Probability ratio and likelihood ratio measures of inductive support and related notions have appeared as theoretical tools for probabilistic approaches in the philosophy of science, the psychology of reasoning, and artificial intelligence. In an effort of conceptual clarification, several authors have pursued axiomatic foundations for these two families of measures. Such results have been criticized, however, as relying on unduly demanding or poorly motivated mathematical assumptions. We provide two novel theorems showing that probability ratio and likelihood ratio measures can be (...) axiomatized in a way that overcomes these difficulties. (shrink)

The current state of inductive logic is puzzling. Survey presentations are recurrently offered and a very rich and extensive handbook was entirely dedicated to the topic just a few years ago [23]. Among the contributions to this very volume, however, one finds forceful arguments to the effect that inductive logic is not needed and that the belief in its existence is itself a misguided illusion , while other distinguished observers have eventually come to see at least the label as “slightly (...) antiquated” .What seems not to have lost any of its currency is the problem which inductive logic is meant to address. Inference from limited ascertained information to uncertain hypotheses is ubiquitous in learning, prediction and discovery. The logical insight that such kind of inference is fallible m .. (shrink)

Proponents of the no-miracles argument contend that scientific realism is “the only philosophy that doesn’t make the success of science a miracle.” Bas van Fraassen argued, however, that the success of our best theories can be explained in Darwinian terms—by the fact they are survivors of a winnowing process in which unsuccessful theories are rejected. Critics of this selectionist explanation complain that while it may account for the fact we have chosen successful theories, it does not explain why any particular (...) one of those theories succeeds. Against this I defend the claim that if selectionists manage to account for the former, they have no burden to account for the latter; the success of any particular one of our best theories might as well be an extraordinary coincidence. I refer to this enhanced selectionist reply as “coincidentalism” and argue that it is a serious but underappreciated response to the no-miracles argument. More generally, I argue the considerations raised in favor of this response show that versions of the no-miracles argument focusing on the success of particular theories are misguided. (shrink)

Two powerful arguments have famously dominated the realism debate in philosophy of science: The No Miracles Argument (NMA) and the Pessimistic Meta-Induction (PMI). A standard response to the PMI is selective scientific realism (SSR), wherein only the working posits of a theory are considered worthy of doxastic commitment. Building on the recent debate over the NMA and the connections between the NMA and the PMI, I here consider a stronger inductive argument that poses a direct challenge for SSR: Because it (...) is sometimes exactly the working posits which contradict each other, i.e., that which is directly responsible for empirical success, SSR cannot deliver a general explanation of scientific success. (shrink)

Howson famously argues that the no-miracles argument, stating that the success of science indicates the approximate truth of scientific theories, is a base rate fallacy: it neglects the possibility of an overall low rate of true scientific theories. Recently a number of authors has suggested that the corresponding probabilistic reconstruction is unjust, as it concerns only the success of one isolated theory. Dawid and Hartmann, in particular, suggest to use the frequency of success in some field of research \ to (...) infer a probability of truth for a new theory from \. I here shed doubts on the justification of this and similar moves and suggest a way to directly bound the probability of truth. As I will demonstrate, my bound can become incompatible with the assumption specific testing and Dawid and Hartmann’s estimate for success. (shrink)

De Finetti is one of the founding fathers of the subjective school of probability. He held that probabilities are subjective, coherent degrees of expectation, and he argued that none of the objective interpretations of probability make sense. While his theory has been influential in science and philosophy, it has encountered various objections. I argue that these objections overlook central aspects of de Finetti’s philosophy of probability and are largely unfounded. I propose a new interpretation of de Finetti’s theory that highlights (...) these aspects and explains how they are an integral part of de Finetti’s instrumentalist philosophy of probability. I conclude by drawing an analogy between misconceptions about de Finetti’s philosophy of probability and common misconceptions about instrumentalism. (shrink)

Autobiographical memories typically give rise either to memory reports (“I remember going swimming”) or to first person past-tense judgements (“I went swimming”). This article focuses on first person past-tense judgements that are (epistemically) based on autobiographical memories. Some of these judgements have the IEM property of being immune to error through misidentification. This article offers an account of when and why first person past-tense judgements have the IEM property.

