It is a privilege to be invited to contribute to the Festschrift dedicated to Professor Johan Buitendag, Emeritus Dean, Faculty of Theology and Religion at the University of Pretoria, South Africa. While his own work often examined the relationship between theology and natural science, he was also passionate about ecumenism and, in that spirit, the present essay utilised what might be described as an inductive approach to an important ecumenical question, the unity between Methodists and Catholics. Ecumenical dialogue (...) is often undertaken from a theological and dogmatic perspective. This essay took a different approach in that it sought to inductively examine what might be described as the inner logic of two ecclesial systems (Methodist and Catholic). In doing so, it was premised upon an Aristotelian philosophical principle, epistemic fit, in that it presupposed that both these ecclesial bodies possess an intrinsic logic that can be brought to the surface in order to exhibit parallel contours in the wider ecclesial terrain.Contribution: This article fits well within the scope of HTS Teologiese Studies/Theological Studies in that it contributed to a new subdiscipline in epistemology, which explores the conceptual and epistemological dimensions of ecclesiology. Using the concept of epistemic fit, the article offered an inductive approach to some of the practical issues that emerge in ecumenical dialogue. (shrink)

We present the notion of finite high-order Gowers games, and prove a statement parallel to Gowers's Combinatorial Lemma for these games. We derive ‘quantitative’ versions of the original Gowers Combinatorial Lemma and of Gowers's Dichotomy, which place them in the context of the recently introduced infinite dimensional asymptotic theory for Banach spaces.

Without inductive reasoning, we couldn't generalize from one instance to another, derive scientific hypotheses, or predict that the sun will rise again tomorrow morning. Despite the widespread nature of inductive reasoning, books on this topic are rare. Indeed, this is the first book on the psychology of inductive reasoning in twenty years. The chapters survey recent advances in the study of inductive reasoning and address questions about how it develops, the role of knowledge in induction, how (...) best to model people's reasoning, and how induction relates to other forms of thinking. Written by experts in philosophy, developmental science, cognitive psychology, and computational modeling, the contributions here will be of interest to a general cognitive science audience as well as to those with a more specialized interest in the study of thinking. (shrink)

The aim of this contribution is to broaden the concept of musical meaning from an abstract and emotionally neutral cognitive representation to an emotion-integrating description that is related to the evolutionary approach to music. Starting from the dispositional machinery for dealing with music as a temporal and sounding phenomenon, musical emotions are considered as adaptive responses to be aroused in human beings as the product of neural structures that are specialized for their processing. A theoretical and empirical background is (...) provided in order to bring together the findings of music and emotion studies and the evolutionary approach to musical meaning. The theoretical grounding elaborates on the transition from referential to affective semantics, the distinction between expression and induction of emotions, and the tension between discrete-digital and analog-continuous processing of the sounds. The empirical background provides evidence from several findings such as infant-directed speech, referential emotive vocalizations and separation calls in lower mammals, the distinction between the acoustic and vehicle mode of sound perception, and the bodily and physiological reactions to the sounds. It is argued, finally, that early affective processing reflects the way emotions make our bodies feel, which in turn reflects on the emotions expressed and decoded. As such, there is a dynamic tension between nature and nurture, which is reflected in the nature-nurture-nature cycle of musical sense-making. (shrink)

This paper is an effort to realize and explore the connections that exist between nonmonotonic logic and confirmation theory. We pick up one of the most wide-spread nonmonotonic formalisms – default logic – and analyze to what extent and under what adjustments it could work as a logic of induction in the philosophical sense. By making use of this analysis, we extend default logic so as to make it able to minimally perform the task of a logic of induction, having (...) as a result a system which we believe has interesting properties from the standpoint of theory of confirmation. It is for instance able to represent chains of inductive rules as well as to reason paraconsistently on the conclusions obtained from them. We then use this logic to represent some traditional ideas concerning confirmation theory, in particular the ones proposed by Carl Hempel in his classical paper "Studies in the Logic of Confirmation" of 1945 and the ones incorporated in the so-called abductive and hy-pothetico-deductive models. (shrink)

