Peter Lipton argues that inference to the best explanation involves the selection of a hypothesis on the basis of its loveliness. I argue that in optimal cases, a form of eliminative induction takes place, which I call ‘Holmesian inference’. I illustrate Holmesian inference by reference to examples from the history of medicine.

In this article I take a loose, functional approach to defining induction: Inductive forms of reasoning include those prima facie reasonable inference patterns that one finds in science and elsewhere that are not clearly deductive. Inductive inference is often taken to be reasoning from the observed to the unobserved. But that is incorrect, since the premises of inductive inferences may themselves be the results of prior inductions. A broader conception of inductive inference regards any ampliative inference as inductive, where an (...) ampliative inference is one where the conclusion ‘goes beyond’ the premises. ‘Goes beyond’ may mean (i) ‘not deducible from’ or (ii) ‘not entailed by’. Both of these are problematic. Regarding (i), some forms of reasoning might have a claim to be called ‘inductive’ because of their role in science, yet turn out to be deductive after all—for example eliminative induction (see below) or Aristotle’s ‘perfect induction’ which is an inference to a generalization from knowledge of every one of its instances. Interpretation (ii) requires that the conclusions of scientific reasoning are always contingent propositions, since necessary propositions are entailed by any premises. But there are good reasons from metaphysics for thinking that many general propositions of scientific interest and known by inductive inference (e.g. “all water is H2O”) are necessarily true. Finally, both (i) and (ii) fail to take account of the fact that there are many ampliative forms of inference one would not want to call inductive, such as counter-induction (exemplified by the ‘gambler’s fallacy’ that the longer a roulette wheel has come up red the more likely it is to come up black on the next roll). Brian Skyrms (1999) provides a useful survey of the issues involved in defining what is meant by ‘inductive argument’. Inductive knowledge will be the outcome of a successful inductive inference. But much discussion of induction concerns the theory of confirmation, which seeks to answer the question, “when and to what degree does evidence support an hypothesis?” Usually, this is understood in an incremental sense and in a way that relates to the rational credibility of a hypothesis: “when and by how much does e add to the credibility of h?”, although ‘confirms’ is sometimes used in an absolute sense to indicate total support that exceeds some suitably high threshold.. (shrink)

Whereas an inference (deductive as well as inductive) is usually viewed as being valid in virtue of its argument form, the present paper argues that scientific reasoning is material inference, i.e., justified in virtue of its content. A material inference is licensed by the empirical content embodied in the concepts contained in the premises and conclusion. Understanding scientific reasoning as material inference has the advantage of combining different aspects of scientific reasoning, such as confirmation, discovery, and explanation. This approach explains (...) why these different aspects (including discovery) can be rational without conforming to formal schemes, and why scientific reasoning is local, i.e., justified only in certain domains and contingent on particular empirical facts. The notion of material inference also fruitfully interacts with accounts of conceptual change and psychological theories of concepts. (shrink)

We present a framework that provides a logic for science by generalizing the notion of logical (Tarskian) consequence. This framework will introduce hierarchies of logical consequences, the first level of each of which is identified with deduction. We argue for identification of the second level of the hierarchies with inductive inference. The notion of induction presented here has some resonance with Popper's notion of scientific discovery by refutation. Our framework rests on the assumption of a restricted class of structures in (...) contrast to the permissibility of classical first-order logic. We make a distinction between deductive and inductive inference via the notions of compactness and weak compactness. Connections with the arithmetical hierarchy and formal learning theory are explored. For the latter, we argue against the identification of inductive inference with the notion of learnable in the limit. Several results highlighting desirable properties of these hierarchies of generalized logical consequence are also presented. (shrink)

Reichenbach held that all scientific inference reduces, via probability calculus, to induction, and he held that induction can be justified. He sees scientific knowledge in a practical context and insists that any rational assessment of actions requires a justification of induction. Gaps remain in his justifying argument; for we can not hope to prove that induction will succeed if success is possible. However, there are good prospects for completing a justification of essentially the kind he sought by showing that while (...) induction may succeed, no alternative is a rational way of trying.Reichenbach's claim that probability calculus, especially via Bayes' Theorem, can help to exhibit the structure of inference to theories is a valuable insight. However, his thesis that the weighting of all hypotheses rests only on frequency data is too restrictive, especially given his scientific realism. Other empirical factors are relevant. Any satisfactory account of scientific inference must be deeply indebted to Reichenbach's foundation work. (shrink)

The Rescorla–Wagner model has been a leading theory of animal causal induction for nearly 30 years, and human causal induction for the past 15 years. Recent theories (especially Psychol. Rev. 104 (1997) 367) have provided alternative explanations of how people draw causal conclusions from covariational data. However, theoretical attempts to compare the Rescorla–Wagner model with more recent models have been hampered by the fact that the Rescorla–Wagner model is an algorithmic theory, while the more recent theories are all computational. This (...) paper provides a detailed derivation of the long-run behavior of the Rescorla– Wagner model under a wide range of parameters and experimental setups, so that the model can be compared with computational theories. It also shows that the model agrees with competing theories on a wider range of cases than had previously been thought. The paper concludes by showing how recently suggested modifications of the Rescorla–Wagner model impact the long-run behavior of the model. (shrink)

