Lange offers an argument that, according to him, “does not show merely that some proofs by mathematical induction are not explanatory. It shows that none are […]”. The aim here is to present a counterexample to his argument.

In this paper, I argue that there are cases of explanatory induction in mathematics. To do so, I first introduce the notion of explanatory definition in the context of mathematical explanation. A large part of the paper is dedicated to introducing and analyzing this notion of explanatory definition and the role it plays in mathematics. After doing so, I discuss a particular inductive definition in advanced mathematics—CW\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${ CW}$$\end{document}-complexes—and (...) argue that it is explanatory. With this, we see that there are cases of explanatory induction. (shrink)

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

This paper considers how explanatory factors can play a role in our ampliative inferential practices. Van Fraassen has argued that there is no possible rational rule that governs ampliative inferences and includes weightings for explanatory beauty. In opposition to van Fraassen, Douven has argued that ampliative inferential rules that include weightings for explanatory factors can be rationally followed. There is, however, a crucial difficulty with Douven's approach: applying the ampliative rule that he suggests leads into irrational belief (...) states. A way to remove the difficulties with Douven's account is suggested. The implications of rationally including explanatory factors in ampliative inferences are then considered. Introduction The proposed interpretations Van Fraassen's justification of the Bayesian approach A rational non-Bayesian interpretation? Further restrictions on D(A,B) Conclusion. (shrink)

Statements that share an explanation tend to lend inductive support to one another. For example, being told that Many furniture movers have a hard time financing a house increases the judged probability that Secretaries have a hard time financing a house. In contrast, statements with different explanations reduce one another s judged probability. Being told that Many furniture movers have bad backs decreases the judged probability that Secretaries have bad backs. I pose two questions concerning such discounting effects. First, does (...) the reduction depend on explanations being mutually incompatible or does it occur when explanations are deemed irrelevant to one another? I found that a small discounting effect occurred with statements that were blatantly unrelated. However, the discounting effect also depended on a factor external to the argument being judged; the composition of the argument set. Second, are explanation effects attributable to changes in the belief afforded statements or to response-specific changes resulting from misunderstanding of the probability rating task or response bias? The results implicate changes in belief. Prior belief influenced conditional probability more than argument strength judgements, as it would if participants understood the tasks in the same way as the experimenter. Also, conditional probability true and false judgements were complementary, suggesting no response bias. (shrink)

Philosophers who regard some mathematical proofs as explaining why theorems hold, and others as merely proving that they do hold, disagree sharply about the explanatory value of proofs by mathematical induction. I offer an argument that aims to resolve this conflict of intuitions without making any controversial presuppositions about what mathematical explanations would be.

The essay deals with problems that emerge in new interpretations of Hume’s famous argument concerning induction. In modern Hume scholarship there is a growing tendency to view Hume’s argument not as reasoning concerning the evidential value of our inductions but rather as a kind of explanation of the cognitive process of making causal inferences. The essay describes the main tenets of two currently dominant interpretations . In addition to discussing both interpretations, the article engages in a discussion about the (...) meaning of Hume’s argument by confronting the old skeptical reading of Hume with new interpretations. My contribution to the discussion consists of two arguments against the explanatory tradition of viewing Hume’s argument. (shrink)

Marc Lange argues that proofs by mathematical induction are generally not explanatory because inductive explanation is irreparably circular. He supports this circularity claim by presenting two putative inductive explanantia that are one another’s explananda. On pain of circularity, at most one of this pair may be a true explanation. But because there are no relevant differences between the two explanantia on offer, neither has the explanatory high ground. Thus, neither is an explanation. I argue that there is (...) no important asymmetry between the two cases because they are two presentations of the same explanation. The circularity argument requires a problematic notion of identity of proofs. I argue for a criterion of proof individuation that identifies the two proofs Lange offers. This criterion can be expressed in two equivalent ways: one uses the language of homotopy type theory, and the second assigns algebraic representatives to proofs. Though I will concentrate on one example, a criterion of proof identity has much broader consequences: any investigation into mathematical practice must make use of some proof-individuation principle. (shrink)

The Minimum Description Length principle is the modernformalisation of Occam's razor. It has been extensively and successfullyused in machine learning, especially for noisy and long sources ofdata. However, the MDL principle presents some paradoxes andinconveniences. After discussing all these, we address two of the mostrelevant: lack of explanation and lack of creativity. We present newalternatives to address these problems. The first one, intensionalcomplexity, avoids extensional parts in a description, so distributingcompression ratio in a more even way than the MDL principle. (...) The secondone, information gain, forces that the hypothesis is informative wrt. the evidence, so giving a formaldefinition of what is to discover. (shrink)

