Inductive Reasoning

We information-theoretically reformulate two measures of capacity from statistical learning theory: empirical VC-entropy and empirical Rademacher complexity. We show these capacity measures count the number of hypotheses about a dataset that a learning algorithm falsifies when it finds the classifier in its repertoire minimizing empirical risk. It then follows from that the future performance of predictors on unseen data is controlled in part by how many hypotheses the learner falsifies. As a corollary we show that empirical VC-entropy quantifies the message (...) length of the true hypothesis in the optimal code of a particular probability distribution, the so-called actual repertoire. (shrink)

The paper demonstrates that falsifiability is fundamental to learning. We prove the following theorem for statistical learning and sequential prediction: If a theory is falsifiable then it is learnable -- i.e. admits a strategy that predicts optimally. An analogous result is shown for universal induction.

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: (...) does the existence of fabricated or otherwise failed accounts of Black swans give me a reason to ignore future arguments or doubt their existence? I argue that while faulty or fabricated reports do not give us a logical reason to reject a claim, they can give us a practical one for refusing to consider future arguments. This practical vs logical distinction gives an inductive reason for believing that future arguments will be invalid, but keeps one from being able to necessarily deny the claim in question without further argumentation. (shrink)

A comprehensive history of how induction has been conceived, from Socrates to Karl Popper.

The grue paradox, also called the new riddle of induction, posed a great challenge to the common understanding about induction. This paper shows that there is a close relation between the grue paradox and the problem of conditionals. This paper presents a general form of the grue predicate. Based on the general form, this paper argues that this kind of predicates can not be used for induction and prediction.

There are (at least) three approaches to quantifying information. The first, algorithmic information or Kolmogorov complexity, takes events as strings and, given a universal Turing machine, quantifies the information content of a string as the length of the shortest program producing it [1]. The second, Shannon information, takes events as belonging to ensembles and quantifies the information resulting from observing the given event in terms of the number of alternate events that have been ruled out [2]. The third, statistical learning (...) theory, has introduced measures of capacity that control (in part) the expected risk of classifiers [3]. These capacities quantify the expectations regarding future data that learning algorithms embed into classifiers. Solomonoff and Hutter have applied algorithmic information to prove remarkable results on universal induction. Shannon information provides the mathematical foundation for communication and coding theory. However, both approaches have shortcomings. Algorithmic information is not computable, severely limiting its practical usefulness. Shannon information refers to ensembles rather than actual events: it makes no sense to compute the Shannon information of a single string – or rather, there are many answers to this question depending on how a related ensemble is constructed. Although there are asymptotic results linking algorithmic and Shannon information, it is unsatisfying that there is such a large gap – a difference in kind – between the two measures. This note describes a new method of quantifying information, effective information, that links algorithmic information to Shannon information, and also links both to capacities arising in statistical learning theory [4, 5]. After introducing the measure, we show that it provides a non-universal analog of Kolmogorov complexity. We then apply it to derive basic capacities in statistical learning theory: empirical VC-entropy and empirical Rademacher complexity. A nice byproduct of our approach is an interpretation of the explanatory power of a learning algorithm in terms of the number of hypotheses it falsifies [6], counted in two different ways for the two capacities. We also discuss how effective information relates to information gain, Shannon and mutual information. (shrink)

Some learning strategies that work well when computational considerations are abstracted away from become severely limiting when such considerations are taken into account. We illustrate this phenomenon for agents who attempt to extrapolate patterns in binary data streams chosen from among a countable family of possibilities. If computational constraints are ignored, then two strategies that will always work are learning by enumeration (enumerate the possibilities---in order of simplicity, say---then search for the one earliest in the ordering that agrees with your (...) data and use it to predict the next data point) and Bayesian learning. But there are many types of computable data streams that, although they can be successfully extrapolated by computable agents, cannot be handled by any computable learner by enumeration. And while there is a sense in which Bayesian learning is a fully general strategy for computable learners, the ability to mimic powerful learners comes at a price for Bayesians: they cannot, in general, become highly confident of their predictions in the limit of large data sets and they cannot, in general, use priors that incorporate all relevant background knowledge. (shrink)

Calibration inductive logics are based on accepting estimates of relative frequencies, which are used to generate imprecise probabilities. In turn, these imprecise probabilities are intended to guide beliefs and decisions — a process called “calibration”. Two prominent examples are Henry E. Kyburg's system of Evidential Probability and Jon Williamson's version of Objective Bayesianism. There are many unexplored questions about these logics. How well do they perform in the short-run? Under what circumstances do they do better or worse? What is their (...) performance relative to traditional Bayesianism? -/- In this article, we develop an agent-based model of a classic binomial decision problem, including players based on variations of Evidential Probability and Objective Bayesianism. We compare the performances of these players, including against a benchmark player who uses standard Bayesian inductive logic. We find that the calibrated players can match the performance of the Bayesian player, but only with particular acceptance thresholds and decision rules. Among other points, our discussion raises some challenges for characterising “cautious” reasoning using imprecise probabilities. Thus, we demonstrate a new way of systematically comparing imprecise probability systems, and we conclude that calibration inductive logics are surprisingly promising for making decisions. (shrink)

