Abductive Reasoning

by Douglas Walton

Overview

A study of the role of abductive inference in everyday argumentation and legal evidence
Examines three areas in which abductive reasoning is especially important: medicine, science, and law. The reader is introduced to abduction and shown how it has evolved historically into the framework of conventional wisdom in logic. Discussions draw upon recent techniques used in artificial intelligence, particularly in the areas of multi-agent systems and plan recognition, to develop a dialogue model of explanation. Cases of causal explanations in law are analyzed using abductive reasoning, and all the components are finally brought together to build a new account of abductive reasoning.
 
By clarifying the notion of abduction as a common and significant type of reasoning in everyday argumentation, Abductive Reasoning will be useful to scholars and students in many fields, including argumentation, computing and artificial intelligence, psychology and cognitive science, law, philosophy, linguistics, and speech communication and rhetoric.
 

Product Details

ISBN-13:	9780817387617
Publisher:	University of Alabama Press
Publication date:	05/31/2014
Sold by:	Barnes & Noble
Format:	eBook
Pages:	320
File size:	1 MB

About the Author

Douglas Walton has published 33 books including Legal Argumentation and Evidence, One Sided Arguments: A Dialectical Analysis of Bias, Ad Hominem Arguments, Argumentation Schemes for Presumptive Reasoning, and A Pragmatic Theory of Fallacy.

Read an Excerpt

Abductive Reasoning

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By Douglas Walton

The University of Alabama Press

Copyright © 2005 The University of Alabama Press
All rights reserved.
ISBN: 978-0-8173-8761-7

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CHAPTER 1

Abductive, Presumptive, and Plausible Arguments

Three kinds of inference—abductive argument, presumptive argument, and plausible argument—are often confused. And it is not too surprising that they are confused. They seem to be quite similar in representing a kind of uncertain and tentative reasoning that is very common in everyday thinking, as well as in special contexts such as legal argumentation and scientific hypothesis construction. And although there is quite a bit of writing on all three types of argument in logic, artificial intelligence (AI), philosophy of science, and cognitive science, there seems at this point to be no widely agreed upon systematic theory that clearly distinguishes between (or among) the three in any precise way. A related notion in the same category is inference to the best explanation, now widely taken (see below) to be the same as abductive argument. The purpose of chapter 1 is to survey how these related terms are used in the literature and to determine what the main differences are between (or among) them. The aim is thereby to elicit a basis for making a clear distinction between (or among) them that should help to explain and clarify these differences. On the basis of this survey and analysis, tentative definitions of all these related concepts will be proposed. The definitions are not meant to be the final word that closes off all discussion of the matter. They are put forward as tentative hypotheses meant to clarify the discussion and move it forward constructively.

The current convention is typically to postulate three kinds of argument—deductive, inductive, and the variously named third category: abductive, presumptive, defeasible, or plausibilistic. This convention poses an important question. Should one of these variously named types fit in as the third kind of inference contrasting with the other two? Or should all of them fit into that category? Or should some subset of them fit? Or should some of them be nested under others as subcategories? The situation is complicated, and the terminology is unsettled. Many logic textbooks either do not recognize the third category at all or show uncertainty about what to call it. Recent work in argumentation theory has studied forms of argument fitting into the third category. These forms are called argumentation schemes. The arguments fitting the schemes appear to be neither deductive nor inductive. Could they be classified as abductive, or is that the wrong word? These questions are perplexing, but seem to be very important not only for logic and computer science but also for many other fields, such as law, where such arguments are so commonly used as evidence. Another question is how abduction is related to argumentation schemes. These stereotypical forms of argument, such as argument from witness testimony and argument from expert opinion, have traditionally been classified as fallacies but can often be reasonable forms of argument used as legal evidence. Some examples of schemes are introduced in this chapter, and it is shown how they can be used in a new automated method of argument diagramming.

