The aim of this paper is to show that the logical approach to philosophy of science could be further improved with tools like the ones put forward by Schurz in his proposal to model scientific theory development. Section 2 is a presentation of the basics in AGM epistemology of logical abduction and of their connection. In Sect. 3 several operations for theory change proposed by Schurz (2011; 2018) are presented, followed by my own proposal of a further case of hypothesis (...) refinement, consisting of the instantiation of an existential abduction. Section 4 offers a discussion and conclusions. (shrink)

Work in online learning traditionally considered induction-friendly (e.g. stochastic with a fixed distribution) and induction-hostile (adversarial) settings separately. While algorithms like Exp3 that have been developed for the adversarial setting are applicable to the stochastic setting as well, the guarantees that can be obtained are usually worse than those that are available for algorithms that are specifically designed for stochastic settings. Only recently, there is an increasing interest in algorithms that give (near-)optimal guarantees with respect to the underlying setting, even (...) in case its nature is unknown to the learner. In this paper, we review various online learning algorithms that are able to adapt to the hardness of the underlying problem setting. While our focus lies on the application of adaptive algorithms as meta-inductive methods that combine given base methods, concerning theoretical properties we are also interested in guarantees that go beyond a comparison to the best fixed base learner. (shrink)

According to the Feigl–Reichenbach–Salmon–Schurz pragmatic justification of induction, no predictive method is guaranteed or even likely to work for predicting the future; but if anything will work, induction will work—at least when induction is employed at the meta-level of predictive methods in light of their track records. One entertains a priori all manner of esoteric prediction methods, and is said to arrive a posteriori at the conclusion, based on the actual past, that object-level induction is optimal. Schurz’s refinements largely solve (...) the notorious short-run problem. A difficulty is noted, however, related to short-run worries but based on localized disagreement about the past, a feature characteristic of real debates (especially early modern) involving induction in intellectual history. Given the evidence about past events, _unfiltered by induction_, meta-induction might support a partly non-inductive method—especially as judged by proponents of esoteric prediction methods, who presumably believe that their methods have worked. Thus induction is justified meta-inductively in contexts where it was uncontroversial, while not obviously justified in key contexts where it has been disputed. This objection, momentarily sensed by Reichenbach regarding clairvoyance, is borne out by the Stoics’ use of meta-induction to justify both science and divination and by ancient Hebrew examples of meta-induction. Schurz’s recently introduced criteria for acceptance of testimony play a crucial role in arriving at object-level induction using meta-induction, but one might question them. Given the need for judgment in accepting testimony, it is unclear that the subjectivity of Howson’s Bayesian answer to Hume’s problem is overcome. (shrink)

In this paper, the contributions to the account of meta-induction (Schurz 2019) collected in this volume are critically discussed and thereby, new insights are developed. How broad and expandable the program of meta-induction is can be learned from Ortner’s contribution. New insights about the transition from the a priori justification of meta-induction to the a posteriori justification of object-induction emerge from the reflection of Shogenji’s paper. How meta-induction may be applied also to religious prophecies and that their meta-inductive justification does (...) not fail for a priori reasons but because of missing evidence for predictive success is learned from the discussion of Pitts’ contribution. That meta-induction does not rely on a particular prior distribution, while the no free lunch theorem depends implicitly on a uniform prior, is the major conclusion drawn from the discussion of Wolpert’s article. How the problem of induction is treated in different versions of the Bayesian account is learned from the discussion of Willliamson’s paper. That meta-induction can also be employed for abduction, and that abductive theory-revision can offer meta-inductive aggregation methods is a new insight emerging from the reflection of Aliseda’s contribution. (shrink)

This paper examines a twofold tension in Gerhard Schurz’s (2019) recent proposal to solve Hume’s problem of induction. Schurz concedes to the skeptic that there is no non-circular epistemic justification of the reliability of induction, but then argues for the optimality of meta-induction so that if any prediction method is reliable, then meta-induction is. There is a tension in this proposal between meta-induction and our inductive practice: Are we supposed to abandon our inductive practice in favor of meta-induction? Schurz claims (...) that given the actual way the world has been, the meta-inductive method supports the standard inductive method. There then arises a second tension: The challenges Schurz cites against the reliability of induction—such as the anti-inductive hypothesis and the state-uniform probability distribution—cast doubt on Schurz’s claim that meta-induction supports induction. The reasoning in this paper moves in the opposite direction: There are ways of answering these challenges in defense of Schurz’s claim that meta-induction supports induction, but these ways also point to ways of defending induction directly without the mediation of meta-induction. (shrink)

This is the introduction to the special issue “The Meta-Inductive Approach to Hume’s Problem”. The introduction includes introductory remarks and brief comments on each of the papers appearing in the special issue.

