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)

This volume will be of particular interest to researchers working in the history, and in the philosophy, of logic and mathematics, and more generally, to ...

The paper is a detailed reconstruction of Bernard Bolzano’s account of merely possible objects. According to Bolzano, there are some objects which are merely possible. They are neither denizens of space and time nor members of the causal order, but they could have been so. Examples are merely possible persons, mountains etc., objects which are neither actual nor persons or mountains, but which could have been both. Bolzano’s views are contrasted with the theory of Alexius Meinong, and it is shown (...) that they have a modern counterpart in the accounts of merely possible objects that were developed by Bernard Linsky & Ed Zalta, and by Timothy Williamson. (shrink)

My working hypothesis is based on the project of a theory of science (Wissenschaftslehre) at the very beginning of the Prolegomena and it consists in conceiving this theory of science as the program which insures their cohesion to the whole of the Investigations in this work. In order to test this hypothesis, I will first examine the different steps which led to the project of a theory of science in the pre-phenomenological period. I will secondly expound the guidelines of the (...) theory of science, insisting in particular on its relation to pure logic. In the third section, I will attempt to define the function of the theory of knowledge and of phenomenology in such a programme. I will conclude with some remarks on the fate of this theory of science after the Logical Investigations. Most of Husserl’s allusions to the theory of science, be it in his lecture notes, the manuscripts that were written after 1901 or other works published during Husserl’s lifetime, seem to suggest that the theory of science kept on assuming the very role it was playing in Husserl’s seminal work: the theory of science provides its basis to Husserl’s philosophical agenda. (shrink)

Souvent aujourd'hui on présente Bolzano comme ayant jeté les bases d'une « ontologie formelle ». On lui impute une théorie du « quelque chose en général » qui serait ontologique. Il est vrai que sa théorie combinatoire des représentations en soi permet de rendre compte de la constitution de « quelques choses » de différents degrés, sur un mode récursif. Pourtant, on pourra douter de ce que le réalisme strict qui est celui de Bolzano, et qui s'applique même aux représentations (...) en soi, laisse réellement un espace pour ce qui pourrait être appelé à proprement parler des « objets formels ». Bolzano is often mentioned today as having layed the foundations for a « formal ontology ». He is supposed to have a theory of the « something in general » that is an ontological one. In fact his combinatory theory of representations in themselves allows an accounting for constituting « somethings » of different degrees, in a recursive way. However you must doubt whether Bolzano's strict realism, even concerning the representations in themselves, makes room for what could really be called « formal objects ». (shrink)

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)