Primarily between 1833 and 1840, Whewell attempted to accomplish what natural philosophers and scientists since at least Galileo had failed to do: to provide a systematic and broad-ranged study of the tides and to attempt to establish a general scientific theory of tidal phenomena. In the essay at hand, I document the close interaction between Whewell’s philosophy of science (especially his methodological views) and his scientific practice as a tidologist. I claim that the intertwinement between Whewell’s methodology and his tidology (...) is more fundamental than has hitherto been documented. (shrink)

In this essay, my aim is twofold: to clarify how the late Mill conceived of the certainty of inductive generalizations and to offer a systematic clarification of the limited domain of application of the Mill’s Canons of Induction. I shall argue that Mill’s views on the certainty of knowledge changed overtime and that this change was accompanied by a new view on the certainty of the inductive results yielded by the Canons of Induction. The key message of the later editions (...) of The System of Logic as conceived by the late Mill was no longer that by the Canons of Induction we can establish scientific certainty and true causes, but rather that the Canons are useful in establishing causal laws in a provisional way. (shrink)

Finland is internationally known as one of the leading centers of twentieth century analytic philosophy. This volume offers for the first time an overall survey of the Finnish analytic school. The rise of this trend is illustrated by original articles of Edward Westermarck, Eino Kaila, Georg Henrik von Wright, and Jaakko Hintikka. Contributions of Finnish philosophers are then systematically discussed in the fields of logic, philosophy of language, philosophy of science, history of philosophy, ethics and social philosophy. Metaphilosophical reflections on (...) the nature of philosophy are highlighted by the Finnish dialogue between analytic philosophy, phenomenology, pragmatism, and critical theory. (shrink)

One of the first to criticize the verifiability theory of meaning embraced by logical empiricists, Reichenbach ties the significance of scientific statements to their predictive character, which offers the condition for their testability. While identifying prediction as the task of scientific knowledge, Reichenbach assigns induction a pivotal role, and regards the theory of knowledge as a theory of prediction based on induction. Reichenbach’s inductivism is grounded on the frequency notion of probability, of which he prompts a more flexible version than (...) that of Richard von Mises. Unlike von Mises, Reichenbach attempts to account for single case probabilities, and entertains a restricted notion of randomness, more suitable for practical purposes. Moreover, Reichenbach developed a theory of induction, absent from von Mises’s perspective, and argued for the justification of induction. This article outlines the main traits of Reichenbach’s inductivism, with special reference to his book Experience and prediction. (shrink)

Since Hume, philosophers of induction have debated the question of whether we have any reason for assuming that nature is uniform. This debate has always presumed that the uniformity hypothesis is itself coherent. In Part 1 of the following I argue that a proper appreciation of Nelson Goodman's so-called grue-green problem1 should lead us to the conclusion that the uniformity hypothesis, under its usual interpretation as a strictly ontological thesis, is incoherent. In Part 2 I argue that further consideration of (...) the grue-green problem leads to the conclusion that certain popular versions of the thesis of physical supervenience/the primacy of physics, under their usual interpretation as strictly ontological theses, are false. In Part 3 I argue that the notions of natural kinds and nature's joints should not be taken as ontologically objective notions but as interest relative. Together Parts 1, 2, and 3 provide support for the Nietzsche-Goodman thesis that philosophers are prone to mistakenly identify as absolute, mind and language independent, features of the world which are in fact only features of a particular discourse, or of the world relative to a particular discourse. (shrink)

In his new foreword to this edition, Hilary Putnam forcefully rejects these nativist claims.

I argue that Goodman's puzzle of grue at least poses no real challenge about inductive inference. By drawing on Stove's characterisation of Hume's characterisation of inductive inference, we see that the premises in an inductive inference report experienced impressions; and Goodman can be interpreted as posing a real challenge about inductive inference only if we treat an epistemic subject's observations more as logical contents and less as experienced impressions. So, even though the grue puzzle was effective against its stated logicist (...) targets, it is not thereby an enduring difficulty regarding experience's ability to impart epistemic justification via inductive evidence. (shrink)

