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 epistemic probability of A given B is the degree to which B evidentially supports A, or makes A plausible. This paper is a first step in answering the question of what determines the values of epistemic probabilities. I break this question into two parts: the structural question and the substantive question. Just as an object’s weight is determined by its mass and gravitational acceleration, some probabilities are determined by other, more basic ones. The structural question asks what probabilities are (...) not determined in this way—these are the basic probabilities which determine values for all other probabilities. The substantive question asks how the values of these basic probabilities are determined. I defend an answer to the structural question on which basic probabilities are the probabilities of atomic propositions conditional on potential direct explanations. I defend this against the view, implicit in orthodox mathematical treatments of probability, that basic probabilities are the unconditional probabilities of complete worlds. I then apply my answer to the structural question to clear up common confusions in expositions of Bayesianism and shed light on the “problem of the priors.”. (shrink)

Where E is the proposition that [If H and O were true, H would explain O], William Roche and Elliot Sober have argued that P(H|O&E) = P(H|O). In this paper I argue that not only is this equality not generally true, it is false in the very kinds of cases that Roche and Sober focus on, involving frequency data. In fact, in such cases O raises the probability of H only given that there is an explanatory connection between them.

A defense of the rationality of adductive inference from the criticisms of Bayesian theorists.

According to the Nomological Argument, observed regularities in nature are best explained by an appeal to a supernatural being. A successful explanation must avoid two perils. Some explanations provide too little structure, predicting a universe without regularities. Others provide too much structure, thereby precluding an explanation of certain types of lawlike regularities featured in modern scientific theories. We argue that an explanation based in the creative, intentional action of a supernatural being avoids these two perils whereas leading competitors do not. (...) Although our argument falls short of a full defense, it does suggest that the Nomological Argument is worthy of philosophical attention. (shrink)

In a series of papers over the past twenty years, and in a new book, Igor Douven has argued that Bayesians are too quick to reject versions of inference to the best explanation that cannot be accommodated within their framework. In this paper, I survey their worries and attempt to answer them using a series of pragmatic and purely epistemic arguments that I take to show that Bayes’ Rule really is the only rational way to respond to your evidence.

A major open question in the borderlands between epistemology and philosophy of science concerns whether Bayesian updating and abductive inference are compatible. Some philosophers—most influentially Bas van Fraassen—have argued that they are not. Others have disagreed, arguing that abduction, properly understood, is indeed compatible with Bayesianism. Here we present two formal results that allow us to tackle this question from a new angle. We start by formulating what we take to be a minimal version of the claim that abduction is (...) a rational pattern of reasoning. We then show that this minimal abductivist principle, when combined with Bayesian updating by conditionalization, places surprisingly strong and controversial constraints on how we must measure explanatory power. The lesson is not that Bayesianism is definitely incompatible with abduction, but that both compatibilism and incompatibilism have hitherto unrecognized consequences. We end the paper by formulating these consequences in the form of a trilemma. (shrink)

It has recently been argued that a non-Bayesian probabilistic version of inference to the best explanation (IBE*) has a number of advantages over Bayesian conditionalization (Douven [2013]; Douven and Wenmackers [2017]). We investigate how IBE* could be generalized to uncertain evidential situations and formulate a novel updating rule IBE**. We then inspect how it performs in comparison to its Bayesian counterpart, Jeffrey conditionalization (JC), in a number of simulations where two agents, each updating by IBE** and JC, respectively, try to (...) detect the bias of a coin while they are only partially certain what side the coin landed on. We show that IBE** more often prescribes high probability to the actual bias than JC. We also show that this happens considerably faster, that IBE** passes higher thresholds for high probability, and that it in general leads to more accurate probability distributions than JC. (shrink)