Bayesians often assume, suppose, or conjecture that for any reasonable explication of the notion of simplicity a prior can be designed that will enforce a preference for hypotheses simpler in just that sense. But it is shown here that there are simplicity-driven approaches to curve-fitting problems that cannot be captured within the orthodox Bayesian framework.

A piece of folklore enjoys some currency among philosophical Bayesians, according to which Bayesian agents that, intuitively speaking, spread their credence over the entire space of available hypotheses are certain to converge to the truth. The goals of the present discussion are to show that kernel of truth in this folklore is in some ways fairly small and to argue that Bayesian convergence-to-the-truth results are a liability for Bayesianism as an account of rationality, since they render a certain sort of (...) arrogance rationally mandatory. (shrink)

The notion of a severe test has played an important methodological role in the history of science. But it has not until recently been analyzed in any detail. We develop a generally Bayesian analysis of the notion, compare it with Deborah Mayo’s error-statistical approach by way of sample diagnostic tests in the medical sciences, and consider various objections to both. At the core of our analysis is a distinction between evidence and confirmation or belief. These notions must be kept separate (...) if mistakes are to be avoided; combined in the right way, they provide an adequate understanding of severity. Those who think that the weight of the evidence always enables you to choose between hypotheses “ignore one of the factors (the prior probability) altogether, and treat the other (the likelihood) as though it ...meant something other than it actually does. This is the same mistake as is made by someone who has scruples about measuring the arms of a balance (having only a tape measure at his disposal ...), but is willing to assert that the heavier load will always tilt the balance (thereby implicitly assuming, although without admitting it, that the arms are of equal length!). (Bruno de Finetti, Theory of Probability)2. (shrink)

The paper offers a partial vindication of Sterelny’s view on the role of error rates and reliability in his theory of decoupled representation based on modelling techniques borrowed from the biological literature on evolution in stochastic environments. In the case of a tight link between tracking states and behaviour, I argue that in its full generality Sterelny’s account instantiates the base-rate fallacy. With regard to non-tightly linked behaviour, I show that Sterelny’s account can be vindicated subject to an adequate evolutionary (...) model and a suitable notion of reliability. (shrink)

In a recent Philosophy of Science article Gerhard Schurz proposes meta-inductivistic prediction strategies as a new approach to Hume's. This comment examines the limitations of Schurz's approach. It can be proven that the meta-inductivist approach does not work any more if the meta-inductivists have to face an infinite number of alternative predictors. With his limitation it remains doubtful whether the meta-inductivist can provide a full solution to the problem of induction.

Since the mid-1970s, scholars have recognized that the skeptical interpretation of Hume's central argument about induction is problematic. The science of human nature presupposes that inductive inference is justified and there are endorsements of induction throughout "Treatise" Book I. The recent suggestion that I.iii.6 is confined to the psychology of inductive inference cannot account for the epistemic flavor of its claims that neither a genuine demonstration nor a non-question-begging inductive argument can establish the uniformity principle. For Hume, that inductive inference (...) is justified is part of the data to be explained. Bad argument is therefore excluded as the cause of inductive inference; and there is no good argument to cause it. Does this reinstate the problem of induction, undermining Hume's own assumption that induction is justified? It does so only if justification must derive from "reason", from the availability of a cogent argument. Hume rejects this internalist thesis; induction's favorable epistemic status derives from features of custom, the mechanism that generates inductive beliefs. Hume is attracted to this externalist posture because it provides a direct explanation of the epistemic achievements of children and non-human animals — creatures that must rely on custom unsupplemented by argument. (shrink)

