In the mid-eighteenth century David Hume argued that successful prediction tells us nothing about the truth of the predicting theory. But physical theory routinely predicts the values of observable magnitudes within very small ranges of error. The chance of this sort of predictive success without a true theory suggests that Hume's argument is flawed. However, Colin Howson argues that there is no flaw and examines the implications of this disturbing conclusion; he also offers a solution to one of (...) the central problems of Western philosophy, the problem of induction. (shrink)

In Generalizing Generalizability in Information Systems Research Lee and Baskerville (2003) attempt to clarify generalization and distinguish four types of generalization. Although this is a useful objective, what they call generalization is often not generalization at all in the proper sense of the word. We elucidate generalization by locating their major errors. A main source of these is their failure to understand the depth of Hume’s problem of induction. We give a thorough explication of the problem (...) and then give a solution. Lastly, we propose an alternative taxonomy of generalization: theoretical, within-population, cross-population, contextual, and temporal. (shrink)

Necessity holds that, if a proposition A supports another B, then it must support B. John Greco contends that one can resolve Hume's Problem of Induction only if she rejects Necessity in favor of reliabilism. If Greco's contention is correct, we would have good reason to reject Necessity and endorse reliabilism about inferential justification. Unfortunately, Greco's contention is mistaken. I argue that there is a plausible reply to Hume's Problem that both endorses Necessity and is (...) at least as good as Greco's alternative. Hence, Greco provides a good reason for neither rejecting Necessity nor endorsing inferential reliabilism. (shrink)

This paper explains what’s wrong with a Hume-inspired argument for skepticism about induction. Hume’s argument takes as a premise that inductive reasoning presupposes that the future will resemble the past. I explain why that claim is not plausible. The most plausible premise in the vicinity is that inductive reasoning from E to H presupposes that if E then H. I formulate and then refute a skeptical argument based on that premise. Central to my response is a psychological (...) explanation for how people judge that if E then H without realizing that they thereby settled the matter rationally. (shrink)

This chapter contains sections titled: Hume's Problem of Induction Hume's Negative Argument concerning Induction.

The Problem of Induction This article discusses the problem of induction, including its conceptual and historical perspectives from Hume to Reichenbach. Given the prominence of induction in everyday life as well as in science, we should be able to tell whether inductive inference amounts to sound reasoning or not, or at least we should be … Continue reading Induction, The Problem of →.

This paper aims to advance two claims. First, it aims to show that Hume's argument against the rationality of induction is sound. However, I claim that the conclusion does not follow merely from the self-defeating attempts to justify the rule of induction, unlike traditional readings of the argument. Rather, the skeptical conclusion must also take into account Hume's argument that the secret powers that are present in bodies and give rise to sensible qualities are unknowable. The (...) paper's second aim is to show that Newtonian induction escapes Hume's secret powers argument, given that it includes a transductive inference, from observable phenomena to the powers present in the ultimate parts of matter. Consequently Hume's argument against the rationality of induction does not demonstrate the non-rational nature of Newtonian induction. (shrink)

This paper aims to advance two claims. First, it aims to show that Hume’s argument against the rationality of induction is sound. However, I claim that the conclusion does not follow merely from the self-defeating attempts to justify the rule of induction, unlike traditional readings of the argument. Rather, the skeptical conclusion must also take into account Hume’s argument that the secret powers that are present in bodies and give rise to sensible qualities are unknowable. The (...) paper’s second aim is to show that Newtonian induction escapes Hume’s secret powers argument, given that it includes a transductive inference, from observable phenomena to the powers present in the ultimate parts of matter. Consequently Hume’s argument against the rationality of induction does not demonstrate the non-rational nature of Newtonian induction. (shrink)

This paper addresses Harman’s approach to enumerative induction as a case of inference to the best explanation. Αfter taking under brief consideration Hume’s critique to induction, the paper argues that Harman’s proposal does not improve the situation since the same characteristics of induction and the kind of skepticism associated with it reappear in case of inference to the best explanation. Then the paper questions Armstrong’s attempt to upgrade Harman’s suggestion by regarding a necessitation relation among two (...) universals (a natural law) as the best explanans of the n observed cases of an enumerative induction procedure. It holds that Armstrong’s modification of Harman’s approach faces some difficulties which arise in the context of his views about instantiated universals. Instead, the paper investigates the possibility to assign the role of the explanans to a metaphysically stronger condition. It suggests that accounts of natural laws as metaphysically necessary facts concerning natural kinds can contribute in an attempt for a more fertile application of Harman’s approach. (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)

Scottish philosopher David Hume provided some of the most novel and important insights into the nature of causation. This article introduces his most important lines of thought regarding cause and effect, specifically, his analysis of causation culminating in his two definitions of causation and the Problem of Induction.