This paper tries to extend Hintikka's inductive logic so that we can confirm a causally necessary statement. For this purpose, a joint system of inductive logic and logic of causal modalities is constructed. This system can offer a plausible explication of the distinction between nomic and accidental universality, as well as a good formulation of a causal law. And the transition from actuality to causal necessity is construed, in this system, as essentially probabilistic; i.e. no statements about actuality (...) can entail a necessary statement, but certain statements about actuality can single out a most probable causal law. (shrink)

Theories of truth approximation in terms of truthlikeness almost always deal with approaching deterministic truths, either actual or nomic. This paper deals first with approaching a probabilistic nomic truth, viz. a true probability distribution. It assumes a multinomial probabilistic context, hence with a lawlike true, but usually unknown, probability distribution. We will first show that this true multinomial distribution can be approached by Carnapian inductive probabilities. Next we will deal with the corresponding deterministic nomic truth, that is, the set (...) of conceptually possible outcomes with a positive true probability. We will introduce Hintikkian inductive probabilities, based on a prior distribution over the relevant deterministic nomic theories and on conditional Carnapian inductive probabilities, and first show that they enable again probabilistic approximation of the true distribution. Finally, we will show, in terms of a kind of success theorem, based on Niiniluoto’s estimated distance from the truth, in what sense Hintikkian inductive probabilities enable the probabilistic approximation of the relevant deterministic nomic truth. In sum, the truth approximation perspective on Carnapian and Hintikkian inductive probabilities leads to the unification of the inductive probability field and the field of truth approximation. (shrink)

The purpose of this paper is twofold. First we want to extent a specific paranormal modal logic in such a way as obtain a paraconsistent and paracomplete multimodal logic able to formalize the notions of plausibility and certainty. With this logic at hand, and this is our second purpose, we shall use a modified version of Reiter‘s default logic to build a sort of inductive logic of plausibility and certainty able to represent some basic principles of epistemic inductive (...) reasoning, such as a negative autoepistemic principle, an `error-prone feature of induction' principle and a confirmation by enumeration principle. (shrink)

Governments, institutions, and brands try various intervention strategies for countering growing cyberbullying, but with questionable effectiveness. The authors use hypocrisy induction, a technique for subtly reminding consumers that they have acted contrary to their moral values, to see whether it makes consumers more willing to support brand-sponsored anti-cyberbullying CSR campaigns. Findings demonstrate that hypocrisy induction evokes varying reactions depending on regulatory focus, mediated by guilt and shame. Specifically, consumers who have a dominant promotion (prevention) focus feel guilt (shame), which motivates (...) them to overcome their discomfort by supporting (avoiding) an anti-cyberbullying campaign. Moral regulation is drawn as a theoretical underpinning to explain various consumer reactions to hypocrisy induction, the moderating role of regulatory focus, and mediating role of guilt and shame. The research contributes to the literature and provides practical implications by explaining when and why brands can use hypocrisy induction to persuade consumers to support social causes through the lens of moral regulation theory. (shrink)

We propose a new hybrid data mining method for predicting protein-protein interactions combining Likelihood-Ratio with rule induction algorithms. In essence, the new method consists of using a rule induction algorithm to discover rules representing partitions of the data, and then the discovered rules are interpreted as “bins” which are used to compute likelihood ratios. This new method is applied to the prediction of protein-protein interactions in the Saccharomyces Cerevisiae genome, using predictive genomic features in an integrated scheme. The results show (...) that the new hybrid method outperforms a pure likelihood ratio based approach. (shrink)

Pure Inductive Logic is the study of rational probability treated as a branch of mathematical logic. This monograph, the first devoted to this approach, brings together the key results from the past seventy years, plus the main contributions of the authors and their collaborators over the last decade, to present a comprehensive account of the discipline within a single unified context.