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

The Problem of Old Evidence is a perennial issue for Bayesian confirmation theory. Garber famously argues that the problem can be solved by conditionalizing on the proposition that a hypothesis deductively implies the existence of the old evidence. In recent work, Hartmann and Fitelson :712–717, 2015) and Sprenger :383–401, 2015) aim for similar, but more general, solutions to the Problem of Old Evidence. These solutions are more general because they allow the explanatory relationship between a new hypothesis and old (...) evidence to be inductive, rather than deductive. In this paper, I argue that these solutions are either unsound or under-motivated, depending on the case of inductive explanation that we have in mind. This lends support to the broader claim that Garber–Style Bayesian confirmation cannot capture the sense in which new hypotheses that do not deductively imply old evidence nevertheless seem to be confirmed via old evidence. (shrink)

The Problem of Old Evidence is a perennial issue for Bayesian confirmation theory. Garber (Test Sci Theor 10:99–131, 1983) famously argues that the problem can be solved by conditionalizing on the proposition that a hypothesis deductively implies the existence of the old evidence. In recent work, Hartmann and Fitelson (Philos Sci 82(4):712–717, 2015) and Sprenger (Philos Sci 82(3):383–401, 2015) aim for similar, but more general, solutions to the Problem of Old Evidence. These solutions are more general because they allow the (...) explanatory relationship between a new hypothesis and old evidence to be inductive, rather than deductive. In this paper, I argue that these solutions are either unsound or under-motivated, depending on the case of inductive explanation that we have in mind. This lends support to the broader claim that Garber–Style Bayesian confirmation cannot capture the sense in which new hypotheses that do not deductively imply old evidence nevertheless seem to be confirmed via old evidence. (shrink)

Ever since Aristotle it has been accepted that there exists a combination of inductive and deductive reasoning and a sort of unified inductive-deductive methodology. If one analyzes the procedures and logic of scientific explanation and the methods of generating and justifying scientific knowledge, one recognizes the prototype of philosophy of science found in Aristotle’s inductive and deductive procedure that is described in his Posterior Analytics, Physics and Metaphysics, where heviewed scientific inquiry as a progression from observations to general principles and (...) back to observation. He maintained that the scientist should induce explanatory principles from the phenomena to be explained, and then deduce statements about the phenomena from premisses which include these principles. (shrink)

Ever since Aristotle it has been accepted that there exists a combination of inductive and deductive reasoning and a sort of unified inductive-deductive methodology. If one analyzes the procedures and logic of scientific explanation and the methods of generating and justifying scientific knowledge, one recognizes the prototype of philosophy of science found in Aristotle’s inductive and deductive procedure that is described in his Posterior Analytics, Physics and Metaphysics, where heviewed scientific inquiry as a progression from observations to general principles and (...) back to observation. He maintained that the scientist should induce explanatory principles from the phenomena to be explained, and then deduce statements about the phenomena from premisses which include these principles. (shrink)

Phenomenal knowledge is knowledge of what it is like to be in conscious states, such as seeing red or being in pain. According to the knowledge argument (Jackson 1982, 1986), phenomenal knowledge is knowledge that, i.e., knowledge of phenomenal facts. According to the ability hypothesis (Nemirow 1979; Lewis 1983), phenomenal knowledge is mere practical knowledge how, i.e., the mere possession of abilities. However, some phenomenal knowledge also seems to be knowledge why, i.e., knowledge of explanatory facts. For example, someone (...) who has just experienced pain for the first time learns not only that this is what pain is like, but also why people tend to avoid it. Some philosophers have claimed that experiencing pain gives knowledge why in a normative sense: it tells us why pain is bad and why inflicting it is wrong (Kahane 2010). But phenomenal knowledge seems to explain not (only) why people should avoid pain, but why they in fact tend to do so. In this paper, I will explicate and defend a precise version of this claim and use it as a basis for a new version of the knowledge argument, which I call the explanatory knowledge argument. According to the argument, some phenomenal knowledge (1) explains regularities in a distinctive, ultimate or regress-ending way, and (2) predict them without induction. No physical knowledge explains and predicts regularities in the same way. This implies the existence of distinctive, phenomenal explanatory facts, which cannot be identified with physical facts. I will show that this argument can be defended against the main objections to the original knowledge argument, the ability hypothesis and the phenomenal concept strategy, even if it turns out that the original cannot. In this way, the explanatory knowledge argument further strengthens the case against physicalism. (shrink)

We present an explanatory objection to Norton's material theory of induction, as applied to predictive inferences. According to the objection we present, there is an explanatory disconnect between our beliefs about the future and the relevant future facts. We argue that if we recognize such a disconnect, we are no longer rationally entitled to our future beliefs.