ABDUCTIVE INFERENCE

To begin, it is useful to review the definitions of "deductive argument" and "inductive argument" offered in the most widely used logic textbook. According to Hurley (2000, p. 33), a deductive argument is "an argument in which the premises are claimed to support the conclusion in such a way that it is impossible for the premises to be true and the conclusion false." Or to put it another way, if the premises are true, then necessarily the conclusion is true, where the adverb "necessarily" applies to the inferential link between the premises and the conclusion. An inductive argument (Hurley, 2000, p. 33) is "an argument in which the premises are claimed to support the conclusion in such a way that it is improbable that the premises be true and the conclusion false." The inferential link between the premises and the conclusion here is not one of necessity but of probability. But what is probability? Although logic textbooks generally agree on how they define a deductively valid argument, there are many differences on how they define probability. The most popular approach is called the Bayesian interpretation, which defines probability in terms of degrees of belief about events. In the Bayesian formalism, measures of belief follow the basic axioms of the probability calculus (Pearl, 2000, p. 3). One is that probability is measured as a fraction between zero and one. Another is that the probability of an event not occurring is defined as one minus the probability that the event does occur. Conditional probability, the probability of one event given the probability of another, is a very important defining characteristic of the Bayesian approach. Independence of events is assumed as a requirement of applying the Bayesian formalism to them. When it is said that event A is independent of event B, it means that our belief in A remains unchanged on learning the truth of B (Pearl, 2000, p. 3). To apply Bayesian probability to a set of data to infer a conclusion, one has to assume that each event in the data set is independent of the other events. At any rate, this rough account gives the beginner a basis to contrast the abductive type of inference to what can be taken, on commonly held criteria, to be deductive and inductive inference.

Abductive inference is a notion that has become familiar to some of us, but the idea is a relative newcomer as something that is widely known or accepted in logic. There seems to be quite a bit of uncertainty about exactly how the notion should be defined. It is thought that the American philosopher Charles Saunders Peirce was the originator of the notion of abduction. But that, too, is somewhat uncertain, in my opinion, even though Peirce's work on abduction is strikingly original and deep. An article by Harman (1965) is also often assumed to introduce the notion of abduction to philosophy. Harman's article makes no specific mention of Peirce's work on abduction. Perhaps Peirce's work had not been "rediscovered" in 1965. Many readers of this book may have only a fuzzy notion about what abduction is, or is taken to be, although they can be expected to have firm opinions on how to define deductive and inductive inference. Hence the best way of introducing the notion is to begin by describing some examples used by Peirce to contrast abductive inference with deductive and inductive inference.

The definitions from Hurley above are about premises "claimed" to support a conclusion. But such claims contain success conditions. A good point at which to begin is to describe what are usually taken to be the success criteria for all three types of inference. In a deductively valid inference, it is impossible for the premises to be true and the conclusion false. In an inductively strong inference, it is improbable (to some degree) that the conclusion is false given that the premises are true. In an abductively weighty inference, it is implausible that the premises are true and the conclusion is false. The abductive type of inference tends to be the weakest of the three kinds. A conclusion drawn by abductive inference is an intelligent guess. But it is still a guess, because it is tied to an incomplete body of evidence. As new evidence comes in, the guess could be shown to be wrong. Logicians have tended to be not very welcoming to the idea of allowing abductive inference as part of logic, because logic is supposed to be an exact science, and abductive inference appears to be inexact. Certainly it is not final. It would seem to be more fallible and conjectural than the other two types of inference.

Abductive inference has often been equated with inference to the best explanation. Harman (1965, pp. 88–89) wrote that "inference to the best explanation corresponds approximately to what others have called abduction." According to Harman, various kinds of reasoning can be shown to be instances of inference to the best explanation. One kind he cited is that of a detective who puts the evidence together to arrive at the conclusion that in a murder case the butler did it (p.89). Another kind of case is that of a scientist inferring the existence of atoms and other subatomic particles (p. 89). Another is the use of witness testimony in which we infer that the witness is telling the truth (p. 89). Harman explicated the latter case of inference to the best explanation as follows (p. 89). Our confidence in the testimony is supported by there being no other plausible explanation than that the person actually did witness the situation described. Hence we draw the conclusion, by inference, that the witness is telling the truth of the matter. It is interesting to note that two of the three kinds of cases cited by Harman show the fundamental importance of abductive inference in legal argumentation.

Abduction is often associated with the kind of reasoning used in the construction of hypotheses in the discovery stage of scientific evidence. A good idea of how abductive inference works in scientific reasoning can be gotten by examining Peirce's remarks on the subject. Peirce (1965II, p. 375) described abduction as a process "where we find some very curious circumstance, which would be explained by the supposition that it was a case of a certain general rule, and thereupon adopt that supposition." The description given by Peirce suggests that abduction is based on explanation of a given fact or finding, a "curious circumstance." The words "supposition" and "adopt" suggest the tentative nature of abduction. As noted above, you can accept an abductively derived conclusion as a provisional commitment even if it is subject to retraction in the future. The expression "general rule" is significant. Abductive inferences are derived from the way things can normally be expected to go in a familiar kind of situation, or as a "general rule." A general rule may not hold in all cases of a certain kind. It is not based on a warrant of "for all x," as deductive inferences so often are. It is not even based on a finding of most or countably many cases, as inductive inferences so often are. It holds only for normal or familiar cases and may fall outside this range of "general rule" cases.