In this article, I will provide a critical overview of the form of non-deductive reasoning commonly known as “Inference to the Best Explanation” (IBE). Roughly speaking, according to IBE, we ought to infer the hypothesis that provides the best explanation of our evidence. In section 2, I survey some contemporary formulations of IBE and highlight some of its putative applications. In section 3, I distinguish IBE from C.S. Peirce’s notion of abduction. After underlining some of the essential elements of IBE, (...) the rest of the entry is organized around an examination of various problems that IBE confronts, along with some extant attempts to address these problems. In section 4, I consider the question of when a fact requires an explanation, since presumably IBE applies only in cases where some explanation is called for. In section 5, I consider the difficult question of how we ought to understand IBE in light of the fact that among philosophers, there is significant disagreement about what constitutes an explanation. In section 6, I consider different strategies for justifying the truth-conduciveness of the explanatory virtues, e.g., simplicity, unification, scope, etc., criteria which play an indispensable role in any given application of IBE. In section 7, I survey some of the most recent literature on IBE, much of which consists of investigations of the status of IBE from the standpoint of the Bayesian philosophy of science. (shrink)

Quine taught us the difference between a theory’s ontology and its ideology. Ontology is the things a theory’s quantifiers must range over if it is true, Ideology is the primitive concepts that must be used to state the theory. This allows us to split the theoretical virtue of parsimony into two kinds: ontological parsimony and ideological parsimony. My goal is help illuminate the virtue of ideological parsimony by giving a criterion for ideological innocence—a rule for when additional ideology does not (...) count against parsimony. I propose the expressive power innocence criterion: if the ideology of theory one is expressively equivalent to that of theory two, then neither is ideologically simpler than the other. In its favor I offer the argument from accuracy, showing that any account of a theoretical virtue that is supposed to make theories that have it more likely to be true than theories that do not must respect it. Next I consider its ramifications, eliminating rival views and passing judgment on some arguments from parsimony that can be found in the literature. Finally, I consider two objections. First: I address an objection arising from the possibility of languages with a ‘primitive’ operator that allows us to list a theory’s primitives in the object-language. Second: I address an objection raised by Nelson Goodman against attempts to reckon simplicity by expressive power. Both objections fail. (shrink)

Fundamental Causation addresses issues in the metaphysics of deterministic singular causation, the metaphysics of events, property instances, facts, preventions, and omissions, as well as the debate between causal reductionists and causal anti-reductionists. The book also pays special attention to causation and causal structure in physics. Weaver argues that causation is a multigrade obtaining relation that is transitive, irreflexive, and asymmetric. When causation is singular, deterministic and such that it relates purely contingent events, the relation is also universal, intrinsic, and well-founded. (...) He shows that proper causal relata are events understood as states of substances at ontological indices. He then proves that causation cannot be reduced to some non-causal base, and that the best account of that relation should be unashamedly primitivist about the dependence relation that underwrites its very nature. The book demonstrates a distinctive realist and anti-reductionist account of causation by detailing precisely how the account outperforms reductionist and competing anti-reductionist accounts in that it handles all of the difficult cases while overcoming all of the general objections to anti-reductionism upon which other anti-reductionist accounts falter. This book offers an original and interesting view of causation and will appeal to scholars and advanced students in the areas of metaphysics, philosophy of science, and philosophy of physics. (shrink)

Most philosophers agree that abduction (in the sense of Inference to the Best Explanation) is a type of inference that is frequently employed, in some form or other, both in everyday and in scientific reasoning. However, the exact form as well as the normative status of abduction are still matters of controversy. This entry contrasts abduction with other types of inference; points at prominent uses of it, both in and outside philosophy; considers various more or less precise statements of it; (...) discusses its normative status; and highlights possible connections between abduction and Bayesian confirmation theory. (shrink)