We argue that a particular approach to satisfying the broad predictive ambitions of the sciences demands law confirmation. On this approach we confirm non-nomic generalizations by confirming there are no actually realized ways of causing disconfirming cases. This gives causal generalizations a crucial role in prediction. We then show how rational judgements of relevant causal similarity can be used to confirm that causal generalizations themselves have no actual disconfirmers, providing a distinctive and clearly viable methodology for inductively confirming them. Finally, (...) we argue that for agents in our epistemic position using this methodology to confirm causal generalizations of adequate breadth will commonly demand law confirmation. We make a prima facie assessment of the methodology’s fit with scientific practice and briefly consider the prospects for an associated analysis of laws. (shrink)

Reasoning from inconclusive evidence, or 'induction', is central to science and any applications we make of it. For that reason alone it demands the attention of philosophers of science. This element explores the prospects of using probability theory to provide an inductive logic: a framework for representing evidential support. Constraints on the ideal evaluation of hypotheses suggest that the overall standing of a hypothesis is represented by its probability in light of the total evidence, and incremental support, or confirmation, indicated (...) by the hypothesis having a higher probability conditional on some evidence than it does unconditionally. This proposal is shown to have the capacity to reconstruct many canons of the scientific method and inductive inference. Along the way, significant objections are discussed, such as the challenge of inductive scepticism, and the objection that the probabilistic approach makes evidential support arbitrary. (shrink)

In this paper I show that James Africanus Beale Horton launched an internal critique of race science as it developed in the hands of Robert Knox, Carl Vogt, and James Hunt. The latter three held an inductivist Baconian conception of science. Horton shows that their practices as scientists and natural philosophers contradict their own conception of what one must do in order to do good science. Horton’s critique of race science has important implications for philosophical anthropology as it took shape (...) over the course of the nineteenth century and for our understanding of the history of African philosophy in its global context. (shrink)

The present research aims to examine the different accounts of induction given by Aristotle, Leibniz, Hume, Carnap and De Finetti, trying to support that probability calculus offers a sufficient grounding of inductive logic. The term induction had been contrasted to deduction, by Aristotle. The Neoplatonic philosopher Alcinous suggested that dialectic firstly investigates the substances and then the accidents. There are five kinds of dialectic reasoning: division, definition, analysis, induction and syllogistic. The first three concern with substances, the last two with (...) accidents. Although Leibniz regarded probability theory as a basis of inductive logic, Hume’s skepticism was seminal for the reappraisal of the role of induction in modern philosophy. Enhancing Hume’s criticism, Popper and Wittgenstein completely denied that scientists use induction. Hans Reichenbach, however, attempted to build a theory of justification for the use of induction, based on a factual basis of other successful predictive methods that make induction feasible (Earman & Salmon 1999). Moreover, Buchdall (1969) stressed that we must distinguish the inductive process of the scientist from the inductive conclusion, which comes after the completion of observation and experimentation. (shrink)

Douven 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 article, 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.

According to the sensitivity account of knowledge, S knows that p only if S’s belief in p is sensitive in the sense that S would not believe that p if p were false. The sensitivity condition is usually relativized to belief-formation methods to avoid putative counterexamples. A remaining issue for the account is where methods should be mentioned in sensitivity subjunctives. In this paper, I argue that if methods are mentioned in the antecedent, then the account is too strong to (...) accommodate inductive knowledge; if methods are mentioned in the consequent, then the account is too weak to eliminate some luckily true beliefs from the realm of knowledge. Therefore, the strategy to relativize the sensitivity condition is undermined by inductive knowledge and some luckily true beliefs. (shrink)

In the last quarter of 2024 four articles on survival after death were published online ahead of print in the International Review of Psychiatry. Two of these included gratuitous attempts to discredit the work of a well-known survival critic. After correcting these misrepresentations, in this response Keith Augustine lays out how those who appeal to survival research to support their beliefs bungle their purportedly scientific assessments of the evidence concerning whether or not individual human minds survive death in a discarnate (...) state (without a normal physical body). The response also lays out why the still-common arguments that the late eminent thanatologist Robert Kastenbaum offered in favor of a discarnate afterlife are fallacious. It canvasses erroneous tropes about discovering white crows and the supposed impossibility of proving negatives, how scientific facts are established as highly probable, how psychical research is grounded on fallacious arguments from ignorance, and when all else fails, how survival researchers resort to psychologizing their critics rather than address their critics' arguments. Their collective failure to engage their critics' actual arguments raises the issue of whether survival proponents are able to adequately answer them—and if not, why not. Augustine submits that they are unable to answer their critics because the scientific evidence against their afterlife beliefs is incredibly strong. 1. Introduction -- 2. Gregory Shushan -- 3. Andreas Sommer -- 3.1 The Irrelevance of My Work to Sommer’s Thesis -- 3.2 How My Use is Comparable to What Robert Kastenbaum Intended -- 3.3 Sommer’s Characterization of The Myth of an Afterlife -- 3.4 The Context of What Kastenbaum was Trying to Do -- 3.5 Where Kastenbaum Fell on the Survival Question—and Why -- 3.5.1 Fallacious White Crows -- 3.5.2 Proof, Certainty, and Proving Negatives -- 3.5.3 Causal Ignorance is not Causal Evidence -- 3.5.4 Psychologizing Opponents -- 4. Conclusion: A Belief in Search of Evidence, or Evidence-Driven Belief? (shrink)

