Dialectics and the Macrostructure of Arguments: A Theory of Argument Structure 9783110875843, 9783110133905

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Dialectics and the Macrostructure of Arguments

Studies of Argumentation in Pragmatics and Discourse Analysis (PDA) This series contains reports on original research in both pragmatics and discourse analysis. Contributions from linguists, philosophers, logicians, cognitive psychologists, and researchers in speech communication are brought together to promote interdisciplinary research into a variety of topics in the study of language use. In this series several kinds of studies are presented under headings such as 'Argumentation', 'Conversation' and 'Interpretation'. Editors Frans Η. van Eemeren Rob Grootendorst University of Amsterdam Department of Speech Communication

Dialectics and the Macrostructure of Arguments A Theory of Argument Structure

James B. Freeman

FORIS PUBLICATIONS Berlin · N e w York 1 9 9 1

Foris Publications Berlin · New York (formerly Foris Publications, Dordrecht) is a Division of Walter de Gruyter & Co., Berlin.

© Printed on acid-free paper which falls within in the guidelines of de ANSI to ensure permanence and durability. Library of Congress Cataloging in Publication Data Freeman, James B. Dialectics and the macrostructure of arguments : a theory of argument structure / James B. Freeman. p. cm. - (Studies of argumentation in pragmatics and discourse analysis) Includes bibliographical references and index. ISBN 3-11-013390-3 (cloth : alk. paper) 1. Logic. 2. Reasoning. I. Title. II. Series. BC71.F738 1991 91-34309 168-dc20 CIP

Die Deutsche Bibliothek Cataloging in Publication Data Freeman, James B.: Dialectics and the macrostructure of arguments : a theory of argument structure / James B. Freeman. - Berlin ; New York : Foris Publ., 1991 (Studies argumentation in pragmatics and discourse analysis ; 10) ISBN 3-11-013390-3 NE: GT

© Copyright 1991 by Walter de Gruyter & Co., D-1000 Berlin 30 All rights reserved, including those of translation into foreign languages. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Printing: ICG Printing, Dordrecht Printed in The Netherlands.

THIS BOOK IS DEDICATED TO DR. BEN KIMPEL MY FIRST TEACHER IN LOGIC AND PHILOSOPHY IN DEEP APPRECIATION FOR OUR MANY YEARS OF FRIENDSHIP

Contents

Preface

xi

Chapter 1 The Need for a Theory of Argument Structure 1.1. The Standard Approach 1.2. Toulmin's Rival Account 1.3. Problems for a Theory of Argument Structure 1.4. Further Problems Posed by the Standard Approach

1

Chapter 2 Basic Theoretical Considerations 2.1. The Dialectical Nature of Argument 2.2. Desiderata for Theory and Practice 2.3. The Central Questions in a Basic Dialectical Situation

1 3 6 8 17

17 33 37

Chapter 3 What Are the Basic Elements of Arguments? 3.1. Claims Versus Conclusions 3.2. Toulmin's Problematic Notion of Warrant 3.3. Data, Warrant, Backing or Just Plain Premises?

49

Chapter 4 How Do the Basic Elements Fit Together? 4.1. The Acceptability Question and Serial Structure 4.2. The Relevance Question and

91

49 50 84

93

viii

Contents Linked Structure 4.3. The First Ground Adequacy Question and Convergent Structure 4.4. The Linked-Convergent Distinction

Chapters

93

95 96 111

What Should We Do With Modalities? 5.1. Modalities — What Are They? 5.2. How Do Modalities Fit into Arguments? Chapter 6 Rebuttals — What is Their Place in Argumentation? 6.1. Introduction 6.2. Are Rebuttals Separable Elements in Arguments? 6.3. Are Only Exceptional Conditions Rebuttals? 6.4. How Do We Represent Rebuttals Diagrammatically? 6.5. Implication of Rebuttals for The Linked-Convergent Distinction 6.6. Counterrebuttals 6.7. Comparison with Other Authors Chapter 7 Further Considerations on Argument Structure 7.1. Mixed Structure 7.2. Rebuttals to Claims 7.3. Arguments Countering Defended Rebuttals 7.4. Refutations by Logical Analogy 7.5. Arguments Involving Suppositions Chapter 8 Adequacy Considerations 8.1. Individuation of Arguments 8.2. Satisfaction of Desiderata

113 127 131 131 134 152 155

158 161 165 183 184 187 188 203 212 233 233 247

Contents

ix

Conclusion Dialectics, Macrostructure, and the Logical Enterprise Appendix Two

255

259 Variations on the Standard Diagramming Arguments

Approach

to

Bibliography

263

Index

269

Preface

This is an essay in logical theory. However, the topics we shall explore are by and large not those one would ordinarily associate with logical theory. We shall not be discussing the nature of entailment, or how well or how poorly it is captured by the '3* of material implication. We shall not be discussing how many truth-values there are or whether some modes of statement compounding leave truth-value gaps. We shall not be exploring interpretations of quantifiers or patterns of inference involving them. All of these themes pertain to deductive logic. A hallmark of deductive logic is its concern with logical form or structure. Determining the form of an argument is central to assessing whether or not it is deductively valid. We shall be concerned here with the structure of arguments also, but structure in a radically different sense. Whereas deductive logic is concerned with the microstructure of arguments, we shall be concerned with their macrostructure. What do we mean by this distinction? In deductive logic, analysing the logical form of an argument involves looking, to some degree, at the internal structure of the statements which compose it. Whether we are dealing with truth-functional validity, syllogistic validity, generalized quantificational validity, or even validity in some modal system, we shall be concerned with how at least some statements in our argument are built up from their constituent parts. Even with so simple a form as modus ponens, one must see that one premise is a conditional, that the other is the antecedent of that conditional, and that the conclusion is the consequent. Thus this involves looking at the internal structure of at least one statement in the argument. By contrast, when we speak of structure in this essay, we shall be concerned principally with how statements as wholes enter into arguments. What statements are put forward to support, give evidence for, allegedly entail, what other statements? What configuration does this support relationship display? These are macrostructural issues. It is macrostructure which is displayed through the tree or circle and arrow diagramming technique currently presented in many informal logic texts. In diagramming an argument in natural language, we are concerned to portray how the component statements as wholes hang together, rather than look at their internal structure. In constructing circle and arrow diagrams, we are not concerned with whether a component

xii

Preface

statement in an argument is a conditional, disjunction, categorical proposition, or an instance of some generalization. It is easy to appreciate that macrostructural analysis is far more general or generic than analysis for microstructure. Issues of microstructure arise for specific families of arguments. We may identify various classes of arguments — those whose validity depends on their truth-functional structure, syllogistic structure, or generalized quantificational structure. Different types or degrees of microstructural analysis are needed in each case. Furthermore, such analyses might not be at all revealing of logical cogency if applied to inductive arguments of various types. (Notice however that microstructural issues are also adjunct to evaluating inductive arguments. To assess the strength of a categorical inductive generalization argument, it is necessary to see its premises as instances of some generalization which constitutes the conclusion. Likewise, for arguments by analogy, it is crucial to identify reference items, target item, similarities argued from, similarity argued for. But all this involves looking at the internal structure of the statements out of which an argument is composed.) But in any text purporting to express an argument, we should be able to distinguish statements presenting evidence from claims that evidence purportedly supports. This indicates why macrostructural analysis is especially important in informal logic. A central goal, if not the goal, of informal logic is to develop means of appraising arguments in ordinary language. But such arguments are of all types. Some are deductive. Others are instances of some standard inductive family. Still others may not obviously fit into any of these categories. Generic tools which could be applied in the analysis and evaluation of any of these arguments would be far more in line with the informal logician's goal than tools restricted to some particular family. Furthermore, recognizing that an argument was a member of a particular family, that it was an instance of a pattern pre-identified as logically important, might require some degree of sophistication. To gain this sophistication, one might have to practice on artificial arguments or formal argument schemata, the very thing informal logic seeks to eschew. The generic aspect of macrostructure is not the only reason why it is interesting and important in informal logic. Indeed, enthusiasm for constructing tree diagrams to picture the macrostructure of arguments is not hard to understand. The tree diagraming method provides a way of displaying the logical support structure of arguments in ordinary language. And without seeing how an argument hangs together, without being able to recognize what supports what, how can we meaningfully have argument evaluation? How can we evaluate just how well an argument supports its main conclusion until we see what reasons are given to directly support the main conclusion, which of those reasons in turn are supported by argumentation, what implicit assumptions, if any are entertained in each of these various reasonings? Diagrammatic representations allow us to identify the

Preface

xiii

subarguments out of which a complex argument is built. Once identified, we can apply critical questions to assess the cogency of each subargument and the cogency of the whole. This essay differs from logical theory developed under the deductive logic paradigm in another way. Our very understanding of the nature of argument is different. As an emphasis on macrostructure is a distinctive feature of much informal logic pedagogy, so an emphasis on the dialogical or dialectical nature of argument is becoming a prominent feature of the theory of informal logic and argumentation. In standard logical theory, one would define an argument as a passage, a set of statements, in which some statements, the premises, are put forward to support other statements, the conclusions. Such discourses could be prepared and presented by one person. This is the monological view of argument. Against this, there is a strong emphasis in much informal logic theory that argument must be viewed primarily as an interchange between two or more persons. Argument is basically dialogical, not monological. In Chapter Two, we develop the notion that certain interchanges, basic dialectical situations, are fundamental to modelling how argument develops. We see arguments generated through a challenge-response dialogue where the proponent of some thesis answers critical questions posed by a challenger. We may view arguments in the monological sense as products of such dialogical exchange processes. We thus accept the process/product distinction for argument put forward by a number of authors. And we agree that process is fundamental to understanding argument. Indeed, the fundamental thesis of this book asserts that we can properly motivate and understand the structure of arguments as products through considering the various challenges which may arise in basic dialectical situations, arguments as process. We shall thus present a dialectical theory of argument macrostructure. This emphasis on process and dialectical exchange explains why we devote so much attention to the work of Stephen Toulmin, in particular to his essay, The Uses of Argument. In that work, Toulmin advocated replacing what he called the geometrical model of understanding argument with a jurisprudential model. But surely just as a geometrical demonstration is a paradigm example of a monological argument, a paradigm example of a dialogical argument is the exchange between two opposing attorneys. In The Uses of Argument, Toulmiri contributed an account of argument macrostructure where certain structural distinctions are motivated by distinct questions which an interlocutor can ask someone prepared to advance and defend some thesis. In this account, Toulmin introduces novel categories for the analysis of arguments. Although Toulmin motivates only some of these categories by distinct questions, this motivation could be straightforwardly extended to the others. Not only can we do this, we contend that doing so

xiv

Preface

is very illuminating in most cases for understanding argument macrostructure. Hence, our approach owes a very distinct debt to Toulmin's work. This does not mean, however, that we have simply appropriated Toulmin's categories in our work. Although we believe that Toulmin's scheme is highly profitable for the analysis and ultimately the evaluation of arguments, we reject some of his categories as proper for analysing the macrostructure of arguments as products, and we radically rethink Toulmin's conception of certain other categories. It is incumbent on us, therefore, to argue for our adaptation of Toulmin's scheme and overall approach. This can only be done by critically examining at length both Toulmin's views on the nature of these structural categories and the interpretation of them as categories of macrostructure for arguments as products. Toulmin's system for analysing arguments also highlights why we need a theory of argument macrostructure. Someone approaching the issue of macrostructure from the perspective of standard logical theory might be quite puzzled over the proposal to present a theory of argument macrostructure. After all, are there not just two macrostructural categories — premises and conclusions? Premises give support; conclusions receive support. What could be simpler than that? What is there to theorize over? Let us move on to more substantive issues! The advent of informal logic has changed this situation completely. As we point out in Chapter One, the tree or circle and arrow method for displaying argument macrostructure now popular in informal logic pedagogy envisages premises and conclusions combining in a number of different ways. Properly distinguishing these ways raises theoretical issues. The need for theory becomes much more acute when we are confronted with Toulmin's rival system of categories. The purpose of this paper is to develop a theory-backed account of argument macrostructure. Work on this essay began while I held a Fellowship Leave from Hunter College of The City University of New York. I hereby wish to thank Hunter College for granting me this leave. The camera-ready copy was produced in the Hunter College Academic Computing Services. I again wish to thank Hunter College for making the proper facilities available to me, and to thank Mr. Andrew Blaner, microcomputer specialist, for his technical assistance. Professors George Bowles and Gerald Press read an earlier draft of this manuscript. I thank them for their comments. Thanks are also due to an anonymous referee of Foris Publications whose comments helped greatly in focusing this essay. The responsibility for any views expressed here is, of course, completely mine. Finally, this preface contains certain brief excerpts from my paper, "The Place of Informal Logic in Logic," which appears in Ralph H. Johnson and J. Anthony Blair (eds.), Informal Logic: Second Series (Informal Logic Publications, 1991). J. B. F.

Chapter 1

The Need for a Theory of Argument Structure 1.1. THE STANDARD APPROACH

The approach to argument diagramming which we call standard was originated, to the best of our knowledge, by Monroe C. Beardsley in Practical Logic [1950], renamed Thinking Straight in later editions. Beardsley's system is simple to describe. It calls for identifying the component assertions in an argument, bracketing and numbering them. In diagramming, these numbers encircled represent the component assertions of the argument. Those which are basic reasons, which are not supported, at least in that argument, by further reasons, appear at the top of the diagram. Downward directed arrows point from these reasons to the assertions they directly or immediately support. If any of these are intermediate conclusions, further downward directed arrows will point from them to the assertions they directly support. This continues until we reach the final conclusion or conclusions of the argument. In Practical Reasoning in Natural Language [1986],1 Stephen N. Thomas significantly refined Beardsley's procedure. He first contributed names to the various basic patters which diagrams may display. If two or more statements are immediately supported by the same premise, we have divergent structure. If one statement supports an intermediate conclusion, that supports a further conclusion (and that a further...), we have serialstructure. But Thomas noted that two or more statements could immediately support a single conclusion in two distinct ways. In some cases, the reasons are independent of each other. In others, each of the reasons is somehow dependent on the others to support the conclusion. The first pattern Thomas calls convergent the second, linked. Both Beardsley and Thomas accept then the quite conventional view that the component elements in arguments are statements or assertions. There are two different structural roles statements may play, premise or conclusion, and these roles are not exclusive. We may schematically represent the four basic structures this way:2

The Need for a Theory of Argument Structure

2

©

©

1 Θ ® ©-Γ-©

/ \ 0?I \© / T ©

©

©

DIVERGENT

SERIAL

CONVERGENT

LINKED

Of course, we can have complex arguments displaying several, even all, of these patterns. In such arguments, we can recognize subarguments which are serial, divergent, linked, or convergent. For example, the following diagram might represent the structure of a given argument:

Θ

G

I

0J, ©-

IΘ ©

\ Θ/

©

G

Many other textbook writers have followed Thomas by incorporating this diagramming procedure in some form into their texts.3 This approach has become so well received that we may refer to it as the standard approach. It would be wrong to infer, however, that this approach appears only in textbooks and is interesting only as an informal logic pedagogical technique. In Galileo and the Art of Reasoning, [1980], Maurice A.

Toulmin's Rival Account

3

Finocchiaro uses argument diagrams to analyze several arguments appearing in Galileo's Dialogue Concerning the Two Chief World Systems. These are substantial arguments concerning the scientific controversies of Galileo's day. Finocchiaro regards the diagrams as essential preparation for evaluating these arguments. In Speech Acts in Argumentative Discussions, [1984], Frans Η. van Eemeren and Rob Grootendorst present a diagramming scheme which also employs the same structural configurations as the standard approach.4 This has especial interest in the light of our discussion in Chapter Two, where we argue that argument is basically dialectical or dialogical. Van Eemeren and Grootendorst include their remarks in their discussion of analyzing arguments arising in discussions, exchanges between a proponent and a challenger. This indicates that the standard structures can be used to represent the structure of arguments arising in such dialogues, and not merely the structure of arguments put forward by a single arguer speaking or writing in monologue. We shall have much more to say of these matters in due course. But the standard approach is not the only approach to analyzing argument structure. It has a noteworthy rival in the Toulmin model, which we consider in the next section.

1.2. TOULMIN'S RIVAL ACCOUNT

In Chapter Three, "The Layout of Arguments," of The Uses of Argument [1958], Stephen Toulmin presents a distinctly different view of how arguments are structured. We must, however, raise one issue at the outset. The standard approach to diagramming arguments is clearly intended as a method for analyzing argumentative texts, written or spoken discourses which contain arguments. Although one would naturally presume in reading Toulmin's account that he is also presenting a method of textual analysis, this view is open to question. We must here anticipate a distinction we shall develop later in this essay, the distinction between argument as process and argument as product. Argumentative texts are products. They are in a straightforward sense the finished results of some deliberative process. This process, as we shall argue, can be appropriately modelled as a dialogical interchange between the arguer as proponent and a challenger as questioner and rational judge. The argument as product develops and evolves through a challenge-response process. Given this distinction, the question arises as to whether Toulmin's model is intended to describe the structure of the argument as process or the argument as product. In the Introduction to The Uses of Argument, Toulmin makes this significant remark: Logic (we may say) is generalized jurisprudence....A main task of jurisprudence is to characterize the essentials of the legal process: the procedures by which claims-at-law are put forward, disputed and

4

The Need for a Theory of Argument Structure

determined, and the categories in terms of which this is done. Our own inquiry is a parallel one: we shall aim, in a similar way, to characterize what may be called 'the rational process', the procedures and categories by using which claims-in-general can be argued for and settled. 5

Again, Toulmin says that the question he is addressing in his account of the layout of arguments concerns "the functions of the different propositions invoked in the course of an argument and the relevance of the different sorts of criticism which can be directed against it. "6 Not just the function of the different sorts of propositions which could be incorporated into the argument as product, but the relevance of the criticisms, e.g. the critical questions which a rational judge could raise in the course of the argument as process, are part of argument analysis. These passages suggest that Toulmin is developing a means of analyzing argument as process rather than product. Yet, there are other passages which suggest that Toulmin is ambivalent about this issue. The introductory paragraphs of "The Layout of Arguments" suggest that Toulmin intends to present a method for analyzing arguments as products. He begins by observing that arguments can be set out on printed pages or delivered in oral address, i.e. arguments can be presented monologically. Such arguments are ultimately composed of sentences, and it is these sentences which can be "laid out" in various ways. Toulmin questions the adequacy of the traditional layout of "three propositions at a time, 'minor premiss; major premiss; so conclusion'."7 He believes a more elaborate layout is necessary if arguments are to be properly —"candidly" is his term—analyzed. This all suggests that Toulmin intends his model as a tool for analyzing argumentative texts. However, Toulmin also suggests that the proper layout of arguments must be developed with an eye to procedure and logical process on analogy with legal process. I believe this ambivalence may be resolved faithful to Toulmin*s intentions this way: The statements composing arguments as products have various functions, functions which are derived from or reflective of their role in arguments as process. A proper understanding of the structure of arguments as products must reflect the functional roles statements may play in arguments as process. In this light, Toulmin is offering a mode of analyzing argumentative texts, but one which sees product structure dependent upon process structure. There are other reasons why it is natural to interpret Toulmin as describing the structure of argumentative texts. First of all, our training,

Toulmin's Rival Account

5

and we would expect the training of the vast majority of Toulmin's audience, leads us to identify argument with argumentative product. Arguments «^discourses in which certain statements are put forward to support others. Hence, we on our first reading of Toulmin and we believe others have taken him to be proposing a structural analysis of arguments as products. In addition, despite Toulmin's intentions, we may simply take his account as a proposed method for analyzing argumentative texts. We may examine this proposal on its own merits, independently of whether Toulmin would explicitly endorse it. Having given these caveats concerning Toulmin interpretation, we can now proceed to present this rival account of argument structure. Premises and conclusions—every argument needing at least one of each—are the two functional roles for statements standardly distinguished in arguments. By contrast, Toulmin distinguishes six roles for argumentative elements, six types of elements in his account of the layout of arguments. Conclusions, or as he ordinarily calls them, claims are one of these six types. Facts given to support, justify, ground a claim are data. Data are potential answers to the question "What have you got to go on?" asked to challenge a claim, and the range of facts which may be presented in various arguments is quite broad.8 Data would be counted as premises under the standard analysis. But when data are offered to support a claim, the arguer may be challenged further to explain why the data are pertinent to the claim; why do the data constitute evidence for the claim? Why are we justified in making a move from the premises to the conclusion? The element providing this explanation, answering the question "How do you get there?" Toulmin calls a warrant. Warrants may be presented as hypothetical or generalized hypothetical statements. "Data such as D entitle one to draw conclusion, or make claims such as C" or "Given data D, one may take it that C" constitute their canonical form.9 Consideration of warrants leads Toulmin directly to identify two further types of elements in argument, not part of the standard analysis. First, different warrants permit asserting our conclusions with different degrees of force, given our data. "Necessarily" is appropriate in some cases, while "probably," "presumably" properly describe the warranted force in others. Expressions indicating various degrees of force Toulmin calls (modal) qualifiers. That there are such differences indicates we should be able to include qualifiers in the layout of arguments. Secondly, warrants which apply ordinarily may have to be set aside in certain cases. Given that a decedent has bequeathed a piece of property to an individual in his or her will, we may take it that the individual will be the rightful owner of that property upon settlement of the will. But wills may be legally invalidated and in such cases this warrant must be set aside. Toulmin believes we should also be able to represent such "conditions of exception or rebuttal,"10 in the layout of arguments, which he standardly refers to as rebuttals.

6

The Need for a Theory of Argument Structure

The final type of element Toulmin distinguishes is the backing an arguer may give for a warrant. Warrants may be challenged and backing offered to certify their authority. Why is it that given the provisos of a will, we may take it that certain individuals have rights as beneficiaries? The proper answer involves citing the appropriate provisions of probate law. Such provisions then would be backing for the warrant. Toulmin structures these elements he has distinguished in the following way to diagram the layout of arguments: ^

Since

W

So,

Q,

c

Unless R

On a c c o u n t of

Β

This is all straightforward. We appeal to data D to justify claim C. The arrow indicates this evidential support. The warrant W licenses the move from D to C and so is "attached to" the arrow. The backing Β authenticates the warrant and so is attached to it. The modal qualifier Q is understood to modify the claim, indicating the force with which it is asserted, and so is written next to the claim. Rebuttals R indicate conditions when the warrant would have to be set aside and so the force of the claim invalidated. Hence they are attached to the modality. Here then we have Toulmin's approach to argument structure, a distinctly different layout from the standard approach.

1.3. PROBLEMS FOR A THEORY OF ARGUMENT STRUCTURE

Toulmin poses a challenge to the standard approach because his account is radically different. On the standard approach, there are basically just two types of elements in arguments—premises and conclusions. These are the two, and the only two, functional roles statements may play. Function is indicated by the position of the statement, or the encircled number representing the statement, in the argument diagram. Appearing at the head of an arrow, it is a conclusion. Appearing at the tail, perhaps linked together with other statements, it is a premise. Arguments then are structured entities built out of statements. Also on the standard approach,

Problems for a Theory of Argument Structure

7

argument structure itself is very multiform. Given as basic the convergent, serial, divergent, and linked patterns, together with the primitive pattern of one premise supporting a conclusion, we can generate a myriad of patterns by successively combining simpler structures into more complex. The standard approach then envisions a basic homogeneity in the type of elements that may enter into arguments together with an astonishing multiplicity in the structural patterns into which they may enter. With Toulmin's approach, on the other hand, there is a multiplicity of elements together with a basically fixed pattern into which they may enter. Notice also that not all the elements in an argument are statements playing some functional role. Data, claims, and backing are statements. As we shall discuss at length in Chapter Three, just what warrants are is problematic, but there is ample reason not to count them simply as statements. Modalities and rebuttals do not make complete assertions, and so are not statements. There are then six different types of elements which may occur in arguments, according to Toulmin. But the structural pattern arguments display is by and large fixed. It is the pattern presented in the previous section. Although we may not need always to include modalities, rebuttals, or backing, and so some arguments will have simpler structures than others, when an element appears in an argument, it will in general appear in a specific position." Toulmin's rival account thus raises two central questions about argument structure: 1. What are the fundamental elements of arguments? 2. How do these elements fit together? Just what are the structural categories, the types of elements to be discovered in arguments? Are they the standard two or Toulmin's six? There is no dispute over claims—conclusions on the standard approach. There cannot be argument without an attempt to establish at least one point. But Toulmin's other elements are controversial. Data, warrants, and backing might all be counted as premises on the standard approach. Do we have distinct types of elements here? Modalities and rebuttals have no standard counterparts. Are such elements to be found in arguments? Much of the novelty of Toulmin's approach lies in distinguishing these elements. What value does this have as a potential contribution to a theory of argument structure? Even with these issues settled, we must address the question of whether there is essentially just one pattern for argumentative elements or whether they may combine in myriad ways. To answer all these questions, indeed to decide between these two approaches, to appraise properly what contribution each makes to our understanding of structural issues, we need to develop a theory of argument structure. We need to have some theoretical backing or framework within which to develop our answers.

8

The Need for a Theory of Argument Structure

Toulmin's rival account even raises the theoretical issue of just what is to count as one argument. Toulmin readily admits that data may need defending and may be supported by argument. However, for Toulmin, such argumentation constitutes a separate argument, distinct from the argument for the main claim at issue, rather than a subargument of the overall reasoning for that claim. We argue for the data as a lemma. When that argument is completed, we proceed to use the data to support the main claim. On the standard approach, argumentation for lemma and subsequent argumentation for main claim might all be viewed as constituting one argument involving serial structure. Toulmin's alternative approach raises this question: Just how do we individuate arguments? When do we have one argument, as opposed to two? Can we answer such a question without a theory of argument structure? These problems, then, raised by Toulmin's approach, show the need for such a theory.

1.4. FURTHER PROBLEMS POSED BY THE STANDARD APPROACH

Even without the Toulminian challenge, the standard approach would still need a theory of argument structure. This can be argued very persuasively from the problems persons have encountered in constructing argument diagrams. Some have raised complaints that instructions in informal logic texts are unclear or misleading—that one might plausibly follow them and yet diagram arguments incorrectly. Two answers may seem possible, without there being a way to justify one over the other. The approach may seem intuitive, with all the vagaries of intuition. More seriously, one might flat out disagree with an author of a text over the correct diagramming of an argument. But should we feel that a certain diagram does not correctly picture the structure of an argument, how can we argue against the diagram unless there are some clear criteria for determining correct answers? If the provided diagramming instructions will not help in this instance, we need to develop andjustify alternative or revised instructions. But where shall we find that justification except in looking at the theory behind what diagrams are about, the theory of argument structure? The problem here is not simply how to diagram certain ambiguous, problematic cases. To some extent, ambiguity may be unavoidable, since we are working with proverbially "messy" natural language. We might expect a diagramming technique for natural language arguments to inherit some of the vagueness of natural language. In some instances, what we are trying to diagram may be just plain ambiguous. But it does not follow that all

Further Problems Posed by the Standard Approach

9

ambiguity is unavoidable. Nor is the problem how to construct diagrammatic representations of structures we can already clearly define or characterize. The problem goes much deeper than that. The problem is with the very characterization of certain basic argument structures. How certain structures are distinguished has seemed so ambiguous in application as to call the enterprise of structural representation, and so most issues of argument macrostructure, into question. The central problem confronting the standard approach to argument diagramming is making clear the distinction between convergent and linked structure. Open disagreements arise over whether a particular example is linked or convergent. In [1986], Thomas characterizes linked structure this way: When a step of reasoning involves the logical combination of two or more reasons, they are diagrammed as linked}2 Reasoning is linked when it involves several reasons, each of which needs the others to support the conclusion.13 In general, suitably related pieces of evidence that fit together to support or justify a given hypothesis, scientific or otherwise, can be diagrammed as linked.14

Thomas gives convergent structure this characterization: When two or more reasons do not support a conclusion in a united or combined way, but rather each reason supports the conclusion completely separately and independently of the other, the reasoning is convergent." If neither reason needs the other reason (or anything like the other) in order to support the conclusion, then the reasoning can be diagrammed as convergent reasoning.16

What are the key words in these characterizations? They are "logical combination," "needs the others," "that fit together," "in a united or combined way," "completely separately and independently." Without the benefit of theory, these are all highly intuitive, ambiguous concepts. Without some explanation of what logical combination—or the lack of it, one reason needing another, or two or more reasons fitting together mean, we can easily imagine persons disagreeing over whether two reasons need each other. Indeed, we might expect situations to arise where we feel two or more reasons need each other in some sense to support the conclusion properly, but not in the sense required for linked structure. But how do we explicate that sense? Thomas offers one other criterion for distinguishing linked from convergent structure—to our mind a lot clearer. He says if each separate reason still would support the conclusion just as well even if the other (separate, independent) reason(s) were false, and each

10

The Need for a Theory of Argument Structure

separate line of reasoning could still be equally good even if the other line(s) of reasoning happened to be no good, 17

then the reasoning is convergent. However, if the falsity of one reason were to undercut the force of the others, the reasons should be linked. Thomas of course admits that there will be hard cases to adjudicate, for various reasons. He also admits the theoretical difficulty here. "Natural logic still has not fully solved the difficult problem of giving a general, exhaustive formula for distinguishing linked from convergent inference in natural languages." 18 Thomas is not the only one to have problems with making a clear distinction between linked and convergent structure. Recent discussions in the APA Newsletteron Teaching Philosophy are significant. In [1984a], Lee Rowen first characterizes an argument with linked (in her terminology "conjoint") structure as one where "a conclusion is supported by two or more premises each of which contributes to the support which the others in the set give to the conclusion." 19 We have convergent ("disjointly supporting premises") structure when the reasons are logically independent, are not contributing any "logical connection" to the support the other(s) give to the conclusion.20 She also speaks of premises giving "partial support." Frequently, such premises must be linked with supplied suppressed premises to get complete support. Here again, we note a problem with lack of clarity. What do "each of which contributes to," "logical connection," "partial support" mean? (In fairness to Rowen, we should point out that she develops in [1984b] a criterion for distinguishing linked from convergent arguments free of such intuitive, ambiguous terminology. We cite her discussion in [1984a] to illustrate how problematic terminology is associated with the linked/convergent distinction.21 In [1984], Robert Yanal said he used such phrases as "conceptually similar," "in the same line of thought," "logically dependent," "fill in the logical gaps," "support each other" to informally characterize when premises should be linked.22 Again, we have rather unclear descriptions of the conditions for linked structure. How do these characterizations of linked and convergent argument structure lead to disagreements or unintuitive determinations of particular examples? How by following them might we produce "wrong" diagrams? Let us examine particular cases. I

Cigarette smoking poses a substantial health risk to the smoker. It also poses a risk to those nearby who must breathe the smoke secondarily. Therefore people should not smoke cigarettes.

Many would regard this argument as having convergent structure, two separate, independent reasons being given for the conclusion. But surely although each premise by itself gives some support to the conclusion, taken

Further Problems Posed by the Standard Approach

11

together do not we have a stronger case? If so, does not one contribute to the support of the other? Don't they both "fit together"—both report adverse effects of smoking? Aren't they in the same line of thought? Isn't the structure then linked? In example I, the first premise gives a strong reason for not smoking. The second premise gives a significant reason against smoking in public if not against smoking in general. This suggests that one reason does not need the other to support the conclusion, and makes a convergent diagram plausible. But suppose we had several premises each of which gives only some support to the conclusion? II

La Petite Coloumb has the best chef in town. The live entertainment there is outstanding. The menu is also quite varied. Thus we should go there for dinner.