In this paper, I explore one of the most important but least discussed components of an evidentialist case for or against theism: its intrinsic plausibility and simplicity as a theory aside from the evidence. This is a crucial consideration in any inductive framework, whether Inference to the Best Explanation, probabilism, or another. In the context of Bayesian reasoning, this corresponds to an assessment of theism's intrinsic probability. I offer a survey of how philosophers of science have attempted to evaluate the (...) intrinsic plausibility and simplicity of scientific theories more generally, before applying these considerations to the question of God's existence. (shrink)

Inference to the Best Explanation (IBE) is widely criticized for being an unreliable form of ampliative inference – partly because the explanatory hypotheses we have considered at a given time may all be false, and partly because there is an asymmetry between the comparative judgment on which an IBE is based and the absolute verdict that IBE is meant to license. In this paper, I present a further reason to doubt the epistemic merits of IBE and argue that it motivates (...) moving to an inferential pattern in which IBE emerges as a degenerate limiting case. Since this inferential pattern is structurally similar to an argumentative strategy known as Inferential Robustness Analysis (IRA), it effectively combines the most attractive features of IBE and IRA into a unified approach to non-deductive inference. (shrink)

In the philosophical literature, the term “abduction” is used in two related but different senses. In both senses, the term refers to some form of explanatory reasoning. However, in the historically first sense, it refers to the place of explanatory reasoning in generating hypotheses, while in the sense in which it is used most frequently in the modern literature it refers to the place of explanatory reasoning in justifying hypotheses. In the latter sense, abduction is also often called “Inference to (...) the Best Explanation.” -/- This entry is exclusively concerned with abduction in the modern sense, although there is a supplement on abduction in the historical sense, which had its origin in the work of Charles Sanders Peirce—see the Supplement: Peirce on Abduction. See also the entry on scientific discovery, in particular the section on discovery as abduction. -/- Most philosophers agree that abduction (in the sense of Inference to the Best Explanation) is a type of inference that is frequently employed, in some form or other, both in everyday and in scientific reasoning. However, the exact form as well as the normative status of abduction are still matters of controversy. This entry contrasts abduction with other types of inference; points at prominent uses of it, both in and outside philosophy; considers various more or less precise statements of it; discusses its normative status; and highlights possible connections between abduction and Bayesian confirmation theory. (shrink)

We examine two leading theories of rational belief, the Lockean view and the explanationist view. The first is appealing because it fits with some independently plausible claims about the ways that rational persons pursue their aims. The second is appealing because it seems to account for intuitions that cause trouble for the Lockean view. While fitting the intuitive data is desirable, we are troubled that the explanationist view seems to clash with our theoretical beliefs about what rationality must be like. (...) We think that upon further examination, the intuitive appeal of the explanationist view starts to diminish. We also think that these further intuitions that spell trouble for the explanationist spell trouble for any theory that is not expectationist. We propose a novel expectationist theory of rational belief that improves upon the Lockean and the explanationist views. We think that recent defences of the Lockean view contain an important insight. A substantive theory of rational response should be based on a suitable theory of prizes and a suitable theory of how we should pursue prizes in the face of uncertainty. Most theories of rational belief typically take for granted a truth-centred picture of epistemic prizes (e.g., that epistemic desirability and undesirability can be fully understood in terms of accuracy) and then differ in terms of how they recommend pursuing prizes so understood. We think the Lockeans embrace plausible principles of how prizes should be pursued. We trace the difficulties that this view faces to veritistic assumptions about prizes. We suggest that some prizes are epistemically loaded in that a complete description of the prize will itself make reference to our epistemic states or standards. We argue that knowledge matters to rational belief and choice because in the epistemic domain, knowledge is the prize. We see this in practical domains, too. In some choice settings, what's desired is desired, in part, because it involves a kind of connection to reality only knowledge provides. (shrink)

It is widely thought in philosophy and elsewhere that parsimony is a theoretical virtue in that if T1 is more parsimonious than T2, then T1 is preferable to T2, other things being equal. This thesis admits of many distinct precisifications. I focus on a relatively weak precisification on which preferability is a matter of probability, and argue that it is false. This is problematic for various alternative precisifications, and even for Inference to the Best Explanation as standardly understood.

