Comparing action-at-a-distance electrodynamics in the tradition of Coulomb and Ampère with electromagnetic field theory of Faraday and Maxwell provides an example for a relation between theories, that are on a par in many respects. They have a broadly overlapping domain of applicability, and both were widely successful in explanation and prediction. The relation can be understood as an inhomogeneous reduction without a clear distinction between reducing and reduced theory. It is argued in general, when a clear hierarchy between competing theories (...) cannot be determined, the plurality of standpoints should be preserved and the bridge laws carefully developed. (shrink)

I argue for the causal character of modeling in data-intensive science, contrary to widespread claims that big data is only concerned with the search for correlations. After discussing the concept of data-intensive science and introducing two examples as illustration, several algorithms are examined. It is shown how they are able to identify causal relevance on the basis of eliminative induction and a related difference-making account of causation. I then situate data-intensive modeling within a broader framework of an epistemology of scientific (...) knowledge. In particular, it is shown to lack a pronounced hierarchical, nested structure. The significance of the transition to such “horizontal” modeling is underlined by the concurrent emergence of novel inductive methodology in statistics such as non-parametric statistics. Data-intensive modeling is well equipped to deal with various aspects of causal complexity arising especially in the higher level and applied sciences. (shrink)

Recent claims, mainly from computer scientists, concerning a largely automated and model-free data-intensive science have been countered by critical reactions from a number of philosophers of science. The debate suffers from a lack of detail in two respects, regarding the actual methods used in data-intensive science and the specific ways in which these methods presuppose theoretical assumptions. I examine two widely-used algorithms, classificatory trees and non-parametric regression, and argue that these are theory-laden in an external sense, regarding the framing of (...) research questions, but not in an internal sense concerning the causal structure of the examined phenomenon. With respect to the novelty of data-intensive science, I draw an analogy to exploratory as opposed to theory-directed experimentation. (shrink)

The old antagonism between the Quinean and the Duhemian view on underdetermination is reexamined. In this respect, two theses will be defended. First, it is argued that the main differences between Quine's and Duhem's versions of underdetermination derive from a different attitude towards the history of science. While Quine considered underdetermination from an ahistorical, a logical point of view, Duhem approached it as a distinguished historian of physics. On this basis, a logical and a historical version of the underdetermination thesis (...) can be distinguished. The second thesis of the article is that the main objections against underdetermination are fatal only to the logical rendering. Taken together, the two theses constitute a defence of underdetermination. (shrink)

In this article, I present a case study of underdetermination in nineteenth-century electrodynamics between a pure field theory and a formulation in terms of action at a distance. A particular focus is on the question if and how this underdetermination is eventually resolved. It turns out that after a period of overt underdetermination, during which the approaches are developed separately, the two programmes are merged. On the basis of this development, I argue that the original underdetermination survives in hidden form (...) in ontological and methodological redundancies of the subsequent particle–field electrodynamics. Implications regarding criteria for theory choice and the realism debate are briefly addressed. (shrink)

Analogical reasoning addresses the question how evidence from various phenomena can be combined and made relevant for theory development and prediction. In the first part of my contribution, I review some influential accounts of analogical reasoning, both historical and contemporary, focusing in particular on Keynes, Carnap, Hesse, and more recently Bartha. In the second part, I sketch a general framework. To this purpose, a distinction between a predictive and a conceptual type of analogical reasoning is introduced. I then take up (...) a common intuition according to which analogical inferences hold if the differences between source and target concern only irrelevant circumstances. I attempt to make this idea more precise by addressing possible objections and in particular by specifying a notion of causal irrelevance based on difference making in homogeneous contexts. (shrink)

