, one may (...) develop a coherent general account of collections. But it is most difficult to take Bolzano's view to fit modern set theory. So while Krickel's positive thesis is rejected, his negative thesis is confirmed. (shrink)

In this paper I argue that Bolzano's concept of deducibility and Tarski's concept of logical consequence differ with respect to their philosophical intent. I distinguish between epistemic and ontic approaches to logic, and argue that Bolzano's deducibility presupposes an epistemic approach, while Tarski's logical consequence presupposes an ontic approach.

Bolzano holds that every sentence can be paraphrased into a sentence of the form "A has b". Bolzano's arguments for this claim are reconstructed and discussed. Since they crucially rely on Bolzano's notion of paraphrase, this notion is investigated in detail. Bolzano has usually been taken to require that in a correct paraphrase the sentence to be paraphrased and the paraphrasing sentence express the same proposition. In view of Bolzano's texts and systematical considerations this interpretation (...) is rejected: Bolzano only holds that the sentence to be paraphrased and the paraphrasing sentence must be equipollent ("gleichgeltend"). It is shown that even this modest view of paraphrase does not help Bolzano in sustaining his claim that all sentences have the form "A has b". (shrink)

A theory of aesthetic normativity states what makes it the case that the fact that an item is beautiful is reason to appreciate it. Aesthetic hedonists characteristically hold that the fact that an item is beautiful is reason to appreciate it because anyone always has reason to do what yields pleasure. Bernard Bolzano was an aesthetic hedonist who is best interpreted as offering a mixed theory of aesthetic normativity. The fact that an item is beautiful is reason to appreciate (...) it because anyone always has reason to do what yields pleasure and because anyone also has reason to do what fosters virtue, the capacity to act well. The argument for this interpretation knits together Bolzano’s aesthetics, his ethics, and his philosophy of science. In doing so, this argument opens up a new perspective on aesthetic normativity. (shrink)

Kant -- Decomposition -- Meaning and analysis -- A substitutional theory -- Analyticity -- Consequence -- Justification and proof -- A priori knowledge -- Things, collections and numbers -- Frege -- Husserl, logical psychologism, and the theory of knowledge.

The dissertation provides a reconstruction of Bernard Bolzano's theory of grounding (both in early and late works) against the background of a classical conception of science and scientific explanation.

In this paper, I provide a thorough discussion and reconstruction of Bernard Bolzano’s theory of grounding and a detailed investigation into the parallels between his concept of grounding and current notions of normal proofs. Grounding (Abfolge) is an objective ground-consequence relation among true propositions that is explanatory in nature. The grounding relation plays a crucial role in Bolzano’s proof-theory, and it is essential for his views on the ideal buildup of scientific theories. Occasionally, similarities have been pointed out (...) between Bolzano’s ideas on grounding and cut-free proofs in Gentzen’s sequent calculus. My thesis is, however, that they bear an even stronger resemblance to the normal natural deduction proofs employed in proof-theoretic semantics in the tradition of Dummett and Prawitz. (shrink)

In his Foundations of a General Theory of Manifolds, Georg Cantor praised Bernard Bolzano as a clear defender of actual infinity who had the courage to work with infinite numbers. At the same time, he sharply criticized the way Bolzano dealt with them. Cantor’s concept was based on the existence of a one-to-one correspondence, while Bolzano insisted on Euclid’s Axiom of the whole being greater than a part. Cantor’s set theory has eventually prevailed, and became a formal (...) basis of contemporary mathematics, while Bolzano’s approach is generally considered a step in the wrong direction. In the present paper, we demonstrate that a fragment of Bolzano’s theory of infinite quantities retaining the part-whole principle can be extended to a consistent mathematical structure. It can be interpreted in several possible ways. We obtain either a linearly ordered ring of finite and infinitely great quantities, or a partially ordered ring containing infinitely small, finite and infinitely great quantities. These structures can be used as a basis of the infinitesimal calculus similarly as in non-standard analysis, whether in its full version employing ultrafilters due to Abraham Robinson, or in the recent “cheap version” avoiding ultrafilters due to Terence Tao. (shrink)