Earlier in this volume, Wesley Salmon has given a characteristically clear and trenchant critique of the account of non-demonstrative reasoning known by the slogan `Inference to the Best Explanation'. As a long-time fan of the idea that explanatory considerations are a guide to inference, I was delighted by the suggestion that Wes and I might work together on a discussion of the issues. In the event, this project has exceeded my high expectations, for in addition to the intellectual gain that (...) comes from the careful study of his essay, I have benefited enormously from the stream of illuminating emails and faxes that Wes has sent me during our collaboration. Doing philosophy together has been an education and a pleasure. Salmon's essay would place Inference to the Best Explanation beyond the pale of acceptable philosophical accounts of inference. According to Salmon, Inference to the Best Explanation has serious internal difficulties and compares very unfavourably with Bayesian approaches to these matters. My aim in the following remarks is irenic. I hope to show that a number of the claimed difficulties either are not really difficulties or are avoidable. In some cases, the avoidance will require a mild reinterpretation of the account that lies behind the slogan `Inference to the Best Explanation'; in others, it will require admitting limits to the scope of the account. For I accept at the outset that Inference to the Best Explanation cannot possibly be the whole story about the assessment of scientific hypotheses. For me, the interesting idea is simply that we sometimes decide how likely a hypothesis is to be correct in part by considering how good an explanation it would provide, if it were correct. This is the idea of explanatory considerations providing a guide to inference, and this is the idea that I will here promote. (shrink)

From a reliabilist point of view, our inferential practices make us into instruments for determining the truth value of hypotheses where, like all instruments, reliability is a central virtue. I apply this perspective to second-order inductions, the inductive assessments of inductive practices. Such assessments are extremely common, for example whenever we test the reliability of our instruments or our informants. Nevertheless, the inductive assessment of induction has had a bad name ever since David Hume maintained that any attempt to justify (...) induction by means of an inductive argument must beg the question. I will consider how the inductive justification of induction fares from the reliabilist point of view. I will also consider two other wellknown arguments that can be construed as inductive assessments of induction. One is the miracle argument, according to which the truth of scientific theories should be inferred as the best explanation of their predictive success; the other is the disaster argument, according to which we should infer that all present and future theories are false on the grounds that all past theories have been found to be false. (shrink)

The problem of underdetermination is thought to hold important lessons for philosophy of science. Yet, as Kyle Stanford has recently argued, typical treatments of it offer only restatements of familiar philosophical problems. Following suggestions in Duhem and Sklar, Stanford calls for a New Induction from the history of science. It will provide proof, he thinks, of “the kind of underdetermination that the history of science reveals to be a distinctive and genuine threat to even our best scientific theories” (Stanford 2001, (...) p. S12). This paper examines Stanford’s New Induction and argues that it – like the other forms of underdetermination that he criticizes – merely recapitulates familiar philosophical conundra. (shrink)

In 1958, to refute the argument known as the theoretician's dilemma, Hempel suggested that theoretical terms might be logically indispensable for inductive systematization of observational statements. This thesis, in some form or another, has later been supported by Scheffler, Lehrer, and Tuomela, and opposed by Bohnert, Hooker, Stegmüller, and Cornman. In this paper, a critical survey of this discussion is given. Several different putative definitions of the crucial notion inductive systematization achieved by a theory are discussed by reference to the (...) properties of inductive inference. The consequences of the following differences between deductive and inductive inference are emphasized: the lack of simple transitivity properties (even in a modified sense) of inductive inference, and the failure of the inductive analogue of the converse of The Deduction Theorem. The main conclusions are: (i) Hempel's original thesis may very well be right but his argument for it is unsatisfactory, (ii) theoretical terms can be logically indispensable for a non-Hempelian kind of inductive systematization, relative to both Craigian and Ramseyan elimination, (iii) Lehrer's attempt to prove the indispensability of theoretical terms for inductive-probabilistic systematization is, as a modification of Hempelian kind of inductive-deterministic systematization, unsatisfactory, and (iv) there does not seem to be much hope of escaping the conclusion (ii), if it is true, by extending the Craigian replacement programme along the lines suggested by Cornman. (shrink)

For several years, through the “material theory of induction,” I have urged that inductive inferences are not licensed by universal schemas, but by material facts that hold only locally (Norton, 2003, 2005). My goal has been to defend inductive inference against inductive skeptics by demonstrating when and how inductive inferences are properly made. Since I have always admired Peter Achinstein as a staunch defender of induction, it was a surprise when Peter..

Bayesian probabilistic explication of inductive inference conflates neutrality of supporting evidence for some hypothesis H (“not supporting H”) with disfavoring evidence (“supporting not-H”). This expressive inadequacy leads to spurious results that are artifacts of a poor choice of inductive logic. I illustrate how such artifacts have arisen in simple inductive inferences in cosmology. In the inductive disjunctive fallacy, neutral support for many possibilities is spuriously converted into strong support for their disjunction. The Bayesian “doomsday argument” is shown to rely entirely (...) on a similar artifact, for the result disappears in a reanalysis that employs fragments of inductive logic able to represent evidential neutrality. Finally, the mere supposition of a multiverse is not yet enough to warrant the introduction of probabilities without some factual analog of a randomizer over the multiverses. (shrink)