It is argued that in deterministic contexts evidence for causal relations states whether a boundary condition makes a difference or not to a phenomenon. In order to substantiate the analysis, I show that this difference/indifference making is the basic type of evidence required for eliminative induction in the tradition of Francis Bacon and John Stuart Mill. To this purpose, an account of eliminative induction is proposed with two distinguishing features: it includes a method to establish the causal irrelevance of boundary (...) conditions by means of indifference making, which is called strict method of agreement, and it introduces the notion of a background against which causal statements are evaluated. Causal statements thus become three-place-relations postulating the relevance or irrelevance of a circumstance C to the examined phenomenon P with respect to a background B of further conditions. To underline the importance of evidence in terms of difference/indifference making, I sketch two areas, in which eliminative induction is extensively used in natural and engineering sciences. One concerns exploratory experiments, the other engineering design methods. Given that a method is discussed that has been used for centuries, I make no claims to novelty in this paper, but hope that the combined discussion of several topics that are still somewhat underrepresented in the philosophy of science literature is of some merit. (shrink)

This book addresses controversies concerning the epistemological foundations of data science: Is it a genuine science? Or is data science merely some inferior practice that can at best contribute to the scientific enterprise, but cannot stand on its own? The author proposes a coherent conceptual framework with which these questions can be rigorously addressed. Readers will discover a defense of inductivism and consideration of the arguments against it: an epistemology of data science more or less by definition has to be (...) inductivist, given that data science starts with the data. As an alternative to enumerative approaches, the author endorses Federica Russo’s recent call for a variational rationale in inductive methodology. Chapters then address some of the key concepts of an inductivist methodology including causation, probability and analogy, before outlining an inductivist framework. The inductivist framework is shown to be adequate and useful for an analysis of the epistemological foundations of data science. The author points out that many aspects of the variational rationale are present in algorithms commonly used in data science. Introductions to algorithms and brief case studies of successful data science such as machine translation are included. Data science is located with reference to several crucial distinctions regarding different kinds of scientific practices, including between exploratory and theory-driven experimentation, and between phenomenological and theoretical science. Computer scientists, philosophers and data scientists of various disciplines will find this philosophical perspective and conceptual framework of great interest, especially as a starting point for further in-depth analysis of algorithms used in data science. (shrink)

A difference-making account of causality is proposed that is based on a counterfactual definition, but differs from traditional counterfactual approaches to causation in a number of crucial respects: it introduces a notion of causal irrelevance; it evaluates the truth-value of counterfactual statements in terms of difference-making; it renders causal statements background-dependent. On the basis of the fundamental notions 'causal relevance' and 'causal irrelevance', further causal concepts are defined including causal factors, alternative causes, and importantly inus-conditions. Problems and advantages of the (...) proposed account are discussed. Finally, it is shown how the account can shed new light on three classic problems in epistemology, the problem of induction, the logic of analogy, and the framing of eliminative induction. (shrink)

A case study is presented of a recent proposal by the major metrology institutes to redefine four of the physical base units, namely kilogram, ampere, mole, and kelvin. The episode shows a number of features that are unusual for progress in an objective science: for example, the progress is not triggered by experimental discoveries or theoretical innovations; also, the new definitions are eventually implemented by means of a voting process. In the philosophical analysis, I will first argue that the episode (...) provides considerable evidence for confirmation holism, i.e. the claim that central statements in fundamental science cannot be tested in isolation; second, that the episode satisfies many of the criteria which Kuhn requires for scientific revolutions even though one would naturally classify it as normal science. These two observations are interrelated since holism can provide within normal science a possible source of future revolutionary periods. (shrink)

Data-intensive techniques, now widely referred to as 'big data', allow for novel ways to address complexity in science. I assess their impact on the scientific method. First, big-data science is distinguished from other scientific uses of information technologies, in particular from computer simulations. Then, I sketch the complex and contextual nature of the laws established by data-intensive methods and relate them to a specific concept of causality, thereby dispelling the popular myth that big data is only concerned with correlations. The (...) modeling in data-intensive science is characterized as 'horizontal'—lacking the hierarchical, nested structure familiar from more conventional approaches. The significance of the transition from hierarchical to horizontal modeling is underlined by a concurrent paradigm shift in statistics from parametric to non-parametric methods. (shrink)

