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Summary The problem of induction, usually attributed to David Hume, is the problem of justifying inductive inferences. Induction is widely taken to be an essential component of rational and scientific reasoning, yet Hume's skeptical argument casts doubt on the possibility of justifying (giving good epistemic reasons for) this kind of inference. Responses to the problem range from attempted justifications (like probabilistic arguments) to dissolutions of the problem (like Strawson's ordinary language approach or Popper's claim that science doesn't actually rely on induction), with several proposals that fall between these two extremes (like Reichenbach's pragmatic "vindication" of induction). Recent systematic approaches to induction and its justification include Norton's material theory of induction and Schurz's meta-inductive justification of induction.
Introductions A good overview article is Lange 2011. A classical introductory book is Salmon 1967. A book-length discussion of the problem from a Bayesian perspective is Howson 2000.
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  1. Goodman Paradox, Hume's Problem, Goodman-Kripke Paradox: Three Different Issues.Beppe Brivec - manuscript
    This paper reports (in section 1 “Introduction”) some quotes from Nelson Goodman which clarify that, contrary to a common misunderstanding, Goodman always denied that “grue” requires temporal information and “green” does not require temporal information; and, more in general, that Goodman always denied that grue-like predicates require additional information compared to what green-like predicates require. One of the quotations is the following, taken from the first page of the Foreword to chapter 8 “Induction” of the Goodman’s book “Problems and Projects”: (...)
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  2. O velho e novo problema da indução.Eros Carvalho - manuscript
    Neste texto inrodutório, apresento brevemente o que normalmente se entende pelo velho problema da indução e, em seguida, apresento um pouco mais detidamente, acentuando as diferenças e semelhanças, o novo enigma da indução.
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  3. Logical vs Practical Reasons.Paul Mayer - manuscript
    For years, the European world saw millions of swans, and all of them without exception were white. If inductive reasoning is valid, one may conclude that all swans are white. However, this would be incorrect: in 1667 Dutch explorer Willem de Vlamingh observed black swans in Australia, falsifying the hypothesis that all swans are white. While often used as a cautionary tale for the use of induction, such as with Popper’s falsification principle, I want to explore a slightly different idea: (...)
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  4. Coherence of Inferences.Matheus Silva - manuscript
    It is usually accepted that deductions are non-informative and monotonic, inductions are informative and nonmonotonic, abductions create hypotheses but are epistemically irrelevant, and both deductions and inductions can’t provide new insights. In this article, I attempt to provide a more cohesive view of the subject with the following hypotheses: (1) the paradigmatic examples of deductions, such as modus ponens and hypothetical syllogism, are not inferential forms, but coherence requirements for inferences; (2) since any reasoner aims to be coherent, any inference (...)
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  5. A statistical learning approach to a problem of induction.Kino Zhao - manuscript
    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 (...)
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  6. What if the principle of induction is normative? Means-ends epistemology and Hume's problem.Daniel Steel - manuscript
    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 (...)
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  7. In defence of science: Two ways to rehabilitate Reichenbach's vindication of induction.Jochen Briesen - forthcoming - The British Journal for the Philosophy of Science.
    Confronted with the problem of induction, Hans Reichenbach accepts that we cannot justify that induction is reliable. He tries to solve the problem by proving a weaker proposition: that induction is an optimal method of prediction, because it is guaranteed not to be worse and may be better than any alternative. Regarding the most serious objection to his approach, Reichenbach himself hints at an answer without spelling it out. In this paper, I will argue that there are two workable strategies (...)
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  8. Meta-induction as a solution to the no free lunch theorem: reply to Wolpert.Gerhard Schurz - forthcoming - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie.
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  9. Meta-induction and religious world-views: reply to Pitts.Gerhard Schurz - forthcoming - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie.
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  10. The meta-inductive justification of object-induction: reply to Shogenji.Gerhard Schurz - forthcoming - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie.
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  11. Induction and direct inference: reply to Williamson.Gerhard Schurz - forthcoming - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie.
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  12. The Unsolvability of Hume's Problem and Local Justification of Induction.Ju Sh - forthcoming - Epistemologia. Genova.
  13. On Explaining the Success of Induction.Tom F. Sterkenburg - forthcoming - British Journal for the Philosophy of Science.
    Douven (in press) observes that Schurz's meta-inductive justification of induction cannot explain the great empirical success of induction, and offers an explanation based on computer simulations of the social and evolutionary development of our inductive practices. In this paper, I argue that Douven's account does not address the explanatory question that Schurz's argument leaves open, and that the assumption of the environment's induction-friendliness that is inherent to Douven's simulations is not justified by Schurz's argument.