My purpose in this chapter is to survey some of the principal approaches to inductive inference in the philosophy of science literature. My first concern will be the general principles that underlie the many accounts of induction in this literature. When these accounts are considered in isolation, as is more commonly the case, it is easy to overlook that virtually all accounts depend on one of very few basic principles and that the proliferation of accounts can be understood as efforts (...) to ameliorate the weaknesses of those few principles. In the earlier sections, I will lay out three inductive principles and the families of accounts of induction they engender. In later sections I will review standard problems in the philosophical literature that have supported some pessimism about induction and suggest that their import has been greatly overrated. In the final sections I will return to the proliferation of accounts of induction that frustrates efforts at a final codification. I will suggest that this proliferation appears troublesome only as long as we expect inductive inference to be subsumed under a single formal theory. If we adopt a material theory of induction in which individual inductions are licensed by particular facts that prevail only in local domains, then the proliferation is expected and not problematic. (shrink)

A model of inductive inquiry is defined within the context of first-order logic. The model conceives of inquiry as a game between Nature and a scientist. To begin the game, a nonlogical vocabulary is agreed upon by the two players, along with a partition of a class of countable structures for that vocabulary. Next, Nature secretly chooses one structure ("the real world") from some cell of the partition. She then presents the scientist with a sequence of facts about the chosen (...) structure. With each new datum the scientist announces a guess about the cell to which the chosen structure belongs. To succeed in his or her inquiry, the scientist’s successive conjectures must be correct all but Hnitely often, that is, the conjectures must converge in the limit to the correct ceH. Different kinds of scientists can be investigated within this framework. At opposite ends of the spectrum are dumb scientists that rely on the strategy of "induction by enumeration," and smart scientists that rely on an operator of belief revision. We report some results about the scope and limits of these two inductive strategies. (shrink)

This paper studies the use of hypotheses schemes in generatinginductive predictions. After discussing Carnap–Hintikka inductive logic,hypotheses schemes are defined and illustrated with two partitions. Onepartition results in the Carnapian continuum of inductive methods, the otherresults in predictions typical for hasty generalization. Following theseexamples I argue that choosing a partition comes down to making inductiveassumptions on patterns in the data, and that by choosing appropriately anyinductive assumption can be made. Further considerations on partitions makeclear that they do not suggest any solution (...) to the problem of induction.Hypotheses schemes provide the tools for making inductive assumptions, but theyalso reveal the need for such assumptions. (shrink)

While standard procedures of causal reasoning as procedures analyzing causal Bayesian networks are custom-built for (non-deterministic) probabilistic structures, this paper introduces a Boolean procedure that uncovers deterministic causal structures. Contrary to existing Boolean methodologies, the procedure advanced here successfully analyzes structures of arbitrary complexity. It roughly involves three parts: first, deterministic dependencies are identified in the data; second, these dependencies are suitably minimalized in order to eliminate redundancies; and third, one or—in case of ambiguities—more than one causal structure is assigned (...) to the minimalized deterministic dependencies. (shrink)

The problem of induction is sometimes motivated via a comparison between rules of induction and rules of deduction. Valid deductive rules are necessarily truth preserving, while inductive rules are not.

The objectivity of Bayesian induction relies on the ability of evidence to produce a convergence to agreement among agents who initially disagree about the plausibilities of hypotheses. I will describe three sorts of Bayesian convergence. The first reduces the objectivity of inductions about simple "occurrent events" to the objectivity of posterior probabilities for theoretical hypotheses. The second reveals that evidence will generally induce converge to agreement among agents on the posterior probabilities of theories only if the convergence is 0 or (...) 1. The third establishes conditions under which evidence will very probably compel posterior probabilities of theories to converge to 0 or 1. (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)

Even though evidence underdetermines theory, often in science one theory only is regarded as acceptable in the light of the evidence. This suggests there are additional unacknowledged assumptions which constrain what theories are to be accepted. In the case of physics, these additional assumptions are metaphysical theses concerning the comprehensibility and knowability of the universe. Rigour demands that these implicit assumptions be made explicit within science, so that they can be critically assessed and, we may hope improved. This leads to (...) a new conception of science, one which we need to adopt in order to solve the problem of induction. (shrink)

J. Richard Gott III (1993) has used the “Copernican principle” to derive a probability density function for the total longevity of any phenomenon, based solely on the phenomenon’s past longevity. John Leslie (1996) and others have used an apparently similar probabilistic argument, the “Doomsday Argument,” to claim that conventional predictions of longevity must be adjusted, based on Bayes’ Theorem, in favor of shorter longevities. Here I show that Gott’s arguments are flawed and contradictory, but that one of his conclusions—his delta (...) t formula—is mathematically equivalent to Laplace’s famous (and notorious) ‘rule of succession’; moreover, Gott’s delta t formula is a plausible worst-case (if one favors greater longevity) bound in some contexts. On the other hand, the Doomsday Argument is fallacious: the argument’s Bayesian formalism is stated in terms of total duration, but all attempted real-life applications of the argument—with one exception, an application by Gott 1994—actually plug in prior probabilities for future duration; moreover, the Self-Sampling Assumption, an essential premise of the Doomsday Argument, is contradicted by the prior information in all known real-life cases. But rejecting the Doomsday Argument does not entail rejecting the possibility of learning about the future from the past. Applying the work of Bruce M. Hill (1968, 1988, 1993) and Frank P.A. Coolen (1998, 2006) in the field of non-parametric predictive inference, I propose and defend an alternative methodology for quantifying how past longevity of any phenomenon does provide evidence for future longevity. In so doing, I identify an objective standard by which to choose among counting time intervals, counting population, or counting any other measure of past longevity in predicting future longevity. This methodology forms the basis of a calculus of induction. (shrink)