In lieu of an abstract, here is a brief excerpt of the content:Inductive Scepticism and Experimental Reasoning in Moral Subjects in Hume's Philosophy Anne Jaap Jacobson According to its title page, Hume's Treatise Concerning HumanNature is An ATTEMPT to introduce the experimental Method ofReasoning INTO MORAL SUBJECTS."1 And from the first section onwards, Hume makes statements about the human mind which are given an unqualified generality;An Enquiry ConcerningHuman Understanding is marked by a similar assurance that much about human understanding can (...) be known. Because of this, exegesis which attributes to Hume an unrestrained scepticism about the experimental method appears to attribute to him inconsistency on such a scale as to render the interpretation itselfquestionable. Nonetheless, there is, atleast on the face ofit, considerable justification for ascribing to Hume just such a scepticism. In this paper I explore sceptical features, some ofthem important but little noticed, in Hume's treatment of causality and our beliefs about the unobserved. Though I end by suggestinghow to avoidviewing Hume in this area as simply lamentably inconsistent, Hume's use of the experimental method doesremain problematic, as, I suggest, Hume himselfthought. The first three of the following sections in this paper treat connected themes in Hume's philosophy which, when taken together, present us with a very sceptical view of experimental reasoning. I. Necessity as projected impression Hume holds that our beliefs about causality in the objects are in large part the result of a projection of an internal impression of (some kind of) necessity. The thesis ofprojection is not entirely straightforward; to see this, let us ask the question, is the impression which is projected semantically simple or complex? There are excellentreasonsforregarding the impression as simple as Hume conceives of "simple" in this context. Hume himselfappears to sayitis simple (E 64, n. 1). Andmuch of Hume's discussion ofnecessity is driven by the principle that there can be no idea without a preceding impression, and this principle applies only to simple ideas. But the consequent reading is far from satisfactory. To see the problem, let us look at what seems to be the Volume XV Number 2 325 ANNE JAAP JACOBSON most entrenched understanding ofHume, one perhaps amark ofKemp Smith's influence. This is the view that Hume is saying that the impression source of our idea of necessity is a feeling of anticipation. The problem is this: ifa feeling ofanticipation is a simple impression, it is not at all clear that the impression can do the job Hume has for it. Remember that if the impression is in content itselfrelational, then it is not a simple impression on Hume's own account, since ideas of relations are for him complex (T 13). Hence, we might take the impression to be of the sort described by Stroud, according to whom the impression yielding our idea of necessity is semantically unrelated to the elements of the relation. But such a reading robs Hume of the explanatory position he so clearly thinks he has. If we have a semantically simple impression it becomes a mystery why the spreading has the effects that it does: when we transfer the determination ofthe thought to external objects, andsuppose any real intelligible connexion betwixt them. (T 168, my emphasis) Why does spreading some simple, indefinable feeling result in our supposing there is a real intelligible connection between the objects on which the mind has spread? To get this result it looks as though the mind will have tomake two mistakes: thefirstmistake is the spreading, and the second mistake consists in the mind's inferring from the experience of the impression as spread that somehow the causal inference itself is also out there in nature as an intelligible connection. But, while Hume does sometimes seem to suggest we make this sort of two-step error (T 223, for example), such a picture makes it seem that the impression spread is not really the semantic source of (that is, wholly determinate of the content of) our idea ofnecessity. Rather, on the two-step error model, our belief that there are connections enters as a result of an inference following upon the spreading; however, for Hume, an inference is not the way an impression ofX gives rise to an idea ofX... (shrink)

Philosophers of mathematics commonly distinguish between explanatory and non-explanatory proofs. An important subclass of mathematical proofs are proofs by induction. Are they explanatory? This paper addresses the question, based on general principles about explanation. First, a recent argument for a negative answer is discussed and rebutted. Second, a case is made for a qualified positive take on the issue.

The hunt for a biologically respectable definition for the folk concept of innateness is still on. I defend Ariew’s Canalization account of innateness against the criticisms of Griffiths and Machery, but highlight the remaining flaws in this proposal. I develop a new analysis based on the notion of environmental induction. A trait is innate, I argue, iff it is not environmentally induced. I augment this definition with a novel analysis of environmental induction that draws on the contrastive nature (...) of causal explanation. Whether a trait is environmentally induced, I argue, depends on a context sensitive contrast class. I argue that a “Noninduction” analysis of innateness allows the concept an explanatory role in biology. I show how my proposal co-opts the successes of the Canalization account whilst avoiding its pitfalls, and I account for why biologists associate a range of disparate properties with innateness. (shrink)