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

Bolzano holds that every sentence can be paraphrased into a sentence of the form "A has b". Bolzano's arguments for this claim are reconstructed and discussed. Since they crucially rely on Bolzano's notion of paraphrase, this notion is investigated in detail. Bolzano has usually been taken to require that in a correct paraphrase the sentence to be paraphrased and the paraphrasing sentence express the same proposition. In view of Bolzano's texts and systematical considerations this interpretation (...) is rejected: Bolzano only holds that the sentence to be paraphrased and the paraphrasing sentence must be equipollent ("gleichgeltend"). It is shown that even this modest view of paraphrase does not help Bolzano in sustaining his claim that all sentences have the form "A has b". (shrink)

In 1817, in the preface to his Rein analytischer Beweis, Bernard Bolzano revealed that he had decided to postpone the publication of any subsequent instalment of his Beyträge zu einer begründeteren Darstellung der Mathematik because of the few and ‘superficial’ reviews of its first instalment, published in 1810. Bolzano’s transcriptions of the only two known reviews of this book are conserved at the Literární archiv Památníku národního písemnictví / Muzea literatury, in Prague, together with another manuscript on his (...) Beyträge, the provenance of which was unknown to Bolzano’s scholars until recently. In this paper it is shown that this latter manuscript is a draft of an announcement that was published at the time and that was indeed written at least to some extent by Bolzano himself. This hitherto unknown announcement of Bolzano’s Beyträge not only solves the mystery surrounding that manuscript, but also helps to date the publication of this book more precisely and provides an unusual insight into what we must take Bolzano himself to have considered most noteworthy about his work, namely his study on logic. The paper includes a transcription of the manuscript and an English translation of the announcement. (shrink)

This chapter has two aims. The first aim is to present an overview of Bolzano's universe from the point of view of his metaphysics and its relationship to logic, relying fundamentally on Bolzano's Wissenschaftslehre. The author's preferred reading of Bolzano is one according to which he is a 'platonistic nominalist': a platonist about propositions and a nominalist about properties. Bolzano's nominalistic tendencies are particularly conspicuous in his mereological analyses, which play a major role in every aspect (...) of his philosophy. The author's second aim is to answer the open question of whether in Bolzano there is any 'ontology of truth'. This chapter argues for a negative answer. Bolzano does not make room for any special object which plays the role of the counterpart of a truth-bearer, or at least his propositions do not connect semantically in a direct way to anything that would count as such a special object. (shrink)

What I propose is to reconsider the interpretation of Bolzano’s concept of analytic propositions which was offered thirty years ago by Bar-Hillel. The claim of Bar-Hillel was that, in a late addition to his book, The Theory of Science, Bolzano actually had been radically improving his concept of analyticity, thus creating some inconsistencies with the previous, uncorrected version. This allows us to equate the new Bolzanian definition of analytic with what was to be defined, a century later, as (...) logical truth by W. V. Quine. Bar-Hillel’s interpretation has been uncritically accepted by commentators, although the historical issue has been rightly challenged by J. Berg. What I want to show is that, in spite of a surface analogy between Bolzano’s phrasing of the definition of ‘logical analytic’ and Quine’s definition, certain considerations should lead us to call that parallel into question. Attractive as it may be for a Quinian, such a view of Bolzano’s analytic can be shown as incompatible with the leading ideas of his philosophy of logic. Furthermore, there is enough evidence in other sections of the Theory of Science to show that Bolzano’s criterion of analyticity is grounded on purely semantical properties and is part of a general account of logical properties in terms of the mapping of propositions to corresponding models. (shrink)

Bernard Bolzano's most fruitful invention was his method of variation. He used it in defining such fundamental logical concepts as logical consequence, analyticity and probability. The following three puzzles concerning this method of variation seem particularly worth considering, (i) How can we define the range of variation of an idea or the categorial conformity of two ideas without already using the concept of variation? This question was raised by Mark Siebel in his M. A. thesis, (ii) Why must we (...) define analyticity by means of (simultaneous or successive) variation of several ideas rather than by means of replacing a single idea? This problem is suggested by an example due to W.V.O. Quine, John R. Myhill and Benson Mates, (iii) Must every 'there is...' sentence be synthetic for Bolzano, as his pupil Franz Příhonský claims in his booklet Neuer Anti-Kant, or can a 'there is...' sentence be logically analytic? (shrink)

L’objectif de Bolzano, dans la Wissenschaftslehre, est d’exposer les conditions générales de la constitution du domaine des sciences particulières comme découpage à l’intérieur du domaine plus général des vérités en soi. Ce qui intéresse plus précisément Bolzano, c’est la manière dont chacune de ces sciences particulières doit se rapporter à son domaine. Dans cette perspective, le concept de représentation...