Schurz (2019, ch. 4) argues that probabilistic accounts of induction fail. In particular, he criticises probabilistic accounts of induction that appeal to direct inference principles, including subjective Bayesian approaches (e.g., Howson 2000) and objective Bayesian approaches (see, e.g., Williamson 2017). In this paper, I argue that Schurz’ preferred direct inference principle, namely Reichenbach’s Principle of the Narrowest Reference Class, faces formidable problems in a standard probabilistic setting. Furthermore, the main alternative direct inference principle, Lewis’ Principal Principle, is also hard to (...) reconcile with standard probabilism. So, I argue, standard probabilistic approaches cannot appeal to direct inference to explicate the logic of induction. However, I go on to defend a non-standard objective Bayesian account of induction: I argue that this approach can both accommodate direct inference and provide a viable account of the logic of induction. I then defend this account against Schurz’ criticisms. (shrink)

The important recent book by Schurz ( 2019 ) appreciates that the no-free-lunch theorems (NFL) have major implications for the problem of (meta) induction. Here I review the NFL theorems, emphasizing that they do not only concern the case where there is a uniform prior—they prove that there are “as many priors” (loosely speaking) for which any induction algorithm _A_ out-generalizes some induction algorithm _B_ as vice-versa. Importantly though, in addition to the NFL theorems, there are many _free lunch_ theorems. (...) In particular, the NFL theorems can only be used to compare the expected performance of an induction algorithm _A_, considered in isolation, with the expected performance of an induction algorithm _B_, considered in isolation. There is a rich set of free lunches which instead concern the statistical _correlations_ among the generalization errors of induction algorithms. As I describe, the meta-induction algorithms that Schurz advocates as a “solution to Hume’s problem” are simply examples of such a free lunch based on correlations among the generalization errors of induction algorithms. I end by pointing out that the prior that Schurz advocates, which is uniform over bit frequencies rather than bit patterns, is contradicted by thousands of experiments in statistical physics and by the great success of the maximum entropy procedure in inductive inference. (shrink)

This paper calls into question one fundamental claim at the basis of an alleged puzzle for veritistic accounts of the value of idealized models: the claim that idealized models cannot be veridical representations of the world. Catherine Elgin has argued that the value of idealized models can only be explained if we construe them as exemplars, which do not represent the world. I argue that Elgin’s proposal is problematic and cannot accommodate central cases of idealization. Nevertheless, there is value in (...) Elgin’s proposal. I rescue her notion of selectiveness in exemplification and incorporate it within a revised account of representation. I provide independent motivation in favour of a form of veritism, which motivates a revision of Elgin’s case against it. I argue that an account based on selective representation has the resources to rescue veritism from the problems raised by Elgin. In the proposal I advance, idealized models are literally veridical representations of the world. (shrink)

This article connects recent work in formal epistemology to work in economics and computer science. Analysing the Dutch Book Arguments, Epistemic Utility Theory and Objective Bayesian Epistemology we discover that formal epistemologists employ the same argument structure as economists and computer scientists. Since similar approaches often have similar problems and have shared solutions, opportunities for cross-fertilisation abound.

Lange (2008) has given an argument elaborating Blackburn’s (1993) dilemma for any account of modal facts. Lange’s argument aims to show that a contingent fact lacks the modal strength required to be responsible for some fact’s necessity. Recently, Wildman (2021) has argued that Lange’s argument appeals to a mistaken premise. This paper shows that Wildman’s argument fails; his case does not constitute a counterexample to that premise.

Otto Neurath’s empiricist methodology of economics and his contributions to political economy have gained increasing attention in recent years. We connect this research with contemporary debates regarding the epistemological status of thought experiments by reconstructing Neurath’s utopias as linchpins of thought experiments. In our three reconstructed examples of different uses of utopias/dystopias in thought experiments we employ a reformulation of Häggqvist’s model for thought experiments and we argue that: (1) Our reformulation of Häggqvist’s model more adequately complies with many uses (...) of thought experiments, especially with the open-ended discussions of utopias and dystopias in thought experiments. (2) As a strict logical empiricist, Neurath is committed to a strictly empiricist account of thought experiments. John Norton’s empiricist argument view can indeed account for the justifications of empirical beliefs and genuine discoveries targeted by scientific utopianism in three distinct (yet connected) ways, all of which Neurath already contemplated: (2.I) Dealing with utopias and thought experiments on a regular basis increases creativity and inventiveness. (2.II) Particular ways of presenting knowledge facilitate scientific discovery and social progress. (2.III) The use of utopias in thought experiments can prompt conceptual change and allow access to new phenomena. We conclude by highlighting that, even though thought experiments support a positive attitude for exploring new social possibilities, Neurath points out that active decisions are unavoidable. The exploration of alternatives and the awareness of a need for decisions in policy discussion avert a technocratic outlook in social science. (shrink)