I present a solution to the epistemological or characterisation problem of induction. In part I, Bayesian Confirmation Theory (BCT) is discussed as a good contender for such a solution but with a fundamental explanatory gap (along with other well discussed problems); useful assigned probabilities like priors require substantive degrees of belief about the world. I assert that one does not have such substantive information about the world. Consequently, an explanation is needed for how one can be licensed to (...) act as if one has substantive information about the world when one does not. I sketch the outlines of a solution in part I, showing how it differs from others, with full details to follow in subsequent parts. The solution is pragmatic in sentiment (though differs in specifics to arguments from, for example, William James); the conceptions we use to guide our actions are and should be at least partly determined by preferences. This is cashed out in a reformulation of decision theory motivated by a non-reductive formulation of hypotheses and logic. A distinction emerges between initial assumptions--that can be non-dogmatic--and effective assumptions that can simultaneously be substantive. An explanation is provided for the plausibility arguments used to explain assigned probabilities in BCT. -/- In subsequent parts, logic is constructed from principles independent of language and mind. In particular, propositions are defined to not have form. Probabilities are logical and uniquely determined by assumptions. The problems considered fatal to logical probabilities--Goodman's `grue' problem and the uniqueness of priors problem are dissolved due to the particular formulation of logic used. Other problems such as the zero-prior problem are also solved. -/- A universal theory of (non-linguistic) meaning is developed. Problems with counterfactual conditionals are solved by developing concepts of abstractions and corresponding pictures that make up hypotheses. Spaces of hypotheses and the version of Bayes' theorem that utilises them emerge from first principles. -/- Theoretical virtues for hypotheses emerge from the theory. Explanatory force is explicated. The significance of effective assumptions is partly determined by combinatoric factors relating to the structure of hypotheses. I conjecture that this is the origin of simplicity. (shrink)

Peter Achinstein (1990, 1991) analyses the scientific debate that took place in the eighteenth and nineteenth centuries concerning the nature of light. He offers a probabilistic account of the methods employed by both particle theorists and wave theorists, and rejects any analysis of this debate in terms of coherence. He characterizes coherence through reference to William Whewell's writings concerning how "consilience of inductions" establishes an acceptable theory (Whewell, 1847) . Achinstein rejects this analysis because of its vagueness and lack of (...) reference to empirical data, concluding that coherence is insufficient to account for the belief change that took place during the wave-particle debate. (shrink)

The paper attempts to elucidate and evaluate William Whewell's notion of a "consilience of inductions." In section I Whewellian consilience is defined and shown to differ considerably from what latter-day writers talk about when they use the term. In section II a primary analysis of consilience is shown to yield two types of consilient processes, one in which one of the lower-level laws undergoes a conceptual change (the case aptly discussed in Butts [1977]), and one in which the explanatory (...) theory undergoes conceptual "stretching." In section III both consilient cases are compared to the non-consilient case in reference to L. J. Cohen's method of relevant variables. In section IV we examine the test procedures of the theory in all three cases, and it is shown that in the event of genuine consilience (consilience of the second type) a theory acquires extraordinarily high support. In the final section something is said of the short-comings of standard Bayesian confirmation theories that are highlighted by Whewellian consilience. (shrink)

John Foster presents a clear and powerful discussion of a range of topics relating to our understanding of the universe: induction, laws of nature, and the existence of God. He begins by developing a solution to the problem of induction - a solution whose key idea is that the regularities in the workings of nature that have held in our experience hitherto are to be explained by appeal to the controlling influence of laws, as forms of natural necessity. (...) His second line of argument focuses on the issue of what we should take such necessitational laws to be, and whether we can even make sense of them at all. Having considered and rejected various alternatives, Foster puts forward his own proposal: the obtaining of a law consists in the causal imposing of a regularity on the universe as a regularity. With this causal account of laws in place, he is now equipped to offer an argument for theism. His claim is that natural regularities call for explanation, and that, whatever explanatory role we may initially assign to laws, the only plausible ultimate explanation is in terms of the agency of God. Finally, he argues that, once we accept the existence of God, we need to think of him as creating the universe by a method which imposes regularities on it in the relevant law-yielding way. In this new perspective, the original nomological-explanatory solution to the problem of induction becomes a theological-explanatory solution. The Divine Lawmaker is bold and original in its approach, and rich in argument. The issues on which it focuses are among the most important in the whole epistemological and metaphysical spectrum. (shrink)

The backward induction controversy in game theory flared up and then practically ended within a decade – the 1990s. The protagonists, however, did not converge on an agreement about the source of the controversy. Why was this the case, if opposing sides had access to the same modelling techniques and empirical facts? In this paper I offer an explanation for this controversy and its unsettled end. The answer is not to be found in the modelling claims made by the (...) opposing protagonists, but in the tacit metaphors they operate under. Aristotle defined metaphor as giving a 'thing a name that belongs to something else' (Poetica, 1457b). The meaning of metaphors has not changed much since then – in contrast to models which are comparatively new, and still not well-understood, scientific tools. The controversy of backward induction in game theory provides a test bed for the explanatory power of metaphors. This paper frames the controversy in terms of metaphor choice to provide a common framework for the protagonists. This results in the identification of three different domains – mathematical logic, game theory and the world – each connected to the other via different metaphors. The controversy around backward induction is placed in, and tentatively explained by, this framework. (shrink)