It has been argued that if the rigidity condition is satisfied, a rational agent operating with uncertain evidence should update her subjective probabilities by Jeffrey conditionalization or else a series of bets resulting in a sure loss could be made against her. We show, however, that even if the rigidity condition is satisfied, it is not always safe to update probability distributions by JC because there exist such sequences of non-misleading uncertain observations where it may be foreseen that an agent (...) who updates her subjective probabilities by JC will end up nearly certain that a false hypothesis is true. We analyze the features of JC that lead to this problem, specify the conditions in which it arises and respond to potential objections. (shrink)

Affirming the consequent is an inferential pattern in which one infers the antecedent of a given conditional from its consequent. Abductive inference is structurally similar: given some evidence, one infers a hypothesis that explains the evidence. I show that a Bayesian analysis of affirming the consequent helps us understand under which conditions abduction may be justified. This provides a Bayesian vindication of explanatory inference.

According to a widely shared generic conception of inferential justification—‘the standard conception’—an agent is inferentially justified in believing that p only if she has antecedently justified beliefs in all the non-redundant premises of a good argument for p. This conception tends to serve as the starting-point in contemporary debates about the nature and scope of inferential justification: as neutral common ground between various competing, more specific, conceptions. But it’s a deeply problematic starting-point. This paper explores three questions that haven’t been (...) given the attention they deserve, that complicate the application of the standard conception to cases, and that reveal it to be underspecified at the core—in ways that aren’t resolved but inherited by more specific (extant) versions of it. The goal isn’t to answer the questions, but to articulate them, explain what turns on them, and invite a critical re-examination of the standard conception. (shrink)

Park (2017, 2018, 2019) argues that Bas van Fraassen uses inference to the best explanation to defend his contextual theory of explanation. If Park is right, then van Fraassen is in trouble because he rejects IBE as a rational rule of inference. In this reply, I argue that van Fraassen does not use IBE in defending the contextual theory of explanation. I distinguish between several conceptions of IBE: heuristic IBE, objective Bayesian IBE, and ampliative IBE. I argue that van Fraassen (...) holds the ampliative conception of IBE and that his rejection of IBE concerns only ampliative IBE. I also argue that van Fraassen’s defense of the contextual theory of explanation, at best, can be interpreted as an instance of heuristic IBE, but not ampliative IBE. Therefore, I argue, Park’s criticism of van Fraassen misfires. (shrink)

This paper draws on the resources of computational neuroscience (an account of active inference under the free energy principle) to address Bas van Fraassen's bad lot objection to the inference to the best explanation (IBE). The general assumption of this paper is that IBE is a finessed form of active inferences that self-organising systems perform to maximise the chance of their survival. Under this assumption, the paper aims to establish the following points: first, the capacity to learn to perform explanatory (...) inferences comes with evolutionary privileges; second, adaptive actions guide beliefs and beliefs are action-oriented; and third, IBE is not inconsistent with (approximate) Bayesianism but plays a heuristic role to it. (shrink)

Journal of Political Philosophy, EarlyView.

Inference to the best explanation (IBE) is a pattern of everyday and scientific reasoning, where a hypothesis is accepted if it gives a better explanation of the known evidence than any alternative hypothesis. This term was introduced by Gilbert Harman in 1965, and ever since IBE has been a central theme in the agenda of logic, artificial intelligence, and philosophy of science. However, a similar idea of a special kind of ampliative reasoning (besides deduction and induction) had been advocated by (...) Charles S. Peirce already a century earlier: “hypothetical reasoning” proceeds backward from effects to causes, or “abduction” leads from surprising facts to explanatory theories. The key issues in the explication of IBE concern the definition of “the best explanation” and the possibility of analyzing the nature of explanatory reasoning by the Bayesian probabilistic approach or by the truthlikeness framework. -/- . (shrink)