Philosophers talk routinely of 'Hume's problem of induction'. But the usual accompanying exegesis is mistaken in a way that has led epistemologists to conceive of 'Hume's problem' in needlessly narrow terms. They have overlooked a way of articulating the conceptual problem, along with a potential way of solving it. Indeed, they have overlooked Hume's own way. In explaining this, I will supplement Hume's insights by adapting Ryle's thinking on knowledge-how and knowledge-that. We (...) will also see why Hume's 'sceptical solution' was a perfectly appropriate response to his 'sceptical argument' -- rather than (as is often thought by analytic epistemologists) a merely descriptive response patently missing the normative sceptical point so strikingly formulated by Hume. (shrink)

Philosophers talk routinely of ‘Hume's problem of induction’. But the usual accompanying exegesis is mistaken in a way that has led epistemologists to conceive of ‘Hume's problem’ in needlessly narrow terms. They have overlooked a way of articulating the conceptual problem, along with a potential way of solving it. Indeed, they have overlooked Hume's own way. In explaining this, I will supplement Hume's insights by adapting Ryle's thinking on knowledge-how and knowledge-that. We (...) will also see why Hume's ‘sceptical solution’ was a perfectly appropriate response to his ‘sceptical argument’ — rather than a merely descriptive response patently missing the normative sceptical point so strikingly formulated by Hume. (shrink)

A new approach to Hume's problem of induction that justifies the optimality of induction at the level of meta-induction. Hume's problem of justifying induction has been among epistemology's greatest challenges for centuries. In this book, Gerhard Schurz proposes a new approach to Hume's problem. Acknowledging the force of Hume's arguments against the possibility of a noncircular justification of the reliability of induction, Schurz demonstrates instead the possibility of a (...) noncircular justification of the optimality of induction, or, more precisely, of meta-induction (the application of induction to competing prediction models). Drawing on discoveries in computational learning theory, Schurz demonstrates that a regret-based learning strategy, attractivity-weighted meta-induction, is predictively optimal in all possible worlds among all prediction methods accessible to the epistemic agent. Moreover, the a priori justification of meta-induction generates a noncircular a posteriori justification of object induction. Taken together, these two results provide a noncircular solution to Hume's problem. Schurz discusses the philosophical debate on the problem of induction, addressing all major attempts at a solution to Hume's problem and describing their shortcomings; presents a series of theorems, accompanied by a description of computer simulations illustrating the content of these theorems (with proofs presented in a mathematical appendix); and defends, refines, and applies core insights regarding the optimality of meta-induction, explaining applications in neighboring disciplines including forecasting sciences, cognitive science, social epistemology, and generalized evolution theory. Finally, Schurz generalizes the method of optimality-based justification to a new strategy of justification in epistemology, arguing that optimality justifications can avoid the problems of justificatory circularity and regress. (shrink)

It would be difficult to overestimate the influence Hume’s problem of induction exercises on contemporary epistemology. At the same time, the problem of induction has not perceptibly slowed the progress of mathematics and science. This ironic state of affairs, immortalized by C. D. Broad’s description of induction as “the glory of science” and “the scandal of philosophy,” ought in all fairness to give both sides some pause. And on occasion, it does: the mathematicians stop (...) to concede that Hume has not yet been answered, the scientists worry about randomization of experiments, and inductive skeptics stir uneasily in their chairs at the mention of certain mathematical theorems that seem palpably to have bearing on the problem. (shrink)

By the middle of the eighteenth century the new science had challenged the intellectual primacy of common experience in favor of recondite, expert and even counter-intuitive knowledge increasingly mediated by specialized instruments. Meanwhile modern philosophy had also problematized the perceptions of common experience — in the case of David Hume this included our perception of causal relations in nature, a fundamental precondition of scientific endeavor.In this article I argue that, in responding to the ‘problem of induction’ as (...) advanced by Hume, Reid reformulated Aristotelian foundationalism in distinctly modern terms. An educator and mathematician self-consciously working within the framework of the new science, Reid articulated a philosophical foundation for natural knowledge anchored in the human constitution and in processes of adjudication in an emerging modern public sphere of enlightened discourse. Reid thereby transformed one of the bases of Aristotelian science — common experience — into a philosophically and socially justified notion of ‘common sense’. Reid's intellectual concerns had as much to do with the philosophy of science as they did with moral philosophy or epistemology proper, and were bound up with wider social and scientific changes taking place in the early modern period. (shrink)

This chapter contains sections titled: * The Problem of Induction * Reid’s Common-Sense Realism * Tradition and Reason in the Principles of Informal Inference * Back to the Rationality of Religion * Notes * Bibliography.