A central problem facing a probabilistic approach to the problem of induction is the difficulty of sufficiently constraining prior probabilities so as to yield the conclusion that induction is cogent. The Principle of Indifference, according to which alternatives are equiprobable when one has no grounds for preferring one over another, represents one way of addressing this problem; however, the Principle faces the well-known problem that multiple interpretations of it are possible, leading to incompatible conclusions. I propose a partial (...) solution to the latter problem, drawing on the notion of explanatory priority. The resulting synthesis of Bayesian and inference-to-best-explanation approaches affords a principled defense of prior probability distributions that support induction. (shrink)

This print edition of Read's account of logical thought includes the original publication's diagrams and tables. In this excellent book, Read commences by offering an overview of past attitudes and definitions of logic. Individual chapters consider the various means by which logical processes are conceived and developed in the mind. Philosophical arguments, spatial reasoning and mathematical forms of logic are discussed in great depth, with illustrations appended where deemed necessary. Read, an academic and philosopher, employs his decades long experience of (...) teaching students about the logical disciplines to write a detailed and comprehensive accounts of logic's aspects. Throughout this work, he attempts to retain a clarity of expression which makes the concepts discussed understandable for readers previously unversed in the types of logical expression. Read also sets out the principles behind setting up a hypothesis, and highlights the common logical fallacies which crop up in human reasoning. Extensive attention is given to the process of syllogism, by which sound conclusions are drawn from the premises offered. Throughout the book, Read is attentive in defining and explaining the esoteric terminology native to logic. As well as allowing the reader swift comprehension of the various subtopics, this explanatory style confers improved flow to the book. At the conclusion we are offered many questions corresponding to each chapter: these are intended to test the reader's understanding, and enforce the mental habits of utilising logical and critical thought. First published in 1898 and subject to several editions with revisions and refinements thereafter, Logic Deductive and Inductive retains a good reputation among academics and logicians. Its successful balance between striking a concise introductory tone with an embrace of the core elements of the subject has served to preserve its popularity into the modern day. (shrink)

The hunt for a biologically respectable definition for the folk concept of innateness is still on. I defend Ariew’s Canalization account of innateness against the criticisms of Griffiths and Machery, but highlight the remaining flaws in this proposal. I develop a new analysis based on the notion of environmental induction. A trait is innate, I argue, iff it is not environmentally induced. I augment this definition with a novel analysis of environmental induction that draws on the contrastive nature (...) of causal explanation. Whether a trait is environmentally induced, I argue, depends on a context sensitive contrast class. I argue that a “Noninduction” analysis of innateness allows the concept an explanatory role in biology. I show how my proposal co-opts the successes of the Canalization account whilst avoiding its pitfalls, and I account for why biologists associate a range of disparate properties with innateness. (shrink)

Many necessitarians about cause and law (Armstrong 1983; Mumford 2004; Bird 2007) have argued that Humeans are unable to justify their inductive inferences, as Humean laws are nothing but the sum of their instances. In this paper I argue against these necessitarian claims. I show that Armstrong is committed to the explanatory value of Humean laws (in the form of universally quantified statements), and that contra Armstrong, brute regularities often do have genuine explanatory value. I finish with a (...) Humean attempt at a probabilistic justification of induction, but this fails due to its assumption that the proportionality syllogism is justified. Although this attempt fails, I nonetheless show that the Humean is at least as justified in reasoning inductively as Armstrong. (shrink)

This paper develops a stronger version of ‘inference-to-the-best explanation’ scientific realism. I argue against three standard assumptions of current realists: realism is confirmed if it provides the best explanation of theories’ predictive success ; the realist claim that successful theories are always approximately true provides the best explanation of their success ; and realists are committed to giving the same sort of truth-based explanation of superseded theories’ success that they give to explain our best current theories’ success. On the positive (...) side, I argue that the confirmation of realism requires explaining theories’ explanatory success, not just their predictive success ; in turn this task requires a richer realist model of explanation that brings into the explanans both successful theories’ epistemic virtues and the standards governing these virtues, as well as truth; this richer realist model is further confirmed because it can better explain the success of theories in gaining wide acceptance among scientists; and the model is further supported because it is superior to ‘preservative realism ’ in providing a plausible rebuttal of the pessimistic meta-induction from the many past successful-but-false theories to the like- lihood that our best current theories are likewise false. (shrink)