Is the structure of this argument linked or convergent? Each premise describes a rather different aspect of La Petite Coloumb. Each independently of the others gives us some reason for the conclusion, leading us to think the structure is convergent. But does any of the three, by itself, properly support, give us a good argument for, the conclusion? Would basing our decision to go to La Petite Coloumb for dinner on just one of these factors be hasty? Besides, all three premises discuss positive factors of one and the same restaurant. Does this mean they are in the same line of thought? Is the structure linked? There is overt disagreement concerning the structure of inductive generalization arguments in the literature. Thomas regards them as linked; Yanal explicitly questions this. Taking (1) e, is an A and a B. (2) e2 is an A and a B. • •

(n) en is an A and a B. Λ (n+1) All A's are B's. as the paradigm schema for inductive generalizations, we may regard each of (1), (2), ..., (n) as providing a bit of evidence—perhaps a very small bit of evidence for the conclusion (n+1). Since each instance is presumably distinct from the others, each premise presents a separate piece of evidence for the conclusion, indicating convergent structure. Thomas argues that inductive generalization arguments are linked because "the strength of support is much greater when the instances are considered in union together, and each reason needs the truth of the others in order for the conclusion to be supported. h23 Suppose we found an ej which was A but not B. Then "the support given the conclusion by the other positive instances

12

The Need for a Theory of Argument Structure

would be greatly reduced."24 Indeed, their support would be undercut altogether. The falsity of the conclusion deductively follows from the truth of ej is A and not B. We must concede that each separate reason would not support the conclusion just as well if any of the other reasons were false. Applying Thomas' last mentioned criterion for distinguishing linked from convergent structure, such arguments then are linked. But does this show that each premise needs the others to support the conclusion? If we say yes, then how can any inductive generalization support its conclusion unless the premises include a complete enumeration of all instances of A's, together perhaps with the assertion that these are all the A's there are? And here we would have a deductively valid argument, not an induction. In [1984], Yanal considers the following argument, which he adapts from Thomas, as a problematic instance of distinguishing linked from convergent structure. III

(1) Forests are cleared to make way for cultivation. (2) Food trees are poisoned to leave space for better timber trees. (3) Whenever chimps are near human settlements they are threatened with epidemics. That's why (4) the spread of agriculture and forestry threaten the life of the chimp.25

Yanal regards this argument as having convergent structure, although he points out that Thomas diagrams it as linked. Each premise gives some evidence that agriculture and forestry, taken as one activity, threaten the life of the chimp. Each mentions a different factor negatively impinging on chimpanzee welfare. One might object that premises (1) and (3) support that the spread of agriculture threatens the life of the chimp, while (2) gives evidence that the spread of forestry is detrimental to chimpanzees. Don't we have to link these premises together to see why all support saying that the spread of agriculture and forestry threaten the life of the chimp? The conclusion in effect is a conjunction, with (1) and (3) supporting one conjunct, (2) the other. This raises the more general question—What is the structure of deductive arguments proceeding by the rule of conjunction: From To Infer

A Β A&Β

Should arguments exhibiting this structure be diagrammed as linked or convergent? Now clearly, unless Ά ' entails 'B,' the argument from Ά ' alone to 'B' is not valid. The situation is symmetric with respect to 'B' and Ά . ' But are Ά ' and 'B' by themselves irrelevant to Ά & Β'? Doesn't each give us "half" of the information we need for Ά & Β'? But if each separately gives us half of what we need, doesn't that mean that each reason

Further Problems Posed by the Standard Approach

13

separately supports the conclusion? Or is it because both reasons are needed to produce a valid argument that neither completely separately supports the conclusion? Suppose we grant that arguments proceeding according to the rule of conjunction are convergent. Does that indicate that the following argument is convergent also? IV

Tom, a Central High School student, won a National Merit Scholarship. Mary, another Central High School student, also won a National Merit Scholarship. So two (at least) Central High School students won National Merit Scholarships.

As with a conjunction argument, doesn't each premise, by itself, give us half the information we need for the conclusion? Does this argument then have convergent structure? But does either premise tell us that two Central High students won National Merit Scholarships? Don't we need both to support that assertion? These examples amply illustrate that drawing the distinction between linked and convergent arguments is problematic. To offer a preliminary diagnosis, we see the heart of the problem lying in an ambiguity of the key concept "logical support" and so also of the downward directed arrow in argument diagrams meant to represent it. When we say that a premise Ρ logically supports a conclusion C, do we mean that Ρ gives some evidence for C, that Ρ is relevant to C, or do we mean that Ρ gives good or sufficient (although not necessarily deductively entailing) evidence for it? Likewise, when we draw an arrow from Ρ alone to C in an argument diagram, are we saying Ρ is a reason for C or Ρ therefore C,26 i.e. Ρ by itself constitutes a complete "case" for C? Now the question of argument strength introduces the issue of modality. To claim that a premise or set of premises gives a strong reason for a conclusion, if the premises are acceptable, or that it gives at most weak support to the conclusion is to make a modal claim. This is to claim something over and above claiming that the premise is relevant to the conclusion. Clearly, a premise can give us some evidence to support a conclusion without giving us sufficiently weighty evidence. Those who tend to look at logical support as making just the relevance claim and the arrow as indicating just that the premise is a reason for the conclusion will tend to favor convergent arguments for all (or all but the last) of our problematic examples. Those who see logical support involving a modal claim and the arrow indicating "therefore," will tend to link the premises in our various examples. Which interpretation of "logical support" and so which reading of the arrow is correct? A justified answer will come in the context of a theory of argument structure. We shall develop our answer in Chapter Four and

14

The Need for a Theory of Argument Structure

discuss various proposals for distinguishing convergent from linked arguments in its light. Given the ambiguity of "logical support" on the issues of relevance and modality, and the attendant confusion it causes in sorting out convergent and linked argument structures, Toulmin's approach has one distinct virtue—it draws a clearcut distinction between relevance and modality. T o ask the warrant-generating question "How do you get there?", i.e. "How do you get from your data to the claim?" is to ask "Why are those data relevant to the claim?" The primary function of warrants is to explain relevance. They are relevance explaining elements. Modal qualifiers, or as we shall call them modalities, explicitly concern argument strength. With how much force may we assert the conclusion, given the data and warrant adduced in its support? By introducing two distinct types of elements, Toulmin clearly separates and distinguishes these two issues. This could have ramifications for any view of argument structure and an associated diagramming procedure, independent of the merits of Toulmin's overall approach. One virtue of Toulmin's presentation, as we see it, is that it gives some theoretical backing to the distinctions it makes. By seeing argument as involving a quasi-judicial or generalized judicial process, one where different questions will arise at different points in the procedure, Toulmin gives us a rationale for distinguishing various elements in an argument. Different elements answer different questions and so serve different purposes or functions. Difference in function justifies drawing structural differences and adopting distinct ways of representing the various elements of arguments. W e might expect, then, that Toulmin's work could make a significant contribution to the theory of argument structure. However, Toulmin's theory is controversial. Some, especially those in rhetoric, find it illuminating.27 Others, especially in philosophy, have been very critical.28 Does Toulmin's approach give us any justified insights into argument structure and its theory? T o answer this question, indeed to deal with the problems which have emerged in this section, we need a theory of argument structure. In the sequel, we shall develop such a theory. W e shall successively direct our attention to the two central questions: What elements are to be discerned in argument structure? How do these elements fit together? But we must first present our theoretical point of departure. Our theory of argument structure is attendant upon a particular theory or understanding of argument. The motivation for the structural distinctions we make, the framework of our entire approach will be determined by this theory. Hence, it is important that we present it "up front." This we proceed to do in the next chapter.

15

Notes NOTES 1. These refinements appeared with the first edition of the text in 1973. 2. Thomas diagrams linked structure this way:

Θ + Θ — I — Θ

This constitutes only a difference in representational notation from our mode of diagramming linked arguments. Nothing substantive hangs on this difference. Our mode may have the advantage of actually connecting, linking the circles representing linked premises. It is how we represented linked structure in [1988] and other writings, and we prefer to retain it in this essay. 3. See, for example, Scriven, [1976], pp. 41-43; Johnson and Blair, [1977], pp. 176-79; Nolt, [1984], pp. 23-51; Govier, [1985], pp. 125-60; Copi, [1986], pp. 18-28, 38-50; Freeman, [1988], pp. 161-222. Copi introduced argument diagramming into his Introduction to Logic text with the sixth edition, [1982]. 4. For a discussion of Finocchiaro's and van Eemeren and Grootendorst's diagramming systems, see Appendix. 5. Toulmin, [1958], p. 7, italics mine. 6. Toulmin, [1958], p. 9. 7. Toulmin, [1958], p. 96. 8. This is pointed out especially in Toulmin et al, [1984]. 9. Toulmin, [1958], p. 98. 10. Toulmin, [1958], p. 101. 11. Toulmin does suggest that his structure can be modified for arguments where a final conclusion C is drawn from a more general statement C', defended by a (fully) structured argument. C, as Toulmin puts it, is one of a number of possible morals we can draw from C ' . The structure might look like this:

>

So, Q, C

Since

UnleBB

W

R

> So. C

On a c c o u n t of Β Toulmin does not explicitly present this diagram. We may ask, then, whether he would require the argument from C' to C to be fleshed out into a fully structured argument, at least with an explicit warrant. He might ultimately regard the move from D to C' and one argument, and from C ' to C as a second. The point is that with at most a few minor exceptions, Toulmin sees the layout of arguments as fixed. 12. Thomas, [1986], p. 58, first italics mine. According to Thomas, he introduced this distinction in the first edition of Practical Reasoning in Natural Language. 13. Thomas, [1986], p. 58, italics mine. 14. Thomas, [1986], p. 59, italics mine. 15. Thomas, [1986], p. 60, all but last italics mine.

16

Notes

16. Thomas, [1986], p. 62, first italics mine. 17. Thomas, [1986], p. 61. 18. Thomas, [1986], p. 461. 19. Rowen, [1984a], p. 7. 20. Rowen, [1984a], p. 7. 21. See footnote 15 of Chapter Four for further comment on Rowen's criterion in [1984b], 22. Yanal, [1984], p. 1. 23. Thomas, [1986], p. 59. 24. Thomas, [1986], p. 59. 25. Yanal, [1984], p. 2. 26. We owe this contrast to a conversation with Prof. Alec Fischer. 27. Wayne Brockriede and Douglas Ehninger regard Toulmin's contributions as valuable for the rhetorician and develop their utility in [I960], J. Michael Sproule in [1980], pp. 14-15 discusses Toulmin's account of argument structure and appraises it positively. In [1966], Peter T . Manicas cites in his first footnote a number of works by rhetoricians which use Toulmin's model. 28. Critical discussions by philosophers of Toulmin's views on argument structure appear in Manicas [1966], Castaneda [1960], and Cooley [1959].

Chapter 2

Basic Theoretical Considerations Our account or theory of argument structure depends on our account of argument, our understanding of just what argument is. Hence we begin by presenting and defending a model of argument on which our theory of argument structure is based. We want both to describe a model for understanding argument and to determine why we are justified in looking at arguments in light of this model. But what should a theory of argument structure, and the system of diagramming it underlies, do? We believe that there are certain desiderata such theories and diagramming methods should satisfy. Such desiderata should help us in evaluating discussions of argument structure—Toulmin's and others. We may also appeal to these desiderata in justifying our own account of argument structure. We regard these desiderata as intuitively straightforward, and we hope to show how they connect with of our model of argument. We are not saying that a system of diagramming or its theory must satisfy all these desiderata. What we do maintain is that meeting these desiderata is a mark in favor, while not meeting them may be a mark against such a system or theory. Hence, this chapter will present the presuppositions of our project.

2.1. THE DIALECTICAL NATURE OF ARGUMENT

Dialogical Situations and Dialectical Situations Imagine a discussion or debate going on between two or more persons over some contested issue, perhaps one of the "hot" topics of current public controversy. Some if not all of the parties to this exchange have distinct views they would like to put across. Each would like to persuade the others of his or her view. In the course of the discussion, these views will be propounded, attacked, defended, and modified in the light of criticism until either a consensus is reached or the parties abandon or recess the argument. We call such an interchange a dialogical situation, for the participants are clearly engaged in some sort of dialogue with each other. It is clear that frequently dialogical situations are very complex systems of personal interaction, where the participants play various roles. To propound a view and to attack it involve two distinct roles, distinct again from drawing out arguments for or against different positions. That role is distinct again from

18

Basic Theoretical

Considerations

criticizing argumentation. Of course, just because these roles are distinct does not mean that a participant cannot play more than one of them. Indeed, in making one and the same contribution, a participant may be playing several roles. One can attempt to draw out an argument for a view by asking questions in a critical manner. One can ask questions to shore up the logical weaknesses of the argument as developed thus far. Here one and the same person plays both the role of questioner and critical judge. Of course, we can also imagine the participants to such an interaction having distinctly different attitudes toward this dialogical situation. Some may be simply interested in presenting their own opinions and having a go at anyone with the temerity to challenge them or present what appears to be a contrary view. If all the participants in our dialogical situation held this attitude, it is hard to see how consensus—much less rational consensus—could ever emerge. The participants would simply bash each other until bashing served no further purpose or the "discussion" was otherwise interrupted or terminated. But we can also imagine dialogical situations where the participants have a very different attitude. Of course, they shall want to present their own points of view. But they will also want to test these points of view by exposing them to different viewpoints and to the critical probing of the other participants in the dialogical situation. Here, genuine consensus might be a possibility. At least, the participants to the situation should leave it with a better appreciation of the strengths and weaknesses of the views expressed. For reasons which will emerge shortly, we want to call such situations dialectical in addition to being merely dialogical. It is with dialectical situations that we shall be principally concerned. Clearly, the complexity of a dialectical situation varies directly with the number of roles its participants are playing. If several protagonists are each trying to defend a separate and distinct view and are challenging each other to defend their own views, we have a much more complex situation than when one respondent develops an argument under the questioning of an interlocutor-challenger. Such a simple basic exchange we call a basic dialectical situation. Here just one person begins by making a claim, the other challenges it, the respondent answers, and based on that response, the challenger may ask further questions.' We understand that the challenger is not interested in putting forward a position of her own or in defeating or discrediting the basic claim of the respondent or proponent. Her role is simply that of constructive interlocutor, trying to draw out from the proponent the most cogent argument of which he is capable. Her role is to initiate and continue dialogue until a successful, logically cogent argument has been formulated, or it becomes apparent such an argument cannot be given. It is not to cut off exchange but to continue exchange by getting answers to questions, where those answers are logically needed. In effect the challenger plays one compound role. To use van Eemeren and

The Dialectical Nature of Argument

19

Grootendorst's terminology, she is a rational judge, someone whom the speaker regards as evaluating what she says and entitled to question his claims overtly and critically, if she finds them not convincing.2 What Makes Dialectical Situations Dialectical? Why do we call these situations dialectical? First of all, what do we mean by "dialectical"? This word has had a rather wide range of meanings in the Western philosophical tradition. But one concept frequently associated with "dialectical" is that of opposition. In Hegelian and Marxist dialectics, we hear of opposites and the struggle of opposed forces. There is certainly opposition in a basic dialectical situation. For a challenger to question a proponent's claim which he has shown himself committed to puts her in opposition to him. But mere opposition is not enough for genuine dialectic. We have distinguished between dialectical and dialogical situations. Where the participants to a "discussion" belligerently propound their own views and seek to discredit opposing positions by any verbal means whatsoever, including outright fallacious argument, we have a dialogical "exchange" with opposition, but not a dialectical situation. It is not enough merely to co-present opposing viewpoints, and bashing to see who can stand up the longest is not the additional condition required. Following Plato, such situations should properly be called eristical, from έ ρ ι ς , strife.3 We flesh out our conception of "dialectic" more when we specify that the exchange must involve questions and answers. We develop the concept further when we specify that through this questioning and answering procedure the participants are seeking to critically test the views that have been propounded. To use van Eemeren and Grootendorst's terminology, the participants are engaged in a critical discussion, "the purpose of the discussion being to establish whether the protagonist's standpoint is defensible against the critical reactions of the antagonist."4 This means that questions will be designed to expose or lead to the weaknesses of a claim. This is in line with the tradition which counts reductio ad absurdum reasoning as dialectical. To the proponent's claim, the challenger may ask a series of questions leading him to infer the very opposite of his claim. We must add one further condition to the concept of dialectic. This applies in particular to basic dialectical situations and makes them paradigmatically dialectical. We can imagine two persons discussing some issue, making claims about it and raising questions about those claims. But we can imagine the proponent, shortly after enunciating his view, raising questions about it. And we can imagine the challenger propounding contrary claims of her own. Such an exchange could get rather chaotic. It would be hard to assess whether the issue had been advanced or advanced properly. But, as we have indicated in defining a basic dialectical situation, the roles of the participants are strictly defined. One participant is the proponent, who

20

Basic Theoretical Considerations

makes an initial claim and subsequently acts as respondent to the challenger's questions. His role is not to ask questions and ordinarily he will not do so.5 The role of the challenger is precisely to ask questions, and not to propound views of her own. She "is supposed to adopt the position of a rational judge.. .who reacts to the argumentation critically, so that a critical discussion ensues. "6 Her role is not to answer questions, and she ordinarily will not do so. 7 So we may add to our conception of dialectical that a situation is dialectical just in case each participant has a clearly defined role.8 This is an instance of being regimented. Regimentation may concern not only what roles the participants in the discussion may play but standards for recognizing when the dialectic is advancing, when the issue is moving toward resolution.® By a situation being dialectical, then, we mean that it involves some opposition among its participants over some claim, that it involves interactive questioning for critically testing this claim, and that this process proceeds in a regimented, rule governed manner. The rules define the roles of participants and standards of the critical process. We believe this account of "dialectical" is in line with the original use of the term in the Western tradition. As Hall points out in [1967], both Zeno and Socrates engaged in dialectic in the sense of drawing out unacceptable consequences from a hypothesis, and Aristotle credits Zeno with inventing dialectic.10 Socrates widened the concept, regarding dialectic as the search for truth by question and answer," and Plato accepted this characterization. The requirement of regimentation reflects the medieval heritage of the formal disputation, a dialectical exercise.12 Given this explication of the concept dialectical, it is obvious why we call basic dialectical situations dialectical. There is opposition in these situations. The proponent's views are challenged. These challenges are critical challenges, intended to critically test the proponent's thesis and the argument he brings forward to support it. Finally, the procedure is regimented. Proponent and challenger have clearly defined roles. Also, there are standards for judging that the dialectic is advancing. Each contribution, be it a question, answer, or some other assertion, should be determined by or apropos to the previous contributions. A challenger's question will be appropriate just when it spots some logical difficulty or problem. A proponent's answer will be appropriate when it meets the issue of that question. The Basic Dialectical Situation as a Model for Argument We contend that this basic dialectical situation can serve as a model of argument. That is, the paradigmatic arena for argumentation is the exchange, discussion, debate between proponent and challenger over some

The Dialectical Nature of Argument

21

issue. Argument is the attempt to convince a skeptical but rational judge of the rightness or rational acceptability of a claim. In saying this, we are not proposing to make an empirical claim about how arguments in fact are generated. Surely, not all arguments as a matter of fact originate in dialogues between a proponent and a challenger playing just the roles assigned to them in a basic dialectical situation. Many arguments may simply be conceived as monologues, as developing a series of reasons supporting some conclusion. Persons composing them might not imagine they are holding conversations with potential interlocutors or even with themselves. On the other hand, in typical adversarial situations, the challenger will have a thesis of her own to support. She will play the roles both of challenger and proponent. We should expect the proponent to challenge her thesis and its argumentation, thus also playing the additional role of challenger. Of course, we can imagine dialectical situations even more complex than this, with more than two participants playing several roles. But dialectical situations where several persons are arguing for distinct claims could in principle be reduced to the basic dialectical situation. Where several arguments are being developed simultaneously, we can imagine each being developed in its own basic dialectical situation. Interior dialogues where one person questions himself about the acceptability of a view are just special basic dialectical situations where one and the same person plays both the proponent and challenger roles. He is somehow divided in himself. Even if a person composing an argument as a monologue does not consciously carry out this interior dialogue, it seems plausible that the reasons put forward and the considerations entertained are instinctively those which would answer anticipated challenges. The dialogue is implicit. Plato makes this point in the Sophist: "Thought and speech are the same thing, but the silently occurring inner dialogue of the soul with itself has been specially given the name of thought. "13 The point is that we can look at arguments presented by one person in written prose or spoken address as presenting the results of such challenger-respondent dialogues, the argument that has been elicited through them. We may fruitfully draw an analogy between basic dialectical situations and the original contract in Rawls' social contract theory of justice. According to this model, what is just is what would accord with "the principles that free and rational persons concerned to further their own interests would accept in an initial position of equality as defining the fundamental terms of their association."14 The original position involves "a veil of ignorance."15 Those in this position do not know what favors or liabilities society or natural endowment have dealt out to them. They choose the principles which will govern their association in complete ignorance of these factors. In fact, since rational endowment and social background put humans from birth in an unequal position, the original contract is purely

22

Basic Theoretical Considerations

hypothetical. Yet it has normative force. "One conception of justice is more reasonable than another, or justifiable with respect to it, if rational persons in the initial situation would choose its principles over those of the other for the role of justice. Conceptions of justice are to be ranked by their acceptability to persons so circumstanced."16 Similarly, the concept of a basic dialectical situation is hypothetical or an idealization. We are not saying that given a particular argumentative text, there was an actual, historical interpersonal exchange between a proponent and a questioner/rational judge which generated the argument. In particular, we are not claiming that there are, as a matter of fact, rational judges. What we are claiming is that given such a text, we can see the development of the reasons presented to justify the conclusion, the exfoliation of the argument, as prompted by the questions a rational judge would ask in the basic dialectical situation. Not only are we claiming that the argument can be viewed this way, but that this gives insight into argument structure. That is the central thesis of this essay. The model of the basic dialectical situation gives us norms for appraising approaches to understanding and representing the structure of arguments. Furthermore, as the original contract is normative for conceptions of justice, so also is the basic dialectical situation normative for the logical cogency of arguments. We can appraise the logical cogency of an argumentative text by determining whether a rational judge would be satisfied with the argumentation as developed in that text. Would her doubts have been satisfied, her objections met? Or would she continue to ask further questions? Viewing an argumentative text as developing through a challenger/ response exchange, should the challenger qua rational judge be completely satisfied with the responses as incorporated into the argumentative text, then we should have a logically cogent argument. Should she not be satisfied, yet this is all the argument that has been given, then it is incomplete, deficient on one or more logical grounds. What those grounds are we shall indicate later in the course of this essay. We have indicated that arguments as monologues can be pictured dialectically. But it is precisely at this point that our theory raises a measure of controversy. It insists that the process aspect of argument be taken as central and essential to the institution of argumentation. We see dialectical exchange as inherent to understanding what argument is. This goes against the standard logical tradition of defining arguments as discourses where various statements are presented to support some further statement. Such discourses are arguments as products on our view. Insisting on the process aspect of argument also goes against the fact that most arguments we meet with in texts, in editorials, essays, speeches are presented in monologues. One might then ask, given that very many of the arguments we meet with are presented monologically, how can you defend your dialectical conception as basic? How can you justify the appropriateness of this dialectical

The Dialectical Nature of Argument

23

model as basic for our understanding of argumentation? To put the challenge most trenchantly, Is your story of arguments arising in basic dialectical situations simply that—a story? Surely, we may take an argumentative text and reconstruct it as a challenger-response dialogue. From the text, we generate a story of how the argument came to be. But here, the text came first and then the story. Is not the argument as monologue then basic? Does the story or the dialectical model it embodies give insight into the argument? How does our model give insight or focus insight into argumentation? We may argue this on two grounds. First, our model is based on and highlights a comprehensive picture of argument. Secondly, it places the very purpose of argument at the center of understanding what argument is. In "Jürgen Habermas and the Dialectical Perspective on Argumentation" [1979], and in "The Significance of a Rhetorical Perspective on Argument" [1989], Joseph W. Wenzel points out that argument involves a family of concepts. We may distinguish process, procedure, and product. Argument is a natural process of human communication. As such, it is basically interpersonal and interactional. It involves "one or more social actors addressing symbolic appeals to others in an effort to win adherence to theses."17 This aspect of argument has been traditionally studied by rhetoric, which is concerned with how effective these appeals are in winning adherence.18 Argument as procedure involves rules for regulating, deliberately controlling argumentative communication, so that the interlocutors will not merely address appeals but will enter into "a uniquely cooperative effort to reach joint understanding or critical decision."1' Such rules have traditionally been incorporated in dialectics, whose central concern "is to determine and promote conditions for candid and critical argumentation."20 Argument as product involves the linguistic reconstruction of what the argumentative process and procedure have generated. It involves first of all identifying premises and conclusions in what has been generated, "laying out" what is perceived as the argument, with a view to evaluating its logical cogency.21 This is the traditional province of logical appraisal. Our dialectical model of argument involves all three of these aspects of argument. It does not truncate the notion of argument, as a monological model, concentrating on argument as product, might very well do. Merely seeing arguments as discourses in which certain premises are put forward to support or deductively entail a conclusion leaves out the whole dynamic of how arguments are generated. By contrast the dialectical model, the image of the basic dialectical situation is motivated by and pictures the very process by which arguments are generated. And the dialectical model includes the aspects of procedure and product also. Dialectical situations are regimented and they seek to subject theses and argumentation to critical test. This comprehensiveness commends the dialectical model to us.

24

Basic Theoretical Considerations

What is the purpose of argument? As Frans van Eemeren has pointed out,22 arguments by definition seek to establish something. That means there is a gap between some claim and acceptance of that claim. The claim is in doubt and argument seeks to remove the doubt, thus closing the gap. Indeed, if a claim were not somehow in doubt, why argue for it except perhaps as a school exercise? Now a claim's being subject to doubt does not mean that it is actually doubted by some particular person. Imagine a researcher who has just gathered evidence he considers sufficient to confirm some hypothesis, a hypothesis he has framed in the light of his research work. He, at least, is convinced of this proposition. But at this point, others will not have thought about the claim and so have no opinion, much less any doubt, about it. But they certainly might very well have doubts if the researcher just baldly stated his hypothesis, and he is sensitive at some level to this. He realizes that he needs to argue for his hypothesis, and should he proceed cogently here, he will consider the objections persons might bring to his claim. Whether or not he actually imagines reasoning with his challengers, what he is doing is tantamount to attempting to convince them. In framing his argument, he is preparing a case to convince potential challengers of his view. This means that the purpose of arguments is not just to make assertions, even assertions that some statements support others, but to convince an audience, at least a potential audience, of some claim. Nicholas Rescher in Dialectics [1977] reinforces this point for arguments presented monologically, in writing or in oral address: Writing of persuasive intent is closely comparable to disputation. The author is cast in the role of a proponent, and his reader is cast in the dual roles of sceptical opponent and determiner....Reasoning in written exposition can and should be regarded as argumentation aimed at winning over an opponent: in both senses of "winning over," namely defeating the objections he made in his role as opponent, and persuading or convincing him in his role as adjudicative determiner. 23

If we accept that the purpose of argument is to win over—convince, then it should be clear that the dialectical model of argument gives insight into what argument is. Dialectical situations are precisely those situations which intend convincing to take place. The dialectical situation, then, offers a comprehensive picture of argument highlighting its essential purpose. These considerations justify taking it as our basic model of argument. Some Other Dialectical Views on Argument We are by no means alone in seeing argument as dialectical. In [1987], Blair and Johnson endorse a dialectical conception of argument in complete agreement with ours. As they see it, argumentation involves at least two roles, that of questioner and answerer. This, as they point out, goes back

The Dialectical Nature of Argument

25

to Aristotle's conception of a dialectical exchange in the Topics. Argumentation begins when some proposition is challenged, put in doubt, although recognizing that a proposition could be challenged, rather than confronting an overt challenge, may be enough to initiate argumentation. Questioner and answerer have compatible purposes in proceeding with the argumentation. The questioner aims at showing the answerer that the proposition should be challenged (at best) or rejected (at worst), or at discovering that it can withstand challenges. The answerer, conversely, seeks to show the questioner that the proposition can withstand the challenges, or to discover that it should not be accepted (at least in the absence of further support) or that it should be rejected. 24

But these are precisely the respective purposes of proponent and challenger in our basic dialectical situation. The dialectical picture of argumentation is central also to another major contribution to argumentation theory, Perelman and OlbrechtsTyteca's The New Rhetoric [1969]. They advocate a fundamental model of argumentation strikingly similar to ours. For them,demonstration and argumentation are distinct. A mathematician or logician may demonstrate a proposition by showing that it follows from certain axioms. The demonstration is monological. The presence of an audience or interlocutor seems accidental here. But arguing means "using discourse to influence the intensity of an audience's adherence to certain theses."25 According to this conception, argumentation by definition involves two parties, a speaker and the audience. There is a two way interaction between these two parties. Not only is the speaker trying to move the audience to accept a certain thesis, the audience will influence how the speaker will carry out this task. Furthermore, certain audiences will be normative for a speaker, as the questions of our interlocutor are normative. Argumentation addressed to these audiences constitutes convincing as opposed to mere persuading, using certain special features and tendencies of an audience to gain adherence. These normative audiences include the universal audience, "the whole of mankind, or at least, of all normal, adult persons,"26 the single interlocutor, and the speaker or subject himself.27 For normative purposes, the universal audience is principal. What does this mean? For Perelman and Olbrechts-Tyteca, each audience which a speaker addresses is a construction of that speaker. He builds an image of the audience which in particular will indicate what argumentation will be effective. What premises will the audience grant? What attitudes will affect the inferences audience members make? Speaker's images may vary in how true they are to the audiences they depict. The goal, of course, is to develop as adequate an image as possible. A speaker will also develop an image of an audience composed of all rational or competent beings. "Every person believes in a set of facts, of truths, which he thinks must be accepted by every 'normal' person, because they are valid for every rational being. Perelman and Olbrechts-

26

Basic Theoretical Considerations

Tyteca are not prepared to grant that these facts and truths considered valid are in fact valid for every rational being. Each speaker must submit his image to empirical test. However, "he will have done all he can to convince, if he thinks he is validly addressing such an audience."29 To address an argument to the universal audience, then, means to give reasons one believes anyone who understands them will have to regard as compelling. The speaker believes he has a right30 to expect the universal audience to recognize the force of his argument. Hence, for the speaker at least, his image of the universal audience gives him his norms for cogent argument. The model of argument before a mass audience, even should that audience be the universal audience, is problematic, however. An argument addressed to a group audience will display certain rhetorical traits. In particular, it will involve "the technique of the long, sustained speech. But this kind of speech, with all the oratorical action involved in it, would be both ridiculous and ineffective before a single hearer."31 Hence, even if such an argument were logically cogent, we could not presume it would be accepted by all members of the universal audience, at least when those members were addressed individually. When addressing a single hearer, it is normal to take his reactions, denials, and hesitations into account, and when he notices them the speaker does not think of evading them. He has to prove the contested point, apprise himself of the reasons for his 32

interlocutor's resistance, and thoroughly understand his objections.

A single hearer is a genuine challenger. This role is just not possible for a general audience. As long as the single hearer is a representative of the universal audience and so her reactions to the argument bear on its logical cogency, by taking these reactions into account and responding to them the speaker may construct, from his perspective, a more cogent or at least logically tighter argument than if he were composing an address to a collective audience. The single hearer's reactions help to generate a cogent argument from the speaker's point of view. Hence the picture of argumentation before a single hearer who is a representative of the universal audience is strikingly analogous to the picture of the basic dialectical situation. This analogy supports the aptness of our model.33 Two Possible Problems for Our Approach: Demonstrations and Inferences Perelman and Olbrechts-Tyteca's distinguishing demonstration and argumentation raises a critical question for our approach. Demonstrations are standardly counted as arguments, at least as argument products. Demonstrations would seem to be among the argumentative texts whose structure we might wish to analyze. We should want to be able to diagram the structure of logical and mathematical proofs just as well as the structure of arguments for some policy. Our system of structural analysis and the

The Dialectical Nature of Argument

27

diagramming scheme which makes it manifest is supposed to be a generic tool of argument analysis. But if demonstrations are not arguments, why should one and the same system of analysis adequately serve to represent the structures of both demonstrations and arguments as products? Are argument texts the products of at least two radically different processes? Some are products of dialectically processes as modelled in the basic dialectical situation. Others are products of monological reasoning processes. Is it a happy accident that these products, at least superficially, seem to share certain structural features, leading us to think both are instances of the same phenomenon? Even if one and the same system of analysis, as a matter of fact, could serve to structurally analyze both arguments (as products) and demonstrations, what about the theory behind that system? In Chapter One, we argued that we need a theory of argument structure as a rationale for our structural analysis, and we have also indicated that such a theory will presuppose an understanding, a theory of argument in turn. Do we, in addition, need a theory of demonstration structure backed by a theory of demonstration? If demonstrations and arguments are distinct, why should a theory of argument adequately disclose the presuppositions of our understanding of demonstration structure? Why should a dialectical theory of dialectically generated arguments throw light on monologically generated demonstrations? Has the distinction between argument and demonstration been drawn too tightly? Is it wrong to attempt to picture demonstration on our model? The issue, as we see it, is this. If someone gives a demonstration, is he or she intending to convince at least a potential critical interlocutor of the correctness of some claim? To answer then, we need to clarify what we mean by "demonstration." Perelman and Olbrechts-Tyteca contrast argumentation with demonstration conceived of as a totally formal exercise, divorced from any consideration of truth or even of meaning. In modern logic,...the formal systems are no longer related to any rational evidence whatever. The logician is free to elaborate as he pleases the artificial language of the system he is building....It is for him to decide which are the axioms,...and to say which are the rules of transformation The only obligation resting on the builder of formal axiomatic systems, the one which gives the demonstrations their compelling force, is that of choosing symbols and rules in such a way as to avoid doubt and ambiguity....When the demonstration of a proposition is in question, it is sufficient to indicate the processes by means of which the proposition can be obtained as the final expression of a deductive series, which had its first elements provided by the constructor of the axiomatic system within which the demonstration is accomplished. 34

Unfortunately, this is a rather stereotyped view of the formal logic enterprise. Logicians ordinarily are not interested in constructing simply arbitrary formal systems, seeing what consequences may be formally

28

Basic Theoretical Considerations

deduced by an arbitrary set of inference rules from an arbitrary set of axioms. A formal system of logic, to be interesting and deemed worthy of consideration, must typically satisfy certain properties—soundness and completeness in particular. A system which allows us to deduce, from a set of premises, what those premises did not entail would not long be the object of logical study. In abstract mathematics, likewise, mathematicians as a rule are not interested in playing around with arbitrary systems. We are able to characterize a group abstractly, but what makes group theory interesting and important is that there are so many different realizations of this concept in a wide variety of mathematical areas. The point is this: Even if some formal logicians and mathematicians are interested just in toying around with formal, abstract systems, this is certainly not true of all. Consequently, it remains to be seen whether all logical and mathematical arguments can be seen as demonstrations in Perelman and Olbrecht-Tyteca's sense, and whether the offering of demonstrations can be seen as merely constructing sequences of statements according to certain rules. When we turn to actual mathematical practice, I believe we shall find Perelman and Olbrecht-Tyteca's characterization of demonstration insufficient as a general characterization of mathematical argument. True, some mathematical arguments take place within the framework of what are called elementary theories. In the elementary theory of groups, a group is characterized as a mathematical structure satisfying certain axioms. The theory is developed by showing that certain other statements, theorems, deductively follow from these axioms. But this is only one way of investigating group theory, and for the mathematician, not nearly the most interesting or important way. Mathematicians will ask whether one group is a homomorphic image of another, whether two groups are isomorphic, whether there is a particular class of groups primary in the sense that any group can be represented as, i.e. shown isomorphic to, some group in that class. To establish these claims, a mathematician must show in particular that certain functions exist or could be constructed which have certain properties. This is a far cry from the elementary theory where the axioms make no mention of functions, homomorphisms, or isomorphisms. And this brings us to our central question: Is it inappropriate to think that such arguments could be offered in response to a challenger's request for justification? It may not be at all obvious that two groups are isomorphic. It may not be at all obvious that if a statement is not provable, then there exists a model in which it is false—a rough version of the completeness theorem. When simply enunciated, a challenger may not know that these statements are true and will not know that they are true until a proof is forthcoming. Certainly, we can imagine a challenger asking "Why?", i.e. initiating a basic dialectical situation. Would not a mathematical demonstration be an attempt to convince such a challenger?