The prospects of a causal interpretation of probability are examined. Various accounts both from the history of scientific method and from recent developments in the tradition of the method of arbitrary functions, in particular by Strevens, Rosenthal, and Abrams, are briefly introduced and assessed. I then present a specific account of causal probability with the following features: First, the link between causal probability and a particular account of induction and causation is established, namely eliminative induction and the related difference-making account (...) of causation in the tradition of Bacon, Herschel, and Mill. Second, it is shown how a causal approach is useful beyond applications of the method of arbitrary functions and is able to deal with various shades of both ontic and epistemic probabilities. Furthermore, I clarify the notion of causal symmetry as a central element of an objective version of the principle of indifference and relate probabilistic independence to causal irrelevance. (shrink)

Big Data and methods for analyzing large data sets such as machine learning have in recent times deeply transformed scientific practice in many fields. However, an epistemological study of these novel tools is still largely lacking. After a conceptual analysis of the notion of data and a brief introduction into the methodological dichotomy between inductivism and hypothetico-deductivism, several controversial theses regarding big data approaches are discussed. These include, whether correlation replaces causation, whether the end of theory is in sight and (...) whether big data approaches constitute entirely novel scientific methodology. In this Element, I defend an inductivist view of big data research and argue that the type of induction employed by the most successful big data algorithms is variational induction in the tradition of Mill's methods. Based on this insight, the before-mentioned epistemological issues can be systematically addressed. (shrink)

Philosophy of physics is a small but thriving research field situated at the intersection between the natural sciences and the humanities. However, what exactly distinguishes philosophy of physics from physics is rarely made explicit in much depth. We provide a detailed analysis in the form of eleven theses, delineating both the nature of the questions asked in philosophy of physics and the methodology with which they are addressed.

This book has grown out of eight years of close collaboration among its authors. From the very beginning we decided that its content should come out as the result of a truly common effort. That is, we did not "distribute" parts of the text planned to each one of us. On the contrary, we made a point that each single paragraph be the product of a common reflection. Genuine team-work is not as usual in philosophy as it is in other (...) academic disciplines. We think, however, that this is more due to the idiosyncrasy of philosophers than to the nature of their subject. Close collaboration with positive results is as rewarding as anything can be, but it may also prove to be quite difficult to implement. In our case, part of the difficulties came from purely geographic separation. This caused unsuspected delays in coordinating the work. But more than this, as time passed, the accumulation of particular results and ideas outran our ability to fit them into an organic unity. Different styles of exposition, different ways of formalization, different levels of complexity were simultaneously present in a voluminous manuscript that had become completely unmanageable. In particular, a portion of the text had been conceived in the language of category theory and employed ideas of a rather abstract nature, while another part was expounded in the more conventional set-theoretic style, stressing intui tivity and concreteness. (shrink)

Gnothi sauton - Erkenne dich selbst! Das Streben nach Erkenntnis und Selbsterkenntnis, das nach antiker Auffassung der Gott selbst in dieser Aufforderung dem Menschen ans Herz legt, bildet ein zentrales Moment von Arbogast Schmitts jahrzehntelanger Beschaftigung mit antiker Literatur und Philosophie, die zugleich immer auch eine kritische Auseinandersetzung mit modernen Konzepten und Positionen darstellt. Die vorliegende Festschrift vereint zwolf neue Beitrage zur antiken Philosophie, Literatur und Literaturtheorie, in denen Schuler, Freunde und Weggefahrten Arbogast Schmitts dieses Erkenntnisstreben beantworten und fortsetzen. Mit (...) Beitragen von: Wolfgang Bernard, Stefan Buttner, Sabine Follinger, Hans Ulrich Gumbrecht, Andreas Kablitz, Michael Krewet, Joachim Latacz, Thomas Leinkauf, Christian Pietsch, Ernst-Richard Schwinge, Rainer Thiel und Gregor Vogt-Spira. (shrink)

The “official” history of connexive logic was written in 2012 by Storrs McCall who argued that connexive logic was founded by ancient logicians like Aristotle, Chrysippus, and Boethius; that it was further developed by medieval logicians like Abelard, Kilwardby, and Paul of Venice; and that it was rediscovered in the 19th and twentieth century by Lewis Carroll, Hugh MacColl, Frank P. Ramsey, and Everett J. Nelson. From 1960 onwards, connexive logic was finally transformed into non-classical calculi which partly concur with (...) systems of relevance logic and paraconsistent logic. In this paper it will be argued that McCall’s historical analysis is fundamentally mistaken since it doesn’t take into account two versions of connexivism. While “humble” connexivism maintains that connexive properties only apply to “normal” antecedents, “hardcore” connexivism insists that they also hold for “abnormal” propositions. It is shown that the overwhelming majority of the forerunners of connexive logic were only “humble” connexivists. Their ideas concerning connexive implication don’t give rise, however, to anything like a non-classical logic. (shrink)