This paper naturalizes inductive inference by showing how scientific knowledge of real mechanisms provides large benefits to it. I show how knowledge about mechanisms contributes to generalization, inference to the best explanation, causal inference, and reasoning with probabilities. Generalization from some A are B to all A are B is more plausible when a mechanism connects A to B. Inference to the best explanation is strengthened when the explanations are mechanistic and when explanatory hypotheses are themselves mechanistically explained. Causal (...) inference in medical explanation, counterfactual reasoning, and analogy also benefit from mechanistic connections. Mechanisms also help with problems concerning the interpretation, availability, and computation of probabilities. (shrink)

Many theorists have proposed that we can use the principle of indifference to defeat the inductive sceptic. But any such theorist must confront the objection that different ways of applying the principle of indifference lead to incompatible probability assignments. Huemer offers the explanatory priority proviso as a strategy for overcoming this objection. With this proposal, Huemer claims that we can defend induction in a way that is not question-begging against the sceptic. But in this article, I argue that (...) the opposite is true: if anything, Huemer’s use of the principle of indifference supports the rationality of inductive scepticism. (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.

Over the last two decades, the debate over scientific realism has been dominated by two arguments that pull in contrary directions: the 'no miracle' argument and the 'pessimistic induction'. The latter suggests that the historical record destroys the realist's belief in an explanatory connection between truthlikeness and genuine empirical success. This paper analyzes the structure of the 'pessimistic induction', presents a move--the divide et impera move--that neutralizes it, and motivates a substantive yet realistic version of scientific realism. (...) This move is also compared with Worrall's and Kitcher's recent reactions to the 'pessimistic induction'. (shrink)

Douven (in press) observes that Schurz's meta-inductive justification of induction cannot explain the great empirical success of induction, and offers an explanation based on computer simulations of the social and evolutionary development of our inductive practices. In this paper, I argue that Douven's account does not address the explanatory question that Schurz's argument leaves open, and that the assumption of the environment's induction-friendliness that is inherent to Douven's simulations is not justified by Schurz's argument.

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)

We discuss the probabilistic analysis of explanatory power and prove a representation theorem for posterior ratio measures recently advocated by Schupbach and Sprenger. We then prove a representation theorem for an alternative class of measures that rely on the notion of relative probability distance. We end up endorsing the latter, as relative distance measures share the properties of posterior ratio measures that are genuinely appealing, while overcoming a feature that we consider undesirable. They also yield a telling result concerning (...) formal accounts of explanatory power versus inductive confirmation, thereby bridging our discussion to a so-called no-miracle argument. (shrink)

In adversarial problem solving (APS), one must anticipate, understand and counteract the actions of an opponent. Military strategy, business, and game playing all require an agent to construct a model of an opponent that includes the opponent's model of the agent. The cognitive mechanisms required for such modeling include deduction, analogy, inductive generalization, and the formation and evaluation of explanatory hypotheses. Explanatory coherence theory captures part of what is involved in APS, particularly in cases involving deception.

This thesis investigates the nature of psychiatric disorders, and to what extent they can form a basis for classification, explanation, and treatment interventions. These questions are important in the light of the “crisis of validity” in psychiatry, according to which current diagnostic categories do not pick out real disorders. I address the questions by defending an account of psychiatric disorders that can better accommodate social aspects and non-epistemic values than the symptom-based model of the Diagnostic and Statistical Manual of Mental (...) Disorders (DSM) and the brain disease model of the biomedical approach, including the Research Domain Criteria (RDoC). I concentrate on three ways that psychiatric disorders can differ from prototypical natural kinds, such as biological species and chemical elements. First, the concept of psychiatric disorder or mental disorder is partly value-laden and cannot be defined based only on scientific facts. Second, the objects of psychiatric classifications are interactive human kinds because people with disorders respond to their classifications through looping effects. Third, sociocultural factors can shape disorders in complex ways, which is indicated by their cross-cultural variation. I argue that these challenges can be overcome with a pluralistic explanatory account that grants an explicit role to value-sensitive considerations and social scientific research. Based on this, I argue that particular disorders can in principle support inductive inferences. ------------------------------------------------------------------------------------------ My key argument is that although whether a condition is considered pathological is partly a value-laden question, this does not rule out a realist account of particular psychiatric disorders as homeostatic property cluster kinds (HPC). I assert that causal mechanisms responsible for psychiatric kinds can be understood non-metaphysically based on the contrastive-counterfactual and interventionist theories of explanation. An advantage of this account is that it can address the concern that psychiatric explanations require one to relate heterogeneous causal factors on different levels, such as genetic, neurological, psychological, and social. My novel argument is that mechanistic explanations of scientific kinds have applicability domains over which they account for specific aspects of kinds and warrant inductive inferences. That is, identifying the applicability domain of an explanation spells out the conditions under which the explanation is expected to be reliable and when it can break down. This helps to understand how different discipline approaches, including social and cultural ones, can be complementary and make an explanation of a psychiatric kind more reliable. On the other hand, the account also shows how the complex nature of psychiatric kinds can license re-classifications for different epistemic and non-epistemic purposes. Finally, in the light of the social implications of psychiatric classifications, I suggest a value-sensitive or ameliorative approach to engineering the concept of psychiatric disorder. In conclusion, my account shows that research on the social and cultural factors that shape psychiatric disorders, and weighing the non-epistemic values that influence classificatory practices, can and should inform classificatory choices as well as policy and treatment interventions. (shrink)