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)

BackgroundHIV molecular epidemiology is increasingly recognized as a vital source of information for understanding HIV transmission dynamics. Despite extensive use of these data-intensive techniques in both research and public health settings, the ethical issues associated with this science have received minimal attention. As the discipline evolves, there is reasonable concern that existing ethical and legal frameworks and standards might lag behind the rapid methodological developments in this field. This is a follow-up on our earlier work that applied a predetermined analytical (...) framework to examine the perspectives of a sample of scientists from the fields of epidemiology, public health, virology and bioethics on key ethical issues associated with HIV molecular epidemiology in HIV network research.MethodsFourteen in-depth interviews were conducted with scientists from the fields of molecular epidemiology, public health, virology and bioethics. Inductive analytical approaches were applied to identify key themes that emerged from the data.ResultsOur interviewees acknowledged the potential positive impact of molecular epidemiology in the fight against HIV. However, they were concerned that HIV phylogenetics research messages may be incorrectly interpreted if not presented at the appropriate level. There was consensus that HIV phylogenetics research presents a potential risk to privacy, but the probability and magnitude of this risk was less obvious. Although participants acknowledged the social value that could be realized from the analysis of HIV genetic sequences, there was a perceived fear that the boundaries for use of HIV sequence data were not clearly defined.ConclusionsOur findings highlight distinct ethical issues arising from HIV molecular epidemiology. As the discipline evolves and HIV sequence data become increasingly available, it is critical to ensure that ethical standards keep pace with biomedical advancements. We argue that the ethical issues raised in this study, whether real or perceived, require further conceptual and empirical examination. (shrink)

The problem of induction is formulated as a set of three questions, namely: ‘What is the nature of the attitude of acceptance that we adopt in relation to certain theories?’ ‘What are the rules according to which we select those theories which we accept?’ and, ‘What is the justification for the adoption of those rules?’. An original answer is proposed for each question in turn, with the help of the new concepts of sub-theory, established sub-theory, aberrant, arbitrary and degenerate theories. (...) The answer to the third question follows the lines of Reichenbach's pragmatic strategy. (shrink)

Eliminative induction is a method for finding the truth by using evidence to eliminate false competitors. It is often characterized as "induction by means of deduction"; the accumulating evidence eliminates false hypotheses by logically contradicting them, while the true hypothesis logically entails the evidence, or at least remains logically consistent with it. If enough evidence is available to eliminate all but the most implausible competitors of a hypothesis, then (and only then) will the hypothesis become highly confirmed. I will argue (...) that, with regard to the evaluation of hypotheses, Bayesian inductive inference is essentially a probabilistic form of induction by elimination. Bayesian induction is an extension of eliminativism to cases where, rather than contradict the evidence, false hypotheses imply that the evidence is very unlikely, much less likely than the evidence would be if some competing hypothesis were true. This is not, I think, how Bayesian induction is usually understood. The recent book by Howson and Urbach, for example, provides an excellent, comprehensive explanation and defense of the Bayesian approach; but this book scarcely remarks on Bayesian induction's eliminative nature. Nevertheless, the very essence of Bayesian induction is the refutation of false competitors of a true hypothesis, or so I will argue. (shrink)

The inductive category formation framework, an influential set of theories of learning in psychology and artificial intelligence, is deeply flawed. In this framework a set of necessary and sufficient features is taken to define a category. Such definitions are not functionally justified, are not used by people, and are not inducible by a learning system. Inductive theories depend on having access to all and only relevant features, which is not only impossible but begs a key question in learning. (...) The crucial roles of other cognitive processes (such as explanation and credit assignment) are ignored or oversimplified. Learning necessarily involves pragmatic considerations that can only be handled by complex cognitive processes.We provide an alternative framework for learning according to which category definitions must be based on category function. The learning system invokes other cognitive processes to accomplish difficult tasks, makes inferences, analyses and decides among potential features, and specifies how and when categories are to be generated and modified. We also examine the methodological underpinnings of the two approaches and compare their motivations. (shrink)