Edmund Gettier (1963) argued that there can be justified true belief (JTB) that is not knowledge. I question the correctness of his argument by showing that Smith of Gettier’s famous examples does not earn justification for his incidentally true beliefs, while a doxastically more conscientious person S would come to hold justified but false beliefs. So, Gettier’s (and analogous) cases do not result in justified _and_ true belief. This is due to a tension between deductive closure of justification and evidential (...) support. For being justified, any believing, disbelieving, or withholding of deductively inferred propositions must be distributed proportionally to given evidential support. This proportionality principle has primacy over deductive closure in case of conflict. My argument does not save the JTB-account. But, instead of merely referring to an intuition, it explains why subjects in Gettier situations do not earn knowledge. (shrink)

Scientific theories are used for a variety of purposes. For example, physical theories such as classical mechanics and electrodynamics have important applications in engineering and technology, and we trust that this results in useful machines, stable bridges, and the like. Similarly, theories such as quantum mechanics and relativity theory have many applications as well. Beyond that, these theories provide us with an understanding of the world and address fundamental questions about space, time, and matter. Here we trust that the answers (...) scientific theories give are reliable and that we have good reason to believe that the features of the world are similar to what the theories say about them. But why do we trust scientific theories, and what counts as evidence in favor of them? (shrink)

This volume examines the limitations of mathematical logic and proposes a new approach to logic intended to overcome them. To this end, the book compares mathematical logic with earlier views of logic, both in the ancient and in the modern age, including those of Plato, Aristotle, Bacon, Descartes, Leibniz, and Kant. From the comparison it is apparent that a basic limitation of mathematical logic is that it narrows down the scope of logic confining it to the study of deduction, without (...) providing tools for discovering anything new. As a result, mathematical logic has had little impact on scientific practice. Therefore, this volume proposes a view of logic according to which logic is intended, first of all, to provide rules of discovery, that is, non-deductive rules for finding hypotheses to solve problems. This is essential if logic is to play any relevant role in mathematics, science and even philosophy. To comply with this view of logic, this volume formulates several rules of discovery, such as induction, analogy, generalization, specialization, metaphor, metonymy, definition, and diagrams. A logic based on such rules is basically a logic of discovery, and involves a new view of the relation of logic to evolution, language, reason, method and knowledge, particularly mathematical knowledge. It also involves a new view of the relation of philosophy to knowledge. This book puts forward such new views, trying to open again many doors that the founding fathers of mathematical logic had closed historically. (shrink)

The volume includes twenty-five research papers presented as gifts to John L. Bell to celebrate his 60th birthday by colleagues, former students, friends and admirers. Like Bell’s own work, the contributions cross boundaries into several inter-related fields. The contributions are new work by highly respected figures, several of whom are among the key figures in their fields. Some examples: in foundations of maths and logic ; analytical philosophy, philosophy of science, philosophy of mathematics and decision theory and foundations of economics. (...) Most articles are contributions to current philosophical debates, but contributions also include some new mathematical results, important historical surveys, and a translation by Wilfrid Hodges of a key work of arabic logic. (shrink)

This is my personal homepage. Find my philosophical papers under "Philosophy".

The evidence from randomized controlled trials (RCTs) is widely regarded as supplying the ‘gold standard’ in medicine—we may sometimes have to settle for other forms of evidence, but this is always epistemically second-best. But how well justified is the epistemic claim about the superiority of RCTs? This paper adds to my earlier (predominantly negative) analyses of the claims produced in favour of the idea that randomization plays a uniquely privileged epistemic role, by closely inspecting three related arguments from leading contributors (...) to the burgeoning field of probabilistic causality—Papineau, Cartwright and Pearl. It concludes that none of these further arguments supplies any practical reason for thinking of randomization as having unique epistemic power. IntroductionWhy the issue is of great practical importance—the ECMO casePapineau on the ‘virtues of randomization’Cartwright on causality and the ‘ideal’ randomized experimentPearl on randomization, nets and causesConclusion. (shrink)