To prevent possible misunderstanding, let me start from one crucial distinction between the logic of science on the one hand and the use of logic in science on the other. The very phrase “inference to the best theory” and the style of its further explication may suggest that it is the former that is at issue. In contrast, the title of the present workshop, “Induction and deduction in the sciences”, suggests the latter to be its focus. And this I (...) find to point to the more adequate way of thinking about the relation between logic and science. I do not believe in “the logic of science” as something that can possibly be read off science in a manner analogous to that of reading logic off mathematics: the classical logic off the classical mathematics or the intuitionistic logic off the intuitionistic mathematics. (shrink)

To prevent possible misunderstanding, let me start from one crucial distinction between the logic of science on the one hand and the use of logic in science on the other. The very phrase “inference to the best theory” and the style of its further explication may suggest that it is the former that is at issue. In contrast, the title of the present workshop, “Induction and deduction in the sciences”, suggests the latter to be its focus. And this I (...) find to point to the more adequate way of thinking about the relation between logic and science. I do not believe in “the logic of science” as something that can possibly be read off science in a manner analogous to that of reading logic off mathematics: the classical logic off the classical mathematics or the intuitionistic logic off the intuitionistic mathematics. (shrink)

In this article, 41 models of covariation detection from 2 × 2 contingency tables were evaluated against past data in the literature and against data from new experiments. A new model was also included based on a limiting case of the normative phi‐coefficient under an extreme rarity assumption, which has been shown to be an important factor in covariation detection (McKenzie & Mikkelsen, 2007) and data selection (Hattori, 2002; Oaksford & Chater, 1994, 2003). The results were supportive of the new (...) model. To investigate its explanatory adequacy, a rational analysis using two computer simulations was conducted. These simulations revealed the environmental conditions and the memory restrictions under which the new model best approximates the normative model of covariation detection in these tasks. They thus demonstrated the adaptive rationality of the new model. (shrink)