The main goal of this dissertation is to provide a solid foundation for a formalization of Inference to the Best Explanation (IBE). This foundation consists of three major components. First, an intuitively adequate and formally precise model of causal explanation. Secondly, an intuitively adequate and formally precise measure of (causal) explanatory power. And third, an intuitively adequate and formally precise criterion of proportionality that is able to identify the most appropriate level of specificity for a causal explanation. While the first (...) component makes it possible to generate and identify causal explanations reliably, the second and third components make it possible to evaluate the strength or quality of causal explanations, which is crucial for identifying the best of a set of competing causal explanations. (shrink)

In abductive reasoning, scientific theories are evaluated on the basis of how well they would explain the available evidence. There are a number of subtly different accounts of this type of reasoning, most of which are inspired by the popular slogan 'Inference to the Best Explanation.' However, these accounts disagree about exactly how to spell out the slogan so as to avoid various problems for abductive reasoning. This Element aims, firstly, to give an opinionated overview both of the many accounts (...) of abductive reasoning that have been proposed and the problems that have motivated them; and, secondly, to critically evaluate these accounts in a way that points toward a systematic view of the nature and purpose of abductive reasoning in science. This title is also available as Open Access on Cambridge Core. (shrink)

A key question in criminal trials is, ‘may we consider the facts of the case proven?’ Partially in response to miscarriages of justice, philosophers, psychologists and mathematicians have considered how we can answer this question rationally. The two most popular answers are the Bayesian and the explanation-based accounts. Bayesian models cast criminal evidence in terms of probabilities. Explanation-based approaches view the criminal justice process as a comparison between causal explanations of the evidence. Such explanations usually take the form of scenarios (...) – stories about how a crime was committed. The two approaches are often seen as rivals. However, this thesis argues that both perspectives are necessary for a good theory of rational criminal proof. By comparing scenarios, we can, among other things, determine what the key evidence is, how the items of evidence interrelate, and what further evidence to collect. Bayesian probability theory helps us pinpoint when we can and cannot conclude that a scenario is likely to be true. This thesis considers several questions regarding criminal evidence from this combined perspective, such as: can a defendant sometimes be convicted on the basis of an implausible guilt scenario? When can we assume that we are not overlooking scenarios or evidence? Should judges always address implausible innocence scenarios of the accused? When is it necessary to look for new evidence? How do we judge whether an eyewitness is reliable? By combining the two theories, we arrive at new insights on how to rationally reason about these, and other questions surrounding criminal evidence. (shrink)

This Element presents and critically examines the relationship between metaphysics and the sciences. Section 1 provides a brief introduction. Section 2 looks at the methodological issues that arise when metaphysics and science get into contact, which is a much-debated aspect of the larger dispute concerning philosophical 'naturalism' and 'anti-naturalism'. A taxonomy of possible views is offered. Section 3 looks more specifically at milder forms of naturalism about metaphysics, which attempt in various ways to make it 'continuous' with science while preserving (...) some degree of autonomy for it. Section 4 adds some reflections on what might be regarded as the most pressing open problem when it comes to doing scientifically oriented metaphysics (but also when practising metaphysics or science in isolation): the problem concerning theory choice and the value of non-empirical factors in determining which explanation of certain phenomena should be preferred. (shrink)

Recent work in cognitive science has uncovered a diversity of explanatory values, or dimensions along which we judge explanations as better or worse. We propose a Bayesian account of these values that clarifies their function and shows how they fit together to guide explanation-making. The resulting taxonomy shows that core values from psychology, statistics, and the philosophy of science emerge from a common mathematical framework and provide insight into why people adopt the explanations they do. This framework not only operationalizes (...) the explanatory virtues associated with, for example, scientific argument-making, but also enables us to reinterpret the explanatory vices that drive phenomena such as conspiracy theories, delusions, and extremist ideologies. (shrink)