Mitchell & Gronenborn ( 2017 ) propose that we account for the presence of multiple models of protein structure, each produced in different contexts, through the framework of integrative pluralism. I argue that two interpretations of this framework are available, neither of which captures the relationship between a model and the protein structure it represents or between multiple models of protein structure. Further, it inclines us toward concluding prematurely that models of protein structure are right in their contexts and makes (...) extrapolation of findings from one context to another seem unwarranted. Instead, protein structure determination ought to be understood as _modestly monistic_. There is one model for every protein in each physicochemical context, and models of the same protein produced in different contexts are compatible with one another. ‘Integrating’ multiple models amounts to extrapolating from one context to another; this is possible because the effect of context on protein folding is relatively weak and predictable. Modest monism better describes the practice of protein structure determination than integrative pluralism and enables greater attention to how context affects protein folding. (shrink)

Most social policies cannot be defended without making inductive inferences. For example, consider certain arguments for racial profiling and affirmative action, respectively. They begin with statistics about crime or socioeconomic indicators. Next, there is an inductive step in which the statistic is projected from the past to the future. Finally, there is a normative step in which a policy is proposed as a response in the service of some goal—for example, to reduce crime or to correct socioeconomic imbalances. In comparison (...) to the normative step, the inductive step of a policy defense may seem trivial. We argue that this is not so. Satisfying the demands of the inductive step is difficult, and doing so has important but underappreciated implications for the normative step. In this paper, we provide an account of induction in social contexts and explore its implications for policy. Our account helps to explain which normative principles we ought to accept, and as a result it can explain why it is acceptable to make inferences involving race in some contexts (e.g., in defense of affirmative action) but not in others (e.g., in defense of racial profiling). (shrink)

Error Management Theory (EMT) suggests that cognitive adaptations evolve to minimize the cost of false negative and false positive errors in detections of consequential environmental conditions. These adaptations manifest as biases tailored to specific environmental conditions. This paper proposes that the same selection pressure fostered the evolution of a self-biasing ability, allowing us to minimize such costs based on experience and culturally transmitted information. The research indicates that this ability specifically applies to productions of belief or doubt about the existence (...) of an environmental condition that is not adequately perceptible to the senses, e.g., doubt that the man is being honest. A model of this self-biasing process, rooted in signal detection theory, is developed and its explanatory reach is demonstrated through many diverse examples from epistemological and social psychological literatures. These examples feature an evidentiary standard for belief that appears too high or low, or seems to have modulated. This study aims to correct and to significantly enhance EMT by introducing this evolved self-biasing ability. (shrink)

When an empirical prediction E of hypothesis H is observed to be true, such observation is said to confirm, i.e., support (although not prove) the truth of the hypothesis. But why? What justifies the claim that such evidence supports the hypothesis? The widely accepted answer is that it is justified by induction. More specifically, it is commonly held that the following argument, (1) If H then E; (2) E; (3) Therefore, (probably) H (here referred to as ‘hypothetico-deductive confirmation argument’), is (...) inductively strong. Yet this argument looks nothing like an inductive generalization, i.e., it does not seem inductive in the term’s traditional, enumerative sense. If anything, it has the form of the fallacy of affirming the consequent. This paper aims to solve this puzzle. True, in recent decades, ‘induction’ has been sometimes used more broadly to encompass any non-deductive, i.e., ampliative, argument. Applying Bayesian confirmation theory has famously demonstrated that hypothetico-deductive confirmation is indeed inductive in this broader, ampliative sense. Nonetheless, it will be argued here that, despite appearance, hypothetico-deductive confirmation can also be recast as enumerative induction. Hence, by being enumeratively inductive, the scientific method of hypothetico-deductive confirmation is justified through this traditional, more restrictive type of induction rather than merely by ampliative induction. (shrink)