Many philosophers argue that Bayesian epistemology cannot help us with the traditional Humean problem of induction. I argue that this view is partially but not wholly correct. It is true that Bayesianism does not solve Hume’s problem, in the way that the classical and logical theories of probability aimed to do. However I argue that in one important respect, Hume’s sceptical challenge cannot simply be transposed to a probabilistic context, where beliefs come in degrees, rather (...) than being a yes/no matter. (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)

Naturalised epistemology has shunned rationality, a hallmark of humanity since ancient Greece. One of Quine's explicit motivations is that Hume's problem of induction cannot be solved. However, Hume himself suggests a solution and the narrow focus of the paper is to present a ‘Humean Solution’ which is an elaboration and defence of Hume's suggestion. What emerges will be argued to be a naturalised conception of rationality which makes naturalised epistemology more continuous with traditional epistemology's focus (...) on rationality. (shrink)

Hume argued that inductive inferences do not have rational justification. My aim is to reject Hume’s argument. The discussion is partly motivated by an analogy with Carroll’s Paradox, which concerns deductive inferences. A first radically externalist reply to Hume (defended by Dauer and Van Cleve) is that justified inductive inferences do not require the subject to know that nature is uniform, though the uniformity of nature is a necessary condition for having the justification. But then the subject (...) does not have reasons for believing what she believes. I defend a moderate externalist account that seeks to partly accommodate that objection to the radical externalist proposal. It is based on an extension of Peacocke’s theory of concepts: possession conditions for predicative concepts standing for natural properties include (fallible) dispositions to project them to new cases in accordance with inductive inferential patterns. (shrink)

The solution is that there can be no justification of induction, "the rule we use to make inferences about unknown events from a sample of data drawn from experience." A principle may be justified either by validation or by vindication; Hume's argument showed conclusively that no validation of induction is possible, but left open the possibility of a vindication. Reichenbach explored this possibility within the framework of a frequency theory of probability. Katz now explores Reichenbach's treatment in (...) detail, finding that it ultimately fails to produce either a "preferability vindication" or an "expediency vindication." Katz then argues that it is in principle impossible ever to modify Reichenbach's account in a way which would allow such vindication-for the inductive rule or, in fact, any convergent rule whatever, whether on a "frequency" or a "degree of confirmation" interpretation of probability. But if no vindication is possible, then no justification of any kind is possible, providing we have correctly reduced the problem; so the problem of induction has received its solution. This in no way calls for skepticism or conventionalism concerning empirical knowledge; we can certainly criticize various inductive procedures and show that one canon is better than another. We can "convince those who are in agreement about basic standards but are interested in more precise versions and their proper application to particular cases"; these are quite different issues from the general "problem of induction." A boldly-outlined argument, drawing upon a good deal of complex material, and handled very skillfully.--B. H. (shrink)

Hume argued that inductive inferences do not have rational justification. My aim is to reject Hume's argument. The discussion is partly motivated by an analogy with Carroll's Paradox, which concerns deductive inferences. A first radically externalist reply to Hume is that justified inductive inferences do not require the subject to know that nature is uniform, though the uniformity of nature is necessary condition for having the justification. But then the subject does not have reasons for believing what (...) she believes. I defend a moderate externalist account that seeks to partly accommodate that objection to the radical externalist proposal. It is based on an extension of Peacocke's theory of concepts: possession conditions for predicative concepts standing for natural properties include dispositions to project them to new cases in accordance with inductive inferential patterns. (shrink)