Gott ( 1993 ) has used the ‘Copernican principle’ to derive a probability distribution for the total longevity of any phenomenon, based solely on the phenomenon’s past longevity. Leslie ( 1996 ) and others have used an apparently similar probabilistic argument, the ‘Doomsday Argument’, to claim that conventional predictions of longevity must be adjusted, based on Bayes’s Theorem, in favor of shorter longevities. Here I show that Gott’s arguments are flawed and contradictory, but that one of his conclusions is plausible (...) and mathematically equivalent to Laplace’s famous—and notorious—‘rule of succession’. On the other hand, the Doomsday Argument, though it appears consistent with some common‐sense grains of truth, is fallacious; the argument’s key error is to conflate future longevity and total longevity. Applying the work of Hill ( 1968 ) and Coolen ( 1998 , 2006 ) in the field of nonparametric predictive inference, I propose an alternative argument for quantifying how past longevity of a phenomenon does provide evidence for future longevity. In so doing, I identify an objective standard by which to choose among counting time intervals, counting population, or counting any other measure of past longevity in predicting future longevity. *Received May 2007; revised October 2008. †To contact the author, please e‐mail: pos@ronpisaturo.com. (shrink)

Hilary Kornblith (1993) has recently offered a reliabilist defense of the use of the Law of Small Numbers in inductive inference. In this paper I argue that Kornblith's defense of this inferential rule fails for a number of reasons. First, I argue that the sort of inferences that Kornblith seeks to justify are not really inductive inferences based on small samples. Instead, they are knowledge-based deductive inferences. Second, I address Kornblith's attempt to find support in the work of Dorrit Billman (...) and I try to show that close attention to the workings of her computational model reveals that it does not support Kornblith's argument. While the knowledge required to ground the inferences in question is perhaps inductively derived, Billman's work does not support the notion that small samples provide a reliable basis for our generalizing inferences. (shrink)

Many people argue that history makes a special difference to the subjects of biology and psychology, and that history does not make this special difference to other parts of the world. This paper will show that historical properties make no more or less of a difference to biology or psychology than to chemistry, physics, or other sciences. Although historical properties indeed make a certain kind of difference to biology and psychology, this paper will show that historical properties make the same (...) kind of difference to geology, sociology, astronomy, and other sciences. Similarly, many people argue that nonhistorical properties make a special difference to the nonbiological and the nonpsychological world. This paper will show that nonhistorical properties make the same difference to all things in the world when it comes to their causal behavior and that historical properties make the same difference to all things in the world when it comes to their distributions. Although history is special, it is special in the same way to all parts of the world. (shrink)

Watkins proposes a neo-Popperian solution to the pragmatic problem of induction. He asserts that evidence can be used non-Inductively to prefer the principle that corroboration is more successful over all human history than that, Say, Counter-Corroboration is more successful either over this same period or in the future. Watkins's argument for rejecting the first counter-Corroborationist alternative is beside the point, However, As whatever is the best strategy over all human history is irrelevant to the pragmatic problem of induction since we (...) are not required to act in the past, And his argument for rejecting the second presupposes induction. (shrink)

Abstract In Peirce's and Hanson's characterization of abductive inference, the abducted hypothesis (but not others) is present in the premises, so that the inference can hardly be taken as ampliative. Abduction has consequently been treated as part of the process whereby already generated hypotheses are judged in terms of their plausibility, simplicity, etc. I propose an interpretation of abduction which supports an ampliative view. It relies on a distinction between two logical stages in the generation of hypotheses, one ?factual? and (...) one ?explanatory?. I also indicate how we may reconstruct Peirce's and Hanson's original inference in an ampliative form. (shrink)

An original study of the philosophical problems associated with inductive reasoning. Like most of the main questions in epistemology, the classical problem of induction arises from doubts about a mode of inference used to justify some of our most familiar and pervasive beliefs. The experience of each individual is limited and fragmentary, yet the scope of our beliefs is much wider; and it is the relation between belief and experience, in particular the belief that the future will in some respects (...) resemble the past and the unobserved the observed, which forms the subject of this book. Dr Blackburn's first aim is to state the problem of induction properly, to show that there does exist a genuine problem immune to the solutions in vogue at present, yet no tin principle insoluble. He gives an extended and original account of the concept of a reason and goes on to discuss prediction. In the end Dr Blackburn produces a rationale for belief in certain short-term predictions based on his reinterpretation of the classical principle of indifference. He claims that a justification for induction can be found along the lines he has suggested and must indeed be found there if anywhere. (shrink)