In a world filled with information overload and complex problems, the ability to think logically is a superpower. "A Little More Logical" is your guide to mastering this essential skill. This engaging and accessible open educational resource is perfect for students, teachers, and lifelong learners who want to improve their critical thinking abilities and make better decisions in all aspects of life. -/- Through a series of fun and interactive chapters, "A Little More Logical" covers a wide range of topics, (...) from the basics of constructing sound arguments to the application of logic in fields like ethics, science, and computing. You'll learn how to spot and avoid common fallacies, analyze real-world arguments, and use logical reasoning to solve problems and make informed choices. -/- But this book isn't just about abstract concepts – it's about the human story behind logic. You'll discover the fascinating lives and ideas of diverse thinkers, from ancient philosophers to modern-day pioneers, who have shaped the development of logical reasoning throughout history. With thought-provoking examples, engaging exercises, and plenty of humor along the way, "A Little More Logical" makes the study of logic both rigorous and entertaining. -/- Whether you're a student looking to ace your philosophy class, a teacher searching for high-quality educational resources, or a curious reader who wants to sharpen your mind, "A Little More Logical" is the perfect companion on your journey to becoming a more effective thinker. Unlock the power of logical thinking today with this one-of-a-kind open educational resource! (shrink)

Consider a set of shuffled observations drawn from a fixed probability distribution over some instance domain. What enables learning of inductive generalizations which proceed from such a set of observations? The scenario is worthwhile because it epistemically characterizes most of machine learning. This kind of learning from observations is also inverse and ill-posed. What reduces the non-uniqueness of its result and, thus, its problematic epistemic justification, which stems from a one-to-many relation between the observations and many learnable generalizations? The paper (...) argues that this role belongs to any complexity regularization which satisfies Norton’s Material Theory of Induction (MTI) by localizing the inductive risk to facts in the given domain. A prime example of the localization is the Lottery Ticket Hypothesis (LTH) about overparameterized neural networks. The explanation of MTI’s role in complexity regularization of neural networks is provided by analyzing the stability of Empirical Risk Minimization (ERM), an inductive rule that controls the learning process and leads to an inductive generalization on the given set of observations. In cases where ERM might become asymptotically unstable, making the justification of the generalization by uniform convergence unavailable, LTH and MTI can be used to define a local stability. A priori, overparameterized neural networks are such cases and the combination of LTH and MTI can block ERM’s trivialization caused by equalizing the strengths of its inductive support for risk minimization. We bring closer the investigation of generalization in artificial neural networks and the study of inductive inference and show the division of labor between MTI and the optimality justifications (developed by Gerhard Schurz) in machine learning. (shrink)

In 2021, the Bigelow Institute for Consciousness Studies (hereafter, BICS) sponsored an essay competition (hereafter, the Contest) designed to solicit the best evidence for the hypothesis that human consciousness survives bodily death, and more specifically, evidence that would prove this hypothesis beyond a reasonable doubt. The summer 2022 issue of the Journal of Scientific Exploration featured a special subsection on the BICS contest and its winning essays. Robert Bigelow and Colm Kelleher outlined the motivation, design, and judging criteria for the (...) competition. Keith Augustine provided an extensive critical commentary on the contest design and eight of its prominent winning essays. Stephen Braude and several coauthors responded to Augustine’s criticisms, and Augustine provided a reply to Braude and his collaborators. Finally, the subsection concluded with a collaborative paper in which Etienne LeBel, Adam Rock, and Augustine proposed a more rigorous experimental design for testing the survival hypothesis. Augustine presented important criticisms of the Contest and several of its prominent winning essays. Moreover, many of his criticisms apply to survival literature in general and so are instructive for the wider survival debate. And Braude, one of the most important contributors to the survival debate since C.D. Broad and C.J. Ducasse, was at the helm of the reply to Augustine. Although the response to Augustine raised important concerns about skeptical assessments of the evidence for survival, it was hamstrung with several defects. 1. Preliminaries 2. Problematic Aspects of the Reply to Augustine 3. What is the Question? Honing in on the Actual Disagreement 4. Inference to Best Explanation 5. Confirmation Approaches to Evidential Support -- 5.1 Evidential Justification -- 5.2 When Does an Observation Favor One Hypothesis Over Another Hypothesis? The Law of Likelihood -- 5.3 When Should We Up Our Confidence in a Hypothesis? Incremental Confirmation -- 5.4 How Can We Determine the Net Plausibility of a Hypothesis? Bayes’ Theorem and Posterior Probabilities -- 5.5 Which of Two Hypotheses is More Probable than the Other? Principle of Contrastive Posterior Probabilities -- 5.6 When Does Evidence Justify Believing a Hypothesis? Principle of Absolute Confirmation -- 5.7 Survivalist Confusions about Bayesian Analyses -- 5.8 The Washing Out of Priors -- 5.9 The Subjectivism Objection -- 5.10 Summing Up Insights from Confirmation Theory -- 6. Back to Braude 7. Varieties of Skepticism 8. Neurophysiological Evidence and the Survival Hypothesis 9. The Data from Mediumship 10. The Alleged Improbability of Fraud and Other Counterexplanations 11. Mediumship and the Logic of Confirmation 12. The Significance of Failed Tests 13. Survivalist Rescues and Contrastive Confirmation 14. Evidential Support without Predictions -- 15. The Testability Problem -- Concluding Remarks. (shrink)