In a recent work, Popper claims to have solved the problem of induction. In this paper I argue that Popper fails both to solve the problem, and to formulate the problem properly. I argue, however, that there are aspects of Popper's approach which, when strengthened and developed, do provide a solution to at least an important part of the problem of induction, along somewhat Popperian lines. This proposed solution requires, and leads to, a new theory of the role of (...) simplicity in science, which may have helpful implications for science itself, thus actually stimulating scientific progress. (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)

The inaugural title in the new, Open Access series BSPS Open, The Material Theory of Induction will initiate a new tradition in the analysis of inductive inference. The fundamental burden of a theory of inductive inference is to determine which are the good inductive inferences or relations of inductive support and why it is that they are so. The traditional approach is modeled on that taken in accounts of deductive inference. It seeks universally applicable schemas (...) or rules or a single formal device, such as the probability calculus. After millennia of halting efforts, none of these approaches has been unequivocally successful and debates between approaches persist. The Material Theory of Induction identifies the source of these enduring problems in the assumption taken at the outset: that inductive inference can be accommodated by a single formal account with universal applicability. Instead, it argues that that there is no single, universally applicable formal account. Rather, each domain has an inductive logic native to it. Which that is, and its extent, is determined by the facts prevailing in that domain. Paying close attention to how inductive inference is conducted in science and copiously illustrated with real-world examples, The Material Theory of Induction will initiate a new tradition in the analysis of inductive inference. (shrink)

A computational theory of induction must be able to identify the projectible predicates, that is to distinguish between which predicates can be used in inductive inferences and which cannot. The problems of projectibility are introduced by reviewing some of the stumbling blocks for the theory of induction that was developed by the logical empiricists. My diagnosis of these problems is that the traditional theory of induction, which started from a given (observational) language in relation to which all inductive (...) rules are formulated, does not go deep enough in representing the kind of information used in inductive inferences. As an interlude, I argue that the problem of induction, like so many other problems within AI, is a problem of knowledge representation. To the extent that AI-systems are based on linguistic representations of knowledge, these systems will face basically the same problems as did the logical empiricists over induction. In a more constructive mode, I then outline a non-linguistic knowledge representation based on conceptual spaces. The fundamental units of these spaces are "quality dimensions". In relation to such a representation it is possible to define "natural" properties which can be used for inductive projections. I argue that this approach evades most of the traditional problems. (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.

A notion of finitary inductively presented (f.i.p.) logic is proposed here, which includes all syntactically described logics (formal systems)met in practice. A f.i.p. theory FS0 is set up which is universal for all f.i.p. logics; though formulated as a theory of functions and classes of expressions, FS0 is a conservative extension of PRA. The aims of this work are (i)conceptual, (ii)pedagogical and (iii)practical. The system FS0 serves under (i)and (ii)as a theoretical framework for the formalization of metamathematics. The general (...) class='Hi'>approach may be used under (iii)for the computer implementation of logics. In all cases, the work aims to make the details manageable in a natural and direct way. (shrink)

The main aim of this paper is to revisit the curve fitting problem using the reliability of inductive inference as a primary criterion for the ‘fittest' curve. Viewed from this perspective, it is argued that a crucial concern with the current framework for addressing the curve fitting problem is, on the one hand, the undue influence of the mathematical approximation perspective, and on the other, the insufficient attention paid to the statistical modeling aspects of the problem. Using goodness-of-fit as (...) the primary criterion for ‘best', the mathematical approximation perspective undermines the reliability of inference objective by giving rise to selection rules which pay insufficient attention to ‘accounting for the regularities in the data'. A more appropriate framework is offered by the error-statistical approach, where (i) statistical adequacy provides the criterion for assessing when a curve captures the regularities in the data adequately, and (ii) the relevant error probabilities can be used to assess the reliability of inductive inference. Broadly speaking, the fittest curve (statistically adequate) is not determined by the smallness if its residuals, tempered by simplicity or other pragmatic criteria, but by the nonsystematic (e.g. white noise) nature of its residuals. The advocated error-statistical arguments are illustrated by comparing the Kepler and Ptolemaic models on empirical grounds. ‡I am grateful to Deborah Mayo and Clark Glymour for many valuable suggestions and comments on an earlier draft of the paper; estimating the Ptolemaic model was the result of Glymour's prompting and encouragement. †To contact the author, please write to: Department of Economics, Virginia Tech 3019 Pamplin Hall (0316), Blacksburg, VA 24061; e-mail: [email protected]. (shrink)

