In the early 1920s, Hans Reichenbach and Kurt Lewin presented two topological accounts of time that appear to be interrelated in more than one respect. Despite their different approaches, their underlying idea is that time order is derived from specific structural properties of the world. In both works, moreover, the notion of genidentity--i.e., identity through or over time--plays a crucial role. Although it is well known that Reichenbach borrowed this notion from Kurt Lewin, not much has been written about their (...) relationship, nor about the way Lewin implemented this notion in his own work in order to ground his topology. This paper examines these two early versions of the topology of time, and follows the extent of Lewin’s influence on Reichenbach’s proposal. (shrink)

This paper is aimed at understanding one central aspect of Bolzano's views on deductive knowledge: what it means for a proposition and for a term to be known a priori. I argue that, for Bolzano, a priori knowledge is knowledge by virtue of meaning and that Bolzano has substantial views about meaning and what it is to know the latter. In particular, Bolzano believes that meaning is determined by implicit definition, i.e. the fundamental propositions in a deductive system. I go (...) into some detail in presenting and discussing Bolzano's views on grounding, a priori knowledge and implicit definition. I explain why other aspects of Bolzano's theory and, in particular, his peculiar understanding of analyticity and the related notion of Ableitbarkeit might, as it has invariably in the past, mislead one to believe that Bolzano lacks a significant account oï a priori knowledge. Throughout the paper, I point out to the ways in which, in this respect, Bolzano's antagonistic relationship to Kant directly shaped his own views. (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)

Recently, Michael Friedman has claimed that virtually all the seeds of Hempel’s philosophical development trace back to his early encounter with the Vienna Circle (Friedman 2003, 94). As opposed, however, to Friedman’s view of the principal early influences on Hempel, we shall see that those formative influences originated rather with the Berlin Group. Hempel, it is true, spent the fall term of 1929 as a student at the University of Vienna, and, thanks to a letter of recommendation from Hans Reichenbach, (...) he even attended some sessions of the Vienna Circle. But he spent much less time in Vienna than in Berlin, where he studied under Reichenbach from 1926 till 1933 and wrote a dissertation on probability, Reichenbach’s specialty. Hempel also attended seminars conducted by Walter Dubislav, another member of the Berlin Group. (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 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)

The Löwenheim-Hilbert-Bernays theorem states that, for an arithmetical first-order language L, if S is a satisfiable schema, then substitution of open sentences of L for the predicate letters of S...

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)

One of Bolzano’s objections to Kant’s way of drawing the analytic-synthetic distinction is that it only applies to judgments within a narrow range of syntactic forms, namely, universal affirmative judgments. According to Bolzano, Kant cannot account for judgments of other syntactic forms that, intuitively, are analytic. A recent paper by Ian Proops also attributes to Kant the view that analytic judgments beyond a limited range of syntactic forms are impossible. I argue that, correctly understood, Kant’s conception of analyticity allows for (...) analytic judgments of a wider range of syntactic forms. (shrink)

This explorative article is organized around a set of questions concerning the concept of a function. First, a summary of certain general facts about functions that are a common coin in contemporary logic is given. Then Frege's attempt at clarifying the nature of functions in his famous paper Function and Concept and in his Grundgesetze is discussed along with some questions which Freges' approach gave rise to in the literature. Finally, some characteristic uses of functional notions to be found in (...) the work of Bernard Bolzano and in Edmund Husserl's early work are presented and elucidated. (shrink)

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 ontological works Kurt Grelling tries to give a rigorous analysis of the foundations of the so-called Gestalt-psychology. Gestalten are peculiar emergent qualities, ontologically dependent on their foundations, but nonetheless non reducible to them. Grelling shows that this concept, as used in psychology and ontology, is often ambiguous. He distinguishes two important meanings in which the word “Gestalt” is used: Gestalten as structural aspects available to transposition and Gestalten as causally self-regulating wholes. Gestalten in the first meaning are, according (...) to Grelling, “equivalence classes of correspondences”, while Gestalten as self-regulating wholes have more to do with relations of ontological dependence. Grelling’s clarification of the concept of Gestalt is doubtless an excellent piece of philosophical analysis, but at the end of the day it turns out that his analysis captures at best only a part of intuitions traditionally connected with the notion of Gestalt. (shrink)

Jakob Friedrich Fries (1773–1843) was the most prolific German philosopher of science in the nineteenth century who strived to synthesize Kant’s philosophical foundation of science and mathematics and the needs or practised science and mathematics in order to gain more comprehensive conceptual frameworks and greater methodological flexibility for those two disciplines. His original contributions anticipated later developments, to some extent, though they received comparatively little notice in the later course of the nineteenth century—a fate which partly can be explained by (...) the unfortunate development of the so-called ‘First Friesian School,’ founded by E. F. Apelt, M. J. Schleiden and O. X. Schlömilch. This situation changed temporarily when Leonard Nelson (1882–1927) arrived on the philosophical stage and founded a second, so-called, ‘New Friesian School’ in 1903. In the following two decades, Fries’ specific transformation of Kantian philosophy gained influence within the vigorous discussions about ‘new’ foundations of mathematics and, thus, also played a role within the Berlin Group surrounding Hans Reichenbach, though his work had no direct impact on the philosophy of physics being expounded therein. -/- This essay will first outline some characteristics of Fries’ development of the Kantian approach. Then it will point out the limited impact of the ‘New Friesian School’ on the Berlin Group, while highlighting some missed chances for fruitful exchange. As the originality of this school and its importance for the development of logic and philosophy of mathematics—by and large merits of its early members Walter Dubislav and Kurt Grelling —is dealt with in separate chapters of this volume, and elsewhere, this article will focus on what Fries called the ‘mathematical philosophy of nature’ (i. e. the philosophical foundations of physics). More specifically, it will show how the New Friesian School reacted to Einstein’s theories of relativity, in a way that contrasts with the approach of the Berlin Group. This discussion about relativity will also be used to reveal different understandings of the nature of ‘scientific philosophy’ in general, as well as different models of how philosophy and the empirical sciences should interact. (shrink)

This compelling reevaluation of the relationship between logic and knowledge affirms the key role that the notion of judgement must play in such a review. The commentary repatriates the concept of judgement in the discussion, banished in recent times by the logical positivism of Wittgenstein, Hilbert and Schlick, and the Platonism of Bolzano. The volume commences with the insights of Swedish philosopher Per Martin-Löf, the father of constructive type theory, for whom logic is a demonstrative science in which judgement is (...) a settled feature of the landscape. His paper opens the first of four sections that examine, in turn, historical philosophical assessments of judgement and reason; their place in early modern philosophy; the notion of judgement and logical theory in Wolff, Kant and Neo-Kantians like Windelband; their development in the Husserlian phenomenological paradigm; and the work of Bolzano, Russell and Frege. The papers, whose authors include Per Martin-Löf, Göran Sundholm, Michael Della Rocca and Robin Rollinger, represent a finely judged editorial selection highlighting work on philosophers exercised by the question of whether or not an epistemic notion of judgement has a role to play in logic. The volume will be of profound interest to students and academicians for its application of historical developments in philosophy to the solution of vexatious contemporary issues in the foundation of logic. ​. (shrink)