In this paper, we analyse conceptions of induction and certainty in Wolff and Crusius, highlighting their competing conceptions of physics. We discuss (i) the perspective of Wolff, who assigned induction an important role in physics, but argued that physics should be an axiomatic science containing certain statements, and (ii) the perspective of Crusius, who adopted parts of the ideal of axiomatic physics but criticized the scope of Wolff’s ideal of certain science. Against interpretations that take Wolff’s proofs in physics to (...) be based on empirical statements that are probable, we show how inductively established statements, coupled with assumptions concerning the uniformity of nature, can be certain according to Wolff. We examine Crusius’ little known work on physics and show that he attacked Wolff, arguing that many statements of physics are probable. We provide a discussion of the reception of methodological rules similar to Newton’s Regulae Philosophandi, discussing different interpretations of such rules. We conclude by briefly hinting at how the debate between Wolff and Crusius provides historical context for understanding Kant’s philosophy of natural science. (shrink)

I examine Du Châtelet’s methodology for physics and metaphysics through the lens of her engagement with Newton’s Rules for Reasoning in Natural Philosophy. I first show that her early manuscript writings discuss and endorse these Rules. Then, I argue that her famous published account of hypotheses continues to invoke close analogues of Rules 3 and 4, despite various developments in her position. Once relevant experimental evidence and some basic constraints are met, it is legitimate to inductively generalize from observations; general (...) hypotheses can thereafter be assumed as true until contrary experiments show otherwise. I conclude by arguing that this account of induction plays an essential role in her metaphysics, both in an argument for simple substances—which has an inductive premise—and in her attempt to distinguish acceptable and unacceptable metaphysical commitments. (shrink)

This paper argues that the linguistic approach to analyzing induction, according to which induction is a type of inference or argument composed of statements or propositions, is unsuitable to account for scientific reasoning. Consequently, a novel approach to induction in model-based science is suggested. First, in order to show their adherence to the linguistic treatment of induction, two strategies are reviewed: (i) Carnap and Reichenbach’s attempts to justify induction and (ii) Norton’s recent material theory of induction. Second, three reasons are (...) provided to support the claim that the linguistic treatment of induction is insufficient in accounting for model-based reasoning in science. Finally, a framework focused on models—rather than statements or propositions—is suggested to address induction in science. William Whewell’s theory of induction is briefly outlined as an example of a non-propositional treatment of induction that is consistent with model-based scientific practice. (shrink)

This chapter presents a typology of the different kinds of inductive inferences we can draw from our evidence, based on the explanatory relationship between evidence and conclusion. Drawing on the literature on graphical models of explanation, I divide inductive inferences into (a) downwards inferences, which proceed from cause to effect, (b) upwards inferences, which proceed from effect to cause, and (c) sideways inferences, which proceed first from effect to cause and then from that cause to an additional effect. I further (...) distinguish between direct and indirect forms of downwards and upwards inferences. I then show how we can subsume canonical forms of inductive inference mentioned in the literature, such as inference to the best explanation, enumerative induction, and analogical inference, under this typology. Along the way, I explore connections with probability and confirmation, epistemic defeat, the relation between abduction and enumerative induction, the compatibility of IBE and Bayesianism, and theories of epistemic justification. (shrink)

The framework of Solomonoff prediction assigns prior probability to hypotheses inversely proportional to their Kolmogorov complexity. There are two well-known problems. First, the Solomonoff prior is relative to a choice of Universal Turing machine. Second, the Solomonoff prior is not computable. However, there are responses to both problems. Different Solomonoff priors converge with more and more data. Further, there are computable approximations to the Solomonoff prior. I argue that there is a tension between these two responses. This is because computable (...) approximations to Solomonoff prediction do not always converge. (shrink)

This paper argues that the linguistic approach to analyzing induction, according to which induction is a type of inference or argument composed of statements or propositions, is unsuitable to account for scientific reasoning. Consequently, a novel approach to induction in model-based science is suggested. First, in order to show their adherence to the linguistic treatment of induction, two strategies are reviewed: (i) Carnap and Reichenbach’s attempts to justify induction and (ii) Norton’s recent material theory of induction. Second, three reasons are (...) provided to support the claim that the linguistic treatment of induction is insufficient in accounting for model-based reasoning in science. Finally, a framework focused on models—rather than statements or propositions—is suggested to address induction in science. William Whewell’s theory of induction is briefly outlined as an example of a non-propositional treatment of induction that is consistent with model-based scientific practice. (shrink)

We are often justified in acting on the basis of evidential confirmation. I argue that such evidence supports belief in non-quantificational generic generalizations, rather than universally quantified generalizations. I show how this account supports, rather than undermines, a Bayesian account of confirmation. Induction from confirming instances of a generalization to belief in the corresponding generic is part of a reasoning instinct that is typically (but not always) correct, and allows us to approximate the predictions that formal epistemology would make.