The Dialectical Nature of Argument

29

. Even in the case of proofs, demonstrations within the elementary theory, we can have convincing. For suppose a challenger accepts the basic axioms from which the demonstration proceeds. By providing this demonstration, surely the proponent is seeking to convince the challenger of the acceptability of some theorem. But there can be convincing in another sense. The point of the argument may not be to convince the challenger of the truth or acceptability of some particular theorem of the elementary theory, but rather to convince her of the truth of the claim that the theorem can be derived from the axioms. In effect the argument seeks to establish the conditional: If the axioms are true—better true of a certain structure—then so is the theorem. This brings us to conditional reasoning. The fact that we can reason from one statement or set of statements to another may be offered as a reason for accepting a conditional statement. The argument itself, then, can be offered to convince someone of the conditional. In those circumstances, it is a proper response to the question "Why?" But what of the chain of inferences in the argument itself moving from antecedent to consequent—Can this be modelled dialectically? We believe that it can, given a suitable modification of our procedural rules for our basic dialectical situations. We shall defend this point explicitly in Chapter Seven. This should not be a surprising thesis. Reductio ad absurdum reasoning is a special case of conditional reasoning, but the reductio is a major type of challenge in Socratic dialectic!35 There would be something very wrong with our dialectical understanding of argument, if such reasoning could not be seen as dialectically motivated. Our mention of inference brings us to another potential challenge to our working hypothesis that all arguments encountered in texts can be seen as dialectically generated. Blair and Johnson distinguish between argumentation and inference in [1987]. They contrast argument and inference on three grounds: (1) Argument is dialectical, while inference is monological. (2) Since the purpose of argument is rational persuasion, arguments deal with controversial issues, while inference need not involve controversy. (3) "Implication and argument differ structurally. An inference can move along one track; but an argument in the complete sense can only develop against the background of heterogeneity of point of view and of other arguments."3® Are some argument texts, then, the products of argumentation and others the products or records of inference? Are there these two sources of arguments as discourses, and does this mean that a dialectical model of argument need not adequately ground a generic theory of the structure of argument texts? To answer this question, we must look more closely at what Blair and Johnson mean by inference. First, they mean more than just "deductive inference" or "deductively valid inference." I see smoke in that direction, so there is a camp-fire over there, so I may be able to get some food by walking in that direction.

30

Basic Theoretical Considerations I left my wallet at home this morning and the five dollars was in it so I can't have lost the five dollars in my office. 37

These are examples of inference. Notice however that although such inferences or chains of inferences may have arisen without any explicit intent to convince anyone, they certainly can be viewed as preparations to convince. If someone asked why we should walk in a certain direction or why the five dollars was not lost in the office, the premises of these inferences would constitute very plausible reasons for our claims. In neither case do we have an example of reasoning which we cannot imagine to have arisen in a basic dialectical situation. But, as we argued above, that is all we require in proposing the dialectical model of argument. Encountering these inferences, then, as argumentative texts, it would be plausible to construe them as results of the dialectical argumentative process. The question remains whether there are any inferences which could not be construed as preparations to convince. Are there argumentative texts, arguments as products, which express these inferences and which could not plausibly be construed as being generated through a basic dialectical exchange? Blair and Johnson consider some further examples in [1987]. In particular they consider these two, taken from Lambert and Ulrich's The Nature of Argument [1980]: Boston is a city and Boston is in the United States. Therefore Boston is in the United States. The sky is blue, grass is green, therefore tigers are carnivorous.38 Both passages constitute argumentative texts. In both passages, statements are put forth which allegedly support some further statement. But both, as attempts to convince, seem distinctly odd. Concerning the latter, Blair and Johnson remark: It is exceedingly difficult for anyone who takes the view that argumentation is dialectical to imagine that [it] constitutes an argument in any sense of the term. Our point is not the trivial one that [it] is an exceedingly bad argument; it is simply that [it], taken by itself, is not an argument.

39

But can we conceive this product as generated through a dialectical exchange? PROPONENT: CHALLENGER: PROPONENT: CHALLENGER: PROPONENT:

Tigers are carnivorous. Why? The sky is blue. Oh, can you perhaps give me another reason? Grass is green.

The Dialectical Nature of Argument

31

This dialectical exchange is conceivable, although very unlikely. It is unlikely because the reasoning is so egregious—the reasons are simply irrelevant to the conclusion. But it would seem that any theory of argument should allow for there to be bad arguments, even spectacularly bad arguments. The dialectical exchange seems no more implausible than the argument product. It is not as if a plausible argument had to be generated through an implausible dialectical exchange. Hence we do not find here a counterexample to our claim that argumentative texts are arguments as products—they can be viewed as generated through argumentative exchanges. The latter argument does not seem to provide grist for the mill of the argumentation/inference distinction. We do not have an argumentative text which could plausibly be construed as expressing an inference, but not as the product of some argumentative process. Whatever inference underlies this "argument" is pretty implausible. This is not the case for the former argument. It expresses a valid inference, but, as Blair and Johnson point out, Someone used to the idea of argumentation as dialectical would have trouble situating this performance in a dialectical setting....We cannot imagine anyone producing such an argument in an effort to persuade an audience of the conclusion, for the premises contain the conclusion in a strikingly obvious fashion.

It is certainly true that trying to construe this argument as an attempt to convince is implausible. But this is not sufficient to show that this inferential move could not occur in a basic dialectical situation. For reasoning according to this pattern might very well occur in an attempt to draw out the consequences of some thesis. α € C and C = Α η Β, but this means that α 6 A and α 6 Β. So a € A. Is this implausible as an attempt to develop one consequence of the thesis that α € C? Surely we can imagine someone arguing this way or incorporating these inferences in an argument to convince someone that α e A i s a consequence of α e C. As we have said above, to properly represent arguments which draw consequences from statements we may need to modify the rules of a basic dialectical situation. Again, we must leave this issue unresolved until Chapter Seven. But, assuming this discussion is cogent, we have not found any examples of argumentative texts which cannot be construed as arising in a basic dialectical situation. Hence, we have blunted the objection that not all argumentative texts express products of the dialectical process. Our dialectical theory of argument, then, is a general theory of the argumentation which may be expressed in argumentative texts. Hence, we can argue that the dialectical model of argument is appropriate to any argumentative

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Considerations

text. We may view the argument involved in any text as the product of a dialectical argument process. A Final Objection We must still admit that there is a tension in our approach at this point. We are aiming to develop a theory of the structure of argument qua argumentative text. Yet, our basic theory of argument is dialectical, seeing process and procedure as fundamental to understanding argument. Do these two aspects of our approach work at cross purposes? We can imagine a critic asking why we think a theory of argument process is germane to understanding argument as product. We are concerned here with a theory of argument text structure, with developing and justifying concepts and categories for analyzing the product of argumentation. Why should a picture, model of how arguments come to be, the process of argumentation, be relevant to understanding the structural features of the product? If the product is typically presented monologically, why is a dialectical model an appropriate tool in its investigation? How may we answer this question? 'The proof is in the pudding," we say. Let's consider again Toulmin's procedure. He sees data and warrants as functioning quite differently in the economy of arguments—the data/warrant distinction as marking a significant structural difference. But we can see that data and warrants have this different function by seeing that they answer different dialectical questions: What have you got to go on? How do you ge there?41 Although Toulmin does not introduce his other elements with dialectical questions, framing such questions is straightforward. In developing our project, we shall argue that certain distinct elements are to be found in arguments, which fit together in various distinct ways, precisely because they serve to answer distinct basic dialectical questions, analogous to Toulmin's questions. If we can show that there is good reason why a rational judge would be constrained to ask the questions we formulate—at least those types of questions—and if the answers to these questions function differently in the economy of arguments, so that different structures appropriately picture their different functions, then our dialectical model will furnish us with an appropriate rationale for a scheme of argument structure. We may justify incorporating different structural patterns in our account of the structural features arguments may display, and justify including certain argumentative elements like modalities and rebuttals in our analytic machinery, by reference to these basic questions. Our saying that a rational judge would be constrained to ask these questions, and so our giving these questions their structure generating role is justified in turn by

33

Desiderata for Theory and Practice

their centrality to issues of logical cogency. These are issues which any rational judge would demand to have settled, should they arise. They are the issues over which she would demand argument from the proponent. Our model of a basic dialectical situation would then furnish an appropriate ground for a theory of argument structure. Before beginning this project in Chapter Three, we want to present certain desiderata for a theory of argument structure and the diagramming system which represents it. These desiderata will further highlight the appropriateness of presenting our dialectical theory of argument at the beginning of our study. We regard these desiderata as basically intuitively straightforward. If they display bias, at least we are confessing our bias at the outset. We are not saying that a system of diagramming or its theory must satisfy all these desiderata. What we do maintain is that meeting these desiderata is a mark in its favor, while not meeting them may be a mark against such a system or theory.

2.2. DESIDERATA FOR THEORY AND PRACTICE

Let us recall what a theory of argument structure is supposed to do. In Chapter One we argued that we needed such a theory for two reasons. First, we are confronted with rival methods of argument diagramming, rival methods of representing the structure of argumentative texts, the standard approach and Toulmin's model. Secondly, within the standard approach, there is distinct confusion over distinguishing two main types of argument structure—convergent and linked. To decide between these approaches, to disentangle these confusions, we need a theory of argument structure. Such a theory would underlie a diagramming technique, a way of representing argument structure. It may help, then, to sharpen our appreciation of a good theory of argument structure to consider what a diagramming technique should do. Desiderata for an Argument Diagramming

Technique

Recall that a main thrust of the informal logic movement is to develop means of analyzing and evaluating arguments in natural language. As a means of analysis, argument diagramming promises to be a generic tool, applicable to any argument we might encounter. Real life arguments are quite varied. Some will be deductive; many will be inductive or probative. They will display many different formal features. Hence it would be a distinct defect if a diagramming technique could be applied only to deductive arguments or only to arguments with singular premise and singular conclusion. The situation would be obviously much worse, if it

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Considerations

could only be applied to the artificial examples of arguments occurring in logic texts! Hence 1. A diagramming technique must be generally applicable—it must allow us to diagram not just some but all arguments. It would likewise seem a fault of an argument diagramming system if it required us to supply all sorts of elements deemed tacit or suppressed to produce a diagram considered correct. A diagramming system should allow us to display the structure of the reasoning manifestly presented in an argument. This is not to say that arguers will leave various notions unexpressed. But if, for example, a premise has been suppressed, we want to be able to diagram the manifest structure of the argument without having to supply that premise. Diagramming an argument is one thing; supplying suppressed premises another. However, it is a virtue of a diagramming system if it suggests where suppressed premises and other elements might go. Argument reconstruction is a legitimate factor in argument analysis and evaluation. But we should engage in argument reconstruction to better understand or criticize an argument, not because we have to complete a diagram. If not all the various structural elements appear in a given argument, there should be no requirement that they all appear in a completed diagram of that argument's manifest structure. Thus 2. The diagramming technique must be straightforwardly applicable, not requiring significant reconstruction of the argument. Finally 3. A diagramming technique must allow us to mirror the structure of real life arguments. The purpose of producing an argument diagram is to gain insight into, to make perspicuous the structure of the argument being analyzed. Hence, it would be a distinct defect in a diagramming technique if it mandated producing structural diagrams which seemed artificial. This might happen if the structural categories of a diagramming system, the elements of argumentation it recognizes and their various configurations, seemed contrived. For example, it would seem plausible to count each complete statement or assertion in an argument as an element of that argument, as one of the units out of which it was built. Suppose we have a sentence, clause, or phrase apparently expressing a complete thought. But suppose also that our diagramming technique tells us to break up this expression into various parts, seeing several argumentative elements involved in it. Without some rationale justifying why this gives a profounder understanding of argument structure (as formal logicians will distinguish surface grammar from depth grammar), this would seem a distinct defect in the diagramming technique. Likewise, if we had to lump together a number of separate

Desiderata for Theory and Practice

35

independent statements into one unit, if we could not see the argument as developed from these statements but rather from the "superunit" into which they were amalgamated, to analyze the argument according to a certain diagramming technique, that would seem a fault in the technique. Again, if it is not a fault, there must be some clear rationale why not. Although this is admittedly vague and intuitive, the structure in the diagram must reflect or mirror the structure of the argument. What this involves will emerge as we proceed with this essay, especially its critical portions. But it will also emerge in considering desiderata for a theory of argument structure, for which we have now set the stage. Desiderata for a Theory of Argument Structure 1. A theory of argument structure must give a rationale for recognizing the different sorts of elements which may appear in an argument, any argument, and the different functions they may play. Any diagramming scheme will analyze an argument according to various sorts of elements and will see these elements entering into various sorts of configurations. We look to our theory to justify this scheme, i.e. to justify saying that these elements and configurations mirror the structure of the argument. In light of our comments above, if any of these elements seem artificial, or if a system mandates always including certain elements in a structural representation which may not always be manifest in arguments in natural language, justification is all the more necessary. Hence an adequate theory of argument structure must furnish us with a roster of the various types of elements which may enter arguments. On the standard theory we have just premises and conclusions, while Toulmin's roster includes data, warrants, claims. Not only do we need a roster of such elements, we need an indication of why these elements are distinct, and why they can fit together in the various ways pictured by our diagramming technique. Both these issues are connected with function. If two elements play radically different functions in an argument, that is a reason for counting them as different types of elements. If an element can fit together with other elements in different ways in an argument, that should be explained in terms of the various functions that elements may play in arguments. A theory of argument structure, then, must involve an explication of the functional roles elements may play in arguments. 2. This rationale for differentiating elements and functions should be justified by a theoretical account of what argument is or involves. Our theory of argument structure should be based on our understanding of what argument is. Ideally we should see it as a development of what our

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Basic Theoretical Considerations

theory indicates is the nature of argument. We shall develop what this involves during the course of this essay. 3. The rationale must be intuitive or "natural." We have said that our diagrams should mirror the structure of arguments and that our theory of argument structure should give us a rationale for justifying this mirror. What then should be the relation between the structure our theory tells us is to be found in arguments and real life arguments? One might like to say that the structure indicated by the theory should be precisely the structure to be found in actual arguments. One might like to say that our theory must not impose a preconceived notion of structure on arguments but display their actual structure. But this is far too simplistic, especially in light of our second desideratum that our rationale for differentiating argument structure should be backed by our theory of argument.42 As Frans van Eemeren points out, Analyzing argumentative discourse...means looking at the text from a specific viewpoint ensuing from the objective of the analysis. The analyst views the textual reality with the help of a special pair of spectacles, as it were, which highlight the aspects he is particularly interested in. He focuses on certain phenomena, so that he gets a better picture of some things, whereas other things fade away or disappear, somewhat as in an X-ray. Of course, a suitable instrument for analysis needs to be available to the analyst. To be able to detect the relevant points, the analysis must rely on a model that differentiates between what, in light of the chosen perspective, is relevant and what is not. 43

To be concerned with analyzing the structural features of argumentative texts means that certain features of arguments will be deemed crucial, all others relatively unimportant. To approach this assay with a dialectical theory of argument may further focus our attention on certain features of the argument deemed salient. Hence, given this framework, we shall be approaching any argumentative text with various preconceptions or presuppositions. However, I think it is possible to exaggerate this point, as van Eemeren suggests it may be exaggerated. There should be a significant difference between highlighting a feature of the text which is already there, and reading some feature into it. As with diagrams, we want our theory to give us insight into an argumentative text, not to paint a wholly or largely fictitious picture of it. Theories are supposed to link up with the real world, and so the argumentative text provides a touchstone for our theorizing. In some sense, our theory of argument structure must be true to the arguments being analyzed. In the sequel, we shall see how these desiderata help us evaluate methods of argument diagramming and their underlying theory. We shall, however, be taking a dialectical approach here. What does this mean?

The Central Questions in a Basic Dialectical Situation

37

Recall first that there are two principal questions in our inquiry: What elements are to be discerned in argument structure? How do these elements fit together? Recall also that in a basic dialectical situation, a proponent is confronted with an opponent who combines the roles of both challenger and rational judge. Since this means that she will be asking questions to probe logical weaknesses and draw out the most cogent argument possible from the proponent, her questions will be indicative of various logical problems which may arise in arguments. This suggests that the challenger's queries may be particularizations of certain broad questions. They raise these issues about certain specific points discussed or debated in a dialectical situation. Appropriate answers to such questions will be elements in an argument fitting together in various ways with other elements. The fact that they answer such questions justifies saying that they are elements in the argument entering into such configurations. Hence, should we develop a stock of broad questions, whose answers function differently in arguments, we would have a rationale for distinguishing different types of argumentative elements and structural configurations. The fact that such a type of question could be asked in a basic dialectical situation and that a certain type of answer appropriately answer it justifies either distinguishing that type of answer as a distinct type of element in argumentation or distinguishing a particular type of structural configuration. But what are these central dialectical questions? They will certainly be basic to our theoretical approach. In the next section, we state what these questions are and why we see them as central.

2.3. THE CENTRAL QUESTIONS IN A BASIC DIALECTICAL SITUATION

What we have said at the end of the last section sets our current agenda. In this section we must enumerate a set of questions and show that these are the sorts of questions a rational judge would ask in drawing out an argument from a proponent. What exactly does the challenger's questioning involve? Since she is a rational judge, she will issue challenges because she perceives deficiencies in the argument thus far developed. As it stands, it does not say enough rationally or logically to convince her to accept the original claim at issue. As we see it, once an argument has been initiated, the challenger could be dissatisfied on any one of three broad grounds where it would be possible to ask questions to elicit further argumentation. First, a premise as it stands could be questionable. From the challenger's perspective, there is no sufficient presumption for it. Given her knowledge, the challenger sees little or no reason to accept the premise. She possesses insufficient, if any, evidence that the premise is either true or plausible. She may possess significant even decisive evidence that the premise is false. The burden of proof is on the proponent to defend, justify that promissory claim.

38

Basic Theoretical Considerations

Secondly, whether or not the challenger accepts a premise, she may not see that it is relevant to the conclusion it is alleged to support. Thirdly, although the premises may be acceptable and relevant, they do not seem weighty enough to establish the conclusion. They either do not given enough direct evidence for the conclusion, fail to address certain counterevidence, or the argument overstates their weight, for example claiming that the conclusion follows necessarily when the premises only make it likely. These issues and problems delimit the broad sense of logical deficiency we mentioned in the last section. These are the three broad grounds on which an argument may be logically deficient. On the contrary, to find an argument logically cogent or logically convincing is to find no problems on any of these grounds. In Thinking Logically [1988], we organized our account of basic argument evaluation around these three issues. Several other authors also recognize these three problems as basic issues in argument evaluation. In Logical Self Defense [1977], Johnson and Blair first present what they term three basic fallacies: irrelevant reason, hasty conclusion, and problematic premise. Obviously these fallacies correspond to the three problems we have just outlined. In A Practical Study of Argument [1985], Govier presents what she calls the ARG conditions— Acceptability (of the premises), Relevance, and adequacy of Grounds.44 A good argument must satisfy all three. To be acceptable, for Govier, the premises must be reasonable for the audience. There must be some good evidence for them and no counterevidence. To be relevant, the premises must give evidence bearing on the conclusion. To be adequate, they must jointly present enough evidence to justify believing the conclusion.43 Basic Dialectical Questions How does perception of problems on these three grounds translate into argument generating questions, questions which a challenger could ask to draw out further argument? We may frame certain questions which we call the basic dialectical questions. As there are three categories of problems with arguments, so there are three categories of questions here. I.

ACCEPTABILITY QUESTIONS Why should I believe that premise? How do you know that reason is true?46

II.

RELEVANCE QUESTIONS Why is that reason relevant to the claim? How do you get there? (Toulmin's warrant-generating

question) III.

GROUND ADEQUACY QUESTIONS

The Central Questions in a Basic Dialectical Situation

39

1. Can you give me another reason? 2. How sure do your reasons make you of the claim? Given your reasons, how confident should I be of your claim? How sure are you that you'll get there? 3. Why do your premises make you so sure (in light of condition or counterevidence R)? Why do your reasons make you sure enough to accept your claim? What might prevent you from getting there? The challenger will pose ground adequacy question (1) when she feels that the reasons given are all right, as far as they go—they do give some plausible evidence for the conclusion, but are simply not weighty enough to constitute adequate grounds for accepting it. Has the protagonist given us all his reasons or all the reasons he could? Further reasons are required. Questions under (2) may very well be a response to argumentation which clearly gives some support to the conclusion, but not conclusive support. Our challenger feels the conclusion needs to be qualified or hedged. On the other hand, she might sense a great deal of confidence from the respondent and want that explicitly enunciated. Questions like those under (3) arise typically when the challenger is aware of rebutting evidence which the respondent has not explicitly addressed. By asking this question, she is raising objections to the argument and asking for argumentation against those objections. That challengers may raise such objections, inviting response, indicates the legitimacy of this third question. Comparison with Grice and Rescher It should be intuitively plausible that these are the sorts of questions a rational challenger would ask in drawing out a logically cogent argument from the respondent. That they concern issues which some authors have identified as central to argument appraisal also indicates their importance for a rational judge. We may get further corroboration of their centrality by comparing them with Grice's maxims for cooperation in rational discussions in "Logic and Conversation" [1975], and the questions which arise in formal disputation, presented by Rescher in Dialectics [1977]. Our three basic grounds for evaluating and challenging arguments parallel three of the four categories of maxims Grice presents. Grice points out that our conversations (of which our proponent-challenger argumentation exchanges are just one type) are not mere sequences of utterances—at least not normally. Rather they involve co-operation, where "each participant recognizes in them, to some extent, a common purpose or set of purposes, or at least a mutually accepted direction."47 Obviously, our respondent and

40

Basic Theoretical Considerations

challenger want to arrive at agreement over the claim at issue—Is it acceptable, believable or not? Hence, at each stage of a conversation some moves are appropriate while others are not. Participants in a conversation may then be expected to abide by what Grice calls the Cooperative Principle: Make your conversational contribution such as is required, at the stage at which it occurs, by the accepted purpose or direction of the talk exchange in which you are engaged.

To make this general maxim more concrete, Grice offers further maxims grouped under the categories of Quantity, Quality, Relation, and Manner. We can very straightforwardly interpret these maxims for argumentative situations. Under Quantity falls the maxim: Make your contribution as informative as is required (for the current purposes of the exchange). 49

That is, when arguing make your grounds full enough to be adequate—say enough to give proper evidence for your conclusion and respond to counterevidence. Under Quality, we have the maxim Try to make your contribution one that is true.

This maxim in turn is made more specific by two further maxims: 1. Do not say what you believe to be false. 2. Do not say that for which you lack adequate evidence. 50

That is, make the premises of your arguments acceptable, not false or questionable. Under Relation, we have one maxim: Be relevant.51

There is no need to comment here. Under the category of Manner, we have various maxims relating to meaning, for example avoid obscure or ambiguous expressions. Now a critical challenger will obviously be sensitive to problems of meaning in the proponent's assertions. If the meaning is obscure for some reason, she will stop him, and demand clarification. But such questions are statement revising or argument revising, rather than argument generating. Hence, in developing a theory of argument structure, we need not be concerned with this category. The first three categories of maxims are important for corroborating what are the expectations of the challenger as rational judge. She will expect that the respondent's argument will be governed by these maxims. She will ask critical, argument generating questions when she perceives some violation of these maxims. But these maxims clearly parallel our three categories of basic dialectical questions—ground adequacy, acceptability, and relevance respectively.

The Central Questions in a Basic Dialectical Situation

41

Considering formal disputation further corroborates our basic dialectical questions and the whole dialectical approach. A formal disputation involves three parties: a protagonist proponent, an antagonist opponent, and a determiner, a referee-judge.52 Strict rules govern the moves proponent and opponent may make. In particular, the proponent must always make some outright categorical assertion, and only the proponent is allowed to make such assertions. On the other hand, the opponent must always challenge an assertion, call some assertion into question, and only the opponent may do this.53 Thus we have an assertor-respondent on one side and a questioner-challenger on the other. The only difference with a basic dialectical situation is that the roles of challenger and judge may be played by different persons. A disputation standardly begins with the proponent making a categorical assertion, claiming that Ρ is the case for some statement P, in symbols !P The opponent will then challenge the proponent in one of two ways. First, she may ask "Why P?" "What entitles you to claim P?"54 This is called a challenge or cautious denial, in symbols t~P-

We may also read this as asserting that ~ P holds for all that you have shown. On the other hand, she may thrust her challenge this way: " ~ Ρ typically obtains given that Q, and Q is the case for all you have shown." In symbols, this appears as ~P/Q & fQ An expression of the form "P/Q," called a provisoed assertion, claims that Ρ generally or typically, but not necessarily or invariably, holds, given that Q.55 We may refer to either "~P/Q" or the entire expression " ~ P / Q & tQ" as a provisoed denial. How may the proponent reply to the challenger? To the cautious denial " f ~ P , " there is just one way to reply, namely to give evidence for "P." The reply has the form P/Q & !Q To the provisoed denial, several replies are available. There are two ways to proceed against "fQ," either by categorical counterassertion !~Q or by the provisoed counterassertion - Q / R & !R.

42

Basic Theoretical Considerations

For simplicity's sake, Rescher does not consider moves directly against the provisoed denial " ~P/Q" (or against provisoed assertions), e.g. counterassertions of the form ! ~(~P/Q) or ~(~P/Q)/R & !R. But there is a way in effect to move indirectly against a provisoed assertion or denial. "P/Q" asserts only that Ρ typically holds given that Q. This suggests that there are atypical situations, "R." Hence "~P/(Q & R)" is perfectly compatible with "P/Q."56 Thus, in reply to the cautious denial " ~P/Q" our proponent may assert P/(Q & R) & !(Q & R). Likewise, to the proponent's provisoed assertion that P/Q, the challenger may attack with ~P/(Q & R) & f(Q & R). These two forms are called distinctions. Since the respondent categorically asserts that Q & R, his is called a strong distinction. Since the challenger only weakly or cautiously asserts Q & R, that Q & R holds for all you have shown, hers is a weak distinction. Once the respondent has replied to her first challenge, the challenger may then challenge again, attacking either the categorical part of the assertion with a cautious or provisoed denial, or challenging the provisoed part of the assertion with a weak distinction. The respondent may reply again, and thus the disputation proceeds. Clearly, given these various possible moves and countermoves, once an exchange has proceeded through several steps, quite a few possibilities are open to respondent and challenger as the next move. How do these forms of assertion and counterassertion, challenge and response, corroborate the centrality of the basic dialectical questions we have presented above? We claim that we may correlate each type of challenge the opponent may make with a type of dialectical question. This further substantiates the importance of those questions to the dialectical enterprise of argument generation. Not all dialectical questions will have some move of the challenger associated with them. However, as we shall show, if we suitably modify the rules for formal disputes, we could generate moves to correlate with these questions which would be completely in the spirit of a formal disputation. Hence, for each of our basic dialectical questions, we can either see how it is embodied in a challenger's assertion or how it might be so embodied, if the rules for such exchanges were altered or relaxed.

The Central Questions in a Basic Dialectical Situation

43

As we have seen, there are three basic types of moves a challenger may make: cautious denial, provisoed denial, and weak distinction. Clearly, to challenge with a cautious denial, " t ~ Q , " a categorical assertion "!Q" made as part of a premise is to ask an acceptability question. Why should I believe that premise (or premise conjunct) Q? Acceptability questions are obviously built into formal disputations. Also, although Rescher does not consider cautious denials of provisoed assertions, he allows that such questions can arise.57 Hence in principle we can ask the acceptability questions of any premise the proponent offers. They are included in the moves of a dialectical exchange. Of course, the challenger can also attack the proponent's initial claim with a cautious denial, the claim which becomes the conclusion of the proponent's argument when he takes up the challenge. But this again is to question acceptability, this time the acceptability of the original claim. Cautious denial is a generalized acceptability question. It in essence asks "Why?" But "Why?" is the fundamental dialectical question, and asking it of a premise is just a special way of asking it. Hence, we can straightforwardly correlate a cautious denial with the general dialectical question of acceptability. To challenge a categorical assertion "!Q" with a provisoed denial " ~Q/R & |R" is again to ask "Why Q?" But it is to ask that question in a particular way. Instead of simply asking for (some) evidence for "Q," this challenge poses an objection to "Q." In supporting "Q," the proponent must either meet that objection, claiming or showing that "R" does not hold or does not constitute an objection in this case (strong distinction), or must concede that the force of whatever evidence he could give for "Q" must be qualified by that condition possibly holding. In effect, the challenger is asking "Given for all that you have shown that R holds, how can you say you have got that Q?" "R" constitutes counterevidence. "Whatever reasons you might have for 'Q,' why do they make you sure enough to accept that claim, in the light of 'R'?" We may thus correlate provisoed denial with the third ground adequacy question. We are not challenging the force of specific reasons given for accepting "Q," but rather the force of any reasons that might be proffered without arguing that the counterevidence does not apply here. The challenger's third move, weak distinction, is even more obviously correlated with the third ground adequacy question. When the proponent has presented an assertion of the form "P/Q & !Q" to support "!P," and the opponent challenges with " ~P/(Q & R) & t(Q & R)," "R" is possible counterevidence. The opponent is conceding that given Q, Ρ ordinarily follows, but not when R holds also. "Q" creates a presumption for "P," unless R. Should "R" hold, the presumption "Q" creates for "P" is undercut. The opponent is in effect asking "Why does 'Q' make you so sure or sure enough to accept 'P' in the light of 'R' or 'R's possibly

44

Basic Theoretical Considerations

holding'?" That is, the opponent is asking the third ground adequacy question. What about the remaining types of basic dialectical questions—the relevance questions and the first two ground adequacy questions? Does the fact that we do not have challenges in formal disputation to correlate with them bring their importance into question? The answer is negative for each of these three types of questions. We claim that the lack of some challenge to correlate with these questions is due to the (over)simplicity of formal disputation or to certain features of the disputation rules. Modifying or loosening the rules will straightforwardly generate the appropriate challenges. The need for a challenge corresponding to the relevance question is obviated by the fact that a counterassertion introducing new material into a disputation is provisoed. It includes a conjunct of the form "P/Q." Proponent (and challenger) are required to explain relevance by the very rules of the disputation. The relevance question has already been anticipated and answered. Hence, the genuineness and legitimacy of this question is recognized. But surely, we can imagine the rules of a disputation relaxed, so that a simple categorical assertion might be offered as a countermove to a challenge. To the opponent's " t ~ P " the proponent answers with "!Q." But then clearly the relevance question could arise in such a disputation if the opponent did not see the relevance of "Q" to "P." The first ground adequacy question — Can you give me another reason? — is not represented in the challenges we have seen principally because the disputational situation has been oversimplified. In replying to our initial challenge, a proponent need not offer just one counterassertion of the form "P/Q & !Q," giving just one ground for his claim. He may offer several, each of which the challenger may go on to attack in various ways. Now we can imagine the rules of a disputation amended, so that before a challenger attacks any of the proponent's grounds, she may ask the proponent whether he has finished presenting his case—Are these all of your grounds? If yes, she may proceed with her challenges. If not, she may say—Give me the other reasons! — in effect incorporating our first ground adequacy question. It certainly seems reasonable for a challenger to want to have all the proponent's reasons for a given claim in front of her before she begins to attack any of them. That the second ground adequacy question does not appear among the opponent's challenges is again in part due to an oversimplification. As Rescher pictures it, all of the "warrants" are provisoed assertions, statements of the form "P/Q." "P/Q & !Q" creates a presumption for "P" but does not entail "P," as does "Q = Ρ & !Q." Hence our grounds are always being alleged to create a presumption for their claims, nothing more. Questions of modality, force of reasons do not arise because in effect we have only one modality—presumably. But could not a whole family of statements serve to proviso assertions? Why if one knows that the stronger

The Central Questions in a Basic Dialectical Situation

45

assertion "Q => P" holds, must he be allowed to assert only the weaker "P/Q"? 58 Should provisoed statements of various strengths be allowed (as they surely are in ordinary exchanges), then the modality question could very well arise. There is another reason why this second ground adequacy question concerning force of reasons does not arise in formal disputation. We have already noted that the rules as presented allow the proponent to offer just one reason for a claim, thus oversimplifying actual reasoning. But the force question arises with peculiar interest when several independently relevant reasons are given for a claim. How strong is their combined weight? If the proponent offered (P/Q, & !Q U & (P/Q2 & !Qj) & (P/Qj & !Q3) as three independent grounds for "P," given the strength of "/," each ground would allegedly create a presumption for "P." But how strong is the presumption created by all three together, gotten in effect by adding together the weights of each? The simplification obviating the need for the first ground adequacy question helps present the second from arising also. These two simplifications, that warranting premises are always of the form "P/Q," and that multiple reasons are not given for a claim, further combine to blunt recognition of the need for modalities. If "Q ( ," "Q 2 , "Q3" could each give differing amounts of evidence for "P," then the question of whether the three taken together create a presumption for "P" and, if so, how strong becomes acute. It is certainly more acute than asking whether the three which severally create a presumption for "P" together create a strong presumption. It might very well be acute enough to force including a challenge corresponding to the second ground adequacy question among the challenges in formal disputation. Hence, the fact that the second ground adequacy question is not among the opponent's challenges reflects more the simplicity of a formal disputation than there being anything illegitimate about the question. Allowing a formal disputation to become more complex would allow such questions to arise. All these considerations then highlight the legitimacy of the role we have assigned to our basic dialectical situations. That our basic dialectical questions are mirrored in formal disputation, and that they are parallel to Grice's conversational maxims and to the issues various authors regard as constituting argument evaluation, all give independent confirmation that these are legitimate, substantial questions which a rational judge would raise in argumentative exchanges. The issues they raise are fundamental to developing argumentation. Hence, should these questions mark off structurally different aspects of arguments, should answers to these various questions function in different ways in arguments, we would have a well-founded rationale for recognizing structural differences in arguments. But how can this be? How could these questions

46

Basic Theoretical Considerations

generate argument structure, or arguments with different types of structure? A significant part of the next four chapters consists of answering this very question. Our discussion will be guided by the two central questions of our inquiry: What type of elements are to be distinguished in arguments? How do they fit together? In these following chapters, we shall critically examine the answers the standard approach and Toulmin's model provide to these questions. In developing our own answer, we shall be guided by these basic dialectical questions and shall see exactly how they generate structural differences. As we have already indicated, the most fundamental dialectical question that could be asked is the simple question "Why?" "Why should I believe that?" This gets argument going. It not only justifies counting the answers a respondent gives to this question as argumentative elements, but the assertions which prompted the question in the first place. On the standard approach, these would be premises and conclusions. But Toulmin has claimed that this dichotomy should be replaced by claims, data, warrants, and backing. Surely this raises the question of the most basic types of elements to be found in arguments. We turn to this question in the next chapter.