Archeology provides many excellent examples of abductive reasoning. Leakey and Lewin (1992, pp. 28–29) described how a fossil hunter recognized a partially exposed bone fragment as part of a hominid skull. It was flattish, the slight curvature indicating it was part of a skull of a large-brained animal. The other observation pointing to the conclusion that the skull was hominid was that the impression of the brain on the inner surface was very faint. The inference to the best explanation of these observations was the fragment was part of a hominid skull. This plausible hypothesis was a reason for carrying the investigation forward and doing some more excavations, leading to the discovery of a nearly complete homo erectus skeleton. Shelley (1996, p. 282) cited this case as illustrating the use of visual abductive reasoning in archeology, because the diagnosis of the bone fragment as hominid was based on an explanation of the data provided by a close inspection of the site. From this data a plausible hypothesis was formed that was then tested by further investigations, providing more data that could support or refute the hypothesis.

Two of the examples given by Peirce not only illustrate what he meant by abductive inference but also show he was aware that abduction is common in everyday reasoning as well as in scientific reasoning. The first example quoted below (which I call "The Four Horsemen Example") came apparently from his personal experience and shows how common abductive inferences are in everyday thinking (1965V, p. 375).

The Four Horsemen Example

I once landed at a seaport in a Turkish province; and, as I was walking up to the house which I was to visit, I met a man upon horseback, surrounded by four horsemen holding a canopy over his head. As the governor of the province was the only personage I could think of who would be so greatly honored, I inferred that this was he. This was an hypothesis.

The second example (p. 375) (which I call "The Fossils Example") illustrates the use of abduction in science, showing that Peirce was aware of its use in scientific fields such as archeology and paleontology.

The Fossils Example

Fossils are found; say, remains like those of fishes, but far in the interior of the country. To explain the phenomenon, we suppose the sea once washed over this land. This is another hypothesis.

The abductive inference in both these cases is easily seen to follow the pattern of inference to the best explanation. In the fossils example, Peirce actually used the word "explain." We all know that fish require water to survive. That could be described as a general rule—a normal or familiar way that fish operate. But it could be subject to exceptions. Some fish can survive on land for some time. But how could fish survive this far into the interior where there is now no water? The observed fact calls for an explanation. A best explanation could be that there was water there at one time. In the four horsemen case, the given facts are also "curious." Why would one man be surrounded by four other men holding a canopy over his head? We could hazard a guess by saying that the general rule might be something like the following: only a very important person (such as the governor) would be likely to have a canopy supported by four horsemen. But the "only" here should not be taken to refer to the "for all x" of deductive logic or to warrant a deductively valid inference to the conclusion that this man must necessarily be the governor. It is just a guess, but it is an intelligent guess that offers the best explanation.

Hintikka (1998) expressed disagreement with the view that Peirce consistently equated abduction with inference to the best explanation. Although this view may represent Peirce's earlier perspective on abduction, according to Hintikka (1998, p. 511), it was not his mature view. Hintikka argued that Peirce took abduction to be the only way that a new hypothesis can be introduced in an inquiry (p. 511). He then (p. 511) cited a passage from Peirce where he seemed to claim that a hypothesis can be introduced into an inquiry even if it is not based on previous knowledge. But inference to the best explanation is always, by its nature, based on the given facts, that is, on previous knowledge in an inquiry. Therefore, Hintikka argued, Peirce's mature notion of abduction has to be wider than merely being inference to the best explanation. Hintikka also based his argument on some cases of scientific discovery drawn from the history of science, and some comment on what he took these cases to show will be made in chapter 7.

As well as being important in scientific and legal reasoning, abduction is abundant in everyday argumentation and in everyday goal-directed reasoning of the kind that is currently the subject of so much interest in artificial intelligence. An excellent and highly useful account of the form of abductive inference has been given in the influential work of Josephson and Josephson (1994). Their analysis is quite compatible with the account given by Peirce. They described abduction as equivalent to inference to the best explanation. Josephson and Josephson cited numerous examples of the use of abductive inference in everyday reasoning showing how common this form of inference is. The one quoted below (p. 6), in the form of a brief dialogue, is a good illustration.