In this thesis I motivate and develop a Hybrid Theory of Induction (HTI), and I explore some of its virtues and implications. The HTI is a hybrid second-order model of inductive support. It is a "hybrid" model of inductive support because it holds that two ingredients play a necessary role in understanding inductive support: rules and facts. It is a "second-order" model of inductive support because it is a model within which first-order models of inductive support (i.e. logics of induction) (...) can fit. In chapter 1 I argue that we need both rules and facts to play a role in a successful account of inductive support. Rules of induction accurately describe relations of inductive support when they are warranted; facts do the warranting work. I call this type of warrant "factual warrant". The resulting account is both functional and accurate, it helps us make sense of how different rules of induction can coexist and it allows us to resolve some current debates in induction. For the purposes of chapter 1 I adopt an existing binary account of factual warrant. In chapter 2 I develop a Graded account of Factual Warrant (GFW), according to which factual warrant comes in degrees. I integrate the GFW in the HTI. I then show that the GFW illuminates the connection between factual warrant and inductive support, and it can successfully account for the role of idealisations and theory in our understanding of inductive support. In chapter 3 I argue that the HTI is also useful for agents, since it can provide methodological guidance to ensure strong inferences and conceptual guidance to assess the strength of our inferences. Finally, in chapter 4, I explore Bayesian inductive logics from the perspective of the HTI. This analysis brings to light the central role that probability models play in Bayesian inductive logics, offering a logical underpinning for some recent suggestions in Bayesian epistemology. Furthermore, throughout this thesis I analyse in detail three rules of induction from the perspective of the HTI: enumerative induction in chapter 2, causal inference in chapter 3 and Bayesian inductive logics in chapter 4. These analyses illustrate how the HTI can help us think more clearly about rules of induction, offering new tools to tackle existing challenges. (shrink)

A volume of papers inspired by the work of George E. Smith on confirmation and evidence in advanced science—from Newton's gravitation theory to the physics of molecules.

The paper presents a comprehensive solution to the new riddle of induction. Gruesome induction is blocked because “grue” is not independent of our sampling and observation methods. Before presenting my theory, I critically survey previous versions of what I call the “independence strategy”, tracing the strategy to three different papers from the 1970s by (respectively) Wilkerson, Moreland, and Jackson. Next I critically examine recent approaches by Okasha, Godfrey-Smith, Schramm, and Freitag. All of these approaches have their virtues, but none of (...) them rules out every problem case. Nor do any of them alone explain exactly what goes wrong in all types of gruesome reasoning. My account aims to do both. Learning lessons from my criticisms of previous theories, I argue that there are several crucial types of independence. All of them are needed to rule out every problem case. I close by suggesting that the independence solution can also be adopted by proponents of other approaches—Bayesians, fans of natural kinds, and pragmatists. (shrink)

Michael Nahm's preceding commentary accuses me of seven misrepresentations. One of these is an acknowledged good-faith error about a peripheral detail, while the remaining six are demonstrably accurate descriptions of Nahm's statements. At the same time, Nahm verifiably misrepresents me frequently and intentionally over issues that he takes to be consequential, which is a much more serious offense. All authors should call out when an interlocutor get their points wrong, but only when they can definitively back up the charge. Where (...) Nahm weakly attempts to show that I misrepresented him, I will show that, if anything, his showcase consists of six verifiably accurate characterizations of his Bigelow Institute contest-winning essay's conclusions. His commentary exemplifies the truism that one can appeal to a million frivolous reasons to dismiss what an opponent has to say if one is absolutely determined not to hear him. Though committed survivalists will undoubtedly be satisfied that survival researchers have responded to me regardless of whether they have responded well, those that care about the underlying issues will hopefully find value in my reply. -/- 1. Introduction -- 2. My (One) Accidental Misattribution -- 3. Nahm's (Repeated) Intentional Mischaracterizations -- 4. Nahm's Mischaracterizations to Shift the Burden of Proof -- 5. Nahm's Seven Wonders of the World -- 6. Conclusion: Assertions Should be Supported. (shrink)