NOTES 1. The challenger/respondent terminology is derived from Wellman, [1971], 2. Van Eemeren and Grootendorst, [1984], pp. 5, 9, 15. 3. Roland Hall points out that Plato used 'eristic* to describe such a degenerate form of dialectic in Sophist 23IE. See [1967], p. 386. 4. Van Eemeren and Grootendorst, [1984], p. 17. 5. We shall discuss an exception to this in Chapter Seven. 6. Van Eemeren and Grootendorst, [1984], p. 15. 7. Again, in Chapter Seven we shall discuss a possible exception here. 8. In [1984], van Eemeren and Grootendorst regard this as a hallmark of being dialectical. "The crux of a dialectical approach is that argumentation is regarded as an attempt to defend a standpoint in respect of an expressed opinion against the critical reactions of a rational judge in a regimented discussion." ([1984], p. 18.) 9. For examples of such rules and standards, see van Eemeren and Grootendorst, [1984], pp. 150-53, 162-73. 10. Hall, [1967], p. 385. 11. Hall, [1967], p. 386. 12. "Perhaps the clearest, and surely historically the most prominent, instance of dialectical process is formal disputation." (Rescher, [1977], p. 1. See pp. 1-3 for an account of formal disputation. 13. Sophist 263E. Quoted in Hall, [1967], p. 386. 14. Rawls, [1971], p. 11. 15. Rawls, [1971], p. 12. 16. Rawls, [1971], p. 17. 17. Wenzel, [1979], p. 84. 18. Wenzel, [1979], p. 84. 19. Wenzel, [1979], p. 84.

Notes

47

20. Wenzel, [1979], p. 84, italics in original. 21. Wenzel, [1979], pp. 84-85. 22. In response to questioning at his presentation "Argumentation and Fallacy Analysis in a Pragma-Dialectical Perspective" at The Fifth International Conference on Critical Thinking and Educational Reform, Sonoma State University, Rohnert Park, California, August 3, 1987. 23. Rescher, [1977], p. 52. 24. Blair and Johnson, [1987], p. 46. 25. Perelman and Olbrechts-Tyteca, [1969], P· 14. 26. Perelman and Olbrechts-Tyteca, [1969], P· 30. 27. Perelman and Olbrechts-Tyteca, [1969], P· 30. 28. Perelman and Olbrechts-Tyteca, [1969], P· 28. 29. Perelman and Olbrechts-Tyteca, [1969], P· 28. 30. Perelman and Olbrechts-Tyteca, [1969], P· 31. 31. Perelman and Olbrechts-Tyteca, [1969], P· 35. 32. Perelman and Olbrechts-Tyteca, [1969], P· 35. 33. Besides these authors, we may also mention that van Eemeren and Grootendorst, [1984], Chapter One explicitly discuss the "dialectifying" approach to argument—that a proper study of argument must include the features we have identified as dialectical. This theme is central to the thought of these authors. The dialectical model appears also in van Eemeren [1987], and van Eemeren, Grootendorst, and Kmiger, [1987]. In [1987], Joseph Kopperschmidt points out that the very act of asserting a claim is at least implicitly intersubjective. To assert a claim is to indicate not only that what is asserted is reliable for oneself, but reliable generally, trans-subjectively, or intersubjectively. ([1987], p. 180) Certain claims are disputable or can become disputable under certain circumstances. Here again we have an interpersonal conception, for although there may be internal disputations, ordinarily disputes arise between two or more persons. Kopperschmidt credits Quintilian with asserting that arguments are necessary only when there are disputes. ([1987], p. 180) Only arguments can legitimate claims. ([1987], p. 180) An argument can legitimate a claim when it can rationally motivate persons to accept that claim ([1987], p. 180) and a claim can be established by argument when it is possible that all participants in a dispute, capable and willing to argue, would agree to that claim. ([1987], p. 180) This conception of argument is again clearly intersubjective and dialectical. 34. Perelman and Olbrechts-Tyteca, [1969], pp. 13, 14. 35. See Hall, [1967], p. 386. 36. Blair and Johnson, [1987], p. 48. 37. Blair and Johnson, [1987], p. 48. 38. Lambert and Ulrich, [1980], p. 71; quoted in Blair and Johnson, [1987], p. 47. 39. Blair and Johnson, [1987], p. 47. 40. Blair and Johnson, [1987], p. 47. 41. Toulmin, [1958], p. 98. 42. We wish to thank the referee of Foris Publications specifically for pointing this out to us. 43. Van Eemeren, [1989], p. 7. 44. Govier, [1985], pp. 60-61. 45. Govier, [1985], pp. 60-61. 46. By phrasing the dialectical question using "true" we are not suggesting or endorsing the view that to be acceptable a premise must be true. At a certain point in time, the balance of evidence available may clearly support some statement which in fact may be false. Burr given the evidential situation, a rational judge would find the statement acceptable. Conversely, a statement may be true, but there may be little or no evidence to support it. There would be no presumption in its favor; it would not be part of "common knowledge." In this case, a rational judge would not find that statement acceptable unless adequate further evidence were presented. However, to question the truth of a statement is to question its rationality or the rationality of accepting it, as Wellman points out in [1971], pp. 118-19. Indeed, why should rational judges weigh the evidence for and against a view if their goal were not to establish the truth of that claim? So to ask why that premise, that reason just given is true is a perfectly legitimate way to question its rational acceptability.

48

Notes

47. Grice, [1975], p. 45. 48. Grice, [1975], p. 45. 49. Grice, [1975], p. 45. Grice also includes a second maxim under this category—Do not make your contribution more informative than is required—but since he himself admits that this maxim is questionable and since it has no obvious connection with our purposes in this essay, we simply note it here. 50. Grice, [1975], p. 46. 51. Grice, [1975], p. 46. 52. Rescher, [1977], p. 4. 53. Rescher, [1977], pp. 17-18. 54. Rescher, [1977], p. 10. 55. See Rescher, [1977], p. 6 for variant readings of "P/Q." 56. As Rescher points out in [1977], p. 7. 57. See Rescher, [1977], p. 8. 58. In [1984], van Eemeren and Grootendorst present patterns of dispositional exchange actually using "a" rather than "/." See [1984], p. 12.

Chapter 3

What Are the Basic Elements of Arguments?

3.1. CLAIMS VERSUS CONCLUSIONS

There is certainly no controversy in saying that there cannot be argument without an attempt to establish at least one point. In a dialectical situation, the challenger's "Why?" transforms a mere assertion into a point at issue. It signals that the challenger will not simply accept the statement, but demands reasons for it. Without such a challenge, at least a potential or anticipated challenge, there would be no call for argument. Should the proponent take up this challenge, we should have an argument, and the initial point expressed would be the point of the argument. That the statement has been challenged by "Why?" in this context identifies it as the point of the argument. On the standard approach, points of arguments are called conclusions, while Toulmin calls them claims. Is there anything in these names? Is there any advantage in adopting one term over the other? Again , the process/product distinction is apropos here. To describe the point of an argument as a claim situates it in the process of argumentation. Claims are put forward for the acceptance of others. By making a claim, as Toulmin points out, we incur an obligation to defend it if challenged. If we cannot defend it, we have spoken irresponsibly.' "Claim" is a dialectical or process notion. When we describe the point of an argument as a conclusion, we are relating it to an argument as product. We can or are giving reasons for claims; we have given reasons for conclusions. A conclusion then is the point of an argument qua product. When after an argumentative process has developed and run its course, the resulting argument is laid out monologically, the point of that argument is its conclusion. Since our overall purpose in this essay is to develop a theory concerning the structure of argumentative texts, "conclusion" is the more appropriate term here. Argumentative texts are argument products. But since we wish to motivate this structure dialectically, we may have recourse to speaking of claims. "Why?" not only flags certain statements as claims or conclusions and so also elements in arguments, it flags appropriate answers as reasons, standardly called premises. But, as we pointed out at the end of the last

50

What Are the Basic Elements of Arguments?

chapter, Toulmin's model raises controversy precisely at this point by distinguishing three types of "premissory elements" — data, warrants, and backing. This distinction is both unorthodox and problematical. Of the three concepts, we find that of warrant both central and the most problematic. In fact, the problems with this notion lead us into some significant philosophical issues. Hence, we turn to this notion first, making it the sole subject of the next section.

3.2. TOULMIN'S PROBLEMATIC NOTION OF WARRANT

It is our contention that although Toulmin's notion of warrant is straightforwardly applicable to arguments as process, its application to arguments as products, to argumentative texts whose structure it is our aim to understand, is highly problematic. It is so problematic in fact that we conclude the concept of warrant is an inappropriate category for analyzing arguments as products. How may we justify these contentions? Warrants and Arguments as Process In analyzing arguments as process, it is straightforward to identify warrants. In arguments as process, we have the participants in our basic dialectical situation in front of us. We witness their exchange. We thus know which statements are warrants because we know, have right in front of us, the questions which the challenger has asked the proponent. Consequently, we know which statements are answers to the warrant-generating question "How did you get there?" Appropriate answers to that question are warrants. Even if warrants should be left implicit in a dialectical exchange, we can imagine entering that exchange and asking the warrant generating question. If the proponent could not answer our question, that should show a defect in his reasoning, not in our system of argument analysis. If we can readily anticipate the proponent's answer, we have already identified the implicit warrant. In The Uses of Argument [1958], Toulmin introduces the very notion of warrant by imagining our being challenged with the warrantgenerating question and pointing out how this calls for a different kind of answer than the data-generating question.2 We are not being asked for more facts, evidence to back up our claim, but for an explanation of why the data presented have a bearing on the claim to be defended. Our providing an answer to this question indicates that we intend our answer as a warrant. If we know what questions are asked, then we know how their answers are intended to function. The problem is that when confronted with an argument as product, an argumentative text, we do not know what generating questions have been

51

Toulmin's Problematic Notion of Warrant

asked. This we must imaginatively reconstruct, to the best of our ability, from the evidence the argument itself provides. Will the argument as product give us unambiguous indications for reconstructing these questions? In an argument as product, will we always know, for sure, whether a given statement should be regarded as offered to answer the data generating question or the warrant generating question? Consider whether we can have an argument in which a conclusion is allegedly supported just by a conditional statement which would ordinarily be taken on Toulmin's view as the warrant. As Clark points out in "Natural Inference" [1956] and Cowan points out in "The Uses of Argument—An Apology for Logic" [1964], we may encounter such arguments. John will not come to the party, because If Mary is coming, John won't. Doesn't the question "How do you get from stated hypothetical premise to conclusion?" arise for this argument? And wouldn't we expect the answer be Mary is coming to the party

?

So in the argument John will not come to the party, because if Mary is coming, John won't and Mary is coming to the party how do we know which statement presents the data and which is the warrant? Diagramming the argument viewed as generated with hypothetical premise presented first and then the categorical "Mary is coming to the party" to explain relevance, we have If Mary is coming to the party, John won't

So, John will not come to the party

Since Mary is coming to the party.

But this seems to get data and warrant reversed, to have them in the opposite positions from what we would expect. Or would Toulmin reply that the warrant in our original argument as product is Given (the datum) that if Mary is coming to the party, John won't, we may take it that John will not come to the party ? But this seems manifestly ad hoc. Yet to claim that the expected diagram

What Are the Basic Elements of Arguments?

52 Mary ia c o m i n g to the party.

->

So,

J o h n will n o t c o m e to t h e p a r t y

Since Ii Mary Is c o m i n g to t h e party, J o h n won't.

correctly diagrams the argument from hypothetical premise to conclusion, or diagrams that argument in a fuller, more developed, more candid form, makes the system of diagramming very revisionistic. It both requires supplying evidence which was not manifestly stated and treating the statement manifestly offered to support the claim not as evidence at all, but as a warrant. Wouldn't it be far simpler and more straightforward to regard the argument from stated conditional alone to conclusion as assuming that Mary is coming to the party is an understood, unstated premise—the reasoner in effect as proceeding from both statements as premises to the conclusion? Proceeding according to the above diagram indicates a preconceived notion of structure which we are imposing on this argument, rather than displaying how the argument actually fits together. But are we not operating precisely with this preconceived notion, should we insist, faced just with the evidence of the argument as product, that "Mary is coming to the party" is the datum and "If Mary is coming to the party, John won't" is the warrant? We can be accused of operating with a preconceived notion of structure unless we can justify our discrimination of datum from warrant here. If we cannot do this, the notion of warrant is problematic for arguments as products. We may certainly attempt to present a rationale for counting certain statements included in arguments as products as warrants. But this account will encounter serious and in the end overwhelming problems. I believe we can develop how by addressing ourselves to three questions in succession: 1. What are warrants? 2. Are there compelling reasons to count certain statements or types of statements which may occur in arguments as warrants? 3. Are warrants properly parts of arguments? We shall organize our discussion in this section around these three questions.

Toulmin's Problematic Notion of Warrant

53

What are Warrants? This question is easy to answer, for Toulmin explicitly says that warrants are inference rules. Warrants answer the question "How do you get there? [i.e. from data to claim]." Such answers require propositions of a rather different kind: rules, principles, inferencelicenses or what you will, instead of additional items of information What are needed are general, hypothetical statements, which can act as bridges, and authorize the sort of step to which our particular argument commits us.

Toulmin says warrants can be expressed in the form "If D, then C," but are better expressed by such forms as "Given data D, one may take it that C. "4 We might call the latter the canonical (or to use Toulmin's term candid) way of expressing warrants. General or hypothetical statements may be taken as expressing warrants elliptically or as having the force of warrants. This last formulation accords very closely with Toulmin's view, as we shall see when we discuss Toulmin on syllogisms. The positioning of the warrant in effect as an annotation on the arrow from D to C further indicates the warrant is an inference rule. It is from the data alone that we infer the claim in accordance with the warrant, rather than from the data together with the warrant. Warrants assert that the step, the movement from D to C is legitimate. Toulmin expresses the situation this way: The explicit appeal...goes directly back from the claim to the data relied on as foundation: the warrant is, in a sense, incidental and explanatory, its task being simply to register explicitly the legitimacy of the step involved and to refer it back to the larger class of steps whose legitimacy is being presupposed.S

Given this discussion, it would seem straightforward to identify warrants or to discriminate warrants from data in arguments as products: Count the conditional or generalized conditional statements appearing in premissory position as warrants. The particular or categorical statements whose relevance to the conclusion they explain are data. Although this seems straightforward, we have reservations. What we have called the standard approach and Toulmin's approach give us two rival or divergent ways of construing the argument If Mary is coming to the party, John won't. Mary is coming to the party. So John won't. The standard approach construes the conclusion as being drawn from, being supported by two premises. The second sees the conclusion being supported by the datum, "Mary is coming to the party" via the warrant "If Mary is coming to the party, John won't." Clearly, Toulmin's second approach is

54

What Are the Basic Elements of Arguments?

novel. Even if we understood how to apply this approach, why should we prefer it over construing the argument with two premises supporting a conclusion? Are there any advantages to be gained? Does Toulmin have some insight into the nature of conditional statements which justifies seeing them as constituting a radically different type of argumentative element than other promissory statements? This brings us to the second principal question organizing our discussion: Are there compelling reasons to count certain statements, namely conditional statements, as warrants?6 Toulmin speaks directly to this issue in The Uses of Argument when he presents his views on certain syllogisms. Will this discussion allay our reservations? Toulmin on Certain Syllogisms In discussing "the layout of arguments" in The Uses of Argument, Toulmin confines himself to just one family of syllogisms, where a particular conclusion is inferred from a particular premise together with a universal or general premise. He says, "We are interested primarily in arguments by which general propositions are applied tojustify particular conclusions about individuals....Many of the conclusions we reach will, in any case, have obvious application — mutatis mutandis — to syllogisms of other types. "7 What these other types of syllogism are is far from clear, as our discussion above suggests. The one obvious application is to modus ponens type reasoning applying a conditional, albeit not a universally generalized conditional, in justifying the conclusion. Hence, it would not be accurate to present Toulmin's views here as a theory of the syllogism in general, but only of certain types. We should note, however, that Toulmin applies his analysis not just to syllogisms where the general premise asserts categorically that "All A are B" or "No A are B," but to statistical syllogisms involving premises of the form "Almost all A's are B's" or "Scarcely any A's are B's." 8 In fact, he feels that such statistical generalizations best reveal "the internal complexity" of general propositions.9 According to Toulmin, the general premise, be it of any of these forms, may very well serve two distinct functions—it may serve as a warrant or serve to make a statistical report, or both. As a statistical report, "All A are B" says or may be expanded as saying The proportion of A's which are also B's is 100%. As a warrant, it should be expanded to read An A may certainly be taken to be a B. Likewise, as a statistical report, "No A are B" asserts The proportion of A's which are B's is nil, 0%. As a warrant, it issues the following authorization:

Toulmin's Problematic Notion of Warrant

55

An A can be taken certainly not to be a B. The expansions of "almost all" and "scarcely any" statements are parallel. We can more explicitly express what "Scarcely any A's are B's" says as a statistical report in the form The proportion of A's which are B's is less than (say) 2% while as a warrant, An A can be taken almost certainly not to be a Β serves as a more "candid" formulation.10 In the context of a syllogism, the statement may serve both functions at once, the statistical report being the backing for the warrant. We should make plain, for future reference, that for Toulmin, when "All A are B," "No A are B" make statistical reports, they are making reports of observed data. "No A are B" says that "Not a single A is recorded to be a B." "All A are Β" says "Every A has been found to be a B" or "The proportion of A's found to be B's is 100%." In all these cases, the universal statements simply summarize data and do not make extrapolations from observation. "All A are B" does not say that "Every A in existence is B," but "Every A observed (which might, but need not, be the entire class of A's) has been found to be a B." Thus, when these universal categoricals are used as backing, they make a statement about a closed, finite, limited class. Whether or not the class of A's is finite and every A has been observed, only a finite number of A's have been observed. The class of observed A's is closed and limited." As Toulmin sees it, a simple form of words masks a "crucial difference in practical function."12 And, Toulmin maintains, frequently in arguments, the universal premise performs both functions. Often enough, especially in arguments, we make the single statement do both jobs at once and gloss over, for brevity's sake, the transition from backing to warrant — from the factual information we are presupposing to the inference-licence which that information justifies us in employing. The practical economy of this habit may be obvious; but for philosophical purposes it leaves the effective structure of our arguments insufficiently candid. 13

The general premise then involves both the functions of warrant and backing, and its simple form conceals its twofold function. To properly represent the structure of the syllogism arguing Socrates' mortality from his humanity on Toulmin's account, we need the following diagram:

56

What Are the Basic Elements of Arguments?

Socrates is human

So, certainly, Socrates is mortal

Since

A human can be taken to be certainly a mortal

I

Because

The proportion of humans which are mortal is 100% To construe such syllogisms as two premise arguments, Toulmin claims, would obscure the structural differences his model makes manifest. The first critical question we can ask of Toulmin's approach is what came first — the syllogism to be analysed or Toulmin's system of structural categories? More precisely, does Toulmin's model reveal or mirror the structure of these syllogisms or are they being structurally distorted to fit his model? Why should we regard the universal premise as functioning to express warrant or backing or both unless we were trying to accommodate these syllogisms to the Toulmin model?14 Toulmin would argue that the roles of data, backing, and warrant are so distinct that we need to supplant the premise/conclusion distinction with "at least the fourfold distinction between 'datum,' 'conclusion,' 'warrant,' and 'backing,'" 15 to properly analyse arguments. But when confronted with syllogisms such as Toulmin is analysing here, and the straightforwardness of representing them as two premise arguments, our inclination is to question Toulmin's categories rather than the standard interpretation. But is Toulmin's interpretation of general statements viable? Toulmin is saying that statements of the form "All A are Β" express either warrants, permitting us to infer a statement of the form "x is B" from one of form "x is A," or statistical reports about a closed class of objects — "Every A (examined) has been found to be a B." Toulmin emphasizes these are the two functions of such expressions. They are either inference warrants or factual reports of observations concerning just that of which we have observational records, or both. This prompts Hector Neri Castaneda in "On a Proposed Revolution in Logic" [1960], to remark, "The central fact seems to be that Toulmin does not acknowledge universal propositions or statements in the customary sense."16 Castaneda asks us to consider

Toulmin's Problematic Notion of Warrant (S)

57

Every Russian is ready to fight for his Motherland.

Is this a warrant or a statistical report? Castaneda argues that it is not a warrant, and Toulmin would agree. There is nothing inference-authorizing in (S) and for Toulmin, universal statements beginning with "every (single)" or "Each" are not permissive.17 But is (S) a statistical report? Does (S) make the assertion that every Russian has been found ready to fight for the Motherland? This does not seem a plausible reading. If anything, we expect this statement goes beyond observation. Has every single Russian that ever was, now is, (or will be) been observed? Is the statement intended to report just about those Russians who have been observed? Castaneda comments, It is odd to insinuate that regardless of how hard we may try, if the class of Russians is not closed, if we have not gone through that class until its complete exhaustion..., then to say that (S)...is not to make a statement, but to issue a warrant, or to quote an already issued warrant, for the making of inferences. 18

It seems that for Toulmin, if a class is subject to augmentation, then we cannot make a descriptive statement about all of it. We either assert a warrant, giving persons permission to infer from the fact that something is a member of this class to its having some other property, or we make a statement understood to describe just the subclass observed. At least, it appears that Toulmin maintains this, should our statement be proffered in a "premissory position" in a syllogism. In terminology we have used in Thinking Logically [1988], Toulmin seems to acknowledge that such universal statements may express summary reports but not descriptions involving inference. A summary report collects or collates data, expressing in summary fashion information expressed in many individual reports: 100 percent of the plants in the experiment injected with the compound survived. Descriptions involving inference go beyond reporting data to making some extrapolation: Every plant injected with the compound will survive. The latter statement would ordinarily be interpreted as making a statement about every plant (at least in a certain species), not just every observed plant. It would be counted true just in case every such plant injected with the compound survived. But aren't such descriptions involving inference, statements of universal form going beyond the data supporting them, asserted all the time? In particular, aren't such statements asserted as conclusions of inductive generalization arguments? How, on Toulmin's account, are we to understand such arguments as

58

What Are the Basic Elements of Arguments? 100 percent of the plants in the experiment injected with the compound survived. Therefore Every plant injected with the compound will survive.

We would ordinarily take this to infer a claim about an entire class on the basis of a sample. Doesn't "every" in the conclusion really mean every — not just all the observed? The truth conditions for premise and conclusion would not be the same, the conclusion obviously being a much stronger statement. We would accord an analogous interpretation to statistical generalizations such as "X% of A's are B's," or quasi-statistical or quasiuniversal statements — "Most A's are B's," "Few A's are B's," "Almost all A's are B's," "Scarcely any A"s are B's" asserted as conclusions of analogous patterns of argument. Toulmin specifically considers such arguments, regarding them as warrant-establishing as opposed to warrant-using: Warrant-establishing arguments will be...such arguments as one might find in a scientific paper, in which the acceptability of a novel warrant is made clear by applying it successively in a number of cases in which both 'data' and 'conclusion' have been independently verified."

Toulmin thus bids us construe all such statements as pn is a plant in the experiment injected with the compound as data, and pn survived as conclusion. These are all summarized in the premise of the original argument. Construing Every plant injected with the compound will survive as Given that ρ is a plant injected with the compound, we may take it that ρ will survive, we then have the warrant which may be applied in these various cases where data and conclusion have been independently verified through observation. This fact then counts as evidence for the warrant. It leads from verified datum to verified claim. General statements, then, occurring as conclusions of such arguments Toulmin understands as warrants. But can Toulmin accept this interpretation of the argument, given what he has said about general statements beginning with "Every"? He does not regard such statements as warrants. So it seems he would reject this interpretation of the conclusion. How then could he construe the conclusion of this argument? If he construes it as backing, as making a summary report of what has been observed, then his interpretation makes the argument

Toulmin's Problematic Notion of Warrant

59

question begging. He apparently would interpret premise and conclusion as making the same statement. But the argument clearly is not question begging. The conclusion goes beyond the premise. If Toulmin were to interpret the conclusion as a description involving inference, then he would be giving the statement an interpretation he otherwise assiduously avoids. Unless Toulmin can bring forward arguments to show that construing general propositions as descriptions involving inference is wrong, we may charge his interpretation of general propositions with false dichotomy or false dilemma. For Toulmin, general propositions are either descriptive summary reports or permissive warrants. He appears not to allow that general statements can go beyond reported data and yet be descriptive. But why should this interpretation be rejected? Construing many general propositions as descriptions involving inference seems a far simpler interpretation than trying to construe them according to Toulmin's warrant/summary report dichotomy, which seems designed to perpetuate his model. The plausibility of Toulmin's position would be greatly increased if he could bring substantial arguments against construing general propositions as descriptions involving inference. We want to underscore how Toulmin incurs a weighty burden of proof at this point. The situation here is distinctly analogous to attempting to justify instrumentalism, a view which Toulmin endorses in his essay The Philosophy of Science: An Introduction [I960]. On the instrumentalist view, the purpose of a scientific theory, ordinarily regarded as a plain statement or composed of plain statements, is to organize data and to operate as an inference rule, leading principle, inference ticket, licensing inferences from observation statements to observation statements.20 Theories are thus not premises, like data statements, but warrants. Toulmin's instrumentalism underlies his claim that A general statement in physical theory, as Newton reminds us, must be construed not as a statistical report about the behaviour of a very large number of objects, but rather as an open warrant or principle of computation.

21

If every scientific theory were expressed by a (multiply) generalized conditional statement, then Toulmin's position in The Uses of Argument could be seen as a generalization applying to all conditionals, including generalized or modified conditionals—insofar as they go beyond summary reports—of the instrumentalist interpretation of scientific theories. Even without regarding Toulmin's position on conditionals as strictly a generalization of his instrumentalism, what he must show here is analogous. As an instrumentalist must argue that all scientific theories function as inference rules whenever scientists appeal to them in scientific arguments, so Toulmin must show that this is the case whenever someone in an argument appeals to generalizations going beyond summary reports. It is open to the critic of

60

What Are the Basic Elements of Arguments?

instrumentalism to object that although the view may give us insight into how scientific theories function on occasion in scientific inquiry, its defenders have not shown that theories always function as inference rules. Nagel, in particular, takes this line of criticism. In his review [1954], of Toulmin's Philosophy of Science, Nagel urges that although laws do function as rules on some occasions, this is not their exclusive or even their characteristic function. Theories do in point of fact frequently function as premises in scientific practice, and indeed this seems to be the usual way they are explicitly employed. Most if not all systematic presentations of physical theory certainly do so; and as far as casual inspection of scientific papers dealing with special experimental phenomena reveals, this is the customary use to which theories and laws are put. 22

Again, in The Structure of Science [1961], Nagel urges Some of the most eminent scientists, both living and dead, certainly have viewed theories as statements about the constitution and structure of a given subject matter; and they have conducted their investigations on the assumption that a theory is a projected map of some domain of nature, rather than a set of principles of mapping ,25

Analogously, unless one can show that all (generalized) conditionals going beyond summary reports always function as inference rules, the critic can protest that Toulmin has not made his point. Although it may be insightful to say that in reasoning, conditionals may function as inference rules or that conditionals may express inference rules appealed to in reasoning, this does not show that when presented in arguments their sole function is to make manifest the rule or leading principle by which the argument proceeds. How does Toulmin argue for his view of conditionals, at least of the generalized conditionals appearing in certain syllogisms? I do not find the arguments Toulmin offers advance his case very far. He argues that the traditional way of construing the universal statement in premissory position as a premise disguises "the great differences between the things traditionally classed together as 'premises.'"24 But if we do not accept Toulmin's analysis of universal propositions applying to all general statements, we will find this claim question begging. Similarly, Toulmin argues that the traditional analysis of the syllogism "leaves it unclear whether the general statement 'All...' is to be construed as a permissive inferencewarrant or as a factual report of our observations.n25 But again this seems to presuppose as established the very dichotomy which is in question. Toulmin also believes he can argue from standard idiom for the warrant/backing distinction. "The contrast between 'Every A' and 'Not a single A', on the one hand, and 'Any A' or 'An A', on the other, points one immediately towards the distinction between statistical reports and the

Toulmin's Problematic Notion of Warrant

61

warrants for which they can be the backing."26 I, for one, find this claim obscure. Every boy is pugnacious. Any boy is pugnacious. Don't these two statements assert the same thing? Now clearly Every boy observed has been pugnacious makes a summary report different from Any boy is pugnacious. But does it make a different statement from Any boy who has been observed has been found to be pugnacious? So far, substantial arguments against construing general propositions as descriptions involving inference are lacking. But Toulmin in developing his position was greatly influenced by Gilbert Ryle's view of conditionals as inference rules. Ryle defended this view both in The Concept of Mind [1949], and "'If,' 'So,' and 'Because'" [1950]. Now the general propositions we have been considering are generalized conditionals of a universal or statistical sort. Can we find arguments in Ryle's considerations on the conditional which will support Toulmin's view of general propositions against the standard view? Ryle on Conditionals In [1950], Ryle asserts that the first purpose of a hypothetical statement, "if p, then q" is to license us in inferring from ρ to q. Knowing "if p, then q" is, then, rather like being in possession of a railway ticket. It is having a license or warrant to make a journey from London to Oxford. (Knowing a variable [universally quantified] hypothetical or "law" is like having a season ticket. 27

In [1949], Ryle develops the notion this way: At least patt of the point of trying to establish laws is to find out how to infer from particular matters of fact to other particular matters of fact, how to explain particular matters of fact by reference to other matters of fact, and how to bring about or prevent particular states of affairs. A law is used as, so to speak, an inference-ticket (a season ticket) which licenses its possessors to move from asserting factual statements to asserting other factual statements. 28

Should Ryle present a successful argument for this view of hypotheticals, then Toulmin would have a rationale for interpreting general hypotheticals

62

What Are the Basic Elements of Arguments?

which go beyond being summary reports as inference rules. That is simply what they are. In [1950], Ryle specifically argues for his position that hypotheticals are inference rules. Given an argument "p, so q" we may form its associated hypothetical, "ifp, then q." For the argument to be valid, the associated hypothetical must be true. Ryle feels it is incumbent on him to explicate just how the validity of an argument requires the truth of its associated hypothetical. He rejects the view that the associated hypothetical is a suppressed premise or a suppressed conjunct of the premise of the argument, necessary for its validity. On this view, to make good our claim that we can argue validly from "p" to "q," we must admit that in a candid formulation of the argument, the premise is "p and (ifp, then q)," not just "p," as might be supposed. But the associated hypothetical of the argument Arg

ρ and (ifp, then q), so q

is AH

if(p and (ifp, then q)), then q.

