Bernard Bolzano, known in his lifetime as ‘the Bohemian Leibniz’, is best known as a logician and mathematician, but he also developed a monadology in which the monads, which he called ‘atoms’, have spatial location and physical properties. This essay summarizes and assesses his monadology.

Bernard Bolzano offers a criterion of individuation for ideas, according to which ideas are distinct if and only if they represent different objects or are composed differently. It fails to individuate ideas that are both simple and fail to represent, in particular syncategorematic ideas and logical constants. However, Bolzano also provides the means to close this gap. He suggests that we can distinguish ideas if they are not substitutable for each other in propositions, which we can, in turn, distinguish in (...) terms of their truth-values. This paper explicates this suggestion and develops it into an improved individuation criterion for ideas: ideas also are distinct if we cannot replace them for one another in propositions salva veritate. (shrink)

In his booklet "Contributions to a better founded presentation of mathematics" of 1810 Bernard Bolzano made his first serious attempt to explain the notion of a rigorous proof. Although the system of logic he employed at that stage is in various respects far below the level of the achievements in his later Wissenschaftslehre, there is a striking continuity between his earlier and later work as regards the methodological constraints on rigorous proofs. This paper tries to give a perspicuous and critical (...) account of the fragmentary logic of Beyträge, and it shows that there is a tension between that logic and Bolzano's methodological ban on ?kind crossing? (shrink)

In his booklet ‘Contributions to a better founded presentation of mathematics’ of 1810 Bernard Bolzano made his first serious attempt to explain the notion of a rigorous proof. Although the system of logic he employed at that stage is in various respects far below the level of the achievements in his later Wissenschaftslehre, there is a striking continuity between his earlier and later work as regards the methodological constraints on rigorous proofs. This paper tries to give a perspicuous and critical (...) account of the fragmentary logic of Beyträge, and it shows that there is a tension between that logic and Bolzano's methodological ban on ‘kind crossing’. (shrink)

La philosophie analytique est, dit-on, an-historique, anti-historique même. Elle s’est souvent présentée comme marquant une rupture avec le passé. L’attitude inspirant la question rhétorique que pose Wittgenstein dans les Carnets, « Was geht mich die Geschichte an ? », est répandue. Les multiples liens entre la réalité historique et l’anthropologie philosophique qui ont fasciné les philosophes depuis Hegel jusqu’à Dilthey, Heidegger, Adorno et Habermas – l’évolution historique, les dimensions historiques de l’éthique, de la politique, l’histoire de l’individu et les deux (...) philosophèmes qu’elle englobe : la Vie et la Mort – y sont singulièrement absents, absents tout court (pas dans le sens parisien du mot). (shrink)

The paper discusses some changes in Bolzano's definition of mathematics attested in several quotations from the Beyträge, Wissenschaftslehre and Grössenlehre: is mathematics a theory of forms or a theory of quantities? Several issues that are maintained throughout Bolzano's works are distinguished from others that were accepted in the Beyträge and abandoned in the Grössenlehre. Changes are interpreted as a consequence of the new logical theory of truth introduced in the Wissenschaftslehre, but also as a consequence of the overcome of Kant's (...) terminology, and of the radicalization of Bolzano's anti‐Kantianism. Bolzano's evolution is understood as a coherent move, once the criticism expressed in the Beyträge on the notion of quantity is compared with a different and larger notion of quantity that Bolzano developed already in 1816. This discussion is enriched by the discovery that two unknown texts mentioned by Bolzano in the Beyträge can be identified with works by von Spaun and Vieth respectively. Bolzano's evolution is interpreted as a radicalization of the criticism of the Kantian definition of mathematics and as an effect of Bolzano's unaltered interest in the Leibnizian notion of mathesis universalis. As a conclusion, the author claims that Bolzano never abandoned his original idea of considering mathematics as a scientia universalis, i.e. as the science of quantities in general, and suggests that the question of ideal elements in mathematics, apart from being a main reason for the development of a new logical theory, can also be considered as a main reason for developing a different definition of quantity. (shrink)

Im folgenden Diskussionsbeitrag werden zunächst starke Spannungen innerhalb von Bolzanos Ausführungen zum Substanzbegriff aufgezeigt. Sodann wird eine kürzlich vorgeschlagene Bolzano-Interpretation besprochen, die geeignet sein soll, besagte Spannungen auszuräumen. Doch der Vorschlag bleibt unbefriedigend; daher wird im Anschluss eine alternative Interpretation ausgeführt und verteidigt.