The recent Bigelow Institute contest rewarding the "best" evidence for life after death epitomizes much of what's wrong with the current state of survival research, its participants constituting a who's who list of contemporary survival researchers. Cases that are regularly hyped as among the best evidence for an afterlife are all too often easily susceptible to normal explanations--if only survival researchers would give them a chance. The consistently negative results of 121 years of experimental survival research ought to have spurred (...) soul-searching questions for survival researchers by now. And if we treat discarnate personal survival as a scientific hypothesis, then researchers are rationally obliged to seriously consider biological facts that tell against it, too. Limiting one's inquiry to attempts to only collect data that might confirm survival is one of the chief hallmarks of pseudoscience, and it's sadly a feature, not a bug, of the survival literature. This systematic review reveals that survival researchers would better serve science by setting aside their feelings and heeding what the data are telling them, for the probabilities should drive our beliefs, not the other way around. Is discarnate personal survival likely to occur in light of the total available evidence? The overall evidence doesn't even make personal survival more probable than not. -/- 1. Introduction 2. In Science the Quality of the Evidence is Paramount -- 2.1 Prospective Experimental Tests of Survival -- 2.2 Where Have All the Deceased Survival Researchers Gone? -- 3. What Does the Total Available Relevant Evidence Tell Us? -- 4. Ranking the Survival Evidence -- 5. The Mind-Body Problem, Botched -- 6. Conclusion: Not Much Better than Religious Faith. (shrink)

What is the relation or connection between formalizations of induction and the actual inductive inferences of scientists? Building from recent works in the philosophy of logic, this paper argues that these formalizations of induction are best viewed as models and not literal descriptions of inductive inferences in science. Three arguments are put forward to support this claim. First, I argue that inductive support is the kind of phenomenon that can be justifiably modeled. Second, I argue that these formalizations have the (...) features that define models—that they have representors, artefacts, and idealizations. Third, I argue that these formalizations being models explains their plurality and revisability. (shrink)

This article compares and contrasts the reception of Comte’s positivism in the works of William Whewell, John Stuart Mill and Franz Brentano. It is argued that Whewell’s rejection of positivism derives from his endorsement of a constructivist account of the inductive sciences, while Mill and Brentano’s sympathies for positivism are connected to their endorsement of an empiricist account. The mandate of the article is to spell out the chief differences between these two rival accounts. In the last, conclusive section, Whewell’s (...) anti-positivist argument is briefly assessed, and rebutted. (shrink)

Prior experimental studies of anomalous information reception (AIR) have been touted as strong evidence for postmortem survival of consciousness yet are plagued by several methodological weaknesses that preclude clear evidence of positive results. The present team provides an adversarial collaboration to identify and compensate for the major limitations of these previous approaches. We outline a more rigorous preregistered study design that eliminates or minimizes researcher bias in (a) data cleaning and (b) statistical analysis. Obtaining positive results with our recommended design (...) would arguably yield data that skeptics and sympathetic researchers would agree is more clearly interpretable and offers stronger support for a survivalist interpretation. However, this proposed study is not intended to be definitive but rather only a next step in a research program that aims to improve on earlier published efforts. It would also admittedly be time-consuming and expensive to implement, as well as raise ethical considerations in utilizing vulnerable research populations. However, these costs are required to achieve the rigor necessary to advance scientific knowledge in survival research. 1. Introduction -- 2. Laying a Working Foundation -- 3. Choice of "Survival Effect" -- 4. The Recommended Preregistered Protocol -- 5. Considerations and Caveats -- 5.1. Strengths of Such Protocol -- 6. Concluding Thoughts. (shrink)

Evaluative studies of inductive inferences have been pursued extensively with mathematical rigor in many disciplines, such as statistics, econometrics, computer science, and formal epistemology. Attempts have been made in those disciplines to justify many different kinds of inductive inferences, to varying extents. But somehow those disciplines have said almost nothing to justify a most familiar kind of induction, an example of which is this: “We’ve seen this many ravens and they all are black, so all ravens are black.” This is (...) enumerative induction in itsfullstrength. For it does not settle with a weaker conclusion (such as “the ravens observed in the future will all be black”); nor does it proceed with any additional premise (such as the statistical IID assumption). The goal of this paper is to take some initial steps toward a justification for the full version of enumerative induction, against counterinduction, and against the skeptical policy. The idea is to explore various epistemic ideals, mathematically defined as different modes of convergence to the truth, and look for one that is weak enough to be achievable and strong enough to justify a norm that governs both the long run and the short run. So the proposal is learning-theoretic in essence, but a Bayesian version is developed as well. (shrink)

This paper addresses the role of analogical reasoning in archaeoastronomy - the discipline which studies the connections between the ancient monuments and the heavens. Archaeoastronomy is a highly interdisciplinary science, placed at the border between the humanities – especially archaeology – and the scientific approach to cultural heritage. As a consequence, its scientific foundations are a delicate matter. We plan to investigate here the question of what constitutes the evidence for analogical inferences in archaeoastronomy and to what extent one can (...) achieve confirmation of archaeoastronomical hypotheses by means of such analogies. Our claim will be that, when deployed in accordance with the methodology articulated in this paper, analogies can be a highly effective epistemic tool for generating and supporting hypotheses about the relation of archaeological sites with astronomical events. (shrink)

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.