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  14. Chapter 12 Introduction.Joel Katzav & Krist Vaesen - 2023 - In Joel Katzav, Dorothy Rogers & Krist Vaesen (eds.), Knowledge, Mind and Reality: An Introduction by Early Twentieth-Century American Women Philosophers. Cham: Springer. pp. 117-129.
    This chapter introduces the articles by Marie C. Swabey, Thelma Z. Lavine, Grace A. de Laguna and Dorothy Walsh on the objectivity of scientific knowledge. We will see Swabey placing herself outside the historicist traditions of (later) authors (e.g., Thomas Kuhn), and arguing that the rationality and objectivity of science are grounded in synthetic a priori justified logical principles. Lavine and de Laguna, by contrast, embrace socio-historical approaches to the study of science, thus anticipating later developments in philosophy of science. (...)
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  15. Ein Plädoyer wider die Annahme einer fundamentalen Unterscheidung von Genese und Geltung in der Erkenntnistheorie.Markus Seidel - 2023 - Zeitschrift für Philosophische Forschung 77 (4):454-483.
    Many epistemologists believe that the distinction between the genesis and the validity of a belief is a fundamental presupposition of adequate epistemological reflection. In this article it will be argued that the arguments for this majority conviction are not convincing. As an alternative it is suggested that the distin- ction between epistemic and non-epistemic procedures should be regarded as fundamental for epistemology.
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  16. Speed-Optimal Induction and Dynamic Coherence.Michael Nielsen & Eric Wofsey - 2022 - British Journal for the Philosophy of Science 73 (2):439-455.
    A standard way to challenge convergence-based accounts of inductive success is to claim that they are too weak to constrain inductive inferences in the short run. We respond to such a challenge by answering some questions raised by Juhl (1994). When it comes to predicting limiting relative frequencies in the framework of Reichenbach, we show that speed-optimal convergence—a long-run success condition—induces dynamic coherence in the short run.
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  17. On the gnoseologic principles of Bertrand Russell.Rafael Andrés Alemañ-Berenguer - 2021 - Naturaleza y Libertad. Revista de Estudios Interdisciplinares.
    Exposed in 1948, within his masterpiece on the scope and limits of human knowledge, the epistemological tenets that Bertrand Russell regarded as fundamental elements in the construction of scientific knowledge, are still worthy of a detailed discussion today. Given the excellence of the author, it will not be surprising to see that Russell's gnoseologic postulates, even for the present scientific view, address some of the most controversial questions still to be solved in the theory of knowledge.
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  18. Chance and the Continuum Hypothesis.Daniel Hoek - 2021 - Philosophy and Phenomenological Research 103 (3):639-60.
    This paper presents and defends an argument that the continuum hypothesis is false, based on considerations about objective chance and an old theorem due to Banach and Kuratowski. More specifically, I argue that the probabilistic inductive methods standardly used in science presuppose that every proposition about the outcome of a chancy process has a certain chance between 0 and 1. I also argue in favour of the standard view that chances are countably additive. Since it is possible to randomly pick (...)
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  19. Improve Popper and procure a perfect simulacrum of verification indistinguishable from the real thing.Nicholas Maxwell - 2021 - Journal for General Philosophy of Science.
    According to Karl Popper, science cannot verify its theories empirically, but it can falsify them, and that suffices to account for scientific progress. For Popper, a law or theory remains a pure conjecture, probability equal to zero, however massively corroborated empirically it may be. But it does just seem to be the case that science does verify empirically laws and theories. We trust our lives to such verifications when we fly in aeroplanes, cross bridges and take modern medicines. We can (...)
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  20. Reichenbach and the Problem of Induction.Flavia Padovani - 2021 - In C. Limbeck Lilienau & Thomas Uebel (eds.), The Routledge Handbook of Logical Empiricism. London, UK: pp. 229-237.
  21. Modal Empiricism: Interpreting Science Without Scientific Realism.Quentin Ruyant - 2021 - Springer International Publishing.
    This book proposes a novel position in the debate on scientific realism: Modal Empiricism. Modal empiricism is the view that the aim of science is to provide theories that correctly delimit, in a unified way, the range of experiences that are naturally possible given our position in the world. The view is associated with a pragmatic account of scientific representation and an original notion of situated modalities, together with an inductive epistemology for modalities. It purports to provide a faithful account (...)
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  22. Induction and Natural Kinds Revisited.Howard Sankey - 2021 - In Benjamin Hill, Henrik Lagerlund & Stathis Psillos (eds.), Reconsidering Causal Powers: Historical and Conceptual Perspectives. Oxford University Press. pp. 284-299.