Four experiments investigated how people judge the plausibility of category-based arguments, focusing on the diversity effect, in which arguments with diverse premise categories are considered particularly strong. In Experiment 1 we show that priming people as to the nature of the blank property determines whether sensitivity to diversity is observed. In Experiment 2 we find that people's hypotheses about the nature of the blank property predict judgements of argument strength. In Experiment 3 we examine the effect of our priming methodology (...) on people's tendency to bring knowledge about causality or similarity to bear when evaluating arguments, and in Experiment 4 we show that whether people's hypotheses about the nature of the blank property were causal predicted ratings of argument strength. Together these results suggest that diversity effects occur because diverse premises lead people to bring general features of the premise categories to mind. Although our findings are broadly consistent with Bayesian and Relevance-based approaches to category-based inductive reasoning, neither approach captures all of our findings. (shrink)

This paper discusses the possibility of modelling inductive inference (Gold 1967) in dynamic epistemic logic (see e.g. van Ditmarsch et al. 2007). The general purpose is to propose a semantic basis for designing a modal logic for learning in the limit. First, we analyze a variety of epistemological notions involved in identification in the limit and match it with traditional epistemic and doxastic logic approaches. Then, we provide a comparison of learning by erasing (Lange et al. 1996) and iterated epistemic (...) update (Baltag and Moss 2004) as analyzed in dynamic epistemic logic. We show that finite identification can be modelled in dynamic epistemic logic, and that the elimination process of learning by erasing can be seen as iterated belief-revision modelled in dynamic doxastic logic. Finally, we propose viewing hypothesis spaces as temporal frames and discuss possible advantages of that perspective. (shrink)

We postulate the Testing Principle : that individuals ''act like statisticians'' when they face uncertainty in a decision problem, ranking alternatives to the extent that available evidence allows. The Testing Principle implies that completeness of preferences, rather than the sure-thing principle , is violated in the Ellsberg Paradox. In the experiment, subjects chose between risky and uncertain acts in modified Ellsberg-type urn problems, with sample information about the uncertain urn. Our results show, consistent with the Testing Principle, that the uncertain (...) urn is chosen more often when the sample size is larger, holding constant a measure of ambiguity (proportion of balls of unknown colour in the urn). The Testing Principle rationalises the Ellsberg Paradox. Behaviour consistent with the principle leads to a reduction in Ellsberg-type violations as the statistical quality of sample information is improved, holding ambiguity constant. The Testing Principle also provides a normative rationale for the Ellsberg paradox that is consistent with procedural rationality. (shrink)

Naive deductivist accounts of confirmation have the undesirable consequence that if E confirms H, then E also confirms the conjunction H·X, for any X—even if X is completely irrelevant to E and H. Bayesian accounts of confirmation may appear to have the same problem. In a recent article in this journal Fitelson (2002) argued that existing Bayesian attempts to resolve of this problem are inadequate in several important respects. Fitelson then proposes a new‐and‐improved Bayesian account that overcomes the problem of (...) irrelevant conjunction, and does so in a more general setting than past attempts. We will show how to simplify and improve upon Fitelson's solution. (shrink)

It is widely recognized that computational theories of learning must posit the existence of a priori constraints on hypothesis selection. The present article surveys the theoretical options available for modelling the dynamic process whereby the constraints have their effect. According to the 'simplicity' theory (exemplified by Fodor's treatment), hypotheses are preference-ordered in terms of their syntactic or semantic properties. It is argued that the same explanatory power can be obtained with a weaker (hence better) theory, the 'minimalist' theory, which dispenses (...) with the preference ordering. According to the 'finitistic' theory, the learner is capable of generating only finitely many hypotheses for evaluation. Chomsky maintains that the occurrence of errorless learning in language acquisition necessitates a finististic explanation. Once again, there is a weaker theory that explains the same data. Finally, Goodman's argument to the effect that there cannot be a computational theory of learning is examined and rejected. (shrink)

Inductive reasoning is a fundamental and complex aspect of human intelligence. In particular, how do subjects, given a set of particular examples, generate general descriptions of the rules governing that set? We present a biologically plausible method for accomplishing this task and implement it in a spiking neuron model. We demonstrate the success of this model by applying it to the problem domain of Raven's Progressive Matrices, a widely used tool in the field of intelligence testing. The model is able (...) to generate the rules necessary to correctly solve Raven's items, as well as recreate many of the experimental effects observed in human subjects. (shrink)

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)

