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.

In a series of publications beginning in the 1980s, John Etchemendy has argued that the standard semantical account of logical consequence, due in its essentials to Alfred Tarski, is fundamentally mistaken. He argues that, while Tarski's definition requires us to classify the terms of a language as logical or non-logical, no such division is guaranteed to deliver the correct extension of our pre-theoretical or intuitive consequence relation. In addition, and perhaps more importantly, Tarski's account is claimed to be incapable of (...) explaining an essential modal/epistemological feature of consequence, namely, its necessity and apriority. Bernard Bolzano (1781-1848) is widely recognized as having anticipated Tarski's definition in his Wissenschaftslehre (or Theory of Science ) of 1837. Because of the similarities between his account and Tarski's, Etchemendy's arguments have also been extended to cover Bolzano. The purpose of this article is to consider Bolzano's theory in the light of these criticisms. We argue that, due to important differences between Bolzano's and Tarski's theories, Etchemendy's objections do not apply immediately to Bolzano's account of consequence. Moreover, Bolzano's writings contain the elements of a detailed philosophical response to Etchemendy. (shrink)

This essay presents a new interpretation of Bolzano's account of necessary truth as set out in ?182 of the Theory of Science. According to this interpretation, Bolzano's conception is closely related to that of Leibniz, with some important differences. In the first place, Bolzano's conception of necessary truth embraces not only what Leibniz called metaphysical or brute necessities but also moral necessities (truths grounded in God's choice of the best among all metaphysical possibilities). Second, in marked contrast to Leibniz, Bolzano (...) maintains that there is still plenty of room for contingency even on this broader conception of necessity. (shrink)

Alongside his groundbreaking work in logic, Bernard Bolzano (1781?1848) made important contributions to ontology, notably with his theory of collections. Recent work has done much to elucidate Bolzano's conceptions, but his notion of a sum has proved stubbornly resistant to complete understanding. This paper offers a new interpretation of Bolzano's concept of a sum. I argue that, although Bolzano's presentation is defective, his conception is unexceptionable, and has important applications, notably in his work on the foundations of arithmetic.

This is the first full English translation of Bernard Bolzano's masterwork, the Theory of Science (1837)--a monumental and revolutionary study in logic, epistemology, heuristics, and scientific methodology. Each volume includes an introduction which illuminates the historical context of Bolzano's work and its continuing relevance.

This paper surveys Bolzano's Beyträge zu einer begründeteren Darstellung der Mathematik (Contributions to a better-grounded presentation of mathematics) on the 200th anniversary of its publication. The first and only published issue presents a definition of mathematics, a classification of its subdisciplines, and an essay on mathematical method, or logic. Though underdeveloped in some areas (including,somewhat surprisingly, in logic), it is nonetheless a radically innovative work, where Bolzano presents a remarkably modern account of axiomatics and the epistemology of the formal sciences. (...) We also discuss the second, unfinished and unpublished issue, where Bolzano develops his views on universal mathematics. Here we find the beginnings of his theory of collections, for him the most fundamental of the mathematical disciplines. Though not exactly the same as the later Cantorian set theory, Bolzano's theory of collections was used in very similar ways in mathematics, notably in analysis. In retrospect, Bolzano's debut in philosophy was a remarkably successful one, though its fruits would only become generally known much later. (shrink)

In the works of Kant and his followers, the notion of form plays an important role in explaining the apriority, necessity and certainty of logic. Bernard Bolzano (1781–1848), an important early critic of Kant, found the Kantians' definitions of form imprecise and their explanations of the special status of logic deeply unsatisfying. Proposing his own conception of form, Bolzano developed radically different views on logic, truth in virtue of form, and other matters. This essay presents Bolzano's views in the light (...) of his criticisms of the Kantian logicians. (shrink)

…all men begin… by wondering that things are as they are…as they do about…the incommensurability of the diagonal of the square with the side; for it seems wonderful to all who have not yet seen the reason, that there is a thing which cannot be measured even by the smallest unit. But we must end in the contrary and, according to the proverb, the better state, as is the case in these instances too when men learn the cause; for there (...) is nothing which would surprise a geometer so much as if the diagonal turned out to be commensurable. (shrink)