The likelihood of a statement is often derived by generating an explanation for it and evaluating the plausibility of the explanation. The explanation discounting principle states that people tend to focus on a single explanation; alternative explanations compete with the effect of reducing one another’s credibility. Two experiments tested the hypothesis that this principle applies to inductive inferences concerning the properties of everyday categories. In both experiments, subjects estimated the probability of a series of statements and the conditional probabilities of (...) those conclusions given other related facts. For example, given that most lawyers make good sales people, what is the probability that most psychologists make good sales people? The results showed that when the fact and the conclusion had the same explanation the fact increased people’s willingness to believe the conclusion, but when they had different explanations the fact decreased the conclusion’s credibility. This decrease is attributed to explanation discounting; the explanation for the fact had the effect of reducing the plausibility of the explanation for the conclusion. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:@ @ Notes and Dlscussaons A NOTE ON CHARLES PEIRCE'S THEORY OF INDUCTION By "Peirce's theory of induction," I refer to a system or collection of ideas which Peirce formulated about the nature and validity of inductive inference or inductive reasoning. This system or collection of ideas covers Peirce's writings from 1867 to 1905.1 During this period of his long philosophical career from 1857 to 1914, Peirce (...) wrote his most important papers on the logic of science and probability. ~ These papers, though only a minor portion of Peirce's philosophical works, constitute a self-explanatory unit of study, simply because they deal with one single subject: the validity of synthetic inference. In the year 1867, Peirce wrote his paper "On the Natural Classification of Arguments," which provides a natural introduction to his treatment of inference and its validity in syllogistic terms and to his trichotomy of inference into deduction, induction, and hypothesis. Through the year 1877 to 1878, Peirce wrote a series of papers on "Illustrations of the Logic of Science." Beside the well-known "The Fixation of Belief" and "How to Make our Ideas Clear," there are four other important but comparatively little discussed papers which are essentially concerned with the logic of science and probability. They are in the following order: "Doctrine of Chances" (with corrections, 1893 and notes, 1910), "The Probability of Induction" (with corrections, 1893), "Deduction, Induction, and Hypothesis" (with corrections, 1893), and "The Order of Nature." In these papers, Peirce laid out his rationale for the validity of ampliative or synthetic inference and indicated a justification of induction in terms of probability. He also made explicit his conception of probabilty in terms of empirical frequency. But very often his ideas concerning the validity of synthetic inference appear disconnected and do not fit into a consistent, not to say wellorganized, whole. It was not until 1883 that Peirce wrote a comparatively systematic treatise on his general theory concerning the validity of ampliative or synthetic inference. This is his "A Theory of Probable inference," in which we find Peirce's statement of what a probable inference is and his argument that inductive inference is valid on account of its being a probable inference. After the year 1883, Peirce's philosophical writings appear to bear little upon his earlier problems in logic of science and probubility. But here and there we find a variety of topics under which Peirce touched the problem of justifying kinds of inference. One significant feature among these is Peirce's recurrent distinction between kinds of induction, a distinction which he had never made in his earlier writings. The distinction is between a "crude induction" (or "pooh-pooh" argument ), a "quantitative induction," and a "qualitative induction." This distinc1See the "Chronological Listing of Peirce's Papers Directly Bearing upon Induction and Probability" in the appendix. 2The earfiest of his papers which we have is dated 1857,and his philosophical activity continued until his death in 1914. [361] 362 HISTORY OF PHILOSOPHY tion is found in the following three short papers: "Three Kinds of Induction" (from "The Logic of Drawing History from Ancient Documents," 1901), "Kinds of Induction" (1903), and "The Varieties and Validity of Induction," (c. 1905). What Peiree calls a "crude induction" is an inference which concludes a universal generalization from what has been found in common in a group of instances. It is induction by simple enumeration. A quantitative induction is an inference from our knowledge of a statistical proportion of individual things having a certain character in a given sample to a conclusion regarding that in the population, from which the sample is chosen. ~ A qualitative induction, on the other hand, is a method of ascertaining factual truths by postulating hypotheses and confirming them on the basis of relevant evidences. That all these three forms of inference are considered induction by Peirce is due to the fact that they do not usually have the form of deduction, and they usually give rise to generalizations which are not deductively warranted by their premises. They differ, nevertheless, because they have different bases for generalizations and their generalizations have different contents. 4 In the light of Peirce's distinction between these three forms... (shrink)

For Hume, one task of logic is “to explain the principles and operations of our reasoning faculties”; this chapter is a study of his logic of inductive reasoning, as presented in Book I of his Treatise and in the Enquiry Concerning Human Understanding. Like other early modern logics—especially those composed, as Hume’s was, under the influence of Locke—Hume’s logic is descriptive, explanatory, and normative. It also aspires to be revelatory. It is descriptive in documenting how our reasoning actually proceeds, (...) explanatory in telling us why it so proceeds, normative in telling us how it should proceed, and revelatory in using those findings to arrive at larger truths about human nature and human life. Hume formulates rules of inductive reasoning and ranks inductive arguments as better and worse. He also advocates the reform of intellectual disciplines. Yet his logic, it is argued, is at the same time deeply skeptical. (shrink)

In this paper, I will discuss accounts to solve the problem of induction by introducing necessary connections. The basic idea is this: if we know that there are necessary connections between properties F and G such that F -ness necessarily brings about G-ness, then we are justified to infer that all, including future or unobserved, F s will be Gs. To solve the problem of induction with ontology has been proposed by David Armstrong and Brian Ellis. In this (...) paper, I will argue that these attempts to solve the problem of induction fail. Necessary connections fail to reliably imply the respective regularities for two main reasons: Firstly, according to an argument originally presented by Helen Beebee, the respective necessary connections might be time-limited, and hence do not warrant inferences about future cases. As I will discuss, arguments against the possibility or explanatory power of time-limited necessary connections fail. Secondly, even time-unlimited necessary connections do not entail strict or non-strict regularities, and nor do they allow inferences about individual cases, which is an important function of inductive reasoning. Moreover, the proposed solution to the problem of induction would only apply to a tiny minority of inductive inferences. I argue that most inductive inferences are not easily reducible to the proposed inference pattern, as the vast majority of everyday inductive inferences do not involve necessary connections between fundamental physical properties or essences. (shrink)

I propose a novel solution to Goodman's new riddle of induction, one on which aspects of scientific methodology preclude significant confirmation of the Grue Hypothesis. The solution appeals to intuitive constraints on the confirmation of explanatory hypotheses, and can be construed as a fragment of a theory of Inference to the Best Explanation. I give it an objective Bayesian formalisation, and contrast it with Goodman's and Sober's solutions, which make appeal to both methodological and non-methodological considerations, and those (...) of Jackson, Godfrey-Smith, and White, on which explanatory considerations play a very different role. (shrink)