Mathematics

This chapter presents an overview of Bolzano’s work in mathematics and its philosophy, while presenting some interesting samples of his work. It begins with a discussion of his views on mathematical method in their historical context, followed by an exposition of some of his best work in real analysis. In particular, the chapter discusses his early work on infinite series and his analysis of continuity, beginning with the Purely Analytic Proof (1817), and extending to his construction of a continuous, nowhere differentiable function in the 1830s, called Bolzano’s function. (85 words)

Political Philosophy

Bolzano’s major work on political philosophy is a treatise called On the Best State, which was first drafted around 1830. Despite its title, it is not a merely utopian work. The best state is considered not in order to avoid practical attempts at reform, but to give them a theoretical underpinning and clearer direction. Chapter 3 presents the main points of the political philosophy set out in On the Best State, followed by a consideration of the program for reform that Bolzano had presented in the sermons (Erbauungsreden) he read at San Salvator church and further developed in his lectures on the “science of religion” at the Charles University and in some later essays. In particular, discussion centers on his views on civil disobedience, revolt, enlightenment, and the rights of women, religious minorities, and the Czech-speaking citizens of Bohemia. (125 words)

Ethics

Bolzano’s ethics is a variant of utilitarianism. As an early utilitarian theory, it lacks some of the refinements later developed with the help of concepts drawn from economic theory. It is nevertheless mostly up to his usual standard, with clear explanations of the key points, and fair consideration of opposing views. This relatively brief chapter presents the main points of Bolzano’s exposition of ethics, before looking at some subtle questions raised by duties with respect to beliefs, which he dealt with in a pair of sermons on self-deception and in the Treatise of the Science of Religion. (97 words)

Bolzano’s Life

This volume provides the most complete biography of Bolzano in English to date. After a brief survey of the history of Bohemia, Chapter 1 recounts the main events of Bolzano’s life: his early upbringing and education, his activity as a young professor at the Charles University, his dismissal and trial, and his later life, including his intense relationship with Anna Hoffmann and his wide-ranging work as an independent scholar. (67 Words)

Introduction

Bolzano’s life coincides almost exactly with what has been called the Age of Revolutions. Born in 1781, he lived through the revolution from above launched by Joseph II in 1780, the French Revolution, the triumphs and defeats of Napoleon, the conservative reaction embodied in the Metternich System, the beginnings of the Industrial Revolution, the July revolution of 1830, and finally the uprisings of 1848, the last year of his life. It was a time of exaggerations, of great hopes and fears, sudden reversals, and crushing disappointments, a time of vast enthusiasms and general confusion, as unprecedented forces were let loose upon a world almost completely unprepared for them. The world of letters was not spared, as authors strove to make their voices count in an ever more crowded and noisy public forum. Novelty was everywhere sought, overreach and passion common on all sides....

Aesthetics, the Science of Beauty

In the last decade of his life, Bolzano turned to aesthetics. He planned to write a series of essays on the subject, and drafted several of them for presentation at the Bohemian Royal Society. In the end, two were published: “On the Concept of the Beautiful” (1843) and “On the Classification of the Fine Arts” (1849). The former presents a careful analysis of the concept of beauty, along with a detailed literature survey; the latter, definitions of the concepts of aesthetics, arts, and artworks, along with a proposed classification of the fine arts. This chapter presents a critical introduction to these works. (103 words)

Catholicism and the Catholic Church

Bolzano’s engagement with Catholicism and the Church was both theoretical and practical. In his Lehrbuch der Religionswissenschaft, he examined Catholicism in light of the conceptual tools he had developed for the study of religions in general. Practically, his concern was to develop interpretations of Catholic teachings that would be compatible with the demands of reason but also maximally conducive to the virtue and happiness of those who accepted them. In many cases, these interpretations put him at odds with strong conservative currents of Catholic opinion. The focus in this chapter is on a relatively small number of points in Bolzano’s presentation of Catholicism which the authors think are especially interesting from a philosophical point of view. In particular, the subjects discussed are his conception of miracles and revelation, the constraints he places on the interpretation of revealed doctrines, the role of consensus in Catholicism, and the sources and kinds of authority within the Church. (150 words)

Ontology and Metaphysics

In many of its claims, Bolzano’s metaphysics appears to belong in the eighteenth century: he elaborates a monadology and an account of the creation which, despite significant differences, resemble those of Leibniz and his successors in many particulars. As in mathematics, he treated the work of his predecessors with respect, seeking foundations for what he took to be solid and modifying where he thought necessary. As in mathematics, too, his search for foundations often produced radically new conceptions. Perhaps the most important of these are found in his theory of collections, with its anticipations of set theory and classical mereology. This chapter gives a survey of Bolzano’s work in metaphysics, covering basic concepts of his ontology (object, attribute, property, relation, determination, collection, substance, adherence, etc.), his account of space and time, and his atom-theory (a variant of Leibniz’s monadology), as well as his conceptions of necessity and possibility. (148 words)

Theory of Knowledge

This chapter presents Bolzano’s theory of knowledge, focusing on the account given in Book 3 of the Theory of Science. It begins with an introduction situating Bolzano in the historical context of modern philosophy and highlighting some of the most innovative features of his epistemology. There follows a section laying out the elements of Bolzano’s account of human knowledge: the nature of subjective ideas and propositions, their relations to their objective counterparts, intuitions and concepts, inference, immediate judgments, a priori and empirical knowledge. It then discusses his notions of knowledge, error, and certainty, followed by a consideration of §303 of the Theory of Science, where Bolzano describes how we might come to form some of our most basic judgments of experience. A final section discusses Bolzano’s critical stance towards the Kantian philosophy. (133 words)

Philosophy of Religion

As professor at the Charles University, Bolzano lectured on religion for many years, developing a theoretical framework for understanding religions in general, which was then applied to Catholicism. The starting point is the notion of a religious proposition, defined as a proposition that if believed, would have an impact on someone’s virtue and happiness, and which one may be inclined to accept or reject based not on reasons but rather on one’s wishes. A person’s religion is then defined as the collection of his religious beliefs. Given this very general conception, it is clear that Bolzano counts as religious far more propositions than most would, to the point where even atheists can properly be said to have a religion. Other inquiries deal with the figurative content of many religious doctrines and with divine revelation, the latter the subject of one of the most subtle of Bolzano’s conceptual analyses. (148 words)