It is undeniable that inductive reasoning has brought us much good. At least since Hume, however, philosophers have wondered how to justify our reliance on induction. In important recent work, Schurz points out that philosophers have been wrongly assuming that justifying induction is tantamount to showing induction to be reliable. According to him, to justify our reliance on induction, it is enough to show that induction is optimal. His optimality approach consists of two steps: an analytic argument for (...) meta-induction (that is, induction over inductive methods) and an application of meta-induction to empirical findings concerning the predictive accuracy of our actual inductive practices as compared to various non-inductive methods. The present article agrees with Schurz’s general conclusion but also argues that it leaves an important aspect of our inductive practices unaccounted for, to wit, that these practices have so far been highly successful; to satisfy the optimality requirement, induction only needs to be as successful as random guessing. To explain the success of induction, I turn to insights from social epistemology, also highlighted in Schurz’s work, and make these formally explicit in a framework that combines the Hegselmann–Krause model for opinion dynamics and Carnap’s system of λ rules. Within this framework, I use a standard evolutionary algorithm to show how communities of interacting agents may, through variation and selection, come to consist of highly successful inductive reasoners. (shrink)

From what norms does the ethics of belief derive its oughts, its attributions of virtues and vices, responsibilities and irresponsibilities, its permissioning and censuring? Since my inductive risk account is inspired by pragmatism, and this method understands epistemology as the theory of inquiry, the paper will try to explain what the aims and tasks are for an ethics of belief, or project of guidance, which best fits with this understanding of epistemology. More specifically, this chapter approaches the ethics of (...) belief from a focus on responsible risk management, where doxastic responsibility is understood in terms of the degree of riskiness of agents’ doxastic strategies, a riskiness which is in turn most objectively measured through accordance or violation of inductive norms. Doxastic responsibility is attributable to agents on the basis of how epistemically risky was the process or strategy of inquiry salient in the etiology of their belief or in their maintenance of what one believes or accepts. (shrink)

I here aim to show that a particular approach to the problem of induction, which I will call “induction by direct inference”, comfortably handles Goodman’s problem of induction. I begin the article by describing induction by direct inference. After introducing induction by direct inference, I briefly introduce the Goodman problem, and explain why it is, prima facie, an obstacle to the proposed approach. I then show how one may address the Goodman problem, assuming one adopts induction by direct (...) inference as an approach to the problem of induction. In particular, I show that a relatively standard treatment of what some have called the “Reference Class problem” addresses the Goodman Problem. Indeed, plausible and relatively standard principles of direct inference yield the conclusion that the Goodman inference (involving the grue predicate) is defeated, so it is unnecessary to invoke considerations of ‘projectibility’ in order to address the Goodman problem. I conclude the article by discussing the generality of the proposed approach, in dealing with variants of Goodman’s example. (shrink)

According to the Bayesian view, scientific hypotheses must be appraised in terms of their posterior probabilities relative to the available experimental data. Such posterior probabilities are derived from the prior probabilities of the hypotheses by applying Bayes'theorem. One of the most important problems arising within the Bayesian approach to scientific methodology is the choice of prior probabilities. Here this problem is considered in detail w.r.t. two applications of the Bayesian approach: (1) the theory of inductive probabilities (TIP) (...) developed by Rudolf Carnap and other epistomologists and (2) the analysis of the multinational inferences provided by Bayesian statstics (BS). ... Zie: Summary. (shrink)

My first goal is to motivate a distinctively metaphysical approach to the problem of induction. I argue that there is a precise sense in which the only way that orthodox Humean and non-Humean views can justify induction is by appealing to extremely strong and unmotivated probabilistic biases. My second goal is to sketch what such a metaphysical approach could possibly look like. After sketching such an approach, I consider a toy case that illustrates the way in which (...) such a metaphysics can help us make progress on the problem of induction. (shrink)