An important debate in the reasoning literature concerns the extent to which inference processes are domain-free or domain-specific. Typically, evidence in support of the domain-specific position comprises the facilitation observed when abstract reasoning tasks are set in realistic context. Three experiments are reported here in which the sources of facilitation were investigated for contextualised versions of Raven's Progressive Matrices (Richardson, 1991) and non-verbal analogies from the AH4 test (Richardson & Webster, 1996). Experiment 1 confirmed that the facilitation observed for the (...) contextualised matrices was in part due to extraneous aspects of commentaries originally intended to activate domainspecific processes. Experiments 2 and 3 indicated that the remainder of the facilitation for the matrices, and all of the facilitation for the analogies, could be explained by visual salience: Converting the item elements into realistic objects had enabled them and their transitions to be identified more easily. Hence, performance at simplified abstract items was as good as, or better than, at contextualised items. It is concluded that facilitation effects cannot be interpreted as showing that domain-specific processes constitute a self-contained system separate from domain-free processes. In turn, this means that domain-free processes cannot be dismissed as being unimportant for reasoning. (shrink)

This paper argues that chance (risk or opportunity) discovery is challenging, from a reasoning point of view, because it represents a dilemma for inductive reasoning. Chance discovery shares many features with the grue paradox. Consequently, Bayesian approaches represent a potential solution. The Bayesian solution evaluates alternative models generated using a temporal logic planner to manage the chance. Surprise indices are used in monitoring the conformity of the real world and the assessed probabilities. Game theoretic approaches are proposed to deal with (...) multi-agent interaction in chance management. (shrink)

It is notoriously difficult to spell out the norms of inductive reasoning in a neat set of rules. I explore the idea that explanatory considerations are the key to sorting out the good inductive inferences from the bad. After defending the crucial explanatory virtue of stability, I apply this approach to a range of inductive inferences, puzzles, and principles such as the Raven and Grue problems, and the significance of varied data and random sampling.

Inferential internalism holds that for one to be inferentially justified in believing P on the basis of E one must be justified in believing that E makes probable P. Inferential internalism has long been accused of generating a vicious regress on inferential justification that has drastic skeptical consequences. However, recently Hookway and Rhoda have defended a more modest form of internalism that avoids this problem. They propose a form of weak inferential internalism according to which internalist conditions are restricted to (...) only certain kinds of inferential justification. In this paper, I clarify and argue against weak internalism. I contend that while weak internalism avoids the vicious regress, it does so at the cost of compromising its internalist credentials. For I show that unless weak internalism makes an arbitrary distinction between individuals who believe for the very same reasons, the view collapses into externalism. (shrink)

In “Weak Inferential Internalism” I defended the frequently voiced criticism that any internalist account of inferential justification generates a vicious regress. My defense involved criticizing a recent form of internalism, “Weak Inferential Internalism” (WII) defended by Hookway and Rhoda. I argued that while WII does not generate a vicious regress, the position is only distinguishable from externalism insofar as it makes an arbitrary distinction between individuals who believe for the very same reason. Either way, WII is not a defensible internalist (...) account of inferential justification. In his “In Defense of Weak Inferential Internalism,” Rhoda has responded to my dilemma argument. He argues that it is mistaken to assume that WII must be incompatible with externalism, and that contrary to my claims, WII is distinguishable from externalism in several ways. In this reply, I explain why none of Rhoda’s replies suggest that there is a defensible internalist account of inferential justification. (shrink)

This paper analyzes the epistemological significance of the problem of induction. In the first section, the foundation of this problem is identified in the thesis of gnoseological dualism: we only know our representations as separate from ‘the world itself’. This thesis will be countered by the thesis of gnoseological monism. In the second section, the implications of Hume’s skeptical thesis will be highlighted and it will be demonstrated how the point of view of gnoseological monism can offer a way out (...) that I call the hermeneutic theory of induction. In the third section, a formal approach is proposed in agreement with this theory. Using tools of the theory of information, this defines the conditions of acceptance or refusal of a hypothesis starting with an experiment. In the fourth section, the epistemological consequences of this approach are analyzed. (shrink)

Watkins proposes a neo-Popperian solution to the pragmatic problem of induction. He asserts that evidence can be used non-Inductively to prefer the principle that corroboration is more successful over all human history than that, Say, Counter-Corroboration is more successful either over this same period or in the future. Watkins's argument for rejecting the first counter-Corroborationist alternative is beside the point, However, As whatever is the best strategy over all human history is irrelevant to the pragmatic problem of induction since we (...) are not required to act in the past, And his argument for rejecting the second presupposes induction. (shrink)

In 1955, Goodman set out to 'dissolve' the problem of induction, that is, to argue that the old problem of induction is a mere pseudoproblem not worthy of serious philosophical attention. I will argue that, under naturalistic views of the reflective equilibrium method, it cannot provide a basis for a dissolution of the problem of induction. This is because naturalized reflective equilibrium is -- in a way to be explained -- itself an inductive method, and thus renders Goodman's dissolution viciously (...) circular. This paper, then, examines how the old problem of induction crept back in while nobody was looking. (shrink)