In his recent book, John Norton has created a theory of inference to the best explanation, within the context of his "material theory of induction". I apply it to the problem of scientific explanations that are false: if we want the theories in our explanations to be true, then why do historians and scientists often say that false theories explained phenomena? I also defend Norton's theory against some possible objections.

Even prior to its publication, John Norton’s book has stimulated debates about induction. Its publication will galvanize these discussions. Does it merit all this attention? Yes, and not just from philosophers of science. Practically all philosophers will find novel and thought-provoking ideas, with implications for their research.

According to John D. Norton's Material Theory of Induction, all reasonable inductive inferences are justified in virtue of background knowledge about local uniformities in nature. These local uniformities indicate that our samples are likely to be representative of our target population in our inductions. However, a variety of critics have noted that there are many circumstances in which induction seems to be reasonable, yet such background knowledge is apparently absent. I call such absences ‘the frontiers of science', where background scientific (...) theories do not provide information about such local uniformities. I argue that the Material Theory of Induction can be reconciled with our intuitions in favour of these inductions. I adapt an attempted justification of induction in general, the Combinatoric Justification of Induction, into a more modest rationalisation at the less foundational level that the critics discuss. Subject to a number of conditions, we can extrapolate from large samples using our knowledge of facts about the minimum proportions of representative subsets of finite sets. I also discuss some of Norton's own criticisms of his theory and argue that he is overly pessimistic. I conclude that Norton's theory at least performs well at the frontiers of science. (shrink)

Many scientists routinely generalize from study samples to larger populations. It is commonly assumed that this cognitive process of scientific induction is a voluntary inference in which researchers assess the generalizability of their data and then draw conclusions accordingly. We challenge this view and argue for a novel account. The account describes scientific induction as involving by default a generalization bias that operates automatically and frequently leads researchers to unintentionally generalize their findings without sufficient evidence. The result is unwarranted, overgeneralized (...) conclusions. We support this account of scientific induction by integrating a range of disparate findings from across the cognitive sciences that have until now not been connected to research on the nature of scientific induction. The view that scientific induction involves by default a generalization bias calls for a revision of the current thinking about scientific induction and highlights an overlooked cause of the replication crisis in the sciences. Commonly proposed interventions to tackle scientific overgeneralizations that may feed into this crisis need to be supplemented with cognitive debiasing strategies against generalization bias to most effectively improve science. (shrink)

An aspect of Peirce’s thought that may still be underappreciated is his resistance to what Levi calls _pedigree epistemology_, to the idea that a central focus in epistemology should be the justification of current beliefs. Somewhat more widely appreciated is his rejection of the subjective view of probability. We argue that Peirce’s criticisms of subjectivism, to the extent they grant such a conception of probability is viable at all, revert back to pedigree epistemology. A thoroughgoing rejection of pedigree in the (...) context of probabilistic epistemology, however, _does_ challenge prominent subjectivist responses to the problem of the priors. (shrink)

Genetic engineering technologies are a subclass of the biotechnology family, and are concerned with the use of laboratory-based technologies to intervene with a given organism at the genetic level, i.e., the level of its DNA. This class of technologies could feasibly be used to treat diseases and disabilities, create disease-resistant crops, or even be used to enhance humans to make them more resistant to certain environmental conditions. However, both therapeutic and enhancement applications of genetic engineering raise serious ethical concerns. This (...) paper examines various objections to genetic engineering (as applied to humans) which have been raised in the literature, and presents a new way to frame these issues, and to look for solutions. Specifically, this paper frames genetic engineering technologies within the ‘design turn in applied ethics’ lens and thus situates these technologies as covarying with societal forces. The value sensitive design (VSD) approach to technology design is then appropriated as the conceptual framework in which genetic engineering technologies can be considered so that they can be designed for important human values. By doing so, this paper brings further nuance to the scholarship on genetic engineering technologies by discussing the sociotechnicity of genetic engineering systems rather than framing them as value-neutral tools that either support or constrain values based on how they are used. (shrink)

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.

John Stuart Mill’s System of Logic (1843) is often considered to be a work that defends an inductivist epistemology. In this article, I propose to question this status by examining the definition of induction set out in Mill’s book, and the consequences that can be deduced from it. I show that Mill’s inductivism implies a methodology of scientific research in which deductive reasoning is just as important, if not more important, than inductive methods, so that the classical opposition between induction (...) and deduction is transformed into a complementarity. I then show how the concepts of natural law and causality emerge from these discussions, and examine how well the methods proposed by Mill are able to account for subsequent scientific discoveries. (shrink)

This introduction consists of two parts. In the first part, the special issue editors introduce inductive metaphysics from a historical as well as from a systematic point of view and discuss what distinguishes it from other modern approaches to metaphysics. In the second part, they give a brief summary of the individual articles in this special issue.