Within analytic philosophy, induction has been seen as a problem concerning inferences that have been analysed as relations between sentences. In this article, we argue that induction does not primarily concern relations between sentences, but between properties and categories. We outline a new approach to induction that is based on two theses. The first thesis is epistemological. We submit that there is not only knowledge-how and knowledge-that, but also knowledge-what. Knowledge-what concerns relations between properties and categories and we argue (...) that it cannot be reduced to knowledge-that. We support the partition of knowledge by mapping it onto the long-term memory systems: procedural, semantic and episodic memory. The second thesis is that the role of inductive reasoning is to generate knowledge-what. We use conceptual spaces to model knowledge-what and the relations between properties and categories involved in induction. (shrink)

Within analytic philosophy, induction has been seen as a problem concerning inferences that have been analysed as relations between sentences. In this article, we argue that induction does not primarily concern relations between sentences, but between properties and categories. We outline a new approach to induction that is based on two theses. The first thesis is epistemological. We submit that there is not only knowledge-how and knowledge-that, but also knowledge-what. Knowledge-what concerns relations between properties and categories and we argue (...) that it cannot be reduced to knowledge-that. We support the partition of knowledge by mapping it onto the long-term memory systems: procedural, semantic and episodic memory. The second thesis is that the role of inductive reasoning is to generate knowledge-what. We use conceptual spaces to model knowledge-what and the relations between properties and categories involved in induction. (shrink)

Inductive generalization, where people go beyond the data provided, is a basic cognitive capability, and it underpins theoretical accounts of learning, categorization, and decision making. To complete the inductive leap needed for generalization, people must make a key ‘‘sampling’’ assumption about how the available data were generated. Previous models have considered two extreme possibilities, known as strong and weak sampling. In strong sampling, data are assumed to have been deliberately generated as positive examples of a concept, whereas in (...) weak sampling, data are assumed to have been generated without any restrictions. We develop a more general account of sampling that allows for an intermediate mixture of these two extremes, and we test its usefulness. In two experiments, we show that most people complete simple one-dimensional generalization tasks in a way that is consistent with their believing in some mixture of strong and weak sampling, but that there are large individual differences in the relative emphasis different people give to each type of sampling. We also show experimentally that the relative emphasis of the mixture is influenced by the structure of the available information. We discuss the psychological meaning of mixing strong and weak sampling, and possible extensions of our modeling approach to richer problems of inductive generalization. (shrink)

The local justification of beliefs and hypotheses has recently become a major concern for epistemologists and philosophers of induction. As such, the problem of local justification is not entirely new. Most pragmatists had addressed themselves to it, and so did, to some extent, many classical inductivists in the Bacon-Whewell-Mill tradition. In the last few decades, however, the use of logic and semantics, probability calculus, statistical methods, and decision-theoretic concepts in the reconstruction of in ductive inference has revealed some important technical (...) respects in which inductive justification can be local: the choice of a language, with its syntactic and semantic features, the relativity of probabilistic evalua tions to an initial body of evidence or background knowledge and to an agent's utilities and preferences, etc. Some paradoxes and difficulties encountered by purely formal accounts of inductive justification, the erosion of the once dominant empiricist position, which most approaches to induction took for granted, and the increasing challenge of noninduc tivist epistemolgies have underscored the need of accounting for the methodological problems of applying inductive logic to real life contexts, particularly in science. As a result, in the late fifties and sixties, several related developments pointed to a new, local approach to inductive justification. (shrink)

Formal topology aims at developing general topology in intuitionistic and predicative mathematics. Many classical results of general topology have been already brought into the realm of constructive mathematics by using formal topology and also new light on basic topological notions was gained with this approach which allows distinction which are not expressible in classical topology. Here we give a systematic exposition of one of the main tools in formal topology: inductive generation. In fact, many formal topologies can be (...) presented in a predicative way by an inductive generation and thus their properties can be proved inductively. We show however that some natural complete Heyting algebra cannot be inductively defined. (shrink)

