Stefan Roski

This chapter contains translations of texts in which Bolzano develops and applies his mature theory of grounding. The heart of the chapter are excerpts from Bolzano’s main work _Theory of Science_, where he gives the most comprehensive account of his conception of grounding and discusses the role of grounding in several philosophical areas ranging from the methodology of science, to the philosophy of causation, to metaphysics. In addition to that, the chapter includes a brief excerpt from a survey of Bolzano’s _Theory of Science_ and his _Theory of the Science of Religion_, in which Bolzano gives a succinct summary of central ideas of his mature theory. Finally, the chapter includes the complete translation of Bolzano’s essay _What Is Philosophy?_ which defends a ground-theoretical conception of philosophy.

This chapter contains translations of excerpts from three early texts by Bolzano (written around 1810): ▪ the 1810 booklet _Contributions to a Better-Grounded Presentation of Mathematics_; ▪ the unpublished manuscript _Aetiology_; ▪ the unpublished manuscript _General Mathematics_. Topic-wise, the texts centre around scientific method and the foundations of mathematics. In the _Contributions_ Bolzano discusses grounding in connection with three topics: the classification of mathematical disciplines, the notion of ground-revealing proofs and its relation to syllogistic inferences, and finally the notion of axioms or basic propositions. In the _Aetiology_ Bolzano presents his first attempt at a rigorous, axiomatic theory of grounding and relates the concept of grounding to several concepts and issues in mathematics. In the part of _General Mathematics_ we present here, Bolzano critically assesses the Principle of Sufficient Reason and some related metaphysical issues.

This paper is devoted to Bolzano’s theory of grounding (Abfolge) in his Wissenschaftslehre. Bolzanian grounding is an explanatory consequence relation that is frequently considered an ancestor of the notion of metaphysical grounding. The paper focuses on two principles that concern grounding in the realm of conceptual sciences and relate to traditionally widespread ideas on explanations: the principles, namely, that grounding orders conceptual truths from simple to more complex ones (Simplicity), and that it comes along with a certain theoretical economy among them (Economy). Being spelled out on the basis of Bolzano’s notion of deducibility (Ableitbarkeit), these principles are revealing for the question to what extent grounding can be considered a formal relation.

This chapter provides an overview of Bernard Bolzano’s views about grounding. On Bolzano’s account, grounding is an objective priority relation among true propositions that has certain explanatory features. The chapter briefly highlights historical influences on Bolzano’s account of grounding and subsequently provides an overview of the most important aspects of it. Bolzano’s account resembles current accounts of metaphysical grounding in many respects and can thus easily be related to many positions in the current debate. The chapter investigates some Bolzanian ideas about grounding that differ from the current orthodoxy but may constitute interesting additions, challenges or inspirations for those working in the current debate. It is striking that Bolzano accepts a number of principles that seem to be motivated by the same kind of intuition that underlies present work on the logic of ground. Bolzano’s thought is that, for instance, general mathematical truths will never be grounded in truths concerned with any individual concrete object in particular.

reality is a complex affair. It comprises a huge variety of different elements. Importantly, though, reality is not a mere aggregate of its elements but rather a structured whole or system whose building blocks are not all on the same level. Instead, they form hierarchical networks ordered by relations of priority. In such networks, derivative aspects of reality obtain in virtue of their grounds, that is, in virtue of more fundamental aspects of reality that are prior to them. This picture of reality as a structured whole is currently enjoying a renaissance in the works of philosophers such as Kit Fine, Jonathan Schaffer, and many others. But far from being a new picture, it has been widely endorsed throughout the...

According to Kant, a true judgement can be called a priori in case it can take place absolutely (schlechterdings) independent of experience. Propositions that are knowable in this way are called a priori propositions by him (Kant 1787 B, 3–4). As is well known, the class of those a priori propositions that are synthetic was particularly important for Kant. In contrast to analytic propositions, they are supposed to contain nontrivial information about the world and yet be irrefutable by experience. Not many of his critics were satisfied with Kant’s way of drawing this distinction.