필자는 본 논문에서 귀납의 문제와 관련하여 흄이 『인성론』 1권에서 이성을 통하여서는 이를 정당화 할 수 없다고 주장한 것으로 해석하는 기존의 회의주의적 해석을 비판적으로 검토한다. 필자의 견해에 따르면, 흄이 『인성론』 1권에서 비판의 대상으로 삼고 있는 것은 인과 추론의 정당성 문제 그 자체가 아니라, 무비판적으로 받아들여져 온 무오류적 이성 개념이다. 흄은 이 무오류적 이성 개념을 부정하고, 이성을 넓은 의미에서의 상상력 아래로 포섭 시킨 후, 그 안에서 무작위로 작동하는 좁은 의미에서의 상상력과 개연성의 논리에 따라 작동하는 이성을 구분함으로써, 인과 추론을 정당화하는 새로운 길을 열고 (...) 있다. 따라서, 흄은 『인성론』 1권에서 인과 추론의 정당성을 부정하고 더 나아가 총체적 회의주의로 빠져드는 것이 아니라, 이성 개념을 새롭게 정립함으로써 오히려 총체적 회의 주의로 빠지지 않고 새로운 방식으로 인과 추론의 정당성을 확보하는 시도를 하고 있는 것이다. 이와 같은 필자의 해석은 『인성론』 1권과 『인성론』 2권, 3권을 단절적으로 해석하지 않고, 오히려 『인성론』 1권에서의 논의가 『인성론』 2권과 3권의 초석이 되어줌을 잘 드러내 보여준다. 다시 말해, 흄이 『인성론』 1권에서 주장하는 바, “우리의 감각들을 넘어서서 추적될 수 있고, 우리가 볼 수 없고 느낄 수 없는 존재들과 대상들을 우리들에게 알려주는 유일한 것은 인과이다”라고 하는 흄의 언명이 『인성론』 2권과 3권에서의 대상 세계에 대한 논의의 출발점이 되어주는 것이다. -/- This paper argues against the common interpretation that, in Book I of the Treatise, Hume attempts to show that inductive arguments concerning matters of fact cannot be justified by reason. It is true that he argues that inductive arguments cannot be justified by the traditional concept of infallible reason. However, it is important to note that contra to the traditional understanding of reason as infallible, he takes it to be open to errors by classifying it under the category of imagination in a broad sense. He then makes a distinction between reason as “the general and more establish’d properties of the imagination” and imagination as a narrow sense. From this, the paper concludes he attempts to justify inductive arguments concerning matters of fact by redefining reason as open to errors. That is, although inductive arguments cannot be justified by probable reasoning in terms of the traditional concept of infallible reason, the former can be justified by the logic of probability, which he calls “general rules” in terms of Hume’s concept of error-prone reason. (shrink)

I develop a critique of Hume’s infamous problem of induction based upon the idea that the principle of induction (PI) is a normative rather than descriptive claim. I argue that Hume’s problem is a false dilemma, since the PI might be neither a “relation of ideas” nor a “matter of fact” but rather what I call a contingent normative statement. In this case, the PI could be justified by a means-ends argument in which the (...) link between means and end is established solely by deductive reasoning. The means-ends argument is an elementary result from formal learning theory that you must be willing to make inductive generalizations if you want to be logically reliable in the types of examples Hume described. This justification of the PI avoids both horns of Hume’s dilemma. Since no contradiction ensues from rejecting logical reliability as an aim, the PI is contingent. Yet since the proof concerning the PI and logical reliability is not based on inductive reasoning, there is no threat of circularity. (shrink)

Hume's Problem comprises two main projects: defending Hume's argument about induction against a dozen or so purported answers, and laying out a logic of induction that incorporates Hume's great insight in a formal theory. In this review, I will look at several instances of Howson's defense of Hume; then I will sketch the broad outlines of Howson's own "answer," the details of which are myriad and sometimes technical.

According to Hume, the paradigm type of inductive reasoning involves a constant conjunction. But, as Price points out, Hume misrepresents ordinary induction: we experience very few constant conjunctions. In this paper, I examine several ways of defending Hume's (psychological) account of our practice against Price's objection, and conclude that the theory cannot be upheld.

The classical Indian Cārvāka (“Materialist”) tradition contains three branches with regard to the means of knowledge (pramāṇas). First, the standard Cārvākas accept a single means of knowledge, perception, supporting this view with a critique of the reliability and coherence of inference (anumāna). Second, the “more educated” Cārvākas as well as Purandara endorse a form of inference limited to empirical matters. Third, radical skeptical Cārvākas like Jayarāśi attempt to undermine all accounts or technical definitions of the means of knowledge (even perception) (...) in order to enjoy a life free from philosophical and religious speculation. These branches respectively present something akin to David Hume’s problem of induction, endorse a fallibilistic, mitigated skepticism, and embody a thoroughgoing skepticism about philosophy itself. While all three branches are skeptics about religious matters, each branch exemplifies a different variety of epistemological skepticism. (shrink)