In recent years, many philosophers of science have rejected the “value-free ideal” for science, arguing that non-epistemic values have a legitimate role to play in scientific inquiry. However, this philosophical position raises the question of how to distinguish between legitimate and illegitimate influences of values in science. In this paper, we argue that those seeking to address this “new” demarcation problem can benefit by drawing lessons from the “old” demarcation problem, in which philosophers tried to find a way of distinguishing (...) between science and non-science. Many of those who worked on this problem ultimately found that efforts to provide necessary and sufficient conditions for defining science failed, and most concluded that the best solution to the problem was to characterize scientific hypotheses, theories, and research programs in terms of some common norms. We suggest that those seeking to distinguish between legitimate and illegitimate value influences on science would do well to adopt a similar approach. Rather than attempting to establish necessary and sufficient conditions for identifying appropriate value influences, it will be more fruitful to evaluate scientific activities based on their adherence to a set of epistemic and ethical norms that can be implemented in scientific practice by means of rules, conventions, policies, and procedures. (shrink)

In a recent article in this journal, Stump argues that pragmatism distances itself from absolutism due to its assent to fallibilism while it rejects relativism at the same time because of its insistence on experience. Therefore, pragmatism can provide a third position between relativism and absolutism. I argue in this note that his argument is profoundly inadequate for both claims. Fallibilism is compatible with both relativism and absolutism, and accordingly cannot be considered as the middle ground. Furthermore, the experience itself (...) and the way it is inferred from is the subject of the relativists’ debates, not a response. (shrink)

We review publications in automated scientific discovery using deep learning, with the aim of shedding light on problems with strong connections to philosophy of science, of physics in particular. We show that core issues of philosophy of science, related, notably, to the nature of scientific theories; the nature of unification; and of causation loom large in scientific deep learning. Therefore, advances in deep learning could, and ideally should, have impact on philosophy of science, and vice versa. We suggest lines of (...) further research, and highlight the role ‘theory-based’ AI could have in future developments of the field. (shrink)

In this paper, I consider the relationship between coming to understand why something must be the case and coming to understand why it actually is the case in some particular instance. Peter Lipton uses the possibility of coming to understand a phenomenon via a necessity proof as an argument that there can be understanding with no explanation. Lipton’s argument has come under criticism, at least partially because one might think that understanding why something must be the case has a different (...) object from understanding the actual phenomenon. In this paper, I argue that that under certain circumstances it is fairly straightforward to come to understand an actual phenomenon on the basis of knowing why it had to be the case. Rather than relying on brute intuitions, my primary strategy will be to show that on least some modern accounts of understanding we can validate Lipton’s general point with respect to a variety of possible necessity relations. (shrink)

Hermann von Helmholtz has been widely acknowledged as one of the forerunners of contemporary theories of measurement. However, his conception of measurement differs from later, representational conceptions in two main respects. Firstly, Helmholtz advocated an empiricist philosophy of arithmetic as grounded in some psychological facts concerning quantification. Secondly, his theory implies that mathematical structures are common to both subjective experiences and objective ones. My suggestion is that both of these differences depend on a classical approach to measurement, according to which (...) the arithmetic laws of addition define what is measurable as a particular domain for their application, and, at the same time, the extensibility of these laws to all known physical processes works as a heuristic principle for empirical research. Such an approach is worth reconsidering, not only because it lends plausibility to some of the controversial aspects of Helmholtz’s theory, but also because it offers a philosophical perspective on quantification problems that originated in the nineteenth-century.This paper draws insights on Helmholtz’s philosophical views from his engagement with the measurability of sensations via Fechner’s psychophysical law. This seems to be in contrast with the fact that the reception of Helmholtz’s theory culminated with the formulation of the theory of extensive measurement. I will contend that Helmholtz reached a no less important standpoint in the nineteenth-century debate on whether sensations are different (i.e., intensive) kinds of magnitudes and on how, if at all, they can be measured. (shrink)