Kant’s theory of cognition centrally builds on his conception of self-consciousness and the transcendental use of the phrase “I think”: the ability to add the phrase “I think” to a representation is a necessary condition of the ability to cognize objects. The paper argues that “I think”, rather than denoting the content of a predicative judgement, is typically an expression of the subject’s thinking. It expresses a kind of self-consciousness that, without assertively representing the subject itself, indicates that representational contents (...) are unified in a single consciousness of a single subject. Our aim is thus to develop and defend an expressivist interpretation of Kant’s “I think”. (shrink)

The aim of the paper is to explicate the concept of causal independence between sets of factors and Reichenbach's screening-off-relation in probabilistic terms along the lines of Suppes' probabilistic theory of causality (1970). The probabilistic concept central to this task is that of conditional stochastic independence. The adequacy of the explication is supported by proving some theorems about the explicata which correspond to our intuitions about the explicanda.

Recently, Bengt Hansson presented a paper about dyadic deontic logic,2 criticizing some purely axiomatic systems of dyadic deontic logic and proposing three purely semantical systems of dyadic deontic logic which he confidently called dyadic standard systems of deontic logic (DSDL1–3). Here I shall discuss the third by far most interesting system DSDL3 which is operating with preference relations. First, I shall describe this semantical system (Sections 1.1–1.3). Then I shall give an axiomatic system (Section 1.4) which is proved to be (...) correct (Section 2) and complete (Section 3) with respect to Hansson's semantics. Finally, in face of these results Hansson's semantics will be discussed from a more intuitive standpoint. After emphasizing its intuitive attractiveness (Section 4.1) I will show that two objections often discussed in connection with preference relations do not apply to it (Section 4.2 and 4.3); more precisely, I will show that the connectedness condition for preference relations can be dropped and that, in a sense, it is not necessary to compare two possible worlds differing in infinitely many respects. (What exactly is meant by this, will become clear later on.) Yet there is a third objection to Hansson's semantics which points to a real intuitive inadequacy of DSDL3. A way of removing this inadequacy, which corresponds to Hansson's own intuitions as well as to familiar metaethical views, is suggested, but not technically realized (Section 4.4). In the last section (section 4.5) I shall briefly show that DSDL3 is decidable, as expected. (shrink)

Kant's theory of cognition centrally builds on his conception of self‐consciousness and the transcendental use of the phrase “I think”: the ability to add the phrase “I think” to a representation is a necessary condition of the ability to cognize objects. The paper argues that “I think”, rather than denoting the content of a predicative judgement, is typically an expression of the subject's thinking. It expresses a kind of self‐consciousness that, without assertively representing the subject itself, indicates that representational contents (...) are unified in a single consciousness of a single subject. Our aim is thus to develop and defend an expressivist interpretation of Kant's “I think”. (shrink)

We present a reconstruction of so-called classical, formal or Mendelian genetics using a notation which we believe is more legible than that of earlier accounts, and lends itself easily to computer implementation, for instance in PROLOG. By drawing from, and emending, earlier work of Balzer and Dawe (1986,1997), the present account presents the three most important lines of development of classical genetics: the so-called Mendel's laws, linkage genetics and gene mapping, in the form of a theory-net. This shows that the (...) set theoretic representation format used in the structuralist approach to the philosophy of science also applies to the domain of genetic theories. There construction is intended to lend more clarity to theme thodological, philosophical and didactical discussions of the foundations of genetics, and on the other hand to defend a formally, logically minded view of theories which seems to have become contested through the work of Feyerabend, Kuhn and Kitcher. (shrink)

