SOPhiA 2017

Salzburgiense Concilium Omnibus Philosophis Analyticis

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Programme - Talk

Grounding in and after Bolzano
(Affiliated Workshop, English)

The aim of this workshop is to discuss Bolzano's theory of grounding (Abfolge) against the background of the recent debate on metaphysical grounding. Early on in the 19th century, Bernard Bolzano developed a very rich account of grounding that resembles modern approaches to metaphysical grounding in several respects. According to Bolzano, grounding is an objective ground-consequence relation among true propositions that can be adequately expressed by the connective 'because'. As is common in modern theories of grounding, Bolzano holds that grounding is irreflexive and asymmetric. Moreover, he systematically distinguishes between complete and partial grounds on the one hand and immediate and mediate grounds on the other. What is most remarkable is his attempt to characterize grounding in terms of entailment by means of certain structural constraints that concern the compositional complexity of grounds and consequences. This workshop brings together researchers with an interest in Bolzano and grounding in order to discuss Bolzano's ideas and shed light on Bolzano as a predecessor of the modern debate on metaphysical grounding. Given the close parallels between Bolzano's theory of grounding and modern accounts, a thorough understanding of Bolzano's ideas seems not only interesting in its own right but also promises to reveal important insights in the context of the current debate.


09:00--09:50 Jan Claas: Grounding the Scope of Philosophy
09:50--10:00 Short break
10:00--10:50 Arianna Betti & Pauline van Wierst: Bolzano in Ones and Zeros: A quantitative study in 19th century philosophy of mathematics
10:50--11:10 Coffee break
11:10--12:00 Edgar Morscher: The Axiomatization of Bolzano's Theory of Abfolge: An Exercise in ''Rational Reconstruction''
12:00--12:10 Short break
12:10--13:00 Stefan Roski: Fundamental Truths and the PSR in Bolzano's Theory of Grounding


Arianna Betti (Amsterdam) and Pauline van Wierst (Pisa): Bolzano in Ones and Zeros: A quantitative study in 19th century philosophy of mathematics
In previous work (Wierst et al. 2016) we have shown that the application of even rather simple, well-known computational techniques to Bolzano's Wissenschaftslehre can yield valuable results. In this talk we extend our computational investigation to three open questions in the interpretation of Bolzano's thought. The first and the second question concern epochal turns in the history of scientific ideas. The first question regards Bolzano's notion of infinity. According to Jan Berg (in Bolzano 1975), four months before his death Bolzano threw overboard his whole life's work on the infinite, and accepted the Cantorian criterion of 1-1 correspondence as a sufficient criterion for equality of size. According to Mancosu (2009), this can only be partially true: he might have accepted the Cantorian view in the arithmetical context, but not in the geometrical context. The second question regards the emergence of a radically objective account of the concept of a scientific statement in terms of a mind-independent, language-independent and time-independent entity, known to present-day philosophers as a proposition (more specifically, a Fregean proposition). The majority of scholars holds that it was Bolzano to take this turn and introduce Sätze an sich as propositions in this sense, while a minority denies he did (e.g. Cantù 2006). The third and final question regards the uniformity of Bolzano's notion of grounding (Abfolge). Some scholars have conjectured that Bolzano's well-known difficulty with the definition of Abfolge is due to his conflation of different notions (Betti 2010). Indeed Bolzano's examples of grounding are so various that it seems unlikely that there can be one notion of grounding which works for all. The majority of scholars however seem to assume that Bolzano's notion of grounding is uniform. In this paper we endeavour to provide new quantitative evidence to help assessing these three open questions by relying on text-mining software developed by our team to the specific goal of aiding philosophers in the analysis of unusually extended textual corpora.

-- Betti, Arianna. 2010. ''Explanation in Metaphysics and Bolzano's Theory of Ground and Consequence.'' Logique et Analyse 211: 281-316.
-- Bolzano, B. (1975a). Einleitung zur Grössenlehre. Erste Begriffe der allgemeinen Grössenlehre. In Jan Berg, editor. Gesamtausgabe, II A 7. Stuttgart-Bad Cannstatt, Germany: Friedrich Frommann Verlag.
-- Cantù, Paola. 2006. Bolzano et les propositions en soi: une théorie objective des vérités. In Propositions et états de choses, ed. J. Benoist. Paris: Vrin.
Mancosu, Paolo. 2009. ''Measuring the size of infinite collections of natural numbers: was Cantor's theory of infinite number inevitable?'' The Review of Symbolic Logic 2: 612-646.
-- Wierst, Pauline van, Sanne Vrijenhoek, Stefan Schlobach, and Arianna Betti. 2016. Phil@Scale: Computational Methods within Philosophy. In Proceedings of the Third Conference on Digital Humanities in Luxembourg with a Special Focus on Reading Historical Sources in the Digital Age. CEUR Workshop Proceedings,, edited by Lars Wieneke, Catherine Jones, Marten Düring, Florentina Armaselu, and René Leboutte. Vol. 1681. Aachen.