    In ‘Induction and Natural Kinds’, I proposed a solution to the problem of induction according to which our use of inductive inference is reliable because it is grounded in the natural kind structure of the world. When we infer that unobserved members of a kind will have the same properties as observed members of the kind, we are right because all members of the kind possess the same essential properties. The claim that the existence of natural kinds is what grounds (...)
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  23. The no-free-lunch theorems of supervised learning.Tom F. Sterkenburg & Peter D. Grünwald - 2021 - Synthese 199 (3-4):9979-10015.
    The no-free-lunch theorems promote a skeptical conclusion that all possible machine learning algorithms equally lack justification. But how could this leave room for a learning theory, that shows that some algorithms are better than others? Drawing parallels to the philosophy of induction, we point out that the no-free-lunch results presuppose a conception of learning algorithms as purely data-driven. On this conception, every algorithm must have an inherent inductive bias, that wants justification. We argue that many standard learning algorithms should rather (...)
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  24. Epistemic benefits of the material theory of induction.Job de Grefte - 2020 - Studies in History and Philosophy of Science Part A 84:99-105.
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  25. Falsificationism and the Pragmatic Problem of Induction.Danny Frederick - 2020 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 27 (4):494-503.
    I explain how Karl Popper resolved the problem of induction but not the pragmatic problem of induction. I show that Popper’s solution to the pragmatic problem of induction is inconsistent with his solution to the problem of induction. I explain how Popper’s falsificationist epistemology can solve the pragmatic problem of induction in the same negative way that it solves the problem of induction.
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  26. Debunking material induction.Jonathan Livengood & Daniel Z. Korman - 2020 - Studies in History and Philosophy of Science Part A 84:20-27.
    We present an explanatory objection to Norton's material theory of induction, as applied to predictive inferences. According to the objection we present, there is an explanatory disconnect between our beliefs about the future and the relevant future facts. We argue that if we recognize such a disconnect, we are no longer rationally entitled to our future beliefs.
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  27. Induction, Philosophical Conceptions of.John P. McCaskey - 2020 - In Marco Sgarbi (ed.), Encyclopedia of Renaissance Philosophy. Springer.
    How induction was understood took a substantial turn during the Renaissance. At the beginning, induction was understood as it had been throughout the medieval period, as a kind of propositional inference that is stronger the more it approximates deduction. During the Renaissance, an older understanding, one prevalent in antiquity, was rediscovered and adopted. By this understanding, induction identifies defining characteristics using a process of comparing and contrasting. Important participants in the change were Jean Buridan, humanists such as Lorenzo Valla and (...)
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  28. Reviving material theories of induction.John P. McCaskey - 2020 - Studies in History and Philosophy of Science Part A 83:1–7.
    John Norton says that philosophers have been led astray for thousands of years by their attempt to treat induction formally. He is correct that such an attempt has caused no end of trouble, but he is wrong about the history. There is a rich tradition of non-formal induction. In fact, material theories of induction prevailed all through antiquity and from the Renaissance to the mid-1800s. Recovering these past systems would not only fill lacunae in Norton’s own theory but would highlight (...)
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  29. The Inductive Route Towards Necessity.Quentin Ruyant - 2020 - Acta Analytica 35 (2):147-163.
    It is generally assumed that relations of necessity cannot be known by induction on experience. In this paper, I propose a notion of situated possibilities, weaker than nomic possibilities, that is compatible with an inductivist epistemology for modalities. I show that assuming this notion, not only can relations of necessity be known by induction on our experience, but such relations cannot be any more underdetermined by experience than universal regularities. This means that any one believing in a universal regularity is (...)
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  30. The material theory of object-induction and the universal optimality of meta-induction: Two complementary accounts.Gerhard Schurz & Paul Thorn - 2020 - Studies in History and Philosophy of Science Part A 82:88-93.
  31. The meta-inductive justification of induction.Tom F. Sterkenburg - 2020 - Episteme 17 (4):519-541.
    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 (...)
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  32. The material theory of induction and the epistemology of thought experiments.Michael T. Stuart - 2020 - Studies in History and Philosophy of Science Part A 83 (C):17-27.
    John D. Norton is responsible for a number of influential views in contemporary philosophy of science. This paper will discuss two of them. The material theory of induction claims that inductive arguments are ultimately justified by their material features, not their formal features. Thus, while a deductive argument can be valid irrespective of the content of the propositions that make up the argument, an inductive argument about, say, apples, will be justified (or not) depending on facts about apples. The argument (...)