L'auteur expose la tentative faite par Bolzano de définir le concept de proposition en soi analytique à l'aide du concept de variation de représentation. Puis, il discute les difficultés qui résultent de ce modèle quant à la définition bolzanienne du concept étroit de vérité logiquement analytique ou de vérité logique. En conclusion, il compare la définition bolzanienne du concept de proposition en soi analytique et la définition husserlienne: celle-ci se découvre être une application de l'idée fondamentale de Bolzano (...) — employer la variation de représentation pour définir les concepts logiques fondamentaux. The author tries to outline Bolzano's proposal to define the concept of an analytic proposition by using the concept of idea variation. He discusses the problems that arise for Bolzano's attempt to define the concept of a logical truth on the same lines. He ends by comparing Bolzano's and Husserl's definition of the concept of an analytical proposition: Husserl's definition can be seen as an original application of Bolzano's basic idea to define basic logical notions with recourse to the concept of idea variation. (shrink)

Inhaltsverzeichnis/Table of Contents Themenschwerpunkt/Special Topic: Bolzano & Kant Gastherausgeber/Guest Editor: Sandra Lapointe Sandra Lapointe: Introduction Sandra Lapointe: Is Logic Formal? Bolzano, Kant and the Kantian Logicians Nicholas F. Stang: A Kantian Reply to Bolzano¿s Critique of Kant¿s Analytic-Synthetic Distinction Clinton Tolley: Bolzano and Kant on the Place of Subjectivity in a Wissenschaftslehre Timothy Rosenkoetter: Kant and Bolzano on the Singularity of Intuitions Waldemar Rohloff: From Ordinary Language to Definition in Kant and Bolzano Weitere Artikel/Further (...) Articles Christian Damböck: Wilhelm Diltheys empirische Philosophie und der rezente Methodenstreit in der analytischen Philosophie Bernd Prien: Socially Constituted Actions and Objects Daniel Enrique Kalpokas: Two Dogmas of Coherentism Jon Cogburn & Jeff W. Roland: Strong, therefore Sensitive. Misgivings about DeRose¿s Contextualism Andre Abath: Brewer¿s Switching Argument Essay-Wettbewerb/Essay Competition Amadeus Magrabi: The Value of Feelings for Decision-Making Stefan Reining: Do Pain-Accompanying Emotions Mislead Us?¿Considerations in the Light of Reactive Dissociation Phenomena Peter Königs: Patriotism. A Case Study in the Philosophy of Emotions Besprechungsaufsatz/Review Essay Christopher Gauker: What Do Your Senses Say? On Burge¿s Theory of Perception Diskussion/Discussion Georg Brun: Adequate Formalization and De Morgan¿s Argument Buchnotizen/Critical Notes. (shrink)

This paper discusses a novel response to two closely related regress arguments from Bolzano’s Theory of Science and Carroll’s What the Tortoise Said to Achilles. Bolzano’s argument aims to refute the thesis that full grounds must include propositions involving notions such as entailment, grounding or lawhood which link the respective grounds to their groundee. This thesis is motivated, Bolzano’s argument is reconstructed, and a response based on self-referential linking propositions is developed and defended against objections concerning self-reference (...) and Curry’s paradox. Finally, the idea is applied to a reading of Carroll’s dialogue and a corresponding solution to the so-called infinite regress problem of inference is proposed. (shrink)

Gary Kemp: Quine's Relationship with Analytic Philosophy: I try to explain why Quine, for all his fame amongst analytic philosophers, has so few explicit followers within analytic philosophy of the past fifty years – despite the fact that naturalism, at least as broadly conceived, is so popular. Partly it's because Quine's particular version of naturalism is so demanding, partly it's because the nature and seriousness of his commitment to extensionalism are not well recognized, and partly because his views were formulated (...) from an extremely general and abstract point of view in the philosophy of science. I focus on the second and especially on the third. Quine is more radical and more alien than is customarily appreciated. (shrink)