But if for an argument to be valid, its associated hypothetical must be a conjunct of the premise, then to candidly present this argument, Arg, the above formulation of Arg will not do. We have to include the associated hypothetical as a third conjunct in the premise. And thus we are off on a vicious infinite regress.29 In commenting on this, Ryle makes the following statement: The principle of an inference cannot be one of its premisses or part of its premiss. Conclusions are drawn from premises in accordance with principles, not from premisses which embody those principles. 30

But if we are searching for an argument to justify saying that hypotheticals are inference rules, we may already suspect trouble at this point. Is the associated hypothetical "if p, then q" the principle of the inference "p, so q"l Isn't it rather and more precisely "From p, we may infer or take it that q." That expresses a genuine, permissive rule. Ryle here seems to simply have taken associated hypotheticals for inference rules, and his very next statements confirm this impression. It is not merely that the officially recognized Rules of Inference cannot be given the role of premiss components in all the specific inferences that are made in accordance with them. The same thing is true of the most 'meaty' and determinate hypothetical statements, like "If today is Monday, tomorrow is Tuesday."...The argument "Today is Monday, so tomorrow is Tuesday" is an application of "if Today is Monday, tomorrow is Tuesday." 31

In talking of this argument as being an application of its associated hypothetical, Ryle is treating that associated hypothetical as an inference

Toulmin's Problematic Notion of Warrant

63

rule. Ryle needs to justify saying hypothetical can be applied to convince us that they are properly construed this way. This is precisely what Ryle does. He not only maintains that hypothetical, like rules, can be applied, but develops this view. It is Ryle's position that all hypothetical are variable or open in some sense, not just those specifically of the form "For all x, if φχ, then ψχ." How does he argue for this position? Ryle begins by pointing out that to assert "ifρ, then q" is not to assert or claim true either "p" or "q." He regards this as tantamount to saying "Neither the statement 'p' nor the statement 'q' enters into the statement 'if p, then q.'"32 But since the statement "if p, then q" looks as if it incorporates "p" and "q," just as "p and q" incorporates both, Ryle intends to argue that the appearance of the hypothetical statement is misleading. As he puts it, according to this form hypotheticals are misleadingly encoded. But even at this point, the discussion seems to involve a subtle confusion. Ryle seems to confuse containing a statement with containing the assertion of a statement. "Assertion" is a semantic notion. To assert a statement is not just or even to utter it, but to put it forward as true, "truth" being a primary semantic concept. "Containment" or "incorporation," on the other hand, is a syntactic notion. A statement may be viewed as an expression, and an expression is a sequence of symbols. For an expression E, to contain another expression E2, it is necessary and sufficient that E2 be a subsequence of E,. Clearly, just because E, contains E2, we may not infer that to assert Ε, is to assert E2. On Ryle's grounds not only should we say that the "encoding" of hypothetical statements is misleading, but that of a number of compounds, both truth-functional and non-truth-functional. One wonders what Ryle would say of negations, disjunctions, or statements of the form "a believes that ρ"Ί Ryle has a reply to this objection, which he begins quite tartly: The suggestion is that to be asserted is a luxury extra, like italicisation. But this will not do. If nothing is asserted, or no statement is made, then no question is answered, nothing is contradicted, no premiss is used, no conclusion is drawn, no information or misinformation is given. A statement bereft of its employments is not a statement and an expression debarred from doing any of the jobs of a statement has either no job or else a different job. 3 3

But we find this reply confused. The root of the confusion seems to be that for Ryle, "statement" and "assertion" are synonyms. Now although the expressions "to make a statement" and "to make an assertion" may be synonymous, this does not show that "statement" and "assertion" are synonymous, and above we have shown that they are not. Nor is it correct to say that when a statement enters into a hypothetical, it is bereft of its employments. For one of the possible employments of statements is to serve as components of longer statements, which latter may be asserted. If "if p,

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What Are the Basic Elements of Arguments?

then q" is asserted, then it is not true to say that nothing is asserted, even if "p," "q" are not. Ryle's reply falls far short of rebutting our objection. But let us return to Ryle's argument specifically that hypothetical are misleadingly encoded. He points out that sometimes one or both components of a hypothetical are worded subjunctively, and when so, the subjunctively worded components are not independent statements, witness If it be Monday today, it is Tuesday tomorrow. If it were Monday today, it would be Tuesday tomorrow. It cannot be Monday today and not be Tuesday tomorrow.34 Ryle points out that in the third form, what follows "cannot" and "and" "has none of the appearances of a statement. "3S He believes any hypothetical can be reworded according to this pattern, and concludes "The statementlike appearance of the clauses of those 'if-then' statements which are not subjunctively worded is a deceptive appearance and one which always can be and often is obviated in stylistically different paraphrases....The logicians' code style...is deceptive."34 It is open to any logician to vigorously reply here that Ryle has not made his point. First, it is true that any hypothetical can be reworded according to the third pattern or form only if "if-then" means "implies" or "entails." For surely Its being Monday today entails its being Tuesday tomorrow expresses the same proposition as It cannot be Monday today and not be Tuesday tomorrow, and this holds in general. But is it true of every "if-then" statement that "ifthen" means "entails"? Consider (1)

If John is coming to the party, then Mary is coming also.

A mechanical rewrite according to the third pattern produces something ungrammatical: It cannot be John coming to the party and Mary not be coming also. But Ryle did not say that we had to mechanically preserve this form. We may take it that the looser (2)

John cannot be coming to the party and Mary not be coming also,

i.e.

It cannot be that John is coming to the party and Mary is not coming also

is the proper rewrite. Now the denial of this statement is clearly (3)

John can be coming" to the party and Mary not be coming also

Toulmin's Problematic Notion of Warrant

65

which surely expresses the same proposition as (4)

John can come to the party and Mary not come also.

Now we can imagine someone asserting the following statements: Of course, John can come to the party and Mary not come also. That's conceivable. But you can rest assured that if John is coming to the party, then Mary is coming also. Is this a contradictory set of statements? Would asserting all the statements in this set be contradicting oneself? It clearly would not. But this shows that (3)

John can be coming to the party and Mary not be coming also

is not the negation or denial of (1)

If John is coming to the party, then Mary is not coming also.

But (3) is the denial of (2)

John cannot be coming to the party and Mary not be coming also,

as we asserted above. Hence these two statements, (1) and (2), are not the same; the "cannot" form does not express a simple paraphrase of the straight indicative conditional. With this particular conditional, at least, "ifthen" does not mean "implies" or "entails." This is not the place to enter into the controversy of how the concepts of implication or entailment should be analyzed. Suffice it to point out here, as any modal logician would, that there is an element of necessity in It cannot be Monday today and not be Tuesday tomorrow. This statement is logically equivalent to a necessitated conditional. For we may express the same proposition by saying It cannot (is not possible for it to) be the case that (today is Monday and tomorrow is not Tuesday). But this is equivalent to saying It is necessary that (if today is Monday, then tomorrow is Tuesday). The form of this statement is it is necessary that (if ρ, then q) analogous to for all x, (if φχ, then ψχ).

What Are the Basic Elements of Arguments?

66 and not the simple i f p , then q.

But this point opens up a further problem for Ryle. For notice that in our expansion of Ryle's third pattern, and as our schema above indicates, indicative statements are components of these expressions. And expanded versions involving just indicative components of Ryle's first two forms are straightforwardly provided. If it be the case that today is Monday, tomorrow is Tuesday. If it were the case that today is Monday, it would be the case that tomorrow is Tuesday. It appears that Ryle's forms are abbreviations of these expanded versions. But it is open to our logician to argue this way: From the fact that a given letter or sequence of letters does not appear in an abbreviation of a word, it does not follow that those letters are not components of the sequence of symbols constituting that word. Likewise, from the fact that Ryle's abbreviations do not contain the full indicative statement as component, it does not follow that they are not the components of such statements properly understood. Unless Ryle can show that these expansions are illegitimate, and further that indicative conditionals should always be properly or candidly rendered according to one of his patterns, he has not made his point that the logicians' code style "if p, then q" is deceptive in representing"/»," "q" as components of hypothetical. Having thought that he had established his point that hypothetical statements do not contain indicatives as components, Ryle continues, "What the hypothetical statement does embody is not statements but statement specifications or statement indents- bills for statements that statements could fill."37 According to Ryle, these statement indents are analogous to variables. Just as an individual variable can have an individual it ranges over as one of its values, so "'...today be Monday' can have 'Today is Monday' for one of its values."38 Ryle's discussion here is obscure. Hypothetical statements certainly do not appear to involve variables at all. As Clark points out in "Natural Inference" [1956], if we have a genuine schema involving a free variable, such as

φχ the "x" marks a slot into which genuine names of individuals may be inserted. Similarly, if we allowed other styles of variables, such as propositional variables or predicate variables, schemata involving these variables would thereby involve slots into which non-variable expressions of the appropriate category could be asserted. But where are the slots in If today be Monday, tomorrow is Tuesday ?

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There are no slots. As Clark observes, "The hypothetical statement is a statement and not the schema of a statement and there is no appropriate insertion which will render it more of a statement than it is, since there is no possibility of insertion at all." 3 ' He concludes, "This is precisely why hypothetical statements...cannot be variable just as these expressions are variable."40 If hypothetical statements cannot be variable just as schemata are variable, if they do not involve variables or variable expressions in that way, is there any other intelligible sense in which they can be said to be variable? What does it mean for an object to be the value of an individual variable? It means that we could, hypothetically, regard that variable as a name of the object (this is what an assignment function does), and where that variable appears in a propositional function expressing some attribute, we can meaningfully ask whether that attribute is true of the object. It likewise suggests that substituting a name of that object for the variable in the propositional function results in a meaningful statement, one which is true or false. In what sense does "...today be Monday" range over statements or what statements express? As Clark asks, what values, other than "Today is Monday" does it range over?41 The very understanding of a variable is that it can range over a whole set of values. But even taking "Today is Monday" as a value of "...today be Monday" is problematic. If some object is the value of a variable "x," then it makes sense, where the quantifier "for all x" ranges over such objects, to ask whether the result of dropping the quantifier in for all χ, φχ and replacing "x" by a name of that object, results in a true statement. But in If today be Monday, tomorrow is Tuesday not only does there appear to be no quantifier to drop, but on Ryle's grounds literally replacing "...today be Monday" by "Today is Monday" is illegitimate. It should, strictly speaking, result in an expression not well formed, one where the question of truth or falsity would not even arise. Are there, for Ryle, any propositional contexts in which "...today be Monday" can be replaced by "Today is Monday" salva well-formedness? If not, what does it mean to say that "Today is Monday" is a value of "...today be Monday"? Given these problems, we conclude that Ryle has simply not established that hypothetical statements express inference rules. Someone seeking a clear rationale for treating hypothetical statements appearing in promissory position as radically different from the other premises, as warrants as opposed to data, will either have to make better sense of Ryle's

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argument than we can, or look elsewhere. At this point, we still lack an argument to show why hypothetical statements, including quantified or variable hypotheticals, are so different from other statements which appear in premissory position that they should be counted as a distinct type of argumentative element. But there is one other writer who has addressed this issue and whose views initially seem quite persuasive. J. S. Mill in A System of Logic presents a discussion of the syllogism which remarkably resembles Toulmin's, but which sets an account of the general proposition in premissory position within a broader account of how we reason. Let's see whether Mill gives us suitable justification for holding that hypotheticals or conditionals going beyond summary reports always express inference rules. Mill on the Syllogism Mill's account of syllogistic arguments of the form All S are P. a is S. Therefore a is P. strikingly anticipates Toulmin's. In fact, we may use Toulmin's data/warrant/backing distinction to sharpen Mill's exposition. In A System of Logic [1973], Mill holds that a proposition may be regarded either "as a portion of our knowledge of nature, or as a memorandum for our guidance."42 Under the first interpretation, a universal affirmative categorical proposition asserts that whatever has a given attribute has some further attribute. Under the second, the proposition is not "a part of our knowledge" but an inference rule, "enabling us, when we see or learn that an object possesses one of the two attributes, to infer that it possesses the other."43 We compress all our observations of particulars and possible inferences into one general proposition. From instances which we have observed, we feel warranted in concluding, that what we found true in those instances, holds in all similar ones, past, present, and future, however numerous they may be. We then...record all that we have observed, together with all that we infer from our observations, in one concise expression. 44

This is the memorandum or register interpretation of general categorical propositions. This interpretation constitutes the basis of Mill's strategy for resolving a notorious paradox or conflict in syllogistic theory. In a valid syllogism, the conclusion cannot assert anything more than what was asserted in the premises. But it certainly appears that syllogistic reasoning can lead to new knowledge. Through such reasoning, persons come to know or recognize facts they were not previously aware of. How can the conclusion of a syllogism give us new knowledge, when it expresses nothing

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but what was already contained in the premises? As Mill sees it, we must distinguish inferring from registering or deciphering. We infer when we pass by inductive generalization from particular facts — e.g. the mortality of individual persons — to a generalization — "All humans are mortal," or when we pass by analogy from particular facts to some further fact — "The [still alive] Duke of Wellington is mortal." But the general proposition is an inference licence or memorandum that we have such a licence. In syllogistic reasoning per se, we do not infer but decipher the import of this licence. From Mill's perspective, we infer the conclusion of a particular syllogism from the particular facts which serve as evidence for, which back, the general statement which licences, warrants an inference. In ordinary, everyday reasoning the move from backing to warrant, inference licence may actually be omitted, the reasoning from backing to claim proceeding by analogy. (If Mill had the data/warrant/backing distinction here and were speaking carefully, I expect he would say we infer the conclusion from the backing for the warrant together with the datum that an object possesses a certain attribute.) Should we set this backing aside, and reason just from (data and) inference licence or warrant to some further fact, we would be consulting, reading our notes, deciphering what was already registered in our inference licence. In his memorandum theory of general propositions, in his account of how these propositions are backed by observation of particulars, Mill gives us a rationale for the data/warrant/backing distinction. What I find most persuasive about this discussion, besides its neat explanation of why the syllogism is not a petitio principii, is its linking the rationale to an account of the reasoning process. Mill has a conception of reasoning from which the data/warrant/backing distinction grows. But it is right here that we may also raise critical questions. Let us grant for the moment that the universal proposition "All humans are mortal" functions as a warrant in some person's inferring the mortality of the Duke of Wellington from his humanity. But should this reasoner propound the argument All humans are mortal. The Duke of Wellington is human. So the Duke of Wellington is mortal. does the general premise here function as a warrant? Is this how it is to be properly interpreted as it appears in this public argument as product, in contradistinction to how it appears in private reasoning? Should the reasoner present this argument to convince a challenger of the Duke of Wellington's mortality, would his first statement serve merely to remind the challenger of an inference rule? Recall that Mill does allow two interpretations of the general proposition. According to the first, the proposition asserts that whatever has the attribute of being human has also the attribute of being mortal. Why should the first statement not be interpreted this way? As R.

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P. Anschutz points out in "The Logic of J. S. Mill" [1949] about the parallel argument for the mortality of Socrates, Although this may not seem a very convincing argument, tom out of any context, it is not difficult to imagine circumstances in which it may, and should, produce conviction, provided we can imagine a person genuinely in doubt about Socrates' mortality and another anxious to convince him of it. The argument will then take the form of an examination—Well, Socrates is a man, isn't he? And all men are mortal, aren't they? Hence he must be mortal. And so far as we are all open to conviction, and are right to be open to conviction, in this sort of way we are, I take it, admitting the validity of syllogistic argument in its original dialectical form. 4 5

Some comments Nagel makes in criticism of instrumentalism seem especially appropriate here. He claims that the premise/inference rule distinction is contextual. In the above argument about the Duke of Wellington, the general statement is a premise and the inference rule is the formal principle of the syllogism "a statement of the form 'JC is Ρ ' is derivable from two statements of the form 'All S is Ρ ' and 'χ is S.'" 46 But in the argument The Duke of Wellington is a man. Therefore the Duke of Wellington is mortal, the inference rule is the material principle "Any statement of the form 'χ is mortal' is derivable from a statement of the form 'χ is a man'" 47 — "All men are mortal" for short. Further, we may recast or reconstruct the first argument as the second and the second as the first. And this holds for any pair of arguments instancing these two patterns. Nagel concludes, It is clearly a matter of convenience in which of these alternate ways an argument is constructed. Accordingly, though the distinction between premises and rules of inference is both sound and important, a given statement may function as a premise in one context but may in effect be used as a leading principle in another context, and vice versa. 48

What Nagel says here is very much in line with some comments of Peirce on leading principles. As he points out in "What is a Leading Principle?", once the leading principle of an argument is formulated, it may be added to the premise(s) of that argument to form a second argument. The conclusion of both arguments is the same. But the premise set of the second includes exactly the premises of the first together with the leading principle as a premise. In the second argument, the conclusion is drawn from all these statements together. Hence, although we may agree with Mill (and Ryle and Toulmin) that conditional statements of various sorts may have the force of inference rules, to construe them as inference rules when they appear in premissory position in the syllogisms we have been considering is to overlook the contextual nature of the premise/inference rule distinction

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and to misconstrue the structure of these arguments. Surely, when someone offers an argument with a conditional statement in premissory position, we have ample textual evidence that he or she intends to draw the conclusion of that argument from all the statements in premissory position together, including the conditional. By explicitly offering the conditional in premissory position, the arguer creates the presumption that this statement is one of the premises, that the statements from which this argument moves to the conclusion include this conditional, and not just the remaining "data"-type premises. Construing the argument as if the conditional statement were the warrant (together perhaps with its backing) goes against this presumption. Of course, it is open to Mill, or better Mill's advocate, to reply that his analysis of universal categorical propositions and their function in reasoning undercuts this presumption. Such propositions, insofar as they go beyond summarizing observed data, are memoranda, registers of the inferences we may make. When someone manifestly includes such a proposition in premissory position in an argument, he is simply reminding himself or his audience of this memorandum, or perhaps communicating it to his listeners. Inference licenses are just what these statements are. But one may counter this by pointing out that Mill's advocate, like Toulmin, seems to have forgotten that universal categorical propositions can go beyond being summary reports that all observed A's are B's to making a descriptive statement about all A's. At least, this is one standard construal of such propositions which has not yet been decisively refuted. Although the force of "All A's are B's" may be to indicate that we may infer from something's having the attribute A that it also has the attribute B, the proposition makes a claim in its own right going beyond summarizing data, and this is ordinarily taken as its intended sense when it is proffered in premissory position. It seems that after reviewing all these considerations put forward by Toulmin, Ryle, and Mill, we are right back where we started. Let us take stock of our inquiry up to this point. We are asking whether the concept of warrant identifies a basic category of element in arguments as products. Alternatively, we are asking whether the data/warrant distinction can be applied to arguments as products. We saw initially that making this application was problematic, and required a rationale for identifying a statement presented in premissory position as the warrant or as expressing the warrant as one of its functions. To discover such a rationale, we turned to Toulmin's account of certain classes of syllogisms. But this discussion, although suggesting a rationale, that if a statement is of conditional form take it ask the warrant, was problematic. It rejected interpreting generalized conditionals as making statements about the world going beyond summary reports. We did not see that Toulmin satisfactorily argued for this view, nor did we find any satisfactory argument in Ryle's defense of construing conditionals as inference rules. Nor have we found a suitable defense in

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Mill's account of syllogistic reasoning. Hence we still lack a reason for rejecting interpreting general categorical propositions as descriptions involving inference, descriptive statements going beyond just what has been observed. But this is precisely what we needed to see that there was an advantage in counting general categorical propositions as warrants as opposed to premises. Although Toulmin's, Ryle's, and Mill's approach may have the virtue of highlighting that universal categorical propositions and conditionals in general may function as inference rules in certain contexts, this does not entail that they so function when appearing in premissory position in certain syllogisms. We have yet to see an argument establishing the superiority of construing them as inference rules or warrants when they appear in such contexts. In fact, if Nagel is correct, this may even misconstrue the structure of such arguments. Hence, we have not found any compelling reason or advantage in following Toulmin's approach, but rather have identified a distinct possible disadvantage. Further, we feel there are a number of other disadvantages to Toulmin's approach which will provide telling reasons against taking warrants as a structural category for arguments as products. By presenting his model of the layout of arguments, Toulmin suggests that in any argument, we should be able to identify the distinct types of elements — claims, data, warrants, modalities, rebuttals, backing — in his model. Further, Toulmin's including warrants in "the first skeleton of a pattern for analysing arguments"49 certainly suggests that every argument includes a warrant. Indeed, Toulmin speaks directly to this point when he says "unless, in any particular field of argument, we are prepared to work with warrants of some kind, it will become impossible in that field to subject arguments to rational assessment....The warrants to which we commit ourselves are implicit in the particular steps from data to claims we are prepared to take and to admit." 30 This passage is significant, in that it allows that warrants may be implicit in an argumentative text, not manifestly stated. Indeed, Toulmin seems quite emphatic about this when he says "Data are appealed to explicitly, warrants implicitly."51 Hence, in analysing an argument according to the Toulmin model, it is not incumbent on us to identify one of the explicit statements or expressions as the warrant. However, it is fair to say that on Toulmin's view, given any responsibly presented argument, any argument worthy of rational assessment, we may identify warrants held at least implicitly. Of course, if warrants are inference rules, this view is not surprising. For it is a commonplace that whenever we move from premises to conclusion in inference, there must be some rule according to which we make that move, even if we are not aware of it explicitly. But warrants, as we saw above, are inference rules. That was the answer to the first of the three questions we asked to evaluate whether warrants constituted a genuine

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category of elements occurring in arguments as products. In answering the second, we have failed to find compelling reasons for counting certain statements or types of statements which may occur in arguments as warrants, even in the syllogisms which apparently lend themselves to this analysis. But in other arguments, at least as manifestly stated, we cannot readily identify an explicit warrant or distinguish warrant from data. Indeed, attempting to do so seems only to lead to puzzlement. We shall give plenty of evidence for this shortly. If warrant is a basic category of argumentative element, then in many instances we shall have to supply the warrant. One main evaluative question remains — Even if warrants, implicit or explicit, can be identified, is it right to count them as elements in arguments as products, are they properly parts of arguments? To prepare ourselves for answering that question, let's see why we need, in a number of cases, to supply warrants. Warrants as Always Implicit, if not Explicit in Arguments as Products Let us remind ourselves of Toulmin's apparent position. In at least some arguments as products, some manifestly stated proposition functions as warrant, or does double duty representing (and masking) both warrant and backing. The point is that from some statement explicitly in the argument we may generate the warrant and contrast it with data, other statements manifestly in the argument. With many other arguments as products, this is not possible. Consider any instance of conjunction, for example Uncle Henry will come. So will Aunt Annie. Therefore Uncle Henry and Aunt Annie will come. Which premise is the data, which involves the warrant? In a disjunctive syllogism, does the disjunctive premise serve the warranting function? Does a statement of the form Ρ or Q say, in part, that Given not P, we may take it that Q? Are the premises of a pure hypothetical syllogism data, warrants, or is one data while the other expresses a warrant? How are we to tell? Consider the familiar syllogism in Barbara. On analogy with our singular syllogism, should we count the minor premise as asserting the data and the major premise as involving the warrant? Can this rule be generalized? In a syllogism of the form

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Some Β are C All Β are A Therefore Some A are C the major premise is particular, the minor universal. But surely here if we want to analyse as Toulmin does, don't we want to count the major premise as data, the minor as furnishing the warrant? Things become even more perplexing when we consider invalid argument forms. In Some Β are C Some A are Β Therefore Some A are C does either premise involve a warrant? The problem is not confined to syllogisms or other two premise deductive arguments. Where is the warrant in arguments proceeding by immediate inference, obversion, conversion, contraposition? How are we to analyse arguments proceeding by some form of the rule of replacement, i.e. arguments where the conclusion is just like the premise except at some component, which is distinct from but logically equivalent to the corresponding component in the premise? For example, consider an argument of the form Ρ & (O 5 R) Ρ & (~~Q = R) Is the equivalence of Q with ~ - Q the warrant here? Especially problematic would seem to be arguments proceeding by some special strategy — conditional proof, reductio ad absurdum, separation of case. Recall that in a conditional proof argument, one establishes a conditional as conclusion by showing that we can argue cogently from the antecedent of the conditional to its consequent. The entire argument is put forward to justify the conditional. What here is the warrant licensing the move from the argument to the conditional? Would it be the formal rule of conditional proof? Problems go further than just deductive arguments or — like these arguments utilizing special strategies — arguments which are frequently deductive. As we noted in Chapter One, inductive generalization arguments proceed this way: (1) e, is an A and a B. (2) &2 is an A and a B. •

(n) e„ is an A and a B. .*. (n+1) All A's are B's.

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Clearly, the premises constitute a body of data, but where is the warrant? Such arguments seem warrant-establishing as opposed to warrant-using. Toulmin indicates that arguments establishing warrants themselves use warrants,52 but he does not give examples. It would seem that in many of such warrant-establishing arguments, the warrant would have to be supplied. If we agree that it is improper to take one of the assertions in these arguments as expressing or involving the warrant, but yet also agree that every argument involves a warrant, then we shall have to say that the warrant is implicit in these arguments. But if we agree that the warrants are implicit, the question arises: How should we frame these warrants? What shall we supply to make the implicit warrants explicit? There is a distinct disanalogy between Toulmin*s examples motivating recognizing warrants as a separate element in arguments and the examples we have just reviewed. Harry's hair is red. Therefore It is not black.

Petersen is a Swede. Therefore He is not a Roman Catholic.

Wilkinson was timed driving at 45 mph in a built-up area. Therefore Wilkinson has committed an offence against the Road Traffic Acts.

Harry was born in Bermuda. Therefore Harry is a British subject.53

Each of these arguments involves an intuitively obvious logical gap. Something is needed to connect data and claim, manifestly stated premise and conclusion. What Toulmin offers as warrants clearly fills in the gaps: If anything is red, it will not also be black. A Swede can be taken almost certainly not to be a Roman Catholic. A man who is proved to have driven at more than 30 m.p.h. in a built up area can be found to have committed an offence against the Road Traffic Acts. A man born in Bermuda will be a British subject.54 But where is the gappiness in the move from the data "Uncle Henry will come; Aunt Annie will come" to the claim that "Uncle Henry and Aunt Annie will come"? Likewise, where is the gappiness in the argument: Either Jim will get the promotion or he'll resign. Jim will not get the promotion. Therefore He will resign.

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Where is the gap when we argue according to the form "All Β are C/All A are B/Therefore All A are C", or when I infer that Jones will come from the assertion that he will not refrain from coming? Again, where is the gap in arguing according to the form On assumption that P, we have shown that Q. Therefore If P, then Q. Does the question, "How do you get there?" naturally arise for these arguments? Now it is open for one to reply that although these arguments involve no substantive or material gap, they still require inference rules to licence or enjoin moving from the data or manifestly stated premises to the conclusion. These examples differ from Toulmin's, since only purely formal inference rules are involved here. In fact, the formal inference rules to which we have alluded in describing the forms of these arguments are the warrants here. By describing the argument as being of a certain form, we have already indicated its warrant. From a statement that Ρ and a statement that Q, we may take it that Ρ and Q. From a statement that either Ρ or Q and a statement that Ρ does not hold, we may take it that Q. The difference between these warrants and those which Toulmin supplies is the difference between formal and material inference rules. The paradigm case of a warrant for Toulmin is a material inference rule. But this is in no way incompatible with admitting formal inference rules as warrants. We could, quite consistently, take the class of warrants as including both formal and material inference rules. Indeed, it seems we must, if we are to regard any argument as involving a warrant. Some Problems With This View Although this view is consistent, we feel that it raises a number of questions and problems. Consider first Toulmin's apparent insistence that warrants be always included in argument diagrams. Consider the sample arguments we have been discussing. On the standard approach, arguments proceeding according to rules of conjunction, disjunctive syllogism, Barbara might all be diagrammed as linked:

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< s >

Vl·'

© As we noted in Chapter One, some might want to diagram conjunction arguments as convergent. But in spite of this disagreement, the diagramming appears straightforward. On the Toulmin model, it would appear that conjunction arguments would be diagrammed this way: Dl, D2

So C Since

From statements ρ anH q we may Infer a statement of form ρ Se q The diagrams for disjunctive syllogism and syllogism in Barbara would be parallel, inserting their respective inference rules in warrant position. An argument proceeding by double negation would be diagrammed this way: D

J

^

So C

Since

From a statement of form — ρ , we may Infer ρ In the current and earlier editions of Practical Reasoning in Natural Language [1986], Stephen Thomas has shown how the standard method of argument diagramming can be extended to display the structure of conditional and reductio ad absurdum arguments. Toulmin says nothing about them. Assuming that we could diagram the move from an argument with a conditional assumption to a conclusion where that assumption is

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discharged, we would again supply some inference rule as warrant for that move. Notice that in each case, we have had to supply the warrant. Deductive arguments in general do not explicitly state the inference rules they are instances of and to which they appeal. Toulmin's approach, apparently requiring us to supply these warrants, conflicts with our second desideratum for an argument diagramming technique given in Chapter Two. We there proposed that our method of diagramming arguments not require significant reconstruction of the argument. Why, if an argument does not include a warrant, should we be required to supply one just to satisfy a requirement of our diagramming system? This makes the diagramming system less straightforward. Why is it incumbent on us to account for warrants — and indeed all the other elements in Toulmin's layout — when our first concern is getting a picture of how the argument as manifestly stated hangs together? This perceived defect in Toulmin's approach could be easily overcome by a simple modification of his system: Keep the general approach, the structural categories of the Toulmin model, but do not require all these categories to be represented in every diagram of an argumentative text. If a text includes only data and a claim, then a proper diagram of that argument's manifest structure would display only data and claim. This does not mean that one could not attempt to supply the other elements deemed implicit in the argument. But that is not now required in constructing a diagram. We have broadened Toulmin's approach to allow diagrammatic representation just of what a text manifestly includes. That frequently, indeed generally, we would have to supply warrants and other elements to complete a diagram according to the Toulmin model again raises the question of whether Toulmin's model applies primarily to arguments as process rather than arguments as product. Are we really describing process rather than product structure here? As we have seen, Toulmin motivates recognizing data and warrants as distinct categories of elements in arguments through questions which a challenger in a basic dialectical situation might ask. It would furthermore be straightforward to frame such questions to introduce modalities, rebuttals, and backing. Toulmin's categories, then, seem attuned to giving us as challengers a framework for asking critical questions of the proponent, for drawing out his argument or imagining what answer he might give. This leaves open how revealing these questions are for discerning the structure of argumentative texts. This does not in any way gainsay the value of these questions for properly evaluating an argument. To determine just how cogently or with what force someone has argued for a claim, one may have to engage him imaginatively in a dialogue by asking these questions. To see the structure of this developing argument as process as instancing the Toulmin model

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might be quite illuminating. But this is different from discerning the structure of an argumentative text. Even with this modification to allow diagramming just the manifest structure, there is still a problem on this approach. Compare these two familiar arguments: (1) (2) (3)

Socrates is human. All humans are mortal. Therefore Socrates is mortal.

(1) (2) (3)

All Greeks are human. All humans are mortal. Therefore All Greeks are mortal.