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  33. A Coherentist Justification of Induction.Byeong D. Lee - 2019 - Erkenntnis 87 (1):35-52.
    In this paper I offer a coherentist justification of induction along the lines of a Sellarsian coherence theory. On this coherence theory, a proposition is justified if we can answer all objections raised against it in our social practice of demanding justification and responding to such demands. On the basis of this theory of justification, I argue that we are justified in accepting the uniformity of nature partly because we have no alternative but to accept it for rationally pursuing our (...)
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  34. Direct Inference in the Material Theory of Induction.William Peden - 2019 - Philosophy of Science 86 (4):672-695.
    John D. Norton’s “Material Theory of Induction” has been one of the most intriguing recent additions to the philosophy of induction. Norton’s account appears to be a notably natural account of actual inductive practices, although his theory has attracted considerable criticism. I detail several novel issues for his theory but argue that supplementing the Material Theory with a theory of direct inference could address these problems. I argue that if this combination is possible, a stronger theory of inductive reasoning emerges, (...)
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  35. Reichenbach, Russell and the Metaphysics of Induction.Michael J. Shaffer - 2019 - Argumenta 8:161-181.
    Hans Reichenbach’s pragmatic treatment of the problem of induction in his later works on inductive inference was, and still is, of great interest. However, it has been dismissed as a pseudo-solution and it has been regarded as problematically obscure. This is, in large part, due to the difficulty in understanding exactly what Reichenbach’s solution is supposed to amount to, especially as it appears to offer no response to the inductive skeptic. For entirely different reasons, the significance of Bertrand Russell’s classic (...)
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  36. Putnam’s Diagonal Argument and the Impossibility of a Universal Learning Machine.Tom F. Sterkenburg - 2019 - Erkenntnis 84 (3):633-656.
    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 (...)
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  37. The Metainductive Justification of Induction: The Pool of Strategies.Tom F. Sterkenburg - 2019 - Philosophy of Science 86 (5):981-992.
    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.
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  38. Goodman e o projeto de uma definição construtiva de “indução válida”.Eros Moreira de Carvalho - 2018 - Principia: An International Journal of Epistemology 22 (3):439-460.
    In Fact, Fiction and Forecast, Nelson Goodman claims that the problem of justifying induction is not something over and above the problem of describing valid induction. Such claim, besides suggesting his commitment to the collapse of the distinction between the context of description and the context of justification, seems to open the possibility that the new riddle of induction could be addressed empirically. Discoveries about psychological preferences for projecting certain classes of objects could function as a criterion for determining which (...)
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  39. Induction and Epistemological Naturalism.Lars-Göran Johansson - 2018 - Philosophies 3 (4):31.
    Epistemological naturalists reject the demand for a priori justification of empirical knowledge; no such thing is possible. Observation reports, being the foundation of empirical knowledge, are neither justified by other sentences, nor certain; but they may be agreed upon as starting points for inductive reasoning and they function as implicit definitions of predicates used. Making inductive generalisations from observations is a basic habit among humans. We do that without justification, but we have strong intuitions that some inductive generalisations will fail, (...)
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  40. Universal Prediction: A Philosophical Investigation.Tom F. Sterkenburg - 2018 - Dissertation, University of Groningen
    In this thesis I investigate the theoretical possibility of a universal method of prediction. A prediction method is universal if it is always able to learn from data: if it is always able to extrapolate given data about past observations to maximally successful predictions about future observations. The context of this investigation is the broader philosophical question into the possibility of a formal specification of inductive or scientific reasoning, a question that also relates to modern-day speculation about a fully automatized (...)
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  41. On the justification of deduction and induction.Franz Huber - 2017 - European Journal for Philosophy of Science 7 (3):507-534.
    The thesis of this paper is that we can justify induction deductively relative to one end, and deduction inductively relative to a different end. I will begin by presenting a contemporary variant of Hume ’s argument for the thesis that we cannot justify the principle of induction. Then I will criticize the responses the resulting problem of induction has received by Carnap and Goodman, as well as praise Reichenbach ’s approach. Some of these authors compare induction to deduction. Haack compares (...)
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  42. The Metaphysical Requirement for Models of Prediction and Explanationist Approaches to the Problem of Induction.Jaeho Lee - 2017 - Axiomathes 27 (3):225-242.
    David Armstrong once argued that to solve the problem of induction with inference to the best explanation we need an anti-Humean conception of law. Some Humeans have argued that this argument begs the question against Humeanism. In this paper, I propose a new argument for the same conclusion which is not vulnerable to this criticism. In particular, I argue that explanationist approaches to the problem of induction that are combined with Humeanism is internally incoherent.