It is surely obvious that medicine, like any other rational activity, must be based on evidence. The interest is in the details: how exactly are the general principles of the logic of evidence to be applied in medicine? Focussing on the development, and current claims of the ‘Evidence-Based Medicine’ movement, this article raises a number of difficulties with the rationales that have been supplied in particular for the ‘evidence hierarchy’ and for the very special role within that hierarchy of randomized (...) controlled trials (and meta-analyses of the results of randomized controlled trials). The point is not at all to question the application of a scientific approach to evidence in medicine, but, on the contrary, to indicate a number of areas where philosophers of science can contribute to a proper implementation of exactly that scientific-evidential approach. (shrink)

Objective Bayesianism has been criticised on the grounds that objective Bayesian updating, which on a finite outcome space appeals to the maximum entropy principle, differs from Bayesian conditionalisation. The main task of this paper is to show that this objection backfires: the difference between the two forms of updating reflects negatively on Bayesian conditionalisation rather than on objective Bayesian updating. The paper also reviews some existing criticisms and justifications of conditionalisation, arguing in particular that the diachronic Dutch book justification fails (...) because diachronic Dutch book arguments are subject to a reductio: in certain circumstances one can Dutch book an agent however she changes her degrees of belief . One may also criticise objective Bayesianism on the grounds that its norms are not compulsory but voluntary, the result of a stance. It is argued that this second objection also misses the mark, since objective Bayesian norms are tied up in the very notion of degrees of belief. (shrink)

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)

In this paper I adduce a new argument in support of the claim that IBE is an autonomous form of inference, based on a familiar, yet surprisingly, under-discussed, problem for Hume’s theory of induction. I then use some insights thereby gleaned to argue for the claim that induction is really IBE, and draw some normative conclusions.

A success-to-truth inference has always been at the heart of scientific realist positions. But all attempts to articulate the inference have met with very significant challenges. This paper reconstructs the evolution of this inference, and brings together a number of qualifications in an attempt to articulate a contemporary success-to-truth inference which is realistic. I argue that this contemporary version of the inference has a chance, at least, of overcoming the historical challenges which have been proffered to date. However, there is (...) a price to pay: the developments which help the realist answer the historical challenges also serve to increase the number of non-historical challenges. (shrink)

Does the Bayesian theory of confirmation put real constraints on our inductive behavior? Or is it just a framework for systematizing whatever kind of inductive behavior we prefer? Colin Howson (Hume's Problem) has recently championed the second view. I argue that he is wrong, in that the Bayesian apparatus as it is usually deployed does constrain our judgments of inductive import, but also that he is right, in that the source of Bayesianism's inductive prescriptions is not the Bayesian machinery itself, (...) but rather what David Lewis calls the ``Principal Principle''. (shrink)

This article argues that a successful answer to Hume's problem of induction can be developed from a sub-genre of philosophy of science known as formal learning theory. One of the central concepts of formal learning theory is logical reliability: roughly, a method is logically reliable when it is assured of eventually settling on the truth for every sequence of data that is possible given what we know. I show that the principle of induction (PI) is necessary and sufficient for logical (...) reliability in what I call simple enumerative induction. This answer to Hume's problem rests on interpreting PI as a normative claim justified by a non-empirical epistemic means-ends argument. In such an argument, a rule of inference is shown by mathematical or logical proof to promote a specified epistemic end. Since the proof concerning PI and logical reliability is not based on inductive reasoning, this argument avoids the circularity that Hume argued was inherent in any attempt to justify PI. (shrink)

In the process of scientific discovery, knowledge ampliation is pursued by means of non-deductive inferences. When ampliative reasoning is performed, probabilities cannot be assigned objectively. One of the reasons is that we face the problem of the unconceived alternatives: we are unable to explore the space of all the possible alternatives to a given hypothesis, because we do not know how this space is shaped. So, if we want to adequately account for the process of knowledge ampliation, we need to (...) develop an account of the process of scientific discovery which is not exclusively based on probability calculus. We argue that the analytic view of the method of science advocated by Cellucci is interestingly suited to this goal, since it rests on the concept of plausibility. In this perspective, in order to account for how probabilities are in fact assigned in uncertain contexts and knowledge ampliation is really pursued, we have to take into account plausibility-based considerations. (shrink)

This article poses a challenge to Schurz’s proposed metainductive justification of induction. It is argued that Schurz’s argument requires a notion of optimality that can deal with an expanding pool of prediction strategies.