This paper is devoted to an examination of Bolzano’s notion of necessary existence, which has so far received relatively little attention in the literature. We situate Bolzano’s ideas in their historical context and show how he proposed to correct various flaws of his predecessors’ definitions. Further, we relate Bolzano’s conception to his metaphysical and theological assumptions, arguing that some consequences of his definition which have been deemed counterintuitive by some of his interpreters turn out to be more reasonable given the (...) broadly Leibnizian background of his metaphysics. Finally, we consider some difficulties that arise from Bolzano’s evolving views on freedom, which, at least in his early thought, was intimately linked with contingency. In an appendix, we discuss a recent debate on Bolzano’s notion of necessary truth between Textor and Rusnock that has some bearing on our overall line of interpretation of Bolzano’s notion of necessary existence. (shrink)

This edition provides the first complete English translation of Bernard Bolzano's four-volume Wissenschaftslehre or Theory of Science, a masterwork of theoretical philosophy. First published in 1837, the Wissenschaftslehre is a monumental, wholly original study in logic, epistemology, heuristics, and scientific methodology. Unlike most logical studies of the period, it is not concerned with the "psychological self-consciousness of the thinking mind." Instead, it develops logic as the science of "propositions in themselves" and their parts, especially the relations between these entities. It (...) offers, for the first time in the history of logic, a viable definition of consequence, and a novel view of probability. Giving constant attention to Bolzano's predecessors and contemporaries, with particular emphasis on Kant, this richly documented work is also a valuable source for the history of logic and philosophy. (shrink)

Russell, in his History of Western Philosophy, wrote that modern analytical philosophy had its origins in the construction of modern functional analysis by Weierstrass and others. As it turns out, Bolzano, in the first four decades of the nineteenth century, had already made important contributions'to the creation of "Weierstrassian" analysis, some of which were well known to Weierstrass and his circle. In addition, his mathematical research was guided by a methodology which articulated many of the central principles of modern philosophical (...) analysis. That Russell was able to discover philosophical content within mathematical analysis was thus not surprising, for it had been carefully put there in the first place. Bolzano can and should, accordingly, be viewed as a founder of modern analytical philosophy, and not necessarily as an uninfluential one. This paper considers his work in mathematical and philosophical analysis against some of the relevant historical background. (shrink)

Russell, in his History of Western Philosophy, wrote that modern analytical philosophy had its origins in the construction of modern functional analysis by Weierstrass and others. As it turns out, Bolzano, in the first four decades of the nineteenth century, had already made important contributions'to the creation of "Weierstrassian" analysis, some of which were well known to Weierstrass and his circle. In addition, his mathematical research was guided by a methodology which articulated many of the central principles of modern philosophical (...) analysis. That Russell was able to discover philosophical content within mathematical analysis was thus not surprising, for it had been carefully put there in the first place. Bolzano can and should, accordingly, be viewed as a founder of modern analytical philosophy, and not necessarily as an uninfluential one. This paper considers his work in mathematical and philosophical analysis against some of the relevant historical background. (shrink)

Bernard Bolzano is increasingly recognized as one of the greatest nineteenth-century philosophers. A philosopher and mathematician of rare talent, he made ground-breaking contributions to logic, the foundations and philosophy of mathematics, metaphysics, and the philosophy of religion. Many of the larger features of later analytic philosophy first appear in his work: for example, the separation of logic from psychology, his sophisticated understanding of mathematical proof, his definition of logical consequence, his work on the semantics of natural kind terms, or his (...) anticipations of Cantor's set theory, to name but a few. To his contemporaries, however, he was best known as an intelligent and determined advocate for reform of Church and State. Based in large part on a carefully argued utilitarian practical philosophy, he developed a program for the non-violent reform of the authoritarian institutions of the Hapsburg Empire, a program which he himself helped to set in motion through his teaching and other activities. Rarely has a philosopher had such a great impact on the political culture of his homeland. Persecuted in his lifetime by secular and ecclesiastical authorities, long ignored or misunderstood by philosophers, Bolzano's reputation has nevertheless steadily increased over the past century and a half. Much discussed and respected in Central Europe for over a century, he is finally beginning to receive the recognition he deserves in the English-speaking world. This book provides a comprehensive and detailed critical introduction to Bolzano, covering both his life and works. (shrink)