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  43. Understanding Scientific Progress: Aim-Oriented Empiricism.Nicholas Maxwell - 2017 - St. Paul, USA: Paragon House.
    "Understanding Scientific Progress constitutes a potentially enormous and revolutionary advancement in philosophy of science. It deserves to be read and studied by everyone with any interest in or connection with physics or the theory of science. Maxwell cites the work of Hume, Kant, J.S. Mill, Ludwig Bolzmann, Pierre Duhem, Einstein, Henri Poincaré, C.S. Peirce, Whitehead, Russell, Carnap, A.J. Ayer, Karl Popper, Thomas Kuhn, Imre Lakatos, Paul Feyerabend, Nelson Goodman, Bas van Fraassen, and numerous others. He lauds Popper for advancing beyond (...)
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  44. Grounding Reichenbach’s Pragmatic Vindication of Induction.Michael J. Shaffer - 2017 - Polish Journal of Philosophy 11 (1):43-55.
    This paper has three interdependent aims. The first is to make Reichenbach’s views on induction and probabilities clearer, especially as they pertain to his pragmatic justification of induction. The second aim is to show how his view of pragmatic justification arises out of his commitment to extensional empiricism and moots the possibility of a non-pragmatic justification of induction. Finally, and most importantly, a formal decision-theoretic account of Reichenbach’s pragmatic justification is offered in terms both of the minimax principle and the (...)
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  45. The Principle of Indifference and Inductive Scepticism.Robert Smithson - 2017 - British Journal for the Philosophy of Science 68 (1):253-272.
    Many theorists have proposed that we can use the principle of indifference to defeat the inductive sceptic. But any such theorist must confront the objection that different ways of applying the principle of indifference lead to incompatible probability assignments. Huemer offers the explanatory priority proviso as a strategy for overcoming this objection. With this proposal, Huemer claims that we can defend induction in a way that is not question-begging against the sceptic. But in this article, I argue that the opposite (...)
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  46. Explaining our Moral Reliability.Sinan Dogramaci - 2016 - Pacific Philosophical Quarterly 98 (S1):71-86.
    I critically examine an evolutionary debunking argument against moral realism. The key premise of the argument is that there is no adequate explanation of our moral reliability. I search for the strongest version of the argument; this involves exploring how ‘adequate explanation’ could be understood such that the key premise comes out true. Finally, I give a reductio: in the sense in which there is no adequate explanation of our moral reliability, there is equally no adequate explanation of our inductive (...)
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  47. Natural Properties, Necessary Connections, and the Problem of Induction.Tyler Hildebrand - 2016 - Philosophy and Phenomenological Research 96:668-689.
    The necessitarian solution to the problem of induction involves two claims: first, that necessary connections are justified by an inference to the best explanation; second, that the best theory of necessary connections entails the timeless uniformity of nature. In this paper, I defend the second claim. My arguments are based on considerations from the metaphysics of laws, properties, and fundamentality.
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  48. The Revenge of Ecological Rationality: Strategy-Selection by Meta-Induction Within Changing Environments.Gerhard Schurz & Paul D. Thorn - 2016 - Minds and Machines 26 (1-2):31-59.
    According to the paradigm of adaptive rationality, successful inference and prediction methods tend to be local and frugal. As a complement to work within this paradigm, we investigate the problem of selecting an optimal combination of prediction methods from a given toolbox of such local methods, in the context of changing environments. These selection methods are called meta-inductive strategies, if they are based on the success-records of the toolbox-methods. No absolutely optimal MI strategy exists—a fact that we call the “revenge (...)
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  49. Skeptical Symmetry: A Wittgensteinian Approach to Scientific Reasoning.Erik Nelson - 2015 - Gnosis 14 (2):14-19.
    Many philosophers have wrongly assumed that there is an asymmetry between the problem of induction and the logocentric predicament (the justification of deductive inferences). This paper will show that the demand for justification, for the very inferences that are required for justification, is deeply problematic. Using a Wittgensteinian approach, I will argue that justification has an internal relation with deductive and inductive inferences. For Wittgenstein, two concepts are internally related if my understanding of one is predicated on my understanding of (...)
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  50. Probability.Darrell Patrick Rowbottom - 2015 - Polity.
    When a doctor tells you there’s a one percent chance that an operation will result in your death, or a scientist claims that his theory is probably true, what exactly does that mean? Understanding probability is clearly very important, if we are to make good theoretical and practical choices. In this engaging and highly accessible introduction to the philosophy of probability, Darrell Rowbottom takes the reader on a journey through all the major interpretations of probability, with reference to real–world situations. (...)
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