Das „Problem der Induktion", dessen Formulierung man gewöhnlich David Hume zuschreibt, hat Leibniz schon am Anfang des 18. Jahrhunderts formuliert und gelöst. Die Methode von Leibniz war sowohl „Hume-isch" als auch rationalistisch. Sie begreift in sich eine Herabsetzung des Empirischen und auch den Gebrauch der „Geheimkräfte", die Hume ausschalten wollte. Ohne solche „Geheimkräfte" gibt es keine Harmonie im klassischen Sinn von Leibniz . Für Leibniz ist eine Hypothese vorzuziehen, die eine Harmonie behauptet oder die maximale Verschiedenheit (...) der Phänomene mit der minimalen Kompliziertheit der zugrundeliegenden Regel zusammenfaßt. Hier sind Beispiele von Gesetzen mit „produktiven Mechanismen" oder „Geheimkräften" gegeben, die der Leibnizschen Erklärung in der Physik und der Mathematik entsprechen. Die Schwerkraft entspricht diesen Gesichtspunkten nicht und ist daher unvernünftig im Leibnizschen Sinne; deshalb werden Induktionen über Schwerkraftsysteme als empirische Regeln betrachtet. Die Leibnizsche Theorie zeigt auch, wie man die wohlbekannten Beispiele von Hume erkennen und vorhersagen kann, nämlich aufgrund des richtigen wissenschaftlichen Verständnisses der Natur der Nahrung und des Feuers. Kants Prinzip der zeitlichen Reihenfolge wird zu seinen Ungunsten mit dem sechsten Grundsatz der Leibnizschen Abhandlung über die Metaphysik verglichen. Wir haben nach Leibniz doch einen vernünftigen Zugang zu der Wirklichkeit, die hinter den Empfindungen liegt, und die Verneinung dessen war es, was das empiristische Problem der Induktion erzeugt hat. Das Problem der Induktion ist ein reductio ad absurdum des Empirismus. (shrink)

The subject of this essay is the classical problem of induction, which is sometimes attributed to David Hume and called “the Humean Problem of Induction.” Here, I examine a certain sort of Neo-Aristotelian solution to the problem, which appeals to the concept of natural kinds in its response to the inductive skeptic. This position is most notably represented by Howard Sankey and Marc Lange. The purpose of this paper is partly destructive and partly constructive. (...) I raise two questions. The first is: Are the natural kind solutions to the problem successful? The first thesis of this paper is that they are not, and I will show how and why they fail. And the second question I raise here is: Is there nonetheless some alternative Neo-Aristotelian solution to the problem which is successful and can overcome the shortcomings endemic to the Sankey-Lange account? The second thesis is that there is, and I’ll attempt to sketch one. My stance here may be summarized by saying that, while I agree with Sankey and Lange that the problem of induction can be adequately resolved, and while I am on the whole sympathetic with the Aristotelian spirit of their account, I am, for all that, dissatisfied with the letter of them. Nothing short of a more thoroughgoing Aristotelianism about the epistemology of induction will do. (shrink)

Gerhard Schurz claims to have a solution to Hume’s problem of induction based on results from machine-learning concerning meta-induction. His argument has two steps. The first is to establish a justification for following a certain meta-inductive strategy based on its predictive optimality. The second step is to show how this justification can be transferred to object-induction. I unpack the second step and fail to find a convincing argument supporting the transfer of justification from meta-induction (...) to object-induction. My conclusion is that the problem of induction has not yet been solved by appeal to meta-induction. (shrink)

A necessary refinement of the concept of circular reasoning is applied to the self-and-universally-referential inductive justification of induction. It is noted that the assumption necessary for the circular proof of a principle of induction is that one inference is valid, not that the entire principle or rule of induction governing that inference is true. The circularity in an ideal case is demonstrated to have a value of lin where n represents the number of inferences asserted valid by (...) the conclusion of the justifying argument, and the ‘I’ represents the inference necessarily assumed valid.An induction antinomy modeled after Russell’s antinomy of the set of all and only non-self-containing sets is derived. Isomorphic antinomies are noted to be derivable for other arguments of philosophical interest, including those purported to undermine theories of determinism, relativism, and skepticism, and including the one that Descartes reduced and converted to ‘Cogito, ergo sum’. (shrink)