Largely ignored in Germany during the nineteenth century, Bolzano was certainly better known in Austria, in particular among Brentano’s students, who enthusiastically studied his Theory of science. In this respect it makes sense to speak of Bolzano as belonging to a tradition of Austrian philosophy. Yet an examination of the reception of Bolzano’s ideas among Brentano’s students indicates that he was not always well understood. This article discusses a particular case, Twardowski’s reaction to Bolzano’s theory of representation.

Many contemporary philosophers favor coherence theories of knowledge (Bender 1989, BonJour 1985, Davidson 1986, Harman 1986, Lehrer 1990). But the nature of coherence is usually left vague, with no method provided for determining whether a belief should be accepted or rejected on the basis of its coherence or incoherence with other beliefs. Haack's (1993) explication of coherence relies largely on an analogy between epistemic justification and crossword puzzles. We show in this paper how epistemic coherence can be understood in terms (...) of maximization of constraint satisfaction, in keeping with computational models that have had a substantial impact in cognitive science. A coherence problem can be defined in terms of a set of elements and sets of positive and negative constraints between pairs of those elements. Algorithms are available for computing coherence by determining how to accept and reject elements in a way that satisfies the most constraints. Knowledge involves at least five different kinds of coherence - explanatory, analogical, deductive, perceptual, and conceptual - each requiring different sorts of elements and constraints. (shrink)

The impressive volume before us started out as an attempt to write “the history of epistemology since Kant, the way Carnap would have written it had he been Hegel.” Coffa began his project in 1981 while a fellow at the Center for Philosophy of Science in Pittsburgh and had finished a “good penultimate draft” when he suddenly died, after a brief illness, on 30 Dec., 1984. The title alludes to Edmund Wilson’s classic study of revolutionary ideology, To the Finland Station. (...) This is no accident and would be presumptuous in a lesser work. The two studies cover roughly the same period, from the late eighteenth century to the first part of the present one, and they are both sparkling narratives that boldly project a large picture and then fill it in with canny detail. Coffa begins with Kant, the villain of the piece, and ends with a group of thinkers “in the neighborhood of Vienna” who came to terms with the restrictive framework they had inherited from Kant, finally overcoming it in favor of a new philosophy in which meaning, rather than mind, played the central role. (shrink)

Bernard Bolzano of Prague was one of the few thinkers of his time who combined real talent in mathematics and philosophy. He was especially drawn to the common ground between these fields, interested in questions of method and what would today be called foundations . Interestingly, he was neither a professional mathematician nor a professional philosopher. As a young man, he had decided that his first priority must be to work for the reform and improvement of society. This led him, (...) after much reflection, to become a priest and to occupy a newly-created chair in religious science at the Charles University in 1805. In this post, he was widely known as what would later be called a dissident, denouncing abuses of power and the ills that were the consequence of the still largely feudal institutions and attitudes of the Austrian Empire, and inspiring a generation of students to transform these institutions from within. While his activities brought him a large and committed following, they also gained him powerful enemies in Vienna and Rome, who eventually convinced the Emperor to remove him from his post in December of 1819. Amazingly, during these years of energetic public life, in which he suffered horribly from lung disease and a variety of other ailments, Bolzano remained quite active as a mathematician. As his notebooks attest, he read the latest mathematical literature voraciously and systematically.1 He also made a number of important discoveries, especially in the foundations of real analysis, and published four mathematical works between 1810 and 1817 [Bolzano, 1810; 1816; 1817a; 1817b].2 After his dismissal, he continued his work, pursuing his earlier inquiries with greater depth and precision, …. (shrink)