I evaluate Schurz's proposed meta-inductive justification of induction, a refinement of Reichenbach's pragmatic justification that rests on results from the machine learning branch of prediction with expert advice. My conclusion is that the argument, suitably explicated, comes remarkably close to its grand aim: an actual justification of induction. This finding, however, is subject to two main qualifications, and still disregards one important challenge. The first qualification concerns the empirical success of induction. Even though, I argue, Schurz's argument does not need (...) to spell out what inductive method actually consists in, it does need to postulate that there is something like the inductive or scientific prediction strategy that has so far been significantly more successful than alternative approaches. The second qualification concerns the difference between having a justification for inductive method and for sticking with induction for now. Schurz's argument can only provide the latter. Finally, the remaining challenge concerns the pool of alternative strategies, and the relevant notion of a meta-inductivist's optimality that features in the analytic step of Schurz's argument. Building on the work done here, I will argue in a follow-up paper that the argument needs a stronger dynamic notion of a meta-inductivist's optimality. (shrink)

Algorithmic information theory gives an idealized notion of compressibility that is often presented as an objective measure of simplicity. It is suggested at times that Solomonoff prediction, or algorithmic information theory in a predictive setting, can deliver an argument to justify Occam’s razor. This article explicates the relevant argument and, by converting it into a Bayesian framework, reveals why it has no such justificatory force. The supposed simplicity concept is better perceived as a specific inductive assumption, the assumption of effectiveness. (...) It is this assumption that is the characterizing element of Solomonoff prediction and wherein its philosophical interest lies. (shrink)

Scientific Realism (SR) has three crucial aspects: 1) the centrality of the concept of truth, 2) the idea that success is a reliable indicator of truth, and 3) the idea that the Inference to the Best Explanation is a reliable inference rule. It will be outlined how some realists try to overcome the difficulties which arise in justifying such crucial aspects relying on an adaptationist view of evolutionism, and why such attempts are inadequate. Finally, we will briefly sketch some of (...) the main difficulties the realist has to face in defending those crucial aspects, and how such difficulties are deeply related: they derive from the inability of SR to satisfyingly avoid the sceptical challenge of the criterion of truth. Indeed, SR seems not to be able to fill the so-called ‘epistemic gap’ (Sankey 2008). In fact, the epistemic gap cannot be filled in no way other than obtaining a criterion of truth, but such a criterion cannot be obtained if the epistemic gap obtains. (shrink)

Putnam construed the aim of Carnap’s program of inductive logic as the specification of a “universal learning machine,” and presented a diagonal proof against the very possibility of such a thing. Yet the ideas of Solomonoff and Levin lead to a mathematical foundation of precisely those aspects of Carnap’s program that Putnam took issue with, and in particular, resurrect the notion of a universal mechanical rule for induction. In this paper, I take up the question whether the Solomonoff–Levin proposal is (...) successful in this respect. I expose the general strategy to evade Putnam’s argument, leading to a broader discussion of the outer limits of mechanized induction. I argue that this strategy ultimately still succumbs to diagonalization, reinforcing Putnam’s impossibility claim. (shrink)