We have already noted the first apparently lends itself to Toulmin's data/warrant distinction, whereas the second is problematic. The standard approach sees both arguments instancing the same linked structure:

G>

-© ν ®

On the Toulmin model, the first would be represented this way: Socrates Is human

^ So Socrates Is mortal

Since

We may take whatever is human as also mortal

I On account oi

The proportion of human beings found to be mortal is 100%

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The second, however, would apparently be represented this way: All Greeks are human 7 .„ , , , > All humana are mortal \

\ 7 So All Greeks are mortal

Since

Given statements of form All A are Β and All Β are C, we may infer the statement of form All A are C

Even if we permitted omitting the warrant, on Toulmin's approach we could supply it and it would properly be included in a diagram of the argument's developed structure. This pair of Toulmin diagrams strikes us as being doubly artificial. First, there is a disparity in these diagrammatic representations which does not reflect a disparity in the original texts. Our first diagram represents the first argument as reasoning to its claim (3) from one datum (1) via the material warrant (2). Our second diagram represents the second argument as reasoning to claim (3) from data (1) and (2) via the formal warrant, syllogism in Barbara. But is there this structural disparity in the original texts? Does not each seem to present two premises from which a conclusion is inferred by taking these premises together? This is how the standard approach represents the structure of both arguments. Even using the Toulmin approach, wouldn't it be more perspicuous to represent the structure of the first argument this way: Socrates is human , All human are mortal'

^

Six*

Given statanoita of form asjland ABAareB, *e may take it that aisB

So Socrata is mortal

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This would restore the parallelism between the two arguments, and be faithful to our intuition that in both, two premises are intended to be taken together to support the conclusion. But at this point, we are faced with another problem. Presenting a formal inference rule as the warrant seems distinctly artificial. Why, unless we were trying to fill in the gap in the Toulmin model and find a warrant, would we want to include these inference rules in a representation of the argument's structure? This is the second way in which the approach involves artificiality. It brings the approach into conflict with our third desideratum for a diagramming technique, that the technique should mirror the structure of real life arguments. If we perceive a gap in a diagram, that should be because we perceive the diagram to reflect imperfectly or incompletely the structure of the argument, not because our diagram construction rules tell us to go out and find a certain element. We sense it artificial to include inference rules in argument diagrams because we are bothered by the following question: Are inference rules parts of arguments? Among the elements properly composing or constituting arguments will we find inference rules? Why should we feel constrained to count an inference rule as part of an argument? This is our third main evaluating question for determining whether warrants are elements in arguments. What may we say to this question? Are Inference Rules Parts of Arguments? Let's attack this question by considering formal and material inference rules in turn. First, is a formal inference rule actually part of an argument, the way the premises and the conclusion are parts of the argument? Suppose someone gives an argument, drawing its conclusion from the premises according to one (familiar) deductive inference rule, but not explicitly stating that rule. To take a fresh example, consider constructive dilemma. Suppose all the premises called for by the rule are explicitly stated — as premises we have one disjunctive statement and two conditionals — as is the conclusion. Is this argument still incomplete for not including an explicit statement of the inference rule From statements of the form pVq, ρ r, q => s, we may infer a statement of the form r V j ? I think not. Once we have indicated what the premises and conclusion are and how the argument signals that the premises support the conclusion, what other parts are missing? We may draw an analogy here—arguments are to inference rules as substances are to attributes. An argument — a deductive argument at least — is an instance of an inference rule as a substance is an instance of an attribute. Are attributes parts of substances? Consider a table. We would

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count its legs, top, and any other additional pieces among its parts. Its parts are the physical components of the table. Is the color, then, a part in this sense? It is clearly not. By "color" we do not mean the skin of paint covering the table, if any. We mean the color attribute of which the table is an instance, that color attribute which is true of the table. Categoreally, it is just not right to count this as one of the parts of the table. But if an argument is to an inference rule as a substance is to an attribute, then the inference rule is no more a part of the argument than the attribute is part of the substance. But, as seems clear, as a substance is a concrete instance of some attribute, so an argument is a concrete instance of some inference rule. Turning to material inference rules, we must admit that there is some plausibility in regarding them as parts of arguments. As we have noted, in Toulmin's warrant motivating examples, there is a gap between data and claim, some substantial element seems missing here, which the warrant, a material inference rule, fills. Those argument involving just formal warrants seem disanalogous here. As long as the warrant being instanced is cogent, there is no substantial gap between premises and conclusion. Here we can just see that we can get to claim from data, whereas when a material warrant is called for, we apparently need some explanation. Despite this fact, I believe we may also show that material inference rules are not parts of the arguments involving or instancing them. The question is: Who needs this gap filled — the proponent who presents this argument from data to claim, or the challenger who receives it? It is the challenger who senses the gap and asks that it be filled in. The proponent, we may presume, has "seen" how to get from his premise to conclusion. This is the basis for what we may call the phenomenological argument against counting material inference rules as parts of arguments. This argument is presented quite trenchantly in David Hitchcock's "Enthymematic Arguments" [1985]: I recently reasoned that it would not be difficult to find a house in a nearby city for which I had been given directions, because the house was just off the main road. This simple piece of reasoning is obviously an enthymematic argument, but I was not conscious of having omitted a premiss in articulating it—especially since I articulated it to myself before later verbalizing it to someone else. I invite the reader to try the same exercise with her or his own recently formulated enthymematic argument; I doubt that you will be conscious of having omitted a premiss. 55

Although Hitchcock wants to make the point that certain arguments involving gaps do not involve tacit, suppressed, unstated premises, his considerations can be applied to argue that material inference rules are not parts of arguments. We may agree that in these arguments involving gaps, something substantial may need to be supplied to explain to a challenger

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how we can get from premises to conclusion. We can leave it open whether this substantial element should be expressed as an additional premise or as a material inference rule. But the point is that the proponent has moved from premise to conclusion without consciously consulting this substantial element, whatever it may be. Just as in the case of a formal rule, he has moved from premises to conclusion directly. His reasoning is in accordance with a material inference rule, just as in giving a valid deductive argument, his reasoning is in accord with a formal inference rule. But in neither case is there a conscious appeal to the rule. The rule was not part of the reasoning. If the formal inference rule was not part of the argument instancing it, then neither is the material inference rule part of the argument proceeding in accordance with it. Peirce in "What is Leading Principle?" [1955] develops this phenomenological argument. According to Peirce, our inferring proceeds according to certain habits. In inference, A judgment is formed; and under the influence of a belief-habit this gives rise to a new judgment, indicating an addition to belief... .The antecedent judgment is called the premiss; the consequent judgment, the conclusion·, the habit of thought, which determined the passage from the one to the other (when formulated as a proposition), the leading principle... When the inference is first drawn, the leading principle is not present to the mind, but the habit it formulates is active in such a way that, upon contemplating the believed premiss, by a sort of perception the conclusion is judged to be true. 56

For Peirce, the reasoner should be conscious of proceeding according to a general habit, but ne need not have "a distinct apprehension of the leading principle of the habit which governs his reasoning."57 He may even be mistaken about the leading principle. It is sufficient only that he be conscious of proceeding according to a general method which he regards as generally leading to the truth.58 Peirce's discussion of leading principles seems in essential agreement with Hitchcock's about certain phenomenological facts of inference. In our reasoning, including reasoning in which a challenger might find a gap, we move according to habits of which we are not explicitly conscious. These habits permit and lead us to move from premises to conclusion directly. The propositions we consciously entertain are the premises and conclusion, not the leading principle representing the habit. That leading principle then is not part of the conscious reasoning, of the conscious inferential process, nor, we might add, of an argument which would express this process. As Peirce puts it, the form of inference is Ρ therefore C,59 and here there is no indication of a leading principle. We have thus presented an argument that no inference rules — neither formal nor material inference rules — are parts of arguments. Hence argument diagrams need not, and in fact should not, contain such elements.

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This means that warrants should not be included in diagrams of argument texts. The category of warrant should be jettisoned in analysing arguments as products.

3.3. DATA, WARRANT, BACKING OR JUST PLAIN PREMISES?

Our argument in the previous section against warrants shows that we cannot meaningfully draw the data/warrant distinction in analysing arguments as products. We cannot identify certain statements in premissory position as the data and others as the warrants. Hence, rather than seek to make the data/warrant distinction, we should simply recognize premises. Are there any advantages to distinguishing backing from premises as a distinct type of argumentative element? Premises and Backing? What is backing supposed to do? According to Toulmin, backing is offered to show why a warrant is acceptable. We can even phrase a dialectical question for introducing backing: Why in general should this warrant be accepted as having authority?® Giving backing then constitutes giving reasons for warrants. Should such statements be offered in arguments as products to support a conditional of some type, why should they not be taken as premises supporting that conditional directly, and indirectly the conclusion for which that conditional is a premise? Toulmin has a reason for distinguishing backing, and it is central to the project of The Uses of Argument. Toulmin believes that to evaluate arguments properly, we must identify the fields to which they belong. The type of support needed for warrants in one field will radically differ from the support needed for warrants in some other. In one field, warrants may be supported by the principles of taxonomical classification, in another by statutory law, in another by statistical findings.61 However, if our concern is the structural analysis of arguments as products, it is not at all obvious that we have a telling rationale here. For no matter what field we are dealing with, backing supports warrant. Indeed, as Toulmin emphasizes, the structural pattern is invariant across fields — the relation of backing to warrant is always the same. At this point in our inquiry, then, we must ask Is there anything so radically different in the relation between the backing and the conditional or generalization premises the backing supports, and the relation between

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those premises and the conclusion they support that we need to mark backing by a special category of elements? Compare these two cases: Harry is a British subject. Why? Harry was born in Bermuda and a person born in Bermuda will generally be a British subject. A person born in Bermuda will generally be a British subject. Why? Parliament has enacted laws giving British nationality in general to persons born in the British colonies. Is the word "Why" being used equivocally here? In both cases, are we not asking for justification? We may distinguish the "Why" of justification from the "Why" of explanation, but in turn are there radically different senses of the justificatory "Why" impelling us to recognize structural distinctions in arguments? I do not see that there are. Toulmin argues that backing can be distinguished from warrants. "Warrants...are hypothetical, bridge-like statements, but the backing for warrants can be expressed in the form of categorical statements of fact. "62 But we have discussed at length in the last section how unconvincing and problematical is this distinction applied to arguments as products. Toulmin argues that we can distinguish data form backing in that an argument must always explicitly present some data (a claim we have, in effect, seen as questionable), but need not explicitly present backing. But does this show that such backing, when presented, is so significantly different from data or data-type premises as to constitute a different category of argumentative element? Hence, we can find no advantage in distinguishing certain premissory elements as backing. There is at least one disadvantage. On Toulmin's model, there is a puzzling asymmetry between data and warrants. It appears that warrants may be supported by backing within the context of one argument. Support for data, however, is counted as a separate, numerically distinct argument. One argument consists of reasoning for the data as a lemma. That lemma is then used in a succeeding argument as data to establish some claim. But when a warrant has backing, that backing appears as a component in one and the same argument. Why is there this disparity?63 If both can be supported by further argumentation, there is no reason to count the argumentation for one as part of the argument while counting the argumentation for the other as part of a numerically distinct argument for the premise as lemma. Either both argumentations should be viewed as part of larger arguments or both should be viewed as separate, numerically distinct

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arguments. Which view should prevail is a question of how arguments should be individuated, an issue we discuss specifically in Chapter Eight. But in either case, the asymmetry between data and warrants is removed. Hence we see no reason for distinguishing backing and even a reason against it. So far, we have addressed ourselves to the categories of warrant and backing and found both highly problematic. Is there anything we can say about the notion of data? Although this category seems quite straightforward, even here we can identify problems in Toulmin's approach. Anomalies in the Concept of Data Do the data of an argument constitute just one promissory unit? Consider: "Data" is plural, and in presenting data for a conclusion, as opposed to a daturn, we are presenting a plurality of facts. But Toulmin has allotted just one position in his structural model for data. Clearly, from one argument to the next, we should expect the number of statements presenting data to vary. Should all such data statements be counted as one unit—the data of the argument? Suppose these data statements are scattered throughout the argument. Should we, representing argument structure diagrammatically, simply copy the data-presenting sentences into a single premise position of the argument diagram, our very diagramming procedure would create a single unit (or superunit) out of the disparate statements of data in the argument. Our diagramming procedure would suggest that we structurally analyse various data statements as constituting one argumentative unit, for that is the analysis it reflects. In an argument as process, this analysis may be quite unobjectionable, for there the data might be presented all at once in response to the challenger's "What have you got to go on?" But can we object to this analysis applied to arguments as products? This contrasts with the standard procedure where a number is assigned to each statement entering into an argument,64 and statements are represented in the diagram by these numbers encircled. The statements then are regarded as the units out of which the argument is built. Now if as on the Toulmin model there is to be just one data unit, to adapt the standard procedure we would have to indicate that all the various data statements, scattered throughout our argument, are components of this one unit, and assign one number to that unit. This would seem plainly artificial. It also could be misleading, as writing out the data statement in one data position of a Toulmin model could be misleading. For the Toulmin model provides for just one warrant explaining how we get from data to claim. But in general will one warrant serve to explain why various data are relevant to the conclusion? Clearly, different facts might need different warrants to explain how we get to the claim C. Should these warrants, then, be gathered into one "superwarrant"? Would this not also be artificial? Or

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should each datum needing a separate warrant be furnished with one? But if all the data are gathered into one unit how should this be diagrammed? What structural analysis would that diagram reflect? Here is the moral of this objection. By counting data, warrants, backing among the units of his model, Toulmin has made no provision for representing independent pieces of data, or independent data-warrant pairs, converging on a claim. Suppose we were not to lump each separate datum into one unit, the data, and each separate warrant into one unit, the warrant of the argument. For each separate warrant required then, should there be a separate argument diagram? But then do we have one argument or several? Would we have several arguments, even if all the data were intended to be weighed together in supporting the claim C, i.e. if the modal qualifier Q reflected the sum of force the various data bestowed on C by virtue of their respective warrants? Toulmin's model obscures the fact that various premises can independently support a conclusion, what the standard approach recognizes as convergent argument structure. On Toulmin's model, it appears this cannot be represented perspicuously. Toulmin's model apparently cannot deal with divergent argument structure either. Suppose one datum is offered to support several different claims. Consider: PROPONENT: CHALLENGER: PROPONENT:

CHALLENGER: PROPONENT:

We may expect that sales of camping equipment will rise this summer. What do you have to go on? With the current recession, people cannot afford expensive vacations. We may also expect that the motel business will be very bad this summer. What do you have to go on for that? The same reason—with the current recession, people cannot afford expensive vacations.

Do we have one argument here or two? Clearly, on the standard account we have one argument with divergent structure. On Toulmin's account, it is not obvious we would have one argument, unless it were an argument with a conjunctive conclusion. But is that how the argument is presented—one reason being offered once to support a conjunction of claims? Hence it is not obvious how arguments with convergent or divergent structures would be diagrammed on Toulmin's view, barring diagramming them as separate arguments. As we shall discuss in Chapter Eight, there may be no compelling reasons against viewing divergent arguments as separate arguments. But to view convergent arguments as separate seems not well suited to picture the actual structure of real life argumentation. Now, as with serial structure, convergent and divergent arguments raise the issue of argument individuation. In a given instance, do we have one argument or several? Again, we shall specifically address that question in Chapter Eight.

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But barring there being some strong theoretical reason to regard convergent arguments as a plurality or system of separate arguments, not as one argumentative unit, Toulmin's treatment of data obscures argument structure. Given all these problems, we reject distinguishing data, warrants, and backing as three distinct types of elements in arguments, at least in arguments as products. It seems more faithful to a general account of argument structure, applicable to all arguments, if we recognize just premises as one type of element in arguments. This does not mean that we cannot use the data/warrant/backing distinction to motivate why premises as statements combine in different ways to instantiate different structural patterns in various arguments. It does not show that Toulmin's warrant motivating or warrant introducing question "How do you get there?" is an illegitimate question or that we cannot identify premises in arguments that apparently function to answer such questions. Surely it is also plausible that such premises will combine with other premises in a manner different from the way several premises offered to answer the data-motivating question would combine. The data/warrant distinction then might have significant heuristic value in motivating this structural difference, although it would not mark a theoretical difference in the type of elements that enter into arguments. But this is to anticipate the issue of the next chapter — How do the basic elements in arguments fit together? In this chapter, we have established what those elements are in the face of Toulmin's challenge. The basic elements in arguments are good, old-fashioned premises and conclusions.

NOTES 1. See Toulmin, [1958], p. 97. Compare also van Eemeren and Grootendorst, [1984], p. 85. 2. In [1984], Toulmin et al motivate the notion of warrant through a series of challenger questions. See. p. 45. 3. Toulmin, [1958], p. 98, italics mine. 4. Toulmin, [1958], p. 98. 5. Toulmin, [1958], pp. 99-100. 6. Here we are construing "conditional statement" broadly to include generalized conditionals and modified conditionals such as "Typically If D, then C," or "Usually if D, then C." 7. Toulmin, [1958], p. 108. 8. Toulmin, [1958], p. 108. We are tempted to say then that Toulmin intends his analysis to apply to more than just certain types of deductive syllogism. The problem is that Toulmin advocates redrawing the deductive/inductive distinction, and he would not agree to this formulation. We shall take up this issue explicitly in Chapter Five on modalities. 9. Toulmin, [1958], p. 108. 10. Toulmin, [1958], pp. 108-09. 11. For maximum accuracy, we should also note that in some cases to properly explicate the backing function of a general proposition, we shall have to resort to statements of a somewhat different form than a straight statistical report. "All A's are B"s" may need to be expanded as

89

Notes A's are ruled by statute to count unconditionally as B's or The class of B's includes taxonomically the entire class of A's

(Toulmin, [1958], p. 112.) But in both these cases we are dealing with straight reports, not extrapolations from data. The first reports a statutory condition, while the second reports a taxonomic decision. 12. Toulmin, [1958], p. 111. 13. Toulmin, [1958], pp. 111-12. 14. Manicas also asks this question in [1966], p. 87. 15. Toulmin, [1958], p. 114. 16. Castaneda, [1960], p. 281. 17. See Toulmin, [1958], p. 117. 18. Castaneda, [1960], p. 282. 19. Toulmin, [1958], p. 120. 20. For a critical discussion of the instrumentalist view of theories, see Nagel [1961], pp. 12940. In [1954], Nagel points out that Toulmin's views in [1960] are similar to the instrumentalists, although probably not derived from them historically. 21. Toulmin, [1958], p. 122. 22. Nagel, [1954], p. 406, italics in original. 23. Nagel, [1961], p. 139, italics in original. 24. Toulmin, [1958], p. 113. 25. Toulmin, [1958], p. 115. 26. Toulmin, [1958], p. 117. 27. Ryle, [1950], p. 329. 28. Ryle, [1949], p. 121. 29. Lewis Carroll developed this point with great humor in [1972], Ryle alludes to Carroll's discussion here. 30. Ryle, [1950], p. 328. 31. Ryle, [1950], p. 328. 32. Ryle, [1950], p. 334. 33. Ryle, [1950], p. 337. 34. Ryle, [1950], p. 335. 35. Ryle, [1950], p. 335. 36. Ryle, [1950], p. 335. 37. Ryle, [1950], p. 336. 38. Ryle, [1950], p. 337. 39. Clark, [1956], p. 469. 40. Clark, [1956], p. 469, italics in original. 41. Clark, [1956], p. 470. 42. Mill, [1973], Book II, Chapter ii, § 4, p. 180. 43. Mill, [1973], Book II, Chapter ii, § 4, p. 180. 44. Mill, [1973], Book II, Chapter iii, § 3, pp. 186-87. 45. Anschutz, [1949], pp. 77-78. 46. Nagel, [1961], p. 138. 47. Nagel, [1961], p. 138. 48. Nagel, [1961], p. 138. 49. Toulmin, [1958], p. 99. 50. Toulmin, [1958], p. 100. 51. Toulmin, [1958], p. 100. 52. Toulmin, [1958], p. 106. 53. See Toulmin, [1958], pp. 97-99. 54. Toulmin, [1958], pp. 98-99. 55. Hitchcock, [1985], p. 86. 56. Peirce, [1955], pp. 130-31, italics in original. 57. Peirce, [1955], p. 133.

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58. Peirce, [1955], p. 133. 59. See Peirce, [1955], pp. 131, 132. 60. See Toulmin, [1958], p. 103. A minor permutation in word order here turns Toulmin's characterization into a dialectical question. 61. See Toulmin, [1958], p. 104. 62. Toulmin, [1958], p. 105. 63. Manicas in [1966] draws attention to this disparity on p. 86. 64. This assignment is made unless the statement functions in a special way, for example as a logical indicator.

Chapter 4

How Do the Basic Elements Fit Together?

In Chapter Two, we maintained that the basic dialectical situation, where a proponent is confronted with a challenger, can serve as a model of argument or how argument is generated. The proponent puts forward a thesis and defends it in response to the challenger's questions. The challenger, who is also a rational judge, asks these questions to express her perception of the logical weaknesses of the proponent's argument, as it has been developed thus far in the dialectical situation. We claimed that we could get insight into the structure of an argument as product by thinking of it as generated through such a proponent-challenger exchange. In particular, we identified certain fundamental questions, the basic dialectical questions, which the challenger could ask the proponent. Answers to different questions would function differently, giving the argument a distinct structure. We identified three categories of questions: acceptability, relevance, and ground adequacy. Further, under ground adequacy, we identified three distinct types of questions. It is our contention here that from the acceptability, relevance, and first type of ground adequacy question, we may develop an account of how the basic elements in arguments fit together. Let's restate these questions this way: Acceptability: Relevance: Ground Adequacy 1:

Why should I believe that premise? Why is that reason relevant to the claim? Can you give me another reason?

Clearly, these are distinct questions. We should expect that a premise in an argument as product which plausibly answers one of these questions functions differently from a premise which answers some other. We shall develop this expectation in the first three sections of this chapter, together with indicating how the concomitant structural difference may be diagrammed. But first, as we noted at the end of Chapter Two, there is a dialectical question which is more basic than any of our basic dialectical questions — the simple question "Why?" Clearly a challenger's asking this simple question generates an argument. The proponent's initial claim

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together with his answer constitutes this argument, which has the simplest type of structure possible. Obviously, we must have at least one premise and at least one conclusion to have an argument. Anything less and we have no argument. When that is all we have, when one, but just one, statement is given as a reason for exactly one conclusion, we have basic argument structure. We shall represent one statement's giving a reason for another by a downward directed arrow:

ψ This is the conventional way, now standard in many texts

© \ k

© represents then basic argument structure. We may see this simple question "Why?" generating not only the basic argument structure, but also the standard structure Thomas labels divergent.1

0

®

Such structures are generated by the challenger asking the basic question "Why?" of more than one claim, and the proponent answering each time with the same assertion. Alternatively, as Thomas points out, we could say we have two (or more) distinct basic arguments here, arguments generated just by "Why?", all of which have the same premise.2 We could thus also appropriately diagram the structure this way:

The Acceptability Question and Serial Structure

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© ©

©@ Hence, we can account for divergent structure as a special case of arguments having the basic, simplest possible structure.

4.1. THE ACCEPTABILITY QUESTION AND SERIAL STRUCTURE

Let's assume a dialogue has proceeded through the initial claim-challengeresponse. Should the challenger next ask an acceptability question, the proponent's answer would be offered as a reason for his premise. The statement would function in the argument as a reason, but as a reason for a reason. Where (1) numbers his initial claim, (2) his response to "Why?," and (3) his response to the acceptability question, this diagram

represents the structure. For obvious reasons, following Thomas,3 we call this type of structure serial.

4.2. THE RELEVANCE QUESTION AND LINKED STRUCTURE

Should our challenger ask a relevance question, after the initial exchange in the dialogue, she would be asking Toulmin's warrant generating question—How do you get from your proffered reason to your initial claim as conclusion? This means that the premise, as stated, is somehow incomplete.

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How Do the Basic Elements Fit Together?

It is possible to question why we have a reason for the conclusion here, why the premise gives any support to the conclusion. For example, if the proponent supports his claim that Jones' car uses too much gas with the premise that it is a 1968 model, our challenger may not see why that premise is relevant to the conclusion at all. A proper answer, then, will remedy this incompleteness by explaining the relevance, and a proffered answer will be intended as such a remedy. For example, our proponent could offer Cars made around 1968 are far less fuel efficient than other models and if a car is less fuel efficient than some other model, it uses too much gas. That would certainly explain why being a 1968 model is relevant to using too much gas. Notice that here we do not have a new, further reason to support our conclusion, some new fact or some new data, but a completion of the original reason. In effect, we still have just one reason for the conclusion, but a reason divided, broken over, expressed by two statements,4 the original premise that the car is a 1968 model and the relevance explaining premise. The proponent intends his answer to the relevance question to be taken together with his answer to the "Why?" question as one reason for his original claim. Structurally, these statements link together to constitute a reason for the conclusion. Hence we may represent the structure this way:

\ y

Again, following Thomas' terminology,5 we call this linked structure. We should emphasize that for us, linked structure is exclusively connected with the question of relevance. This is not clearly the case with other authors. According to our conception, premisses are linked when we need to take them together or they are intended to be taken together to see why we have a relevant reason for the conclusion. Notice that although we are in effect asking Toulmin's warrant generating question here, with linked structure we do not identify one element as data and the other as warrant. There is no structural differentiation between the elements linked. All are premises on a par with each other. To be sure, conditionals and universal generalizations may be offered preponderantly in answering the relevance questions. Surely, it is natural to

The First Ground Adequacy Question and Convergent Structure

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regard "All humans are mortal" as explaining why "Socrates is human" is relevant to "Socrates is mortal," and not vice versa. But, as we saw in criticizing the notion of warrants, someone could offer the generalization as a premise and the particular statement to explain why that generalization is relevant to the conclusion. Distinguishing data and warrant in those circumstances is problematic. With linked structure, the order in which the statements are given in immaterial. We simply link them together as premises. The data/warrant distinction may have heuristic value in motivating linked structure. With our approach, however, we do not enshrine something with heuristic value in an actual structural distinction. With linked structure, we recognize the appropriateness of the warrant generating questions, but avoid the problematic notion of warrant completeiy·

4.3. THE FIRST GROUND ADEQUACY QUESTION AND CONVERGENT STRUCTURE

Should our challenger ask for another reason after the initial exchange, i.e. ask the first ground adequacy question, she is not rejecting the premise already offered. She is not questioning its acceptability or relevance to the conclusion. The premise is all right as far as it goes, but it does not go far enough. The challenger senses that more evidence, more data is needed to properly support the conclusion. The proponent's answer then is intended not to support the originally proffered reason, nor to explain how we get from that reason to the conclusion, but to give more evidence for the conclusion. As Toulmin might put it, the proponent is saying, "Here is something more to go on." That the answer is offered in response to the question—Can you give me another reason?—makes the intention clear that this is a new piece of evidence, different from the first. It is independent evidence in the sense that it neither explains why the first reason is relevant to the conclusion nor does the first reason explain why it is relevant to the conclusion. Neither is necessary to see why the other gives evidence for the claim. Both separately answer Toulmin's data-generating question—What have you got to go on? Since we here have two distinct, independent reasons for the original claim, we represent the structure this way:

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©

©

Ο Again following Thomas,6 since the two premises converge on the conclusion, we call this convergent argument structure. We must be very clear at this point that our arrows say "is a reason for" and not "therefore" or "is an argument for." 7 In asking for another reason, our challenger is not asking for a completely new argument, nor is our proponent offering one when he replies. Rather, our challenger is asking for a supplement to the original argument, because she senses that the original premise is not, or may not be, weighty enough to create a presumption for the conclusion. We could modify our diagrams of convergent arguments to make this more perspicuous. We might think of our separate, independent premises as weights which we place on one pan of a balance scale to support some conclusion. Letting a horizontal line represent the pan, we may diagram the argument this way:

This picture makes clear that we have just one argument here, since we have just one arrow head.8 It also indicates that it is the combined weight of two independent premises, two independent lines of reasoning that constitutes the strength of the argument. Although there may in a sense be linkage, it is not the relevance linkage that we saw previously. It is rather "linkage" on the basis of ground adequacy.

4.4. THE LINKED-CONVERGENT DISTINCTION

In Chapter One, we pointed out that the linked-convergent distinction was a highly problematic issue for the standard approach to argument diagram-

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ming. Explanations of the distinction and directions for identifying whether an argument has convergent or linked structure are intuitive, vague, or ambiguous. We now have a clearcut distinction between these two argument patterns. An argument involves linked structure when two (or more) premises must be taken together or are intended to be taken together to see why we have one relevant reason for the conclusion. We can imagine at least one of these linked premises being offered to answer the question—Why is that (the remaining premise or premises) relevant? An argument involves convergent structure when two or more premises are each independently relevant to the conclusion. Each gives a separate piece of evidence for the conclusion. We can imagine each one, after the first, being given to answer the question—Can you give me another reason? What are the merits of how our approach distinguishes linked from convergent structure? The first advantage of our approach is its clarity in distinguishing these two types of structure. We have distinguished linked from convergent structure without resorting to such problematic locutions as "logical combination, connection, dependence, independence," "needing or contributing to the support of others," "fitting together," "being in the same line of thought," "filling logical gaps," which we found in Thomas, Rowen, and Yanal. As long as one understands what it is for one statement to explain why another is relevant to a claim, or what it is for two statements to give distinct, independently relevant evidence for a third, the distinction should be clear. But, as Govier remarks in A Practical Study of Argument, "the concept of relevance is so basic to thought and the development of knowledge that it is difficult to define and explain. "9 Although the notion is intuitive, it is intuitively clear. We understand the notion when we understand what it is for one statement to give a reason for another. The most we can do is to forestall misunderstanding by saying that for one statement to give a reason for another, it must give some evidence, even if that evidence is very slight. Of course, intuitions may vary over whether one statement does give evidence for another. This in turn can be overcome by proper definition of "being relevant." Johnson and Blair present the following characterization in Logical Self Defense: If R is relevant to Q, ...then R's being true would increase the likelihood that Q is true, while R's being false would increase the likelihood that Q is false.... If there is no effect one way or the other, then you have ample grounds for your claim that R is irrelevant to the acceptability of Q. 1 0

So if R is relevant to Q, R's truth or falsity will affect to some degree, however slight, the likelihood of Q's being true or false. R will constitute at least some evidence for Q. Following Govier, we may further distinguish positive and negative relevance. A statement A is positively relevant to a statement Β just in case

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How Do the Basic Elements Fit Together?

A's being true increases, however slightly, the likelihood of B's being true. A is negatively relevant to Β just in case A's being true increases the likelihood that Β is false." Johnson and Blair's criterion then says that A is relevant to Β just in case either A is positively relevant to Β or its denial, not-A is negatively relevant to B. Since our concern is with how premises support conclusions in arguments, we may frame our understanding of relevance just in terms of positive relevance. As Govier points out, "Clearly premises have to be positively relevant in order to support the conclusion."12 Modality-Relevance Ambiguity Not only does our approach dispense with unclear vocabulary in explicating the linked-convergent distinction, it explains why that vocabulary is unclear, ambiguous. To discuss the adequacy of grounds is to discuss an essentially modal question. Modality in part concerns how strong a case the premises make for the conclusion. If the premises are true, how much support does this give the conclusion? Is it as strong as deductive entailment, not that strong but still inductively good, or weaker yet? Since our challenger in a basic dialectical situation is a rational judge, she will ask questions as she perceives logical weaknesses in the argument. Hence, she will ask for more reasons, the first ground adequacy question, not out of idle curiosity, but because she perceives that the reasons, grounds given thus far do not give a sufficiently strong case for the claim or that they could be strengthened. On the other hand, she asks the relevance question when she does not see at all why a stated premise gives any support to the claim it is alleged to support. Hence, our basic dialectical questions clearly separate modal and relevance issues. The central difficulty with the vocabulary Thomas, Rowan, and Yanal use is that it is ambiguous between relevance and modality. Keeping this distinction in mind, a simple review of the problematic vocabulary readily reveals this ambiguity. What does it mean to say that two reasons "logically combine"? It could mean that one explains why the other is relevant to some claim, or it could mean that the two add their weight together in building up a case for the conclusion. The first interpretation concerns relevance; the second, modality. When we say that several reasons each need the others to support the conclusion, what do we mean? We could mean that subtract or remove any one of these reasons, and we shall fail to see (or it is understandable how a rational judge could fail to see) how the remainder, even taken in combination, constitute a relevant reason for the conclusion. On the other hand, we could mean that none of the reasons, by themselves, is strong enough to create a presumption for the conclusion, or a presumption as strong as we would like, but that when all are offered, their weight combined, we do have an appropriately strong presumption.

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Here we could say that each reason needs the others, but not in the sense required for linked structure, as we understand linkage. We could raise these same questions for talk of premises "fitting together," "being in the same line of thought," "filling logical gaps," or supporting a conclusion "in a united or combined way." Likewise talk of premises each contributing to the support the others give for the conclusion or talk of premises giving partial support for the conclusion is ambiguous between relevance and modality. In a sense, a convergent premise gives partial support, presuming that it does give some support to the conclusion. But in "A Diagrammatic Method for Portraying the Structure of Arguments Presented in Ordinary Language," Rowen uses "partial support" in connection with adding suppressed premises; premises which, when added, would be linked to those manifestly stated. If two reasons "completely separately and independently" support a conclusion, are logically independent, or do not contribute any logical connection to the support the others give, does that mean that we can see the relevance of each, by itself, to the conclusion, or does it further mean that the case each makes by itself gains no augmentation from the other? That is, the case made by presenting all of them together is no stronger than the case of each taken separately? This whole vocabulary then is infected with modality-relevance ambiguity. By separating these issues, we can see why the vocabulary is unclear and can give rise to ambiguous diagramming instructions. Testing Our Account of the Distinction Although our method of distinguishing linked from convergent argument structure is free of this ambiguity, does it properly separate these structures? Is it intuitively plausible or defensible to regard as convergent those arguments it counts as convergent, or to regard as linked those arguments it counts as linked? To explore this question, let's see how our approach decides the hard cases we considered in Chapter One. In these cases, persons might disagree whether the structure is linked or convergent. Intuitions might indicate one structure but diagramming instructions could plausibly be understood to indicate the other. Let's review these problematic arguments. Cigarette smoking poses a substantial health risk to the smoker. It also poses a risk to those nearby who must breathe the smoke secondarily. Therefore people should not smoke cigarettes. In Chapter One, we said that many intuitively would regard this argument as convergent, although the vocabulary some authors use would indicate linked structure. According to our account, the structure is clearly convergent. Neither premise explains the relevance of the other to the

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conclusion. Neither would be offered to answer the question "Why is that relevant?" But should either premise be offered first, the other could answer the convergent argument generating question "Can you give me another reason?" To be sure, offering both premises produces a stronger argument than either one alone. But this does not indicate that the structure is linked, because argument strength is a modal, not a relevance concept. Our intuitions for convergent structure are confirmed against the contraindications of the problematic vocabulary. We can repeat this same line of reasoning for the second problematic argument: La Petite Coloumb has the best chef in town. The live entertainment there is outstanding. The menu is also quite varied. Thus we should go there for dinner. Each premise gives another reason for going to La Petite Coloumb for dinner. Each answers the first ground adequacy question, not the relevance question. Again intuitions of convergent argument structure are confirmed. That all the premises speak of the same restaurant may indicate they are in the same line of thought, but this is not germane to determining whether the structure is linked or convergent. What about the fact that each premise, by itself, may give a less than compelling reason for going to La Petite Coloumb for dinner? We many need to consider all of them to see why we have a plausibly convincing reason to go. We shall consider this issue shortly. We can repeat this reasoning for the third argument, claiming that agriculture and forestry threaten the life of the chimp. (See Page 12). We agree with Yanal against Thomas, because we see each premise independently relevant to the conclusion. As we pointed out, a more general issue here is the structure of arguments supporting conjunctions. When some premises support conjunct A, while others support conjunct B, what is the structure of the argument for ( A & B)? Deductive arguments proceeding by the rule of conjunction are classic instances here. Intuitions go both ways. Since each conjunct A , Β is by itself relevant to ( A & B), but each gives another reason for ( A & B), our procedure confirms those intuitions counting for convergent structure. Of course, we need both A and Β to validly argue for ( A & B). Intuitions for linked structure are based on this fact. In effect, each premise gives us only fifty percent of what we need, not enough for a good argument. So this is essentially the same objection which we saw might be mounted against the La Petite Coloumb argument, and which we shall consider in due course. What about the fourth argument, which we admitted was problematic?