A necessary refinement of the concept of circular reasoning is applied to the self-and-universally-referential inductive justification of induction. It is noted that the assumption necessary for the circular proof of a principle of induction is that one inference is valid, not that the entire principle or rule of induction governing that inference is true. The circularity in an ideal case is demonstrated to have a value of lin where n represents the number of inferences asserted valid by (...) the conclusion of the justifying argument, and the ‘I’ represents the inference necessarily assumed valid.An induction antinomy modeled after Russell’s antinomy of the set of all and only non-self-containing sets is derived. Isomorphic antinomies are noted to be derivable for other arguments of philosophical interest, including those purported to undermine theories of determinism, relativism, and skepticism, and including the one that Descartes reduced and converted to ‘Cogito, ergo sum’. (shrink)

This article evaluates Karl Popper's contribution to analytic philosophy, and outlines some of the contradictions in his work which make it difficult to locate in any particular tradition. In particular, the article investigates Popper's own claims to be a member of the rationalist tradition. Although Popper described himself as a member of this tradition, his definition of it diverged quite radically from that offered by other supporters of rationalism, like, for example, Mach, Carnap, and the logical positivists of the Vienna (...) Circle. The reason for this was that Popper believed the rationalist tradition, if it were to remain coherent and relevant, needed to overcome the dilemma posed by Hume's problem of induction. Popper believed that this problem rendered conventional understandings of rationalism, science, and inductive reasoning incoherent. This article suggests that Popper's principal contribution to modern philosophy was to reconfigure the rationalist tradition in such a way as to circumvent the problem of induction while preserving the rationalist commitment to reason, rational debate, and objective knowledge. Popper's reconfiguration of the epistemological bases of the rationalist tradition challenged dominant understandings of rationalist and analytic philosophy, and may be appropriately understood as part of a wider move among philosophers like Quine and Putnam to challenge conventional understandings of analytic philosophy, and of what philosophy itself could and could not achieve. It also informed a vision of social and political life (and of the social and political sciences) as rooted in principles of freedom, equality, and rational debate, but which cannot be fit within the traditional ideological landscape. (shrink)

At its strongest, Hume's problem of induction denies the existence of any well justified assumptionless inductive inference rule. At the weakest, it challenges our ability to articulate and apply good inductive inference rules. This paper examines an analysis that is closer to the latter camp. It reviews one answer to this problem drawn from the VC theorem in statistical learning theory and argues for its inadequacy. In particular, I show that it cannot be computed, in general, (...) whether we are in a situation where the VC theorem can be applied for the purpose we want it to. (shrink)

Marc Lange has criticized my assertion that relative to a Bayesian conception of inductive reasoning, Hume's argument for inductive scepticism cannot be run. I reply that the way in which Lange suggests one should run the Humean argument in a Bayesian framework ignores the fact that in Bayesian models of learning from experience, the domain of an agent's probability measure is exogenously determined. I also show that Lange is incorrect to equate probability distributions which 'support inductive inferences' with probability (...) distributions which assign probability to contingent propositions/events. (shrink)

In this paper I present a game-theoretical approach to the problem of induction. I investigate the comparative success of prediction methods by mathematical analysis and computer programming. Hume's problem lies in the fact that although the success of object-inductive prediction strategies is quite robust, they cannot be universally optimal. My proposal towards a solution of the problem of induction is meta-induction. I show that there exist meta-inductive prediction strategies whose success is universally optimal, (...) modulo short-run losses which are upper-bounded. I then turn to the implications of my approach for the evolution of cognition. In the final section I suggest a revision of the paradigm of bounded rationality by introducing the distinction between local, general and universal prediction strategies. (shrink)

This short paper provides an explanation of Hume's problem of induction.