Poincaré’s conventionalism has been interpreted in many writings as a philosophical position emerged by reflection on certain scientific problems, such as the applicability of geometry to physical space or the status of certain scientific principles. In this paper I would like to consider conventionalism as a philosophical position that emerged from Poincaré’s scientific practice. But not so much from dealing with scientific problems, as from the use of two specific methodologies proper to modern mathematics and the modern natural sciences: methodological (...) structuralism and the hypothetical-deductive method—thus, as a philosophical position which emerged from a way (or rather, two ways) of doing science. With this approach, I try to deepen the analysis of connections between Poincaré’s scientific practice and his philosophy. (shrink)

This paper defends a conceptualistic version of structuralism as the most convincing way of elaborating a philosophical understanding of structuralism in line with the classical tradition. The argument begins with a revision of the tradition of “conceptual mathematics”, incarnated in key figures of the period 1850 to 1940 like Riemann, Dedekind, Hilbert or Noether, showing how it led to a structuralist methodology. Then the tension between the ‘presuppositionless’ approach of those authors, and the platonism of some recent versions of philosophical (...) structuralism, is presented. In order to resolve this tension, we argue for the idea of ‘logical objects’ as a form of minimalist realism, again in the tradition of classical authors including Peirce and Cassirer, and we introduce the basic tenets of conceptual structuralism. The remainder of the paper is devoted to an open discussion of the assumptions behind conceptual structuralism, and—most importantly—an argument to show how the objectivity of mathematics can be explained from the adopted standpoint. This includes the idea that advanced mathematics builds on hypothetical assumptions (Riemann, Peirce, and others), which is presented and discussed in some detail. Finally, the ensuing notion of objectivity is interpreted as a form of particularly robust intersubjectivity, and it is distinguished from fictional or social ontology. (shrink)

Philosophy of science in the twentieth century tends to emphasize either the logic of science (e.g., Popper and Hempel on explanation, confirmation, etc.) or its history/sociology (e.g., Kuhn on revolutions, holism, etc.). This dichotomy, however, is neither exhaustive nor exclusive. Questions regarding scientific understanding and mathematical explanation do not fit neatly inside either category, and addressing them has drawn from both logic and history. Additionally, interest in scientific and mathematical practice has led to work that falls between the two sides (...) of the dichotomy. We might call these less narrow approaches ‘holistic’. Prior to 1918, work in the philosophy of science was also somewhat more holistic and interdisciplinary in nature. An exemplar of this type of approach is found in the work of Henri Poincaré. In this paper I will consider one particularly flexible tool Poincaré uses throughout his philosophical writings about science and mathematics: the tool of the unifying concept. More specifically, I will focus on one unifying concept: that of structure. I aim to show first, that structure is a unifying scientific concept for Poincaré; second, a focus on structure helps explain his scientific and mathematical success; lastly, this case study may provide a model for how unifying concepts can facilitate progress in mathematics and science. (shrink)

This paper has a twofold aim. On the one hand, it explores the extent to which Mach was inspired by Kant’s approach to philosophical inquiry and tried to further elaborate it through his historico-critical method for enlightening scientific knowledge claims. On the other hand, it argues that the focus on the situated character of these claims that is implied in Mach’s epistemology makes it possible to compare his view to recent attempts to defend a perspectival realist account of scientific knowledge, (...) thus revealing the relevance of Mach’s own approach as a methodology in the philosophy of science. (shrink)

The present paper studies Ernst Mach’s experimental work with “spark waves” and other types of shock waves, which brought him to the 1887–88 famous schlieren photographs of supersonic phenomena triggered by bullets shot at high speed. Against what it is traditionally argued, I show (1) that Ernst Mach’s visualization attempts do not depend on his commitment to any particular philosophical doctrine about the role of sensations as the foundation of empirical science, and (2) that his inclination toward experimental research may (...) have crucially contributed to the development of his epistemological and ontological views. (shrink)

Identifications, diagnoses, and treatments of pseudo-problems form a family of classic methodologies in later nineteenth century philosophy and at least partly, as I shall argue, in the philosophy of science. They were devised, not by academic philosophers, but by three of the greatest of the philosopher-scientists. (Later, the idea was taken up by academic philosophers, of course. But I will not discuss that development). Here I show how Ernst Mach, Heinrich Hertz and Ludwig Boltzmann each deployed methods of this general (...) kind, how they identified different pseudo-problems, how they gave different diagnoses of such problems, and how they suggested quite different treatments for them. I argue that it was Mach who really first developed the idea of a pseudo-problem, that he did so in a relatively focused way on the basis of two kinds of examples. Hertz’s contribution was much more limited, identifying two specific pseudo-problems concerning physics, and suggesting a way in which they might be treated. Boltzmann’s conception of pseudo-problems, though, was far less focused, being applied to a very wide range of problems in philosophy and physics. However, his conception was certainly more influential in philosophy, and perhaps ultimately more fruitful and suggestive. I argue for the originality and continuing interest of such approaches, and I try to dissociate them from any problematic ‘positivism’. (shrink)