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Tom, a Central High School student, won a National Merit Scholarship. Mary, another Central High School student, also won a National Merit Scholarship. So two (at least) Central High School students won National Merit Scholarships. As we see it, what makes discerning the structure of this argument tricky is that it has a third premise, implicit because so obvious, to wit: Tom is not identical with Mary.

(Tom * Mary).

To say that at least two Central High School students won National Merit Scholarships is to say that there are persons x, y such that χ is a Central High School student and a National Merit Scholarship winner, y is a Central High School student and a National Merit Scholarship winner, and χ * y. Once the implicit premise is made explicit and the meaning of the conclusion made clear, it is straightforward that each premise can be seen as answering the question "Can you give me another reason?" As long as we are willing to count arguments for conjunctions as convergent, this argument is not problematic. This argument again highlights the problem concerning arguments where the premises individually give weak reasons for the conclusion or where if one of the premises were false, the force of the others would be undercut. There is no doubt that the relevance and ground adequacy dialectical questions provide a clear rationale for distinguishing linked from convergent structure. They give us a straightforward way of determining whether an argument's structure is convergent or linked. The problem is — Does our approach draw the distinction in the right place? Consider the La Petite Coloumb argument again. Suppose we had just the second and third premises and suppose it was not true that La Petite Coloumb had the best chef in town. Suppose, to the contrary, that the chef was pretty bad. Would the force of the remaining two reasons be undercut? Would they support the conclusion just as well? Clearly, they would not. As we pointed out in Chapter One, according to Thomas' final and much clearer criterion, that only when a reason would support the conclusion just as well even if the other reasons were false is the argument convergent—otherwise it is linked (See Page 10), they should be linked. That such arguments have linked structure is the verdict of other authors. Consider the following argument due to John Eric Nolt in Informal Logic: Possible Worlds and Imagination: Mr. A had no motive to cheat on his income taxes, since his annual income reaches six digits and he is not in debt.13

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We count this argument as convergent. Do we need both premises to see why we have a relevant reason for saying Mr. A had no motive to cheat? Although arguing from each reason, and even together, might be easily rebutted, do not both premises give some evidence that Mr. A had no motive to cheat? But the very issue of rebuttal would lead someone like Thomas to say that the premises should be linked. Suppose Mr. A were in debt although his annual income reached six digits. Wouldn't he then have a motive to cheat on his income taxes? Suppose he were not in debt, but his annual income did not reach six digits. Suppose it does not even reach five? Wouldn't Mr. A then also have a motive to cheat? Nolt claims the premises are linked: "They are intended to be taken together, though even together they constitute very weak evidence."14 Our difference with Thomas and Nolt becomes most acute, and our approach may seem most extreme, in dealing with inductive generalization arguments. Our discussion in this chapter confirms our judgment in Chapter One that such arguments have convergent structure. Each premise can answer the question—Can you give me another reason? Thus each premise by itself is independently relevant to the conclusion. None of the several premises, singly or in combination, answers the relevance question. These considerations on inductive generalization arguments make plain that on our account we have convergent structure, even if the evidence each premise gives for the conclusion by itself is quite weak or if the combined weight of the evidence presented by the various premises is stronger than the weight of any premise taken singly. Indeed, even if the inference from each premise to the conclusion were a hasty conclusion fallacy, as it frequently would be in an inductive generalization argument, yet the weight of all premises combined yielded satisfactory evidence for the conclusion, we should have convergent argument structure.15 But, as we pointed out in Chapter One, should any of the premises of an inductive generalization argument prove false, the force of the argument would be undercut. Our account here conflicts with three different intuitions. First, if several premises presented to support some one conclusion are individually weak but together make a stronger case, it would seem intuitively appropriate to link them together to represent how they support the conclusion. Secondly, and closely related, the fact that an arguer has presented several less than deductively strong reasons for one claim which apparently augment one another would intuitively suggest that linked structure appropriately represents the arguer's intentions that these premises be taken together. Finally, if the falsity of one premise would undercut the force of the remaining premises, intuitively it would seem their connection is closer than mere convergent, and so they should be linked. This third intuition, due to Thomas, raises an objection that we cannot answer until we have examined the argument structures generated by our second and third ground adequacy questions.

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Our disagreement with the remaining intuitions rests on our sharp separation of modal from relevance considerations. We have seen that the vocabulary used to characterize linked or convergent structure is ambiguous between modal and relevant connection. In addition, the very discussion some authors use to explain why structures should be linked employs modal considerations. Nolt calls arguments with convergent structure "split-support arguments." In discussing whether an argument is convergent, he says: "We can identify split-support arguments by asking whether the premises are supposed to work separately, each by itself being presumed to imply the conclusion, or whether they are to be taken as a single complex of evidence." 16 A key word here is "imply"—a modal term here meaning very strong if not deductively strong support. Nolt is claiming that separate premises or separate lines of reasoning must each offer strong support if the reasoning is to be convergent. Again, in discussing a particular example, Nolt says of two premises Each, if true, would by itself be good evidence for the conclusion. However, joining the two together produces a single inference which is somewhat stronger than either o f the two inferences obtained by keeping them separate....Hence the author...probably intended the two premises to be taken as a single unit o f evidence. 1 7

This discussion is shot through with modal considerations. If the modal strength is increased, we link according to Nolt. Augmented strength indicates intention to link. Thomas also agrees that increase in strength of support is a reason for linking premises. He is in close agreement with Nolt when he specifically restricts convergent argument structure just to those cases where each premise provides good (note the modal term here) support for the conclusion, where "each reason alone would be enough, if true, to support the conclusion." 18 This raises an important question for our account—Why should such modal considerations be divorced from the criterion for linked argument structure? We may have blunted the force of this question by our modification of how convergent structure may be represented. Let's take again the La Petite Coloumb argument. Numbering each component statement successively, representing its structure as convergent according to the standard method produces this diagram:

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How Do the Basic Elements Fit Together?

\

©

This representation may suggest to some that we have three separate arguments for statement (4) here, or that the reasoning from any one of (1), (2), (3) to (4) is intended to be sufficient, with no need of further augmentation from the others. We, of course, do not intend such suggestions. On the other hand, should we represent the structure according to our alternative method, the diagram would look like this:

Here the suggestion that each reason constitutes a separate argument, that we have three rather than one unit of argumentation for (4) is dispelled by the horizontal bar. There is but one case presented for the conclusion in this argument, albeit that case contains three separate reasons. But that the strength of the argument rests on their combined weight should be plain to all who understand the diagram. The bar allows representation of a modal "linkage" without resorting to representing the structure of the argument as linked. The second diagram does not say the same thing as Thus we have a perspicuous way of accommodating some intuitions of those who want to link, while still keeping modality and relevance issues distinct. But why should we want to keep those issues distinct? Because they are distinct!19 Clearly, the relevance question and the first ground adequacy question are distinct questions. An answer to one will not in general be apposite to the other. More importantly, answers to these questions do function differently in argumentation. No one would think that "All humans are mortal" gives evidence separate from "Socrates is human" for the claim

The Linked-Convergent

Distinction

105

G>

© "Socrates is mortal." Speaking heuristically, the generalization explains the relevance of the data about Socrates to the conclusion. Together they constitute one reason for the claim. But in saying "Socrates was a great man because in his life he pondered the central questions of meaning and value, and in his death he showed an exemplary courage" we have two distinct pieces of evidence for the conclusion, not one. Failure to separate modal and relevance issues leaves us with an account of argument structure and a diagramming system ambiguous in its applications. By clearly separating relevance linkage from modal combination, we gain a clear rationale for representing two different ways premises may join to support a conclusion, ways which may become confused otherwise. The intuitions that the weight of several premises is intended to be combined, that they are intended to make one case for the conclusion, that the strength of the case they make together is stronger than the cases they each make severally can all be accommodated without representing modal connection through linked structure. Representing both types of combination through linked structure makes it unclear how to distinguish linked from convergent structure. Clarity is served by recognizing these two types of combination. In "'Convergent' and 'Linked* Reasons," Yanal has tried to justify through modal considerations a linked-convergent distinction in essential agreement with ours. His attempt is problematic, but this will simply highlight another reason why modal and relevance considerations should be kept distinct. Recall that if a premise is not relevant to the conclusion, then its being true does not increase the likelihood of the conclusion's being true at all. However, should we link a premise which by itself seems irrelevant to the conclusion with a relevance explaining statement, the resulting positively supporting reason does distinctly increase the likelihood of the conclusion. Without some connection being established between "being human" and "being mortal," the premise "Socrates is human" is irrelevant to "Socrates is mortal." The support the premise gives the conclusion is nil. But link the premise with the statement "All humans are mortal" and we have a deductively valid argument. As Yanal puts it, the strength of support "leaps" from 0 to 1. Should we have an inductive argument, the leap would not be as great, but would still be there. On the other hand, should we add a separate, independently relevant premise to one already relevant to the

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conclusion, we should expect their combined strengths to "add" together. In a convergent argument, each individual premise should contribute its weight toward supporting the conclusion. There would not be any leaps. Yanal has actually proposed this difference in modal behavior as theoretically explicating the difference between linked and convergent structure, as presenting "the real distinction between convergent and linked reasons in principle. "a> If an argument is genuinely convergent, then the probability its reasons together lend to the conclusion is the sum of the probabilities of each.21 If the premises are linked, the probability does not sum this way, but leaps. Yanal draws a moral from this that you cannot teach the distinction between linked and convergent structures, allegedly part of the analysis of arguments, without going into the issue of weighing the strength of the evidence, an issue of evaluation. You have to show how probabilities leap with linked reasons,22 and thus you have to get into the issue of probabilities and weight of evidence. Although pointing out how probabilities—better degree of support or amount of evidence—leap in particular, sample arguments with linked structure may be valuable heuristically in illustrating the linked-convergent distinction, it is easy to see that there are real problems with this as a theoretical explication of the distinction. Rowen discusses these problems in "'Convergent* and 'Linked" Reasons Revisited." For many nondemonstrative arguments, it will simply be impossible to assign probabilities in any meaningful way. Furthermore, for some inductive arguments, given background information about probabilities, it may be possible that when linked, the probability actually goes down rather than leaps.23 Our relevance rationale for linkage both explains why we might expect probabilities to leap—at least in a number of cases, and dispenses with this leap as the feature distinguishing linked from convergent arguments. If a premise, taken by itself, is not relevant to the conclusion, then the degree of support it gives is nil. But if taking that premise together with another statement produces a relevant reason, then we do have positive evidence. To be relevant, a premise must give some evidence. So we have had a "jump" from 0 to some positive amount, even if this cannot be quantified. If probabilities would decrease in certain special examples, this would not gainsay the general principle, or show its disutility as an illustration. But since it is because taking premises together gives us a relevant reason as opposed to taking them separately that explains why they should be linked, such anomalies are not theoretically bothersome. For this reason, our relevance criterion, which does not resort to modal considerations, gives a better rationale for identifying linked argument structure. Notice that our ground adequacy criterion for convergent structure itself explains why probabilities should sum with convergent arguments. If each premise gives another reason, the probability of the conclusion given all of them should be the sum of the probabilities of each. However, to apply our criterion we

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need not determine the probability of the conclusion relative to each premise or develop a formula for adding probabilities. All we need do is see that each premise appropriately answers the question—Can you give me another reason? This consideration leads directly to another advantage of our approach. It is a commonplace that we diagram arguments as a preliminary step to evaluating them. We determine how the argument hangs together before we assess its logical cogency. Hence, it would be a distinct disadvantage for a diagramming procedure to require us to make evaluative determinations before we could display the structure. But this is exactly what is required both in Yanal's proposal and in those of Thomas and Nolt. To ask whether each line of reasoning constitutes a good or valid reason for the conclusion to determine whether the structure is convergent or linked is to incorporate evaluation into structural analysis. To ask whether the likelihood or probability of the conclusion "leaps" or merely sums when premises are added, taken together is to ask an evaluative question, and a fairly problematic one at that. However, although relevance is one ground on which we can evaluate an argument, to ask whether one statement explains the relevance of another to the conclusion, or whether two or more premises mutually illuminate why we have a reason for the conclusion, or whether two or more statements were intended to be taken together as one reason for the conclusion, is to keep evaluative issues at a minimum. It is really to ask just how may reasons have been given to support a claim and whether these reasons are spread over various statements—a structural question. To ask whether a statement is positively relevant to another and to ask whether it constitutes a reason or premise for another is to ask the same question. Likewise to ask whether two statements are independently relevant to a claim is just to ask whether we have two distinct reasons here. But in diagramming, the aim is to represent the support structure, the pattern of premises and conclusions in an argument. Furthermore, in many cases, judging whether one statement is relevant to another or whether one statement explains the relevance of another to the conclusion is intuitive. Being able to "see" whether one statement is relevant to another often involves no special training other than to properly assess the sense of both statements. Assessing modality is a different story. Here the concepts of validity, inductive correctness, and comparative strength must be defined, and skills developed for their proper application. Indeed, in some cases, determining deductive validity may involve rather refined skills, while inductive strength can be quite problematic. Hence, making judgments of relevance as part of discerning argument structure does not add to the skills necessary to analyse arguments for structure, while incorporating modal considerations does. So keeping relevance and modality separate is well motivated procedurally. It allows us, insofar as possible, to discern argument structure without considering

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questions of argument evaluation. Giving a clearcut rationale for distinguishing convergent from linked arguments by keeping separate questions and functions which are genuinely separate, and keeping evaluative considerations, as far as possible, out of determining preliminary structural issues are strong reasons for drawing the line between linked and convergent structures as we do. We have now presented our account of how the basic elements of arguments — premises and conclusions — fit together. Premises may appear in different configurations to support conclusions depending upon what functions they serve in the argumentative passage. A premise may directly support a conclusion, either by itself or as an additional independent supplementary reason. It may support some other premise or serve to explain why some premise or premises are relevant to a conclusion. Thinking of the argument expressed by a text as arising through an exchange in a basic dialectical situation, what function a premise serves depends on the question it was intended to answer. Besides the simple question "Why," certain basic dialectical questions — the acceptability, relevance, and first ground adequacy questions — motivate the various structural configurations — serial, linked, convergent — the premises and conclusions of an argument may assume. This perspective indicates a very clearcut demarcation of linked from convergent arguments, but a demarcation not without controversy. The intuitions of some authors run counter to ours. By suitably modifying convergent argument diagramming, we can accommodate some intuitions of those who would regard as linked some arguments we see as convergent. Thus we overcome objections based on those intuitions. We have still not answered Thomas' challenge that if the falsity of one premise should undercut the force of the others, the argument structure is linked. Also, there are two ground adequacy questions we have not yet considered, and Toulmin has introduced two types of argumentative elements, modalities and rebuttals, which we have not discussed. All these issues are related. Our remaining ground adequacy questions give us a rationale for counting modalities and rebuttals as further genuine elements in arguments, besides premises and conclusions. Once we have introduced rebuttals and determined their role in arguments, we should have an answer to Thomas' challenge. These issues will occupy us in the next two chapters.

NOTES 1. 2. 3. 4. 5.

Thomas, [1986], p. 58. See [1986], p. 58. See [1986], pp. 57-58. Clearly, we could have a reason distributed over three, four, or more statements. See [1986], pp. 58-60.

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Notes

6. See [1986], pp. 60-63. 7. We owe this point of clarification to Prof. Alec Fischer. We shall consider Prof. John Hoaglund's recommendations in [1988-89] for distinguishing "reason" from "premise" in section one of Chapter Eight, when we discuss the individuation of arguments. 8. We shall address the controversy surrounding whether convergent arguments should be thought of as one argument or many when we discuss argument individuation in section one of Chapter Eight. 9. Govier, [1985], p. 101. 10. Johnson and Blair, [1977], pp. 15-16. 11. Govier, [1985], p. 102. In Govier's terminology, if A's truth "counts in favor" of B's, "gives us some reason to think" Β is true, then A is positively relevant to B. Similarly with negative relevance. 12. Govier, [1985], p. 103. 13. Nolt, [1984], p. 33. 14. Nolt, [1984], p. 33. 15. Our approach here is how we distinguish linked and convergent structure in our [1988], (See Ch. 6.2.) We should note here, in defense of our position, that we are not alone in drawing the linked-convergent distinction in this manner. We are in substantial agreement with how Trudy Govier makes the distinction in [1985]. (See Ch. 6.) In [1984b], Rowen also sees a connection between relevance and linked structure: "If R2 is epistemically relevant to R l , then Rl and R2 provide conjoint [i.e. linked] support. If not, they provide disjoint support." ([1984b], p. 5.) However, Rowen's account of R2's being epistemically relevant to R l ' s being a reason for a conclusion C has significant points of difference from our account of relevance presented above. This could lead to disagreements over diagramming particular cases, especially inductive generalizations. Rowen's intuitions agree with Thomas', that if the falsity of one premise would undercut the force of another the two should be linked. In Chapter Six of this essay, we discuss how through rebuttals this intuition can be accommodated without linking the premises. 16. Nolt, [1984], p. 32. 17. Nolt, [1984], p. 32. 18. Thomas, [1986], p. 62. 19. Besides the authors cited previously for separating modal from relevance considerations, Govier, Grice, Johnson and Blair, we may also cite the late Alan Ross Anderson and Nuel D. Belnap, Jr. In [1962], they argue that the implicational part of the intuitionist propositional calculus, i.e. the system axiomatized by A (B - A) [A - (B C)] - [(A - B) -> (A - Q ] together with -*E as the sole inference rule, is deficient on the grounds both of necessity and relevance as an analysis or explication of the concept of implication. See pp. 30-31 and pp. 3334. Fixing necessity does not mean fixing relevance. Although at the back of our minds, Anderson and Belnap's distinction of modal necessity and relevance may have been seminal in leading us to keep modality and relevance distinct. 20. Yanal, [1984], p. 1. 21. This is according to a summing formula Yanal describes in the Appendix to [1984], which we need not present here. 22. Yanal, [1984], p. 2. 23. See Rowen's example, [1984b], p. 4.

Chapter 5

What Should We Do With Modalities?

The first ground adequacy question is motivated by doubts about whether the premises offered so far are adequately weighty to support the conclusion plausibly. To remedy this, the challenger asks for more reasons. Now suppose our proponent has presented all the separate independent reasons for his claim. Let's suppose he has actually told the challenger that he has no more reasons to present. She may still have questions. She may perceive that these reasons give some but less than total support to the claim the respondent is arguing. The respondent will not be reasoning cogently if he does not admit this. But he may have stated his conclusion rather categorically, without any modal qualification or hedge. On the other hand, his premises may make a very strong case for his conclusion, a strength which it is appropriate that he recognize. Awareness of such issues motivates the second ground adequacy question—How sure do your reasons make you of the claim? How sure are you that your reasons adequately get you to your claim, i.e. establish a presumption for it? How might the proponent answer such a question? Depending on his logical acumen and basic honesty, he might say I'm completely sure

— My reasons make me certain of my claim

I'm very sure

— Given my reasons, my claim is highly likely, very plausible

I'm basically sure

— My reasons make my claim likely, probable

I'm not at all certain of my claim, but I'm more sure of it than not

— Given my reasons, my claim is more likely than not.

In explicating how sure he is of his conclusion, the proponent has used such modal words as "certain," "likely," "probable." Such words frequently appear in arguments as products, argumentative texts, in adverbial form: "certainly," "necessarily," "obviously," "probably," "presumably," "possibly," introducing or otherwise apparently modifying a conclusion. Even in this form, we may still view them as answers to the second ground

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adequacy question. We would like to argue that the legitimacy of this question, that it may arise in dialectical situations through the challenger's perception of needed logical clarification or qualification, shows that modalities are genuine elements in arguments as products. That the second ground adequacy question presupposes that premises and conclusion have already been presented indicates modalities have a distinct function from premises and conclusions. They are not the main or final claim of argument nor serve to give evidence for such claims. Hence, Toulmin appears quite right to distinguish modal qualifiers as a distinct type of argumentative element in his "layout of arguments," even understanding the layout as a model for analysing argumentative texts. Because these modal qualifiers or modalities answer a distinct basic dialectical question which distinguishes them from premises and conclsuions, we want to say they are distinct, isolable, argumentative elements, distinct structural elements in arguments, deserving their own distinct mode of representation in argument diagrams. Yet, this argument opens up a host of problems. First, although the fact that modalities properly answer the second ground adequacy question shows they have a distinct role in arguments as process, we may have reservations about this for arguments as product. Frequently modal words occur infixed in the conclusions of arguments. Jones is certainly the best candidate to run next year. Smith has apparently won her case. The ball must drop with accelerating velocity. Don't all these statements, in their entirety, including "certainly,' "apparently," "must" function as conclusions when they appear in a conclusion position in argument texts? To justify isolating modalities, we need an argument that they are not properly part of these conclusions. Secondly, just what are modalities? What do they do? The answer we endorse is that a chief function of modalities is to make a description of or claim about just how weighty a case the premise or premises of an argument make for the conclusion they support. As we may claim complete or less than complete support, and such claims are hallmarks of deductive or inductive arguments, so we may straightforwardly distinguish deductive from inductive modalities along familiar textbook lines. Deductive modalities claim that the premises give complete support to the conclusion, that they necessitate it, while inductive modalities make the weaker claim that the premises give sufficient evidence to justify accepting the conclusion, but not necessarily conclusive evidence. Such claims, we may say, are the literal meaning of modalities. However, not all philosophers would immediately agree to this characterization. Furthermore, given most of what he says to characterize modal qualifiers in The Uses of Argument, Toulmin would not agree either. We may draw a distinct analogy between Toulmin's position on modalities and his position on premises which we discussed at length in Chapter Three.

Modalities — What Are They?

113

The justificatory "Why" naturally arises in dialogical and dialectical situations. The answers to such questions are reasons, premises in an argument for the claim questioned. Thus it would seem totally straightforward to count premises as argumentative elements. Yet Toulmin advocates rejecting a unitary concept of premise for the threefold data/warrant/backing distinction. Likewise, the question of how sure the proponent is of his claim arises in dialogical and dialectical situations. To answer this question with more than a subjective report, to give an answer with some claim to intersubjective agreement, the proponent should make a claim about the weight of the premises, how probable is the conclusion given these premises. This is precisely the claim we understand modalities to be making. Yet Toulmin rejects this conception of a modality. It is not what he understands modal qualifiers to be doing. Hence, it is not enough merely to argue that modalities are separate elements in arguments. We must clarify what they are. This is necessary not only for theoretical adequacy. How modalities are included or represented in argument diagrams should reflect their role in argumentation. We cannot then give modalities their proper place in a system of diagramming unless we know what they are. On the other hand, knowing what they are may very well suggest their proper position in diagrams and settle the issue of whether they are distinct elements in arguments. We turn to this question of the nature of modalities first.

5.1. MODALITIES - WHAT ARE THEY?

Let us, for the purpose of this discussion, take "probably" and "certainly" as paradigms of modalities. We want to ask first of all just what do these terms mean when appearing in statements of the form "Probably P" or "Certainly P," e.g. Probably Jack will be subject to the wrath of moral conservatives. Certainly Jack will be subject to the wrath of moral conservatives. We then want to ask in particular what these words mean when they appear in the context of arguments, "Given P,, P2, ..., Pn, probably P" or "Given P„ P2, ..., Pn, certainly P." In "Probability" [1967], Max Black has identified a "common sense of probability." Since when confronted with an argument text, the presumption is that "probably" involves some common notion, Black's analysis should be quite apropos here.

What Should We Do With Modalities?

114 Common Sense of "Probably P"

As Black sees it, when ordinarily someone asserts a statement such as Probably a black ball will be drawn, he makes implicit reference to certain initial or background conditions — or his perception of such conditions. The statement "may be taken as elliptical for 'Given that we have such-and-such an urn, containing suchand-such balls of known colors, etc., a black ball will probably be drawn.'" 1 Different descriptions — or perceptions — of the initial conditions will foster different estimates of probability. For example, given that the most recent poll shows candidate A to have a substantial lead with the election only a few days away, we may judge it highly probable that A will win. But should we learn the additional information that A has just made certain ethnic slurs in public which will offend a sizable proportion of the voters, the probability of A's winning is cut rather dramatically. Even if the speaker or proponent is ignorant, partially or fully, of the initial conditions "(with correspondingly weak reasons for his judgment)," 2 he still makes this implicit reference in his probability assertions. In making this assertion, then, the speaker is first of all attributing a certain probability to the outcome of drawing a black ball in the light of some background conditions. Although in the simple "Probably P," we do not have any assertion of a specific degree or numerical value of probability, yet there is still some probability attribution. The initial conditions do not make drawing a black ball certain, but they do justify us in making that prediction with some degree of confidence. Black points out that in some instances, to assert "Probably a black ball will be drawn," is also in fact to predict that outcome—that the ball drawn will be black. There is an absurdity in saying "Probably a black ball will be drawn, but all the same a black ball will not be drawn." Although the speaker's use of "probably" is intended to intimate that the initial conditions are insufficiently strong to render the designated outcome empirically certain, the whole assertion, however guarded by acknowledgement of fallibility, is intended to commit the speaker to the kernel's truth, 3

i.e. the truth of "A black ball will be drawn." We may thus distinguish the probability-attributing aspect of a probability statement from its predictive aspect. These are independent. We might be justified in predicting some outcome, even though events may prove that prediction false. Likewise, events may confirm our prediction, even though it was not justified on the basis of initial conditions. We should also note that "probably" serves to qualify or hedge our assertion of P. We are predicting an outcome, albeit somewhat guardedly. The modality "probably" then has these three features — probability-asserting, predicting, and hedging.

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In statements of the form "Probably P," we seem to be attributing probability to Ρ or to what Ρ asserts. "Probably" appears as a unary statement operator, and reference to initial conditions, at least by the statement itself, is left implicit. In such statements, we have what Black calls the "absolute sense of 'probability,' where the 'initial conditions'...are identified with the relevant features of the 'state of the world' at the moment of utterance."4 But we also have a relative sense expressed in locutions of the form "Given evidence E, probably (to a certain extent) P." On the evidence presented, probably Jones is guilty. As Black points out, and as we would expect from the above discussion, we may take the relative sense as logically prior to the absolute. We may think of "Probably P" as elliptically asserting "On evidence D, probably P," where 'D' indicates the initial conditions. "Probably P" then attributes probability with respect to these initial conditions, to the way the world is perceived, rather than with respect to some special body of evidence. Hence, as Black points out, there is a "large measure of truth in the commonly accepted dictum that probability is always relative to evidence. "5 This relational aspect of probability appears most strikingly in such locutions as Given D, the probability that Ρ is such-and-such6 Here, the substantive "probability" replaces the adverb "probably," and "the assertive force of the adverbial use is bracketed or suppressed, the point of such uses being solely to estimate the strength with which the relevant enabling conditions (expressed by reference to 'D') favor the realization of the outcome P." 7 The point is that these locutions clearly indicate that we may attribute probability relative to certain bodies of evidence. Such attributions would seem to be presupposed in such locutions as "Given D, probably P," where 'P' is also asserted. What implications does this have for understanding "probably" in the context of arguments, i.e. in contexts of the form P„ P 2 , ..., Pn. Therefore probably Q

?

Clearly in such contexts, "probably" is being used in its relative sense, ascribing some probability to Q in light of or given P[, P 2 , ..., P„. It also serves to reinforce that 'Q' is asserted, albeit in a hedged manner, with acknowledgement that the premises do not totally justify asserting it. They do not deductively entail 'Q.' I believe we should add one refinement to how the probability ascription of "probably" is understood in these argument contexts. As we noted, in "probably P," there is implicit reference to a body of initial conditions, background beliefs about the relevant state of the world. 'P' is probable with respect to that background. In "P,, P 2 , ..., Pn. Therefore probably Q," we should also allow making implicit reference to

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background. To be precise, we should formulate the probability ascription as "Given P„ P2 Pn together with background B, the probability of Q is such-and-such." Of course, in many cases, someone propounding an argument may not have any salient view of such background information. Again, in many cases, this formulation may simply collapse into "Given P,, P2 Pn, the probability of Q is such-and-such" because the background is moot on the question of Q, contains no relevant information affecting Q's probability. However, as will become clear by the next chapter, I believe we need to keep the option of referring to some background open in understanding the probability ascription of "probably" in such argument contexts. Common Sense of "Certainly P" We may argue that the common sense of "certainly P" is quite parallel to "probably P." Although there may be times when "certainly" has no implicit reference to perceived initial conditions or background information, as in Certainly 2 + 2 = 4 or Certainly "everything is what it is, and not another thing," which expresses unqualified agreement with one of Bishop Butler's points, frequently someone asserting a statement of the form "certainly P" has some background or body of assertions in mind which makes 'P' certain. It is implausible to think that someone asserting Certainly the next ball to be drawn will be black or Certainly John will come tomorrow means that these statements are certain, necessarily true in themselves. Far more plausibly, they are alleged certain with respect to some background information, say that all the non-black balls have already been drawn from the urn or that given John's intentions, motivation, and capabilities, his coming tomorrow is guaranteed. In using "certainly," the assertor is claiming that in the light of this initial or background information, the probability of 'Q' is certain. He is also asserting 'Q,' now explicitly without hedge or reservation. Likewise, in the context of arguments, P,, P 2 , ..., Pn. Therefore certainly Q "certainly" serves to ascribe certainty to 'Q,' given P,, P2, .... Pn (together perhaps with certain relevant background information). In the light of the premises, 'Q' is certain and is asserted without qualification. For example, in the argument

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All persons with morally innovative ideas are subject to the wrath of moral conservatives. Jack is a person with morally innovative ideas. So certainly Jack is subject to the wrath of moral conservatives. "certainly" claims that the premises necessitate the conclusion. In both these cases, then, we have seen that the common sense of modal terms has a dual aspect. In argumentative contexts, these terms serve to ascribe a certain degree of probability to the conclusion vis-a-vis the premises — together perhaps with certain background considerations, and to reinforce that the conclusion is asserted, either with some hedge — in the case of "probably," or explicitly without hedge — in the case of "certainly." Implications for Argument Structure What are the structural implications of these considerations for argument analysis, for seeing how arguments are structured? We take it that what we have said about "probability" and "certainly" may be applied, mutatis mutandis, to the other modal qualifiers or modalities. In light of the probability ascriptions modalities make, we are justified in distinguishing them from both premises and conclusions. We should in fact view them as functioning like logical indicator words, such as "therefore" or "because." They constitute part of the material connecting premises and conclusion. As "therefore" serves to flag the statement following as a conclusion and to suggest that the preceding statements are premises supporting that conclusion, so a modality serves to modify this claim, indicating just how strong is this support. Modalities then are not only distinct elements in arguments, distinct from premises and conclusions, the basic elements. They are illation-sign modifiers, serving to modify the claim that the premises support the conclusion with some indication of how strong is this support. We reject the position that modalities are parts of conclusions. Although their appearing as parts of sentences expressing conclusions lends this view some prima facie plausibility, when we consider what such a reading of these sentences entails, this view is no longer a viable candidate. The case is easily made for deductive modalities.8 If we see such a modality as part of the statement expressing the conclusion, then we should read the modality as attributing necessity to the conclusion in its own right. But, unless the kernel of the conclusion is necessary, this will produce an implausible reading. As we saw, reading "Certainly the next ball to be drawn will be black," "Certainly John will come tomorrow," as ascribing necessity to "The next ball to be drawn will be black," "John will come tomorrow," gives these statements a very implausible reading. Consider the argument about Jack. Is the conclusion of this argument the claim that Jack's being subject to the wrath of moral conservatives is certain, a

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necessary truth? Is the arguer trying to defend that in all possible worlds, Jack is subject to the wrath of moral conservatives or that attempting to imagine otherwise is attempting to imagine a contradiction? This is absurd. Clearly the conclusion is the claim that Jack is subject to the wrath of moral conservatives. "Certainly" describes the relation between premise and conclusion. The truth of the premises guarantees the truth of the conclusion. If the premises are true, so will be the conclusion. The arguer is not concluding that given the premises, Jack's being subject to the wrath of moral conservatives is absolutely or necessarily true. Given this argument for deductive modalities, the same result follows for inductive modalities, since they function in a parallel way to indicate how strongly the premises support the conclusion. In Probability and Induction [1949], William Kneale in effect points out that the absolute sense of "probably" may obscure the relative character of this notion. That background knowledge constitutes a body of evidence relative to which probability is estimated may be left understood, just tacitly assumed, and so unnoticed. Alternatively the evidence may be referred to rather obliquely, as in What is the probability that this card, which has been drawn at random from a complete pack, is a court card?9 Here it may not be obvious that the card's being drawn at random from a complete pack is the evidence relative to which the probability is assessed. Kneale also asks us to consider a situation where someone has acted according to his best lights, although his course of action was not successful. We would not blame him, for given his evidence, he chose the course of action which was probably the best. Again, we may say that something is "improbable but true" when we know that something has happened but with reference to our background knowledge (which excludes, of course, the knowledge that the event has happened), its happening seems quite unlikely. These considerations further highlight the relative character of the claim "probably" is making. "Probably" is not a unary statement connective analogous to "not." It is not the case that John will come makes a complete assertion in its own right. It could function as the conclusion of an argument. Probably John will come asserts that "John will come" is probable, given some understood body of evidence. Here only the kernel, "John will come," would function as the conclusion of an argument. But those who would see "probably" (and the other inductive modalities) as part of the conclusion mistakenly construe it as a unary operator.