In this paper I offer a straight solution to Hume's problem of induction by defusing the assumptions on which it is based. I argue that Hume's problem only arises if we accept (i) that there is no necessity but logical necessity, or (ii) that it is unreasonable to believe that there is any form of necessity in addition to logical necessity. I show that Hume's arguments in favour of (i) and (ii) are unsound. I then offer a suggestion as to (...) how the weakness of his arguments has escaped detection. Finally, having claimed that there remains a surmountable problem with inductive arguments, I end by characterising that problem and a possible approach to its solution. (shrink)

No one doubts that philosophers have discussed at length ‘the problem of induction’, but it would also be generally recognized that there would be disagreement as to precisely what that problem is. Rather than tackle the formulation problem, I will borrow from a popular text: Our existence as well as science itself is based on the principle of induction that tells us to reason from past frequencies to future likelihoods, from the limited known of the past and present to the (...) unknown of the past, present, and future ... But though inductive probability is psychologically inescapable, we have trouble providing a rational justification for it. We might say, then, that there is such a practice as induction, and a problem associated with it is that of justifying engaging in it. We engage in reasoning from things we know about the past and present to conclusions about the past, present and future. We can't resist doing this but we have trouble finding a rational justification for doing so. This problem suggests a generalization. We engage in reasoning, reaching new conclusions. It would be hard to resist engaging in this practice. How do we provide a rational justification for it? (shrink)

Of knowledge and probability: a quick tour of part 3, book 1. Of knowledge ; Of probability; and of the idea of cause and effect ; Why a cause is always necessary? ; Of the component parts of our reasonings concerning causes and effects ; Of the impressions of the senses and memory ; Of the inference from the impression to the idea ; Of the nature of the idea, or belief ; Of the causes of belief ; Of the (...) effects of other relations, and other habits ; Of the influence of belief ; Of the probability of chances ; Of the probability of causes ; Of unphilosophical probability ; Of the idea of necessary connexion ; Rules by which to judge of causes and effects ; Of the reason of animals -- Hume on unphilosophical probabilities -- Hume's skepticism with regard to reason -- Of skepticism with regard to the senses -- Of the ancient and modern philosophy -- The soul and the self -- The conclusion of book 1 -- Two openings and two closings. (shrink)

This paper responds to a claim by Christopher Hookway, that Fumerton’s Principle of Inferential Justification (PIJ) is a platitude, and that skeptical arguments that deploy it depend essentially on a substantive thesis about the nature of epistemic kinds. This paper argues that, contrary to Hookway, the thesis about epistemic kinds is not necessary to generate skeptical results, and PIJ is sufficient to do so.

The problem of induction is sometimes motivated via a comparison between rules of induction and rules of deduction. Valid deductive rules are necessarily truth preserving, while inductive rules are not.

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

In a recent paper replying to the inductive sceptic, Samir Okasha says that the Humean argument for inductive scepticism depends on mistakenly construing inductive reasoning as based on a principle of the uniformity of nature. I dispute Okasha's argument that we are entitled to the background beliefs on which (he says) inductive reasoning depends. Furthermore, I argue that the sorts of theoretically impoverished contexts to which a uniformity-of-nature principle has traditionally been restricted are exactly the contexts relevant to the inductive (...) sceptic's argument, and (pace Okasha) are not at all remote from actual scientific practice. I discuss several scientific examples involving such contexts. (shrink)

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

Bacon’s project suggests in theory that the obtaining of absolute certain knowledge is possible but in fact such knowledge is revealed to be impossible. Th e description of the human mind on which Bacon’s account is based seems to imply that the impossibility of obtaining absolute certainty does not depend on the contingent historical situation of a preliminary stage of the scientifi c endeavor. Consequently, a gap emerges between the proposed goal of science and the ways to reach it: Bacon (...) tried to obtain absolute certainty but he only could arrive at degrees of certainty and probability both in theories and in facts. Malgrè lui, Bacon shows himself developing in fact a kind of probabilistic science instead of surpassing the limits to knowledge posed by the skeptical arguments. Th at is the reason why many of his followers could develop a mitigated skepticism in the framework of a Baconian science. (shrink)

The overall aim of this thesis is to understand Hume’s famous argument concerning induction, and to appraise its success in establishing its conclusion. The thesis accordingly falls into two main parts, the first being concerned with analysis and interpretation of the argument itself, and the second with investigation of possible responses to it. Naturally the argument’s interpretation strongly constrains the range of possible replies, and indeed the results of Part I indicate that the only kind of strategy which stands much (...) prospect of defeating Hume’s argument is one based on a priori probabilistic reasoning – hence the overwhelming majority of Part II is devoted to a thorough investigation of this approach. (shrink)

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