1.1 The Concept of Evil The problem of evil, in the sense relevant here, concerns the question of the reasonableness of believing in the existence of a deity with certain characteristics. In most discussions, the deity is God, understood as an omnipotent, omniscient, and morally perfect person. But the problem of evil also arises, as Hume saw very clearly, for deities that are less than all-powerful, less than all-knowing, and less than morally perfect. What is the relevant (...) concept of evil, in this context? Here it is useful to distinguish between axiological concepts and deontological ones. First, there are judgments about whether certain states of affairs make the world better or worse, whether those states are good or bad, desirable or undesirable. Such normative concepts – of good and bad, or desirable and undesirable, states of affairs – are axiological concepts. Secondly, there are judgments about the rightness and wrongness of actions, about what one morally ought or ought not do, of what one’s duty is, of whether a certain action violates someone rights, and these concepts – of the rightness and wrongness of actions, of duties, of the rights of individuals, of what one should or should not do – are deontological concepts. Given this distinction, should the problem of evil be understood axiologically or deontologically? Often, and I think most commonly in this context, evils are equated with states of affairs that, all things considered, are bad or undesirable: they are states of affairs that make the world a worse place. But one can also interpret the problem of evil in a deontological fashion, equating evils with states of affairs that a person should have prevented, if he could have done so. Elsewhere (2008, 105-6), I have argued that the deontological interpretation is preferable. But for present purposes, either interpretation will be fine. 1.2 Evil and the Reasonableness of Belief in the Existence of God That many things in the world – tsunamis, earthquakes, the suffering of non-human animals and innocent children, human actions such as the carrying out of the Holocaust – certainly appear to be evil is not a controversial matter. But whether such things are really evils, all things considered, is disputed. Assume, however, that the world does continue genuine evils, and not merely apparent ones. How, then does the existence of such evils bear upon the reasonableness of belief in the existence of God? First, the existence of evils can be used to show that certain arguments for the existence of God cannot establish that conclusion, or even render it probable. For some arguments, of course, one need not appeal to evil to make that point. If someone argues for the existence of a first cause, or an unmoved mover, or a necessary being having its necessity of itself, and then claims that this is what everyone understands by the term “God”, one can point out that no reason has been offered for thinking that the entity in question is even a person, let alone omnipotent, omniscient, and perfectly good. By contrast, with the type of argument that Hume was concerned with when he discussed the problem of evil – namely, arguments from the existence of order in the world to the existence of a designer, or intelligent cause of that order – one does have a type of argument that, if sound, shows that there is a person who, even if not omnipotent and omniscient, is at least extremely powerful and very knowledgeable. But such arguments do not support for conclusions about the moral character of such a person, and so it is at this point that the existence of evils becomes crucial. For in providing a reason for holding that the one is not justified in attributing even moral goodness to such a being, let alone moral perfection, it supports the conclusion that that argument in question cannot be a successful argument for the existence of God. The existence of evils, then, can serve to block arguments for the existence of God. But a second, and very familiar possibility, is that the existence of evils can also provide the basis of arguments against the existence of God. A very important distinction here is between deductive, or logical incompatibility, versions of the argument from evil, and inductive, or evidential, or probabilistic versions of the argument. According to the former, there are facts about the existence of evils in the world that are logically incompatible with the existence of God. Thus, some have held that the mere existence of any evil whatsoever is incompatible with the existence of God; others, that that certain types of evil – such as natural evils – are incompatible with the existence of God; and others, that it is the amount of evil in the world, or the fact that some people suffer horrendous evils, that logically precludes the existence of God. Inductive (or evidential, or probabilistic) versions of the argument from evil, by contrast, do not claim that there are facts about the evils in the world that are logically incompatible with the existence of God. The claim is rather that there are facts about the evils found in the world that render the existence of God at the very least unlikely, and perhaps extremely so. 1.3 Hume’s Use of the Existence of Evils The preceding discussion suggests two very different ways in which Hume might be employing the existence of evils. First, he might be appealing to the existence of evils simply to undercut certain arguments for the existence of God. In particular, he might be appealing to evils to show that, whatever the merits of the argument from order to design may be, it can nether establish, nor render probable, the existence of a morally good deity. Secondly, Hume might be advancing a version of the argument from evil, and that in turn could take the form either of an argument that claims that facts about evil are logically incompatible with the existence of God, or of an argument that claims, more modestly, that the apparent evils found in the world render the existence of God unlikely. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Hume and the Lockean Background: Induction and the Uniformity Principle David Owen Introduction What has come to be called Hume's problem of induction is special in many ways. It is arguably his most important and influential argument, especially when seen in its overall context of the more general argument about causaUty. It has come to be one of the great "standard problems" ofphilosophyandyetis,by most (...) accounts, almost unique in having no ancient precursor. Interestingly, the argument is frequently presented in terms that the author never used. Itis difficult for us not to think of the problem in terms of the contrast between deductive vs. inductive reasoning (or logic, or whatever). But this is a contrast nowhere to be found in Hume: he talks of demonstrative vs. probable (or moral) reasoning. Hume uses the word "induction" only twice in the Treatise1 and in neither case is it clear that the word is used toreportapieceofprobablereasoning.2One ofthefewoccurrences of"deduce" or "deducing" occurs in the second Enquiry, where he talks about "following the experimental method, and deducing general maximsfrom acomparisonofparticularinstances,"3hardlyaparadigm of what we would call deductive reasoning.4 Many modern studies of Hume that make a real attempt to understand what Hume meant by demonstration and probability, in the context of his argument about induction, tend towards the ahistorical,6 treating Hume's writings as contemporary texts. But failure to take into account some of the background concerning the nature of demonstrative and probable reason makes it unlikely, I think, that we can understand Hume's argument. Part ofthe problem is the failure to identify Hume's targets in that famous negative argument about induction (vague reference is sometimes made to the "rationalists") and part of the problem is identifying the role the uniformity principle plays in Hume's famous argumentand thelightitsheds on the conception ofprobablereasoning Hume was attacking. In this paper I want to argue that a careful look at Locke solves some ofthese problems: he has a well developed view ofdemonstrative and probable reasoning, his confidence in conformity as a ground of probability is a Ukely target of Hume's attack and his Volume XVIII Number 2 179 DAVID OWEN accountshedsmuchlightonwhatrole the principleofuniformitymight play in Hume's account.6 Of course, at a certain level of philosophical abstraction it is irrelevant whether we have understood what Hume "really meant." Theproblemofinductionhas emergedas a central onein epistemology, philosophical logic, and philosophy of science. It would be an interesting question in philosophical historiography to trace the development ofthe "problem" from Hume's time to our own but that is not my task here. I trust one needs no justification for taking an historical look at a famous problem rather than tackling the problem head-on in one's own terms. But if one is needed, here is mine: sometimes, by looking at a problem from a different, historical perspective, one sees a different problem or afamiliar problem in a new light. One's philosophical horizons are broadened. Furthermore, one may make an interesting historical discovery, or at least draw some interesting historical connections. I take it as uncontroversial that Locke, following Descartes, rejected a formal, logical account of demonstrative reasoning. Instead ofusing a formal, syllogistic account ofhow two propositions can entail a third, Locke concentrated on the relation two ideas bear one to another.7 Thus a demonstration, for Locke, getsits force, notfrom what we would call a deductive relation between one set of propositions (.the premises) and anotherproposition (the conclusion), butrather from the relation one idea bears to another, either directly, or via a chain of intermediate ideas. It is true that Locke frequently talks of inferring one proposition from another, but this is always cashed out in terms of relations ofideas via a chain ofintermediate ideas.8 It is also true that Locke occasionally uses the terms "deduce" and "deduction." But these are never used in our sense that has to do with formal deductive validity. Rather, they are simply used loosely in the informal sense of "argue" or "infer," and "argument" or "inference."9 In the rest of this paper, all uses ofthe word"deduction" andits cognates shouldbe taken as having the modern sense, unless flagged as having "Locke... (shrink)