We show that one can solve Post's Problem by constructing generic sets in the usual set theoretic framework applied to tiny universes. This method leads to a new class of recursively enumerable sets: r.e. generic sets. All r.e. generic sets are low and simple and therefore of Turing degree strictly between 0 and 0'. Further they supply the first example of a class of low recursively enumerable sets which are automorphic in the lattice E of recursively enumerable sets with inclusion. (...) We introduce the notion of a promptly simple set. This describes the essential feature of r.e. generic sets with respect to automorphism constructions. (shrink)

The paper analyzes the nature and scope of Moore’s paradox, articulates the desiderata of a successful solution and claims that psychological expressivism best meets these desiderata. After a brief discussion of prominent responses to Moore’s paradox, the paper offers a solution based on a theory of expressive acts: a Moorean utterance is absurd because the speaker expresses mental states with conflicting contents in commissive versions of the paradox and conflicting states of mind in omissive versions. The paper presents a theory (...) of expressivism for self-ascriptions of mental states. In addition, it introduces the idea of expressive denegation—the speaker’s expressing the absence of a mental state—as an analysis of negative self-ascriptions of mental states. Some of the consequences of expressivism for avowals are explored. (shrink)

A comprehensive model for describing various forms of developments in science is defined in precise, set-theoretic terms, and in the spirit of the structuralist approach in the philosophy of science. The model emends previous accounts in centering on single systems in a homogenous way, eliminating notions which essentially refer to sets of systems. This is achieved by eliminating the distinction between theoretical and non-theoretical terms as a primitive, and by introducing the notion of intended links. The force of the model (...) is demonstrated by formally incorporating many of the important, precise meta-theoretic concepts occurring in the literature. (shrink)

It has recently been argued that some cases of naked statistical evidence license a high credence, but not an outright belief. If this is correct, there cannot be an unconditional bridge principle from credence to outright belief. We show that at least one prominent putative counterexample to such a bridge principle is based on a mistake, by demonstrating that the statistical evidence falls short not only of licensing rational belief, but also of justifying a high credence.

One of the main controversies of the Logic Schools of the 12th century centered on the question: What follows from the impossible? In this paper arguments for two diametrically opposed positions are examined. The author of the ‘Avranches Text’ who probably belonged to the school of the Parvipontani defended the view that from an impossible proposition everything follows (‘Ex impossibili quodlibet’). In particular he developed a proof to show that by means of so-called ‘disjunctive syllogism’ any arbitrary proposition B can (...) be logically derived from a pair of contradictory propositions A and Not-A. The author of the Ars Meliduna instead argued that nothing follows from an impossible proposition (‘ex falso nihil sequitur’). This view is supported by various counterexamples which aimed to show that the admission of impossible premises would give rise to inconsistent conclusions. Upon closer analysis these inconsistencies do not, however, have the formal structure of a real contradiction like A and Not-A, but rather the structure of two rivalling conditionals like ‘If B then A’ and ‘If B then Not-A’. Hence these counterexamples rather have to be considered as refutations of the basic principles of ‘connexive logic’. (shrink)

We provide a finite axiomatization of the consequence , i.e. of the set of common sequential rules for and . Moreover, we show that has no proper non-trivial strengthenings other than and . A similar result is true for , but not, e.g., for +.

It is shown that the class of Kolmogorov-Loveland stochastic sequences is not closed under selecting subsequences by monotonic computable selection rules. This result gives a strong negative answer to the question whether the Kolmogorov-Loveland stochastic sequences are closed under selecting sequences by Kolmogorov-Loveland selection rules, i.e., by not necessarily monotonic, partial computable selection rules. The following previously known results are obtained as corollaries. The Mises-Wald-Church stochastic sequences are not closed under computable permutations, hence in particular they form a strict superclass (...) of the class of Kolmogorov-Loveland stochastic sequences. The Kolmogorov-Loveland selection rules are not closed under composition. (shrink)

The systems Kα of transfinite cumulative types up to α are extended to systems K∞α that include a natural infinitary inference rule, the so-called limit rule. For countable α a semantic completeness theorem for K∞α is proved by the method of reduction trees, and it is shown that every model of K∞α is equivalent to a cumulative hierarchy of sets. This is used to show that several axiomatic first-order set theories can be interpreted in K∞α, for suitable α.