Howson's critique of my essay on Hume's problem of induction levels two main charges. First, Howson claims that I have attributed to him an error that he never made, and in fact which he warned against in the very text that I cite. Secondly, Howson argues that my proposed solution to Hume's problem is flawed on technical and philosophical grounds. In response to the first charge, I explain how Howson's text justifies attributing to him the claim that the principle of (...) induction is shown to be inconsistent by Goodman's riddle. In regards to the second, I show that Howson's objections rest on misunderstandings of formal learning theory and on conflating the problem of induction with the problem of unconceived alternatives. (shrink)

This paper develops a probabilistic reconstruction of the No Miracles Argument in the debate between scientific realists and anti-realists. The goal of the paper is to clarify and to sharpen the NMA by means of a probabilistic formalization. In particular, we demonstrate that the persuasive force of the NMA depends on the particular disciplinary context where it is applied, and the stability of theories in that discipline. Assessments and critiques of "the" NMA, without reference to a particular context, are misleading (...) and should be relinquished. This result has repercussions for recent anti-realist arguments, such as the claim that the NMA commits the base rate fallacy. It also helps to explain the persistent disagreement between realists and anti-realists. (shrink)

Structural realists claim that we should endorse only what our scientific theories say about the structure of the unobservable world. But according to Newman’s Objection, the structural realist’s claims about unobservables are trivially true. In recent years, several theorists have offered responses to Newman’s Objection. But a common complaint is that these responses “give up the spirit” of the structural realist position. In this paper, I will argue that the simplest way to respond to Newman’s Objection is to return to (...) one of the standard motivations for adopting structural realism in the first place: the No Miracles Argument. Far from betraying the spirit of structural realism, the solution I present is available to any theorist who endorses this argument. (shrink)

Collin Howson (2000) challenges van Cleve’s reliabilist defense of induction (1984) based on an adaptation of Goodman Paradox (or new riddle of induction). I will try to show that Howson’s argument does not succeed once it is self-defeating. Nevertheless, I point out another way which Howson could have employed the new riddle to undermine the reliabilist defense.

This article suggests a ‘best alternative' justification of induction (in the sense of Reichenbach) which is based on meta-induction . The meta-inductivist applies the principle of induction to all competing prediction methods which are accessible to her. It is demonstrated, and illustrated by computer simulations, that there exist meta-inductivistic prediction strategies whose success is approximately optimal among all accessible prediction methods in arbitrary possible worlds, and which dominate the success of every noninductive prediction strategy. The proposed justification of meta-induction is (...) mathematically analytical. It implies, however, an a posteriori justification of object-induction based on the experiences in our world. *Received November 2005; revised March 2008. †To contact the author, please write to: Department of Philosophy, University of Duesseldorf, Universitaetsstrasse 1, Geb. 23.21, Duesseldorf, Germany D-40225; e-mail: [email protected]. (shrink)

This article describes abductions as special patterns of inference to the best explanation whose structure determines a particularly promising abductive conjecture and thus serves as an abductive search strategy. A classification of different patterns of abduction is provided which intends to be as complete as possible. An important distinction is that between selective abductions, which choose an optimal candidate from given multitude of possible explanations, and creative abductions, which introduce new theoretical models or concepts. While selective abduction has dominated the (...) literature, creative abductions are rarely discussed, although they are essential in science. The article introduces several kinds of creative abductions, such as theoretical model abduction, common cause abduction and statistical factor analysis, and illustrates them by various real case examples. It is suggested to demarcate scientifically fruitful abductions from purely speculative abductions by the criterion of causal unification. (shrink)

Perhaps the strongest argument for scientific realism, the no-miracles-argument, has been said to commit the so-called base rate fallacy. The apparent elusiveness of the base rate of true theories has even been said to undermine the rationality of the entire realism debate. In this paper, I confront this challenge by arguing, on the basis of the Kuhnian picture of theory choice, that a theory is likely to be true if it possesses multiple theoretical virtues and is embraced by numerous scientists, (...) even when the base rate converges to zero. (shrink)