Induction, conceived as the class of rational non-truth preserving inferences, has been a perennial problem in philosophy. Aside from the problem of justification of induction, a less debated issue is the problem of properly describing inductive inferences. The purpose of this book is to conceptually investigate this descriptive problem of induction from the standpoint of the nonmonotonic logical tradition raised inside the field of Artificial Intelligence in the last thirty years. As we try to show, an essential part of (...) this enterprise involves the analysis of a pragmatically oriented notion of probability, called by us inductive plausibility. This in turn is made from the viewpoint of paraconsistency ? which according to some is the unavoidable companion of nonmonotonicity ? and modal logic. We therefore put forward a nonmonotonic, paraconsistent and modal approach to induction and plausibility. The book shall be useful to philosophers, logicians and computer scientists interested in the problem of induction in general and in the logical analysis of induction and plausibility in particular. (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)

Objective Bayesianism has been criticised for not allowing learning from experience: it is claimed that an agent must give degree of belief ½ to the next raven being black, however many other black ravens have been observed. I argue that this objection can be overcome by appealing to objective Bayesian nets, a formalism for representing objective Bayesian degrees of belief. Under this account, previous observations exert an inductive influence on the next observation. I show how this approach can (...) be used to capture the Johnson-Carnap continuum of inductive methods, as well as the Nix-Paris continuum, and show how inductive influence can be measured. (shrink)

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.

Understanding inductive reasoning is a problem that has engaged mankind for thousands of years. This problem is relevant to a wide range of fields and is integral to the philosophy of science. It has been tackled by many great minds ranging from philosophers to scientists to mathematicians, and more recently computer scientists. In this article we argue the case for Solomonoff Induction, a formal inductive framework which combines algorithmic information theory with the Bayesian framework. Although it achieves excellent (...) theoretical results and is based on solid philosophical foundations, the requisite technical knowledge necessary for understanding this framework has caused it to remain largely unknown and unappreciated in the wider scientific community. The main contribution of this article is to convey Solomonoff induction and its related concepts in a generally accessible form with the aim of bridging this current technical gap. In the process we examine the major historical contributions that have led to the formulation of Solomonoff Induction as well as criticisms of Solomonoff and induction in general. In particular we examine how Solomonoff induction addresses many issues that have plagued other inductive systems, such as the black ravens paradox and the confirmation problem, and compare this approach with other recent approaches. (shrink)

In his recent bookThe Advancement of Science,Philip Kitcher endorses eliminative induction, or the view that confirmation of hypotheses proceeds by the elimination of alternatives. My intention here is to critically examine Kitcher's eliminativist view of confirmation, and his rejection of the widely held Bayesian position, according to which an hypothesis H is confirmed by evidence E just in case the probability of H conditional on E is greater than the simple unconditional probability of H [i.e. p(H/E) > p(H)]. Here, I (...) will maintain that while there are aspects of the eliminative approach which Bayesianism must incorporate, as has been argued by John Earman, the eliminativism advocated by Kitcher is unsatisfactory. In addition, I will suggest that Kitcher's reasons for rejecting Bayesian confirmation theory are unconvincing and depend on an overly restrictive version of the position and that indeed Bayesianism has resources needed by an eliminativist account of confirmation. (shrink)

A conceptual analysis of the problem of induction suggests that the difficulty of justifying probabilistic reasoning depends on a mistaken comparison between deductive and inductive inference. Inductive reasoning is accordingly thought to stand in need of special justification because it does not measure up to the standard of conditional absolute certainty guaranteed by deductive validity. When comparison is made, however, it appears that deductive reasoning is subject to a counterpart argument that is just as threatening to the justification (...) of deductive as to inductive inference. Trying to explain induction in such a way that it satisfies a special justificatory requirement in contrast with deduction is therefore not the way to justify induction. An alternative approach is sought in a style of justification developed by Aristotle for the law of noncontradiction and by Kant for the conclusions of transcendental reasoning that with variations can be used to justify both deduction and induction. This strategy upholds a principle when the principle must be presupposed even to raise doubts about the principle's justification. (shrink)