Sustainability and internationalization are considered to be core values of Higher Education Institutions (HEIs), but their relationship is rarely investigated. The current study develops a framework to create a sustainable internationalization policy for an HEI; it analyzes how to measure the sustainability of an internationalization policy in two steps. First, this study presents a theoretical framework for a cost-benefit analysis of HEIs’ sustainable internationalization policies using three sustainability pillars (economic, ecological, and social), each with examples for their own measurable indicators. Second, this research operationalizes the economic pillar of the framework to enable a specific measurement of the economic sustainability of internationalization. The empirical analysis identifies the distribution of funding for internationalization as a promising indicator. To demonstrate the implementation of this part of the framework, this study analyzes how German HEIs distribute their monetary investments in internationalization activities to countries worldwide. Using data from the German academic exchange service (DAAD), this research investigates the distribution using descriptive statistics. In a second step, the methodology of the Lorenz curve is empirically applied to the distribution of funding. Universität Hamburg is used as a case study to visualize the different funding tendencies among German HEIs. The findings suggest that the distribution of resources for internationalization says more about the sustainable character of an HEI than the absolute amount of invested resources. To evaluate the sustainability of an HEI’s internationalization strategy, it is therefore necessary to look at the distribution of target countries in addition to the mere absolute level of funding.

This survey paper pursues three aims. The first aim is to sketch the overall role that grounding plays in Bolzano’s philosophy and to indicate some historical roots of his views, namely Aristotle’s conception of scientific proofs and the rationalist’s debate about the Principle of Sufficient Reason. The second aim is to provide readers coming from the current debate about metaphysical grounding with an accessible overview of Bolzano’s mature conception of grounding. The third and final aim of the paper is to introduce elements and terminology from Bolzano’s conceptual and ontological framework that are required to understand his theory of grounding.

According to an increasingly popular view among philosophers of science, both causal and non-causal explanations can be accounted for by a single theory: the counterfactual theory of explanation. A kind of non-causal explanation that has gained much attention recently but that this theory seems unable to account for are grounding explanations. Reutlinger (Eur J Philos Sci 7(2):239-256, 2017) has argued that, despite these appearances to the contrary, such explanations are covered by his version of the counterfactual theory. His idea is supported by recent work on grounding by Schaffer and Wilson who claim there to be a tight connection between grounding and counterfactual dependence. The present paper evaluates the prospects of the idea. We show that there is only a weak sense in which grounding explanations convey information about counterfactual dependencies, and that this fact cannot plausibly be taken to reveal a distinctive feature that grounding explanations share with other kinds of explanations.

This paper investigates Bolzano’s views on the distinction between logical and non-logical notions. Even though it is crucial for Bolzano’s definitions of logical consequence and logical analyticity, his remarks on how the distinction is to be drawn are few and far between. Bolzano’s adherence to a traditional, pre-Fregean syntax, complicates interpreting these remarks even further. The paper offers an interpretation of the remarks on which they suggest that Bolzano identified logicality with topic-neutrality. It further discusses Bolzano’s views on the systematic relevance of the notion of logical consequence.

In a variety of recent debates, philosophers have found it useful to appeal to a notion of difference-making. Metaphysicians have appealed to difference-making in analysing aspects of relations such as causation and grounding. Following influential work by Michael Strevens, philosophers of science have argued that causal factors are explanatorily relevant only if they make a difference to a given event. Finally, the notion of difference-making has been prominent in debates about free will and responsibility. In the course of these debates, several competing analyses of difference-making have been proposed. Thus far, however, there has been little interaction between these different debates. This special issue aims to bring together recent approaches to difference-making from several different angles in relation to a variety of hotly debated topics.

Explanatory realism is the view that explanations work by providing information about relations of productive determination such as causation or grounding. The view has gained considerable popularity in the last decades, especially in the context of metaphysical debates about non-causal explanation. What makes the view particularly attractive is that it fits nicely with the idea that not all explanations are causal whilst avoiding an implausible pluralism about explanation. Another attractive feature of the view is that it allows explanation to be a partially epistemic, context-dependent phenomenon. In spite of its attractiveness, explanatory realism has recently been subject to criticism. In particular, Taylor :197–219, 2018). has presented four types of explanation that the view allegedly cannot account for. This paper defends explanatory realism against Taylor’s challenges. We will show that Taylor’s counterexamples are either explanations that turn out to provide information about entities standing in productive determination relations or that they are not genuine explanations in the first place.