Historians of philosophy have hitherto either given scant attention to Cournot and Renouvier’s views on scientific revolution, tried to read Kuhn’s concept of scientific revolution back into their works, or did not fully appreciate the extent to which these philosophers were reflecting on the works of their predecessors as well as on developments in mathematics and the sciences. Cournot’s views on cumulative development through revolution resemble Comte’s more than Kuhn’s, and his notion of progressive theoretical simplicity through revolution recalls Whewell’s (...) philosophy of science. Renouvier, far from regarding a scientific revolution as resulting in a new set of conceptual boxes imposing a conformity of thought on the scientific community, recognized that a new theory proposed during a revolution is open to more than one interpretation. (shrink)

William Whewell’s 19th century philosophy of science is sometimes glossed over as a footnote to Kant. There is however a key feature of Whewell’s account worth noting. This is his appeal to Aristotle’s form/matter hylomorphism as a metaphor to explain how mind and world merge in successful scientific inquiry. Whewell’s hylomorphism suggests a middle way between rationalism and empiricism reminiscent of experience pragmatists like Steven Levine’s view that mind and world are entwined in experience. I argue however that Levine does (...) not adequately explain exactly how mind and world entwine. He could nonetheless do so if he appealed to Whewell’s hylomorphic metaphor. We may prefer a reductive metaphysical explanation, but I suggest that pragmatists only have recourse to metaphor in this case. Both reductive and metaphorical explanations can enjoy great explanatory power if they exhibit a suitable measure of what I will call sematic distance. Semantic distance measures how close or how far apart explanandum and explanans are from each other in meaning. Metaphorical explanation - as evident in Whewell’s hylomorphism and as detailed via the notion of semantic distance - presents a valuable new explanatory tool to those who hold that mind and world are entwined sans recourse to metaphysics. (shrink)

Otto Neurath’s empiricist methodology of economics and his contributions to politi- cal economy have gained increasing attention in recent years. We connect this research with contemporary debates regarding the epistemological status of thought experiments by reconstructing Neurath’s utopias as linchpins of thought experiments. In our three reconstructed examples of different uses of utopias/dystopias in thought experiments we employ a reformulation of Häggqvist’s model for thought experiments and we argue that: (1) Our reformulation of Häggqvist’s model more adequately complies with many (...) uses of thought experiments, especially with the open-ended discussions of utopias and dys- topias in thought experiments. (2) As a strict logical empiricist, Neurath is committed to a strictly empiricist account of thought experiments. John Norton’s empiricist argument view can indeed account for the justifications of empirical beliefs and genuine discoveries targeted by scientific utopianism in three distinct (yet connected) ways, all of which Neur- ath already contemplated: (2.I) Dealing with utopias and thought experiments on a regular basis increases creativity and inventiveness. (2.II) Particular ways of presenting knowl- edge facilitate scientific discovery and social progress. (2.III) The use of utopias in thought experiments can prompt conceptual change and allow access to new phenomena. We con- clude by highlighting that, even though thought experiments support a positive attitude for exploring new social possibilities, Neurath points out that active decisions are unavoidable. The exploration of alternatives and the awareness of a need for decisions in policy discus- sion avert a technocratic outlook in social science. (shrink)

Logic diagrams have been increasingly studied and applied for a few decades, not only in logic, but also in many other fields of science. The history of logic diagrams is an important subject, as many current systems and applications of logic diagrams are based on historical predecessors. While traditional histories of logic diagrams cite pioneers such as Leibniz, Euler, Venn, and Peirce, it is not widely known that Kant and the early Kantians in Germany and England played a crucial role (...) in popularising Euler(-type) diagrams. In this paper, the role of the Kantians in the late eighteenth and early nineteenth centuries will be analysed in more detail. It shows that diagrams (or intuition in general) were a highly contentious topic that depend on the philosophical attitude and went beyond logic to touch on issues of physics, metaphysics, linguistics and, above all, mathematics. (shrink)