Jan Claas (Hamburg): Grounding the Scope of Philosophy
Not only does Bolzano develop a detailed theory of grounding. In the short piece Was ist Philosophie? from 1839 he also applies the notion in order to define what philosophy is. He thereby provides us with a necessary and sufficient condition for an investigation being a philosophical one. An investigation is philosophical, we are told, if and only if it is either an investigation into the consequences and effects of given grounds and causes or an investigation into the grounds and causes of given consequences and effects. The aim of my talk is to scrutinize this definition. I will focus on the necessary condition provided and a salient counterexample Bolzano briefly considers. Conceptual analysis appears to be a genuinely philosophical endeavour while, at first glance, it does not seem to be concerned with grounds and consequences or causes and effects. Addressing this worry, Bolzano appeals to something he takes to be closely related to conceptual analysis, namely investigating the ways in which mental states with complex contents arise in us. I will exposit the tight connection Bolzano assumes between mental states and their contents in the Theory of Science (1837) and assess to which extent this connection can be used in order to rule out conceptual analysis as counterexample against Bolzano's definition.

Edgar Morscher (Salzburg): The Axiomatization of Bolzano's Theory of Abfolge: an Exercise in ''Rational Reconstruction''
Bolzano presented his informal theory of Abfolge in admirable clarity in his Wissenschaftslehre, §§ 198--222. A theory is hereby understood as a deductively closed set of sentences. In order to rationally reconstruct an informal theory, we have to make three substantial decisions: first, we have to fix the formal language within which we are going to reconstruct the theory in question; second, we must decide about the primitive term(s) which we take as the basis of the vocabulary in our reconstruction language; and third, we have to choose the primitive theses, i.e. axioms or postulates, on which we base the theory in its reconstructed form. As far as a rational reconstruction of Bolzano's theory of Abfolge is concerned, I propose to answer the three questions in the following way: (1) As my language of reconstructions I take the language of modern quantification logic, augmented with a consistent segment of modern set theory (and not, as some would like to have it, the language of Bolzano's theory of collections or Inbegriffe). (2) The primitive term on which I base the vocabulary of my language of reconstruction will be the 2-place predicate 'M is the complete ground of N', where M and N are sets of (true) propositions (Sätze an sich) and N is a partial or the complete consequence of M (and not, as some would like to have it, the 2-place predicate 'M is the complete ground of P' where P is a single true proposition). (3) For my reconstruction I choose six postulates which determine the formal properties of the grounding relation (among them are not, as some would like to have it, special instances of the Abfolge relation such as 'For every proposition P: P is the complete ground of [P has truth]'). In my contribution I will explain why I make these decisions. In doing so, the focus of my interest turns from Bolzano's theory of Abfolge to the method of rational reconstruction for which Bolzano's theory serves as an illustrative example.

Stefan Roski (Hamburg): Fundamental Truths and the PSR in Bolzano's Theory of Grounding (joint work with Benjamin Schnieder)
Bernard Bolzano is often credited with developing the first rigorous theory of grounding in his main work Theory of Science (1837). One of the motivations to develop this theory was his concern with the Principle of Sufficient Reason (PSR) that, due to the influence of rationalism, was widely endorsed in his time. Against the background of his theory of grounding, Bolzano was in the position to point out that a number of arguments for this principle were wanting. In addition to that, he also developed original arguments to show that the PSR is false. In our talk we will investigate those arguments and show that one of them is of considerable systematic interest for the contemporary debate on grounding and fundamentality.

Organisation: Jan Claas (Hamburg) & Antje Rumberg (Constance). In cooperation with Benjamin Schnieder (Hamburg), with kind support of the SNF.

Chair: Jan Claas & Antje Rumberg
Time: 09:00-13:00, 13 September 2017 (Wednesday)
Location: SR 1.006

Arianna Betti 
(University of Amsterdam, Netherlands)

Arianna Betti is professor of philosophy of language at the University of Amsterdam. Her main research interests are in philosophical methodology and the history of logic in Poland and its Austrian roots. Her recent project ''Concepts in Motion'' is devoted to the history of ideas and focuses on the application of computational techniques in tracing the development of concepts.

Jan Claas 
(University of Hamburg, Germany)

Jan Claas is doctoral researcher at the University of Hamburg with a strong research interest in the history of analytic philosophy. He studied philosophy at the University of Heidelberg and spent a year as visiting student at Yale University. His PhD thesis is devoted to Bolzano's theory of concepts.

Edgar Morscher 
(University of Salzburg, Austria)

Edgar Morscher is professor emeritus at the University of Salzburg. He is president of the International Bernard Bolzano Society and co-editor of the Bernard Bolzano Gesamtausgabe. He has published on a broad range of philosophical topics. Recent publications include a monograph on Bolzano's theory of grounding.

Stefan Roski 
(University of Hamburg, Germany)

Stefan Roski is postdoctoral researcher at the University of Hamburg with a strong research interest in Bolzano and modern theories of grounding. He has recently published a monograph entitled ''Bolzano's Conception of Grounding'', based on his PhD thesis.

Pauline van Wierst 
(Scuola Normale Superiore Pisa, Italy)

Pauline van Wierst is doctoral student at the Scuola Normale Superiore in Pisa. She obtained her undergraduate degree from the VU University Amsterdam with a MA thesis on Bolzano's notion of analyticity and the application of computational methods within philosophical research. In her PhD thesis she is investigating infinite idealizations in physics from the viewpoint of philosophy of mathematics.

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