The extent of harm and suffering caused by the coronavirus pandemic has prompted a debate about whether the epidemic could have been contained, had the gravity of the crisis been predicted earlier. In this paper, the philosophical debate on predictive reasoning is framed by Hume’s problem of induction. Hume argued that it is rationally unjustified to move from the finite observations of past incidences to the predictions of future events. Philosophy has offered two major responses to (...) the problem of induction: the pragmatic induction of Peirce and the critical rationalism of Popper. It is argued that of these two, Popper’s critical rationalism provides a more potent tool for preparing for unanticipated events such as the Covid-19 pandemic. Popper’s notion of risky predictions equips strategic foresight with clear hypotheticals regarding potential crisis scenarios. Peirce’s pragmatic induction, instead, leans on probabilities that are slower to be amended as unexpected events start unfolding. The difference between the two approaches is demonstrated through a case study of the patterns of reasoning within the World Health Organization in the early stages of the coronavirus pandemic. (shrink)

Popper famously claimed that he had solved the problem of induction, but few agree. This paper explains what Popper's solution was, and defends it. The problem is posed by Hume's argument that any evidence-transcending belief is unreasonable because (1) induction is invalid and (2) it is only reasonable to believe what you can justify. Popper avoids Hume's shocking conclusion by rejecting (2), while accepting (1). The most common objection is that Popper must smuggle in (...) induction somewhere. But this objection smuggles in precisely the justificationist assumption (2) that Popper, as here undestood, rejects. Footnotes1 Invited address at the Karl Popper 2002 Centenary Conference, Vienna, 3–7 July 2002. (shrink)