The last couple of decades have witnessed a renewed interest in the notion of inductive risk among philosophers of science. However, while it is possible to find a number of suggestions about the mitigation of inductive risk in the literature, so far these suggestions have been mostly relegated to vague marginal remarks. This paper aims to lay the groundwork for a more systematic discussion of the mitigation of inductive risk. In particular, I consider two approaches to the (...) mitigation of inductive risk—the individualistic approach, which maintains that individual scientists are primarily responsible for the mitigation of inductive risk, and the socialized approach, according to which the responsibility for the mitigation of inductive risk should be more broadly distributed across the scientific community or, even more broadly, across society. I review some of the argument for and against the two approaches and introduce two new problems for the individualistic approach, which I call the problem of precautionary cascades and the problem of exogenous inductive risk, and I argue that a socialized approach might alleviate each of these problems. (shrink)

Inductive probabilistic reasoning is understood as the application of inference patterns that use statistical background information to assign (subjective) probabilities to single events. The simplest such inference pattern is direct inference: from “70% of As are Bs” and “a is an A” infer that a is a B with probability 0.7. Direct inference is generalized by Jeffrey’s rule and the principle of cross-entropy minimization. To adequately formalize inductive probabilistic reasoning is an interesting topic for artificial intelligence, as an (...) autonomous system acting in a complex environment may have to base its actions on a probabilistic model of its environment, and the probabilities needed to form this model can often be obtained by combining statistical background information with particular observations made, i.e., by inductive probabilistic reasoning. In this paper a formal framework for inductive probabilistic reasoning is developed: syntactically it consists of an extension of the language of first-order predicate logic that allows to express statements about both statistical and subjective probabilities. Semantics for this representation language are developed that give rise to two distinct entailment relations: a relation ⊨ that models strict, probabilistically valid, inferences, and a relation that models inductive probabilistic inferences. The inductive entailment relation is obtained by implementing cross-entropy minimization in a preferred model semantics. A main objective of our approach is to ensure that for both entailment relations complete proof systems exist. This is achieved by allowing probability distributions in our semantic models that use non-standard probability values. A number of results are presented that show that in several important aspects the resulting logic behaves just like a logic based on real-valued probabilities alone. (shrink)

Indicators of the reliability of informants are essential for social learning in a society that is initially dominated by ignorance or superstition. Such reliability indicators should be based on meta-induction over records of truth-success. This is the major claim of this paper, and it is supported in two steps. One needs a non-circular justification of the method of meta-induction, as compared to other learning methods. An approach to this problem has been developed in earlier papers and is reported in (...) section 2. It is based on the predictive optimality of meta-inductive learning, under the assumption that objective success records are globally available. The rest of the paper develops an extension of this approach, so-called local meta-induction. Here individuals can access only success records of individuals in their immediate epistemic neighborhood. It is shown that local meta-inductive learning can spread reliable information over the entire population, and has clear advantages compared to success-independent social learning methods such as peer-imitation and authority-imitation.Send article to KindleTo send this article to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle. Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply. Find out more about the Kindle Personal Document Service.META-INDUCTION IN EPISTEMIC NETWORKS AND THE SOCIAL SPREAD OF KNOWLEDGEVolume 9, Issue 2Gerhard SchurzDOI: https://doi.org/10.1017/epi.2012.6Your Kindle email address Please provide your Kindle [email protected]@kindle.com Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Dropbox To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox. META-INDUCTION IN EPISTEMIC NETWORKS AND THE SOCIAL SPREAD OF KNOWLEDGEVolume 9, Issue 2Gerhard SchurzDOI: https://doi.org/10.1017/epi.2012.6Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Google Drive To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive. META-INDUCTION IN EPISTEMIC NETWORKS AND THE SOCIAL SPREAD OF KNOWLEDGEVolume 9, Issue 2Gerhard SchurzDOI: https://doi.org/10.1017/epi.2012.6Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Export citation Request permission. (shrink)