The aim of this contribution is to provide a rather general answer to Hume’s problem. To this end, induction is treated within a straightforward formal paradigm, i.e., several connected levels of abstraction. Within this setting, many concrete models are discussed. On the one hand, models from mathematics, statistics and information science demonstrate how induction might succeed. On the other hand, standard examples from philosophy highlight fundamental difficulties. Thus it transpires that the difference between unbounded and bounded inductive steps is crucial: (...) while unbounded leaps of faith are never justified, there may well be reasonable bounded inductive steps. In this endeavour, the twin concepts of information and probability prove to be indispensable, pinning down the crucial arguments, and, at times, reducing them to calculations. Essentially, a precise study of boundedness settles Goodman’s challenge. Hume’s more profound claim of seemingly inevitable circularity is answered by obviously non-circular hierarchical structures. (shrink)

For several decades, renewed interest in the connection between perception and knowledge has sustained a robust debate over external world skepticism. Recently, however, a growing consensus claims the skeptical challenge has been substantially met, and that realism in some robust form has emerged a clear victor. I invite us to rethink this consensus in a two-part response. The first forges a temporary alliance with skepticism against prominent forms of contemporary realism. That these fail to rebuff ews bolsters Barry Stroud’s call (...) for a new paradigm of objectivity. In the second part I sketch such a paradigm based upon a transactional interpretation of John Dewey’s pragmatism, and indicate its resilience to skeptical attacks. (shrink)

First, I answer the controversial question ’What is scientific realism?’ with extensive reference to the varied accounts of the position in the literature. Second, I provide an overview of the key developments in the debate concerning scientific realism over the past decade. Third, I provide a summary of the other contributions to this special issue.

This paper will make the case that we can find in Kant’s Second Analogy a substantive response to Hume’s argument on induction. This response is substantive insofar as it does not merely consist in independently arguing for the opposite conclusion, but rather, it identifies and exploits a gap in this argument. More specifically, Hume misses the possibility of justifying the uniformity of nature as a synthetic a priori proposition, which Kant looks to establish in the Second Analogy. Note that the (...) focus on the paper is on Kant’s identification of the form that a solution to Hume’s inductive scepticism must take. In making this point, my paper will look to establish two lemmas: Kant identifies synthetic a priori judgments as a means of justifying metaphysical knowledge in a way that circumvents Hume’s dichotomy between matters of fact and relations of ideas; the Second Analogy looks to establish the uniformity of nature of as a synthetic a priori proposition. However, my paper generally abstains from the question of the tenability of Kant’s argument in the Second Analogy. Doing justice to this latter discussion would require more space than I am able to offer here. My paper therefore has a conditional bearing on the philosophical issue of inductive scepticism. If one believes Kant’s Second Analogy to be philosophically cogent, then Kant offers a successful justification of induction against Hume’s scepticism. If not, then at least one can still admire Kant’s identification of the gap in Hume’s argument, which, to a degree, can be exploited independently of Kant’s system. (shrink)

The problem of justifying induction has vexed philosophers for centuries. It has been entangled with issues concerning logic and probability and the philosophy of science. This article proposes a new approach to untangling these issues and resolving the overall problem. This new approach is by way of the perspective of realist ontology. Induction should not be seen as a debased form of logic and the search for inflexible rules for justifying particular sorts of inductive inference should be abandoned. Rather, induction (...) can be justified pragmatically as a general practice because reality possesses ordered patterns. Induction, being dependent on repetition, can sometimes identify aspects of those patterns simply because the instances of repetition really do occur. Thus, confidence in conclusions based on inductive inferences is not properly to be derived from unchanging logical rules governing when and where inductive inferences may be successfully applied, but from the involvement of such inferences with a wider, deeper process in which not only deductive inferences and other inductive inferences are involved, but also a set of relations to broader bodies of relevant knowledge. That is, unlike particular deductive inferences, inductive inferences may not be engaged in isolation from all other information about the world and completely in the abstract. Induction is always connected with a process of retroduction. (shrink)