According to an increasingly popular view among philosophers of science, both causal and non-causal explanations can be accounted for by a single theory: the counterfactual theory of explanation. A kind of non-causal explanation that has gained much attention recently but that this theory seems unable to account for are grounding explanations. Reutlinger :239-256, 2017) has argued that, despite these appearances to the contrary, such explanations are covered by his version of the counterfactual theory. His idea is supported by recent work on grounding by Schaffer and Wilson who claim there to be a tight connection between grounding and counterfactual dependence. The present paper evaluates the prospects of the idea. We show that there is only a weak sense in which grounding explanations convey information about counterfactual dependencies, and that this fact cannot plausibly be taken to reveal a distinctive feature that grounding explanations share with other kinds of explanations.

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.

We define a notion of difference-making for partial grounds of a fact in rough analogy to existing notions of difference-making for causes of an event. Using orthodox assumptions about ground, we show that it induces a non-trivial division with examples of partial grounds on both sides. We then demonstrate the theoretical fruitfulness of the notion by applying it to the analysis of a certain kind of putative counter-example to the transitivity of ground recently described by Jonathan Schaffer. First, we show that our conceptual apparatus of difference-making enables us to give a much clearer description than Schaffer does of what makes the relevant instances of transitivity appear problematic. Second, we suggest that difference-making is best seen as a mark of good grounding-based explanations rather than a necessary condition on grounding, and argue that this enables us to deal with the counter-example in a satisfactory way. Along the way, we show that Schaffer's own proposal for salvaging a form of transitivity by moving to a contrastive conception of ground is unsuccessful. We conclude by sketching some natural strategies for extending our proposal to a more comprehensive account of grounding-based explanations.

According to Hempel’s influential theory of explanation, explaining why some a is G consists in showing that the truth that a is G follows from a law-like generalization to the effect that all Fs are G together with the initial condition that a is F. While Hempel’s overall account is now widely considered to be deeply flawed, the idea that some generalizations play the explanatory role that the account predicts is still often endorsed by contemporary philosophers of science. This idea, however, conflicts with widely shared views in metaphysics according to which the generalization that all Fs are G is partially explained by the fact that a is G. I discuss two solutions to this conflict that have been proposed recently, argue that they are unsatisfactory, and offer an alternative.

This paper is devoted to an examination of Bolzano’s notion of necessary existence, which has so far received relatively little attention in the literature. We situate Bolzano’s ideas in their historical context and show how he proposed to correct various flaws of his predecessors’ definitions. Further, we relate Bolzano’s conception to his metaphysical and theological assumptions, arguing that some consequences of his definition which have been deemed counterintuitive by some of his interpreters turn out to be more reasonable given the broadly Leibnizian background of his metaphysics. Finally, we consider some difficulties that arise from Bolzano’s evolving views on freedom, which, at least in his early thought, was intimately linked with contingency. In an appendix, we discuss a recent debate on Bolzano’s notion of necessary truth between Textor and Rusnock that has some bearing on our overall line of interpretation of Bolzano’s notion of necessary existence.

Not all truths are on a par. The realm of truths is structured: some propositions are only true because others are. The relation that endows the realm of truths with this structure is often called grounding. Grounding has achieved much attention in 21st century metaphysics, but the topic is arguably as old as philosophy itself. This becomes apparent when investigating the works of the 19th-century philosopher Bernard Bolzano, who developed what is perhaps the first comprehensive theory of grounding, drawing on a rich tradition that goes back to Aristotle’s Posterior Analytics. Roski’s book provides, for the first time, a comprehensive study of Bolzano’s theory of grounding in its entirety, paying more attention than previous studies to the interaction between grounding and the consequence-relation of deducibility.

Deux transitions ont eu lieu aux xviiie et xixe siècles dans le déve­loppement de l'analyse mathématique : de l'approche géométrique à l'approche axée sur des formules d'une part ; de l'approche axée sur les formules à l'ap­proche conceptuelle d'autre part. En nous appuyant sur la Preuve purement analytique de Bolzano, nous montrons qu'il adopte une approche que l'on peut qualifier de conceptuelle. Nous parvenons à la conclusion selon laquelle Bolzano n'adopte pas la même attitude selon qu'il se rapporte à l'approche géométrique d'une part, à l'approche axée sur des formules d'autre part ; dans le premier cas, il est question de rejet, dans le second cas de non-participation. Bolzano appuie sa méthodologie conceptuelle sur des opinions philosophiques partagées en partie par certains mathématiciens partisans d'une approche de l'analyse axée sur les formules.