Joe: Why are you pulling into this filling station?

Tidmarsh: Because the gas tank is nearly empty.

Joe: What makes you think so?

Tidmarsh: Because the gas gauge indicates nearly empty. Also, I have no reason to think that the gauge is broken, and it has been a long time since I filled the tank.

The reasoning used in this case follows Peirce's pattern of inference to the best explanation. Tidmarsh derives two alternative explanations for the circumstances presented by the gas gauge. The obvious explanation is that the gas in the tank is nearly empty. But there is also a possible alternative explanation. The gas gauge could be broken. But Tidmarsh does remember that it has been a long time since he filled the tank. This additional evidence tends to make the hypothesis that the tank is nearly empty more plausible. On balance, the best explanation of all the known facts is that the gas tank is nearly empty. This conclusion could be wrong, but it is plausible enough to warrant taking action. Tidmarsh should pull into the next gas station.

(Continues...)

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Table of Contents

Contents
Acknowledgments
Introduction
1 Abductive, Presumptive, and Plausible Arguments
Abductive Inference
Peirce on the Three Types of Reasoning
Peirce on the Form of Abductive Inference
Scientific Discovery and Artificial Intelligence
Abductive Inference in Legal Evidence
Defeasible, Plausible, and Presumptive Reasoning
Tentative Definitions
Argumentation Schemes
Araucaria as a Tool for Argument Diagramming
2 A Dialogue Model of Explanation
Types of Explanation
Models of Scientific Explanation
Simulation, Understanding, and Making Sense
Scripts, Anchored Narratives, and Implicatures
The Dialogue Model of Explanation
The Speech Act of Explanation
Dialogue Models of Scientific Argumentation and Explanation
Examination Dialogue and Shared Understanding
Dialectical Shifts and Embeddings
3 A Procedural Model of Rationality
Computational Dialectics
Reasoning as Chaining of Inferences
Forward and Backward Chaining Rule-Based Systems in Artificial Intelligence
The Problem of Enthymemes
Multiagent Practical Reasoning
Bounded Rationality
4 Defeasible Modus Ponens Arguments
A Typical Case of Abductive Reasoning in Evidence Law
Argumentation from Consequences
Defeasible Inferences and Modus Ponens
Conditionals and Generalizations
Abductive Inference in Medical Diagnosis
Introducing Defeasible Modus Ponens
Using Defeasible Modus Ponens as an Argumentation Scheme
5 Abductive Causal Reasoning
Necessary and Sufficient Conditions
Forms of Causal Argumentation
Argument from Correlation to Cause
Abductive Causal Reasoning in Law
Causal Abduction in Medical Examination and Diagnosis
Causal Reasoning as Dynamic Improvement of a Hypothesis
The Thesis That Causal Reasoning Is Abductive
Causal Explanations
The Chain of Reasoning in the Accident Case
Insights into Causal Argumentation Yielded by the Abductive Theory
6 Query-Driven Abductive Reasoning
Argument Extrapolation by Chaining Forward
Colligation in Chaining Backward
The Form of Abductive Inference Revisited
Belief-Desire-Intention and Commitment Models
The Abductive Profile of Dialogue
Abduction as a Query-Driven Process
Discovery as an Open Process
Retraction of Commitment
The Four Phases of Abductive Reasoning
7 Unsolved Problems of Abduction
Abduction and Argumentation Schemes
Enthymemes, Argumentation Schemes, and the Defeasible Modus Ponens Form of Reasoning
The Role of Examination in Science
Accounts and Explanations
The Problem of Inconsistency
How Abductive Reasoning Moves Forward by Examining Competing Accounts
Question-Answering and Critiquing Systems in Artificial Intelligence
Summary of Abduction as a Heuristic
Notes
References
Index

Editorial Reviews

“Abductive Reasoning makes a significant and original contribution. It is interdisciplinary in the right way: the drawing together of fields is demanded by the nature of the problem and issues, not by ideology or administrative decree.” —Jonathan E. Adler, author of Belief's Own Ethics


“Walton’s book is a good account of abductive reasoning, especially in the field of witness testimony, or argument from expert opinion.” —Artificial Intelligence and Law

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