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To clarify our position, we must make plain that expressing modalities is not the only way modal words may function in arguments or other discourse. Frequently, modal words do double-duty as both logical indicators and modifiers of logical indicators. When words such as "therefore," "thus," "so," "because" are not present in an argument (as product), a modal word may serve to indicate a conclusion and make a claim about how strongly the premises support that conclusion. It is crucial to note that a modal word, in particular one which may express a deductive modality, does not always make a claim about how strongly a premise or set of premises supports a conclusion. Consider (1) (2)

It is necessary that 2 + 2 = 4 2 + 2 necessarily equals 4. It is impossible that there is a rational / 2 .

Isn't asserting (1) claiming that no matter how the world might differ in point of fact, 2 + 2 will still equal 4? 2 + 2 not only equals 4, it has to. (1) is not claiming that relative to certain conditions, this statement has to be true, but rather that the statement must be true in itself or considered just by itself. Likewise, to assert (2) is to assert that no matter how the world might have been different, there still would be no rational / 2 . (1) and (2) express the logical or mathematical necessitation of certain statements, not the claim that a statement is necessary relative to a certain body of evidence. Instead of functioning as a part of the connecting material between premises and conclusion, the modal expressions here are integral components of these statements (1) and (2), functioning as modal statement connectives or operators. They are as much a part of the statement as "not" is a part of "John is not coming." Now we may admit that when a modal word occurs in the context of an argument, it may be ambiguous. It may not be possible to determine definitively whether it should be taken as a modal statement connective or as a modality proper. However, as our discussion above indicates, in a number of instances the context will give a clear indication for taking the expression as a modality.10 Taking it as a modal statement connective would attribute an absurd conclusion to the arguer. Toulmin's View of "Probably" (and Other Modalities) As we have seen, the common sense of "probably" views this expression (and by implication the other modalities) as making a probability ascription to a certain statement given or in light of certain evidence. This probability ascription we might very well regard as the literal meaning of the modality. By contrast, expressing some hedge, reservation, or qualification about the claim in the case of inductive modalities, or lack of any reservation or hedge by deductive modalities, is akin to their emotive meaning. But it is the literal meaning which gives us to key to understanding the structural

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role of modalities in arguments. In the context, "P,, P 2 P n . Therefore probably /certainly Q," the modality ascribes a certain probability to Q given the premises (and perhaps certain background information). Hence the modality is an element separate from premises and conclusion. As the illative "therefore" serves to indicate that the premises are put forward to support the conclusion, the modality serves to modify this claim, in turn making a claim about how strong is the support. I think we may succinctly and fairly characterize Toulmin's view of modalities by saying that he rejects their having this literal meaning. Toulmin insists on distinguishing two aspects of the meaning of modalities — the force of a modal qualifier and the criteria for its use. In Chapter One of The Uses of Argument, Toulmin compares modal words with evaluative terms — "good" in particular. We call many different things "good." Now to call something good is to commend it, whatever that thing is. But certainly a good apple is a very different thing from a good speech. In arguing that an apple is good, we would appeal to quite different considerations from arguing that a speech is good. This motivates Toulmin's distinction between force and criteria. The force of "good" is the same in its various applications, although the criteria for application vary. He sees the situation as parallel for modal words. They have a common force, although disparate criteria for application. "The force of a modal term" means "the practical implications of its use."" For example, to say of some conceivable alternative or concept that it is impossible is to rule it out of further consideration. Consider the concept of being a rational V2. The force of saying that this concept is impossible or an impossibility is to dismiss it, to issue an injunction against giving it any place in any discussion.12 Analogously, the force of saying of some proposed solution that it is possible is to enter it into serious consideration. It is to say that it is worthy of consideration, and to mandate entertaining that proposal with some degree of seriousness. To say that the solution is necessary is to say it is the one solution worthy of consideration. We are directed not to bother to look elsewhere. To say it is probable is to call it the best of the field, while to say it is presumable is to say it is the answer, unless certain exceptions hold. 13 In each of these cases, the force has a directive aspect vis-a-vis various alternatives or concepts which present themselves for consideration. The criteria, by contrast, are the "standards, grounds and reasons, by reference to which we decide in any context that the use of a particular modal term is appropriate."14 If we are being precise, we do not say simply that some concept or alternative is impossible, but that it is mathematically impossible, physically impossible, physiologically impossible, morally, legally, judicially impossible, or impossible in some other way. To say that the rational - Π is mathematically impossible means that assuming there is such a thing leads to a contradiction. Implying or entailing

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a contradiction, then, is the criterion of mathematical impossibility. Other senses of impossibility will have their own distinct criteria. In all these cases, the force of using the modal term "impossibility" is the same. The criteria, grounds for using it, however, are different each time. One of Toulmin's most extensive contributions to a theory of modality is his discussion of probability. Toulmin characterizes the force of "probable" this way: "Starting from what we know, we may accordingly be entitled to take the step to one of the conclusions with more confidence than the step to the others: this conclusion, we say, is more 'probable' than the others."15 In effect, the probable conclusion is the best of the field, as we noted above. The force of "probable" is to express confidence, but not unqualified confidence. To say I know that S is Ρ is to put all the force of one's authority behind asserting that S is P. But to say S is probably Ρ is to make a guarded, hedged assertion. We do not fully commit ourselves to saying that S is P, or give it our full weight of authority. We assert that S is P, but only with reservations. The force of "probably" is to express our guarded attitude. How then does Toulmin understand modalities structurally? As indicating, expressing the force with which we may assert a claim, as qualifying the assertion of the claim, modalities modify conclusions or the assertion of conclusions, rather than the move from premises to conclusions. On Toulmin's conception, modalities qualify the conclusion directly, rather than the arrow from premises to conclusion.16 What we have called the common sense of modalities is distinguished from Toulmin's view by its attributing a literal meaning to modal qualifiers. They literally attribute a certain probability (including certainty) to the conclusion in light of the premises. That modalities have this literal meaning derives from the view that "probably" is always used in the light of some evidence, even if this reference is vague and only implicit. There is substantial agreement with the dictum that probability is relative to evidence. Toulmin, we expect, would reply quite vigorously that the common meaning of "probably" and the other modalities does not contain this literal component, and that we are being contentious by labelling this notion the "common sense." Toulmin is in a position here curiously parallel to his position on generalized conditionals. As we saw in Chapter Three, Toulmin allows generalized conditionals to express summary reports (All observed A's are B's) and to have the force of inference rules (From something's being an A, we may infer that it is a B). But he rejects understanding generalized conditionals as literally asserting descriptions

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involving inference, propositions going beyond what is observed (All A's — observed or not — are B's). The summary report may serve as backing, satisfying the criteria for employing the warrant, which expresses the force of the generalized conditional. But its common literal meaning is denied. Yet, neither Toulmin nor the others who adopt a similar position regarding generalized conditionals had a satisfactory argument against the common literal meaning. Likewise, Toulmin here admits that there are various criteria for employing modalities and that these expressions have a distinctive force, but again denies their literal meaning of making a claim about how strongly premises support conclusion. Can Toulmin succesfully argue that modalities do not have the literal meaning the common sense attributes to them? In Probability and Induction, Kneale specifically endorses the view that probability is relative to evidence.17 Toulmin makes Kneale's conception a prime target of attack in developing his own views on probability. Critically examining his argument, then, may help us decide the issue of whether modalities have this literal meaning. Toulmin objects that Kneale's use of "probability" is hard to square with everyday uses of this and such related words as "probably." He first criticizes Kneale's claim that probability is relative to evidence, in particular its corollary that something can be improbable but true. Toulmin charges that Kneale has confused "seeming probable" with "being probable." Given certain evidence, a claim may seem probable, although it is not, and those with additional evidence may no longer speak of it as being probable. That a course of treatment was the best alternative of those available may have seemed probable to the doctor who prescribed it, although we know it wasn't. Something seemed improbable given our background knowledge, but we know it is not. For Toulmin, unless "probable" is quoted, directly or indirectly, to use "probable" without the "seeming" is to use it with all its force of making a hedged, qualified assertion. Apparently then to say that something was improbable but true or to say that it is probable but false is, if not an outright contradiction, to take away with one assertion what the other states. It is akin to "I promise, but I won't."18 Against Kneale's saying that the stories of Marco Polo were true but improbable for his contemporaries, Toulmin replies, "we...have no business to describe them as ever having been improbable, since for us to do this tends in some measure to lend our authority to a view which we know to be false."19 Yet, Toulmin seems just wrong on his claims about common usage. First, although it would be distinctly anomalous to say It is probable that Ρ but Ρ is false, would it be so anomalous to assert that Given conditions C, Ρ is probable; but nonetheless Ρ is false ?

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It would only be anomalous if the proponent also asserted that conditions C obtained. Without that, we would understand "Given conditions C, Ρ is probable" as simply expressing a conditional, with 'P' not asserted. So there are at least two senses of "P is probable," in only one of which does 'P' seem asserted. As Black points out, "probably," "probable," and "probability" differ on their involvement of assertion. "Probably" has an assertive force. To say Probably Ρ but Ρ is false is distinctly anomalous. 20 When we say, On evidence D, the probability of Ρ is such-and-such are we asserting Ρ or simply making a logical point about the strength of support Ε gives to P? The expression "it is probable that" sometimes functions as a synonym of "probably"; more characteristic, however, is its use to register the strength of the determining conditions as conducive, on balance, to the designated outcome. In many such cases the nonassertion of the kernel is patent. With the use of the substantive, "probability," there is still greater epistemological distance from any act of assertion: to say something of the form "Given D, the probability that Ρ is such-and-such" is to formulate a theoretical judgment about the strength of the enabling conditions without facing the question whether Ρ should be expected 21

with sufficient confidence for its assertion to be warranted.

Hence, Toulmin is just plain wrong in his claim that "probable," "improbable" in oratio recta always have assertive force, especially in the context "probable for...," "improbable for...," where there is some reference to an evidential situation. Only to seem probable is to be probable given certain deficient or incomplete evidence, for those possessing just that evidence. Toulmin has failed to distinguish the assertive from the nonassertive sense of "probable." There is a distinct parallelism between these two senses of "probable" and the absolute and relative senses of "probably" we distinguished earlier. Notice that the nonassertive use of "probable" comes to light when we explicitly relativize our assertion to some body of evidence. When we say that Ρ is probable outright, in a way that intimates asserting P, we make no such explicit relativization. What we mean by making such an assertion can be clarified, I believe, through the notion of epistemic probability. As Nolt points out in Informal Logic: Possible Worlds and Imagination, we may speak of the probability of a statement outright as opposed to its probability given certain evidence, a specific set of evidence statements. The latter is its inductive probability. But ordinarily when we speak of the probability of a statement outright, we mean its epistemic probability, its probability given all the known relevant evidence.22 To say

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that a statement is probable outright, in a way that involves asserting that statement, is to say it is epistemically probable. As Nolt points out, epistemic probability is the most familiar notion of probability in daily life. 23 The probabilities of any prediction, whether of the weather, of the outcome of a horse race, of sending a team of astronauts to Mars and returning them safely, are epistemic probabilities. Furthermore, it makes no sense to say that something is epistemically improbable but true. To say that something is true is to admit it is part of the total evidence which we take into account in assessing epistemic probability. If we know something is the case, if that is part of our knowledge, then its epistemic probability is 100%. So there is no question that Toulmin's notion of probability captures at least part of the most central, everyday notion of probability. However, Toulmin has only captured part of this notion. By sticking to this partial notion exclusively, he has a distorted conception of probability. Although in everyday discourse, reference to the total body of relevant evidence may be only implicit, it is still there, for it is bound up with the very meaning of epistemic probability. This notion, although a monadic property, is nonetheless a relational property of statements. As χ is the son of Socrates expresses a monadic property, albeit a relational property, gotten by filling the second position in χ is the son of y by "Socrates," so assertions of epistemic probability ascribe inductive probability relative to best available relevant evidence (or what is perceived as such). The notion is implicitly relative. Now when a statement is probable relative to our best available relevant evidence, we can say it is simply probable in a way which asserts that statement. But this is a special feature of being epistemically probable, not of being probable in general. Although in ordinary language, the relative character of epistemic probability may be obscured, we may maintain, contra Toulmin, that it is close enough to the surface to justify saying that on the everyday conception, probability is relative to evidence and phrases like "improbable but true" are proper and intelligible. Why do we say that? To say that some statement is epistemically probable to some degree is to speak from the vantage point of our current best available relevant knowledge. But, as Nolt brings out, epistemic probability is still itself a relative notion, relative to time and person. Total available relevant knowledge varies. What was epistemically probable yesterday, is not so today. What is highly improbable, epistemically, for one person, may be quite probable for another. Epistemic probability is defined in terms of a relative sense of probability. So with epistemic probability, it is still true to say that probability is relative to evidence. Hence we may also speak about what is epistemically probable

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for other observers or at other times. Here when we estimate these probabilities, we are estimating the likelihood of the statement given the best relevant knowledge then available. But this is to make a judgment of inductive probability relative to that body of knowledge, not a judgment of epistemic probability for us. Thus, if we say that given the evidence available to the doctor, it was probable that the course of treatment pursued was the best, we are using inductive probability. And, it would seem that frequently in ordinary language, "probable," "improbable" are used in this way. As John King-Farlow points out in "Toulmin's Analysis of Probability," To say that Marco Polo's claims were improbable is simply to say that, judged by the best evidence practically obtainable in the context indicated by 'were', his claims were not belief-worthy. The non-present tensing of the verb may often indicate the context of reasons and judgment to be very different from the present one.24

King-Farlow points out that even such problematic locutions as "is probable but false" or "is probable, but I don't think so" may not be unintelligible on occasion.23 If the reasons, evidence Ε one has for a claim C are of a sort that generally gives good evidence for C, but in this circumstance one knows or suspects that some condition undercutting the probative force of this evidence also operates, then the locution is in order. "Probable" here makes a claim about how strongly the body of evidence Ε in general supports C. We implicitly recognize, then, the relative character of probability when we recognize that probabilities have been estimated relative to other bodies of evidence than our current best available relevant evidence.26 So far, then, Toulmin's attack against Kneale's conception of probability, and by extension what we claim to be the common notion of modalities, cannot be sustained. This interpretation is not in conflict with ordinary usage. Rather, Toulmin seems beguiled by certain special features of epistemic probability—asserting that something is epistemically probable involves asserting the statement and leaving reference to evidence implicit. This leads him to hold a distorted view of the meaning of "being probable." Interestingly, Toulmin in effect accepts the legitimacy of the relative notion of probability, but denies that it should be called "probability." Toulmin believes that Kneale (and also Carnap) have gone wrong in confusing support with probability. Evidential support is a relation between premises and claim, between evidence and hypothesis. Different bodies of evidence support a hypothesis to different degrees. However, for Toulmin, to ascribe probability is to go beyond asserting that a support relation holds. In Toulmin's words, it is to draw a moral from that support relation's holding.27 "That we are entitled to bank"28 so far on hypothesis h in light of our evidence e, is the conclusion we arrive at about h in the light of e.

126

What Should We Do With Modalities? The effect of writing the evidence into all probability-estimates is to conceal the vital logical step, from a hypothetical statement about the bearing of e on A to a categorical conclusion about h—from the inference-licence, 'Evidence e, if available, would suggest very strongly that h\ to an argument in which it is actually applied, namely 'e\ so very likely Λ'. 29

But does "very likely" express a property asserted categorically of h, or only about h in light of or in relation to el Even if "very likely h" occurred independently of an argument context, would not there be implicit reference to some body of evidence? True, the expression can have an emotivedirective force, but Toulmin has not established that there is no reference to evidence or a literal claim made about how strongly evidence supports claim. Curiously enough, at one point, Toulmin himself appears to endorse the view that modal words — at least those coming between premises and conclusions in the context of arguments — express in part support relations. In summarizing his position, he again reiterates that the force of "probably" is to make a qualified assertion, to commit the speaker only to a certain extent. But then he goes on to say, Just how far we are entitled to commit ourselves depends on the strength of the grounds, reasons or evidence at our disposal.... Our probabilityterms come to serve, therefore, not only to qualify assertions, promises and evaluations themselves, but also as an indication of the strength of the backing which we have for the assertion, evaluation or whatever. It is the quality of the evidence or argument at the speaker's disposal which determines what sort of qualifier he is entitled to include in his statements.

30

If to indicate the strength means to make or involve a claim about the strength of the backing or argument, then Toulmin in effect is accepting this central feature of what we have called the common sense of modal terms. Modal words have a force to indicate how strongly the speaker is committed to a claim, but they also serve to make a claim about how strongly the evidence supports the conclusion. What may we say, then, about modal words in arguments? Besides their force in indicating how strongly the speaker accepts the conclusion, to assert the conclusion with a certain force, they serve to make a claim about how strongly the premises support the conclusion. The use of a modality in the context of reasons serves not only to express a degree of confidence in the statement, but to say that the degree of confidence is justified given the reasons. It is a claim about logical support. We think this view is in accord with ordinary usage and is substantiated by standard intuitions. Thus, as we argued above, modal expressions are genuinely part of the linking material between premises and conclusions, and are not properly part of the

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conclusions themselves. What are the implications of these structural considerations for argument diagrams?

5.2. HOW DO MODALITIES FIT INTO ARGUMENTS?

We have seen that a modality in effect modifies the claim that one or more given statements support a conclusion. Hence, if arrows represent such claims in our diagrams, modalities should somehow be attached to arrows to indicate their qualifying or modifying role. Our second diagramming method for convergent arguments (See Page 96) suggests how to do this. We tag with the modality our line indicating that the weight of various premises is being added together in claiming support for our conclusion. Better, we expand that line into a box, writing out the modality within the box:

This basically adapts Toulmin's representation to our system. Many different configurations are possible here. A modality need not make a claim about how strongly several premises support a conclusion, but only one. And that one reason may be divided over several statements.

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128

0

(B>

Μ

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Also, several reasons, some of which are divided over several statements, may be claimed to support a conclusion with a given weight.

© These configurations all represent possible argument structures. Further, should an argument present several independent reasons all converging on a conclusion, a modality may make a claim only about the weight of some of those premises, rather than all.31 Thus

Notes

129

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also displays a possible argument structure involving modalities. This brings us to the issue of mixed structure, which we shall discuss in Chapter Seven.

NOTES 1. Black, [1967], p . 465. 2. Black, [1967], p . 465. 3. Black, [1967], p . 465. 4. Black, [1967], p . 467. 5. Black, [1967], p . 467. 6. Black, [1967], p . 468. 7. Black, [1967], pp. 468-69. 8. We are here following Salmon's argument in [1984], pp. 95-96, contained in an argument for the separability of both deductive and inductive modalities. We have considered these questions at length, especially the issue of the separability of inductive modalities, in [1983]. See pp. 3-8. 9. Kneale, [1949], p. 10. 10. For an argument that inductive modal expressions should be taken uniformly as inductive modalities, see [1983], pp. 4-8. 11. Toulmin, [1958], p. 30. 12. Toulmin, [1958], p. 32. 13. Toulmin, [1958], pp. 18-21. 14. Toulmin, [1958], p. 30. 15. Toulmin, [1958], p. 21. 16. We should note that there are passages in [1958] which suggest a reading far more like the common sense of modalities. But we may also question whether Toulmin was aware of the structural distinction between the two views. He speaks of qualifying the conclusion and qualifying the step from data to conclusion as doing the same thing.

Notes

130 Warrants.. .may confer different degrees of force on the conclusions they justify. Some...entitle us...to qualify our conclusion with the adverb 'necessarily', others authorize us to make the step from data to conclusion either tentatively, or else subject to conditions, exceptions, or qualifications. (Toulmin, [1958], p. 100, italics mine.)

Again, he practically juxtaposes "qualifiers (Q) indicating the strength conferred by the warrant on this step [from data to claim]," with "we may write the qualifier (Q) immediately beside the conclusion which it qualifies (C)." (Toulmin, [1958], p. 101.) There is clearly something unsatisfactory here. A claim is not the same thing as a step from data to claim. What exactly do modalities qualify? We believe however that Toulmin's basic view of modalities is as conclusion qualifiers. 17. Kneale, [1949], p. 9. 18. Compare King-Farlow, [1963], p. 16. 19. Toulmin, [1958], p. 56. 20. Black admits that even this claim about the assertive force of "probably" would be challenged by some philosophers. 21. Black, [1967], p. 468. 22. Nolt, [1984], pp. 193-94. 23. Nolt, [1984], p. 195. 24. King-Farlow, [1963], p. 21. 25. King-Farlow, [1963], pp. 21-22. 26. Is there any sense of probability not relative to a body of knowledge? Nolt mentions only one, inherent, absolute, or logical probability. Using a possible worlds terminology, he defines the inherent probability of a statement as "the frequency among all possible worlds of the worlds in which it is true." ([1984], p. 193.) But this is not Toulmin's notion of probability. Given all the possible worlds there are, in how many was the Emancipation Proclamation issued on January 1, 1863? The percentage is minuscule, yet the statement is true. Given this sense of probability, "improbable but true" is a commonplace. 27. Toulmin, [1958], p. 81. 28. Toulmin, [1958], p. 81. 29. Toulmin, [1958], p. 81. 30. Toulmin, [1958], p. 90. 3 1 . 1 want to thank Ms A. Francisca Snoeck Henkemans for pointing out to me the need to make this explicit.

Chapter 6

Rebuttals — What is Their Place in Argumentation?

6.1. INTRODUCTION

One basic dialectical question remains — the third ground adequacy question, and one category of elements Toulmin introduces — rebuttals — has not yet found a place in our treatment of argument structure. What, for Toulmin, are rebuttals? In introducing the concept in Chapter One, we pointed out that warrants may be general but not unexceptionable. There may be circumstances in which a warrant, hypothetical, or generalized hypothetical must be set aside, as mental incompetence invalidates a will. For Toulmin such circumstances, as long as they are exceptional, are rebuttals. Excepting circumstances, facts which could be cited in a legal proceeding to show that a statute does not apply in a given case or only subject to certain qualifications, 1 whatever conditions would cause some warranting hypothetical or generalization to be set aside, Toulmin regards as rebuttals. As Toulmin et al put it in An Introduction to Reasoning, a rebuttal is "some particular exceptional condition, which would.. .withdraw the authority of the warrant." 2 Since in Chapter Three we have argued at length against distinguishing warrants as elements in arguments as products, we should modify this characterization by saying that a rebuttal is an exceptional condition which would undermine or undercut the force of an argument. Will the third ground adequacy question show rebuttals to be proper elements of arguments the way the previous basic dialectical questions have shown conclusions, premises in various configurations, and modalities to be elements of arguments? On the surface, this might seem quite obvious. Just look at how we have formulated this question: Why do your premises make you so sure (in light of condition or counterevidence R)? Why do your reasons make you sure enough to accept your claim? What might prevent you from getting there? If a condition R served as counterevidence, served to bring the force of the argument into question, to undermine it, it would seem to count as a

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rebuttal. If a condition prevented us from getting from premises to conclusion, would't that condition be a rebuttal? This, however, may move too fast for several reasons. Our first formulation of the question seems practically set up to introduce rebuttals. Would a rational judge be constrained to ask this question in this form? Is this the sort of question that would naturally arise in a dialogical situation? Surely we can imagine the simple questions How can you be so sure? Why do your premises make you sure enough to accept your claim? readily arising in a proponent-challenger interchange. Although there is no explicit mention of a rebuttal in these formulations, our challenger might very well have in mind at least one excepting condition which would reduce the force of the argument, if not undercut it altogether, should that condition hold. Further, this raises real doubts in her mind, since she sees no reason why this excepting condition, rebuttal does not hold. Let us take Toulmin's example about Harry's being a British subject. Should our proponent defend this claim by saying that Harry was born in Bermuda, and yet there be significant doubt about his parents' being British subjects or there be significant question whether Harry has become a naturalized American citizen, our challenger would be constrained to ask the proponent why his reason gives him adequate ground for his claim. Remember that a challenger in a basic dialectical situation is a rational challenger. She issues challenges as she perceives logical weaknesses in arguments. And one way to perceive a logical weakness in an argument, to doubt its cogency as it stands, is to be aware of some excepting or rebutting condition which undercuts the argument. Hence these simple questions do allude to rebuttals, even if they do not mention them explicitly. That the challenger would be constrained to ask them indicates that they would arise legitimately in basic dialectical situations. That they allude to rebuttals suggests the legitimacy of this category. In Chapter Two, we gave further evidence for the centrality and importance of the third ground adequacy question. We saw that it was correlated with two of the challenger's moves in formal dialectic. (See Pages 43 through 44) We shall develop this theme further in the last section of this chapter, where we compare our conception with those of other authors. This correlation, though, further highlights the importance and legitimacy of the third ground adequacy question. Yet, there are other problems at this point. Should our challenger ask this third ground adequacy question in any of its forms, is she asking the proponent to extend, further develop his argument or is she asking him to admit that there are significant criticisms against it? Should she ask the question without indicating an excepting condition, she might very well be

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trying to get the proponent himself to reflect on rebutting conditions, to draw out these conditions from him. But would this be argument-generating, as our previous basic dialectical questions were argument generating, or argument criticizing? By asking this question, have we moved from argument construction to argument criticism? How are rebuttals incorporated into arguments, if at all? Toulmin indicates that rebuttals are introduced into arguments by the word "unless" or similar expressions: unless both Harry's parents were aliens or he has become a naturalized American3 barring accidents, unforeseeable injuries, or a more than usual degree of managerial incompetence absent some quite new kind of investment opportunity that the bank may give us a line on.4 In analysing arguments as products, then, are we to count such unlessclauses, at least those occurring in the vicinity of illatives or modalities, as rebuttals? Are rebuttals properly distinguished and isolated as separate elements in arguments as products? Consider the following argument: Mrs. Wilson's will leaves her daughter exactly $1.00. In general, whatever a will leaves to a specific individual constitutes what that individual will inherit from the estate the will divides. So presumably, unless Mrs. Wilson was mentally incompetent at the time she made her will, her daughter will inherit only $1.00 from the estate. If the notion of rebuttal is to be a viable and proper tool in the analysis of argumentative texts, then we must be able to identify rebuttals confidently when analysing such texts. Given Toulmin's conception, we would expect the unless-clause in the last sentence to be the rebuttal. But what about this sentence, more specifically the material following the modality? Do we have two elements here, a rebuttal (R): "unless Mrs. Wilson was mentally incompetent at the time she made her will," and a claim (C): "her daughter will inherit only $1.00 from the estate"? Or do we have just one element, the compound statement "unless Mrs. Wilson was mentally incompetent at the time she made her will, her daughter will inherit only $1.00 from the estate"? Which claim is being argued here? We can raise this same question with any of the examples Toulmin et al offer to motivate rebuttals in An Introduction to Reasoning: "So presumably—unless there is some other factor that our tests didn't reveal or unless our bacteriological ideas are generally haywire—the food service equipment is the villain of the piece. "5 What is being argued here? Is it everything following "Presumably" or is it just "the food service equipment is the villain of the piece"?

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Regarding such unless-clauses as separate, distinct elements requires argument, if we are to be faithful to the desiderata for an argument diagramming technique we set out in Chapter Two. Our third desideratum requires our diagramming system to let us mirror the structure of real life arguments, and not impose a notion of structure that seems contrived. Intuitively, it seems very natural to count a complete assertion as one argumentative unit. Now, as every beginning logic student knows, in asserting a statement of the form 'Unless P, Q,' we make just one assertion. Neither 'P' nor 'Q' are asserted. Also, apparently, in dealing with claims qualified by unless-clauses, we are dealing with statements of this form. Hence, separating the unless-clause from the claim, regarding them as two independent elements in the argument, requires a plausibly defended rationale to avoid the charge of imposing a structure on arguments. There is a second critical question to raise in connection with Toulmin's characterization of rebuttals: Are only exceptional circumstances properly identifiable as rebuttals? Should any excepting condition, any condition which would undercut the force of the argument, be counted as a rebuttal? Suppose it were not unusual for mentally incompetent persons to make wills—wills which are nonetheless invalid because of this incompetence. Would the clause "unless Mrs. Wilson was mentally incompetent at the time she make her will" no longer be a rebuttal? Two critical issues, then, concern whether rebuttals should count as elements in arguments, and if so, just exactly what are these elements. We examine these issues successively in the next two sections.

6.2. ARE REBUTTALS SEPARABLE ELEMENTS IN ARGUMENTS?

Toulmin's case in The Uses of Argument for the separability of rebuttals, for their constituting distinct elements in arguments rests with his very strong conception of the fundamental differences among the various elements he identifies. The basic idea is that types or categories of elements should be distinguished by the function these elements play. Claims are what are argued for. Data give grounds for claims. Warrants are distinct from data and claims since they indicate that the move from data to claim is legitimate. A warrant confers a certain amount of strength on the move from data to claim, or on the claim in light of the data, described by the modality. Surely, what describes the strength of the warrant is not the warrant itself, and so modalities are distinct from warrants. Likewise, given a warrant holding generally but not universally, holding all things being equal, there will be circumstances where all things are not equal and thus the warrant will have to be set aside. These circumstances in which the warrant is to be set aside are surely not the warrant itself. Nor do they indicate the strength a warrant confers on the move from data to claim.

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They do not function as a modality. So they would appear to be something else again. Such excepting circumstances appear to have a unique function and so we may conclude that they, the rebuttals, are distinct elements in arguments. 6 Now this, in itself, does not argue directly that rebuttals are distinct from claims or conclusions. But given this clear differentiation of function, we could construct such an argument along these lines. We can certainly imagine arguments where a particular, categorical claim ' C , ' not the qualified 'Unless R, C , ' is our intended conclusion. Our premises will be intended to support ' C . ' The premises may include a general statement for which we recognize that there are exceptions. W e need not construe such a statement as a warrant, inference rule to recognize this. But we also recognize that the argument from our premises to the claim has a certain strength. If the excepting circumstances ' R ' hold, then that strength is undercut if not obliterated altogether. In this case, at least, these rebuttals are certainly not identical with or even part of the claim we are seeking to justify. Mentioning them in the course of the argument would be qualifying the claimed force of the argument, not qualifying the conclusion. But from this example, can we not move via a sort of Aristotelian ε π α γ ω γ ή (epagoge - induction) to seeing the overall distinctness of rebuttals and conclusions? The separateness of the elements in our example and their distinctness of function indicate that in general when we meet elements playing these functions in arguments we should regard them as distinct. But does this argument settle the matter? (Does the fact that two elements apparently have different functions mean that they are distinct elements in arguments, as opposed to distinct parts of one argumentative element?) How confident can we be that our argument gives us the correct insight? Consider the argument about Mrs. Wilson's will again. Why couldn't we construe the "in general" qualifying the universal premise, In general, whatever a will leaves to a specific individual constitutes what that individual will inherit from the estate the will divides as saying "if no excepting conditions hold"? One could immediately object that "in general" says more than this, implying any excepting conditions are genuinely exceptional. A more refined view might hold that as for all x, if Fx, then Gx implies if Fa, then Ga but is not exhausted by the latter, so a statement of the form in general, for all x, if Fx, then Gx

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implies but is not equivalent to if no excepting conditions hold, if Fa, then Ga. The view might further maintain that some statement instancing the implied form enters, if only implicitly, into the reasoning of the Wilson will argument. W e might phrase the statement this way: If no excepting conditions hold, then if Mrs. Wilson's will leaves her daughter exactly $1.00, only $1.00 is what the daughter will inherit from the estate. The reasoning infers this statement from the manifestly stated warranting premise. From this statement together with the remaining data, we infer the conclusion. The form of this inference leading directly to the conclusion looks like this: If not-R, then (if D, then C ) D ·"· If not-R (in particular if not mentally incompetent), then C i.e.

Unless R, C

Notice here that the conclusion is not ' C ' but 'Unless R, C . ' This seems plausible. The data-providing premise ' D ' gives us no evidence that the rebutting conditions ' R ' do not hold. Since the first premise is relativized to this condition, so should be the conclusion. Thus when an unless-clause introduces the conclusion, it is proper to take it as part of the conclusion. In ordinary, everyday, natural language, that the reasoning has this form is obscured not only by the fact that the conclusion mentions a particular excepting condition, but by the fact that the concrete conditional implied by the qualified universal need not be explicitly stated. But the point is that in qualifying the universal premise with "in general," we are tacitly relativizing that premise to no rebutting conditions holding. This is the key to seeing that in the conclusion, the claim being argued is relativized to some, if not all, of the possible specific rebutting conditions not holding. It is not true that the premises just concern ' C . ' The "in general" qualifier tacitly introduces a reference to rebuttals, which is made explicit and specific in the conclusion. In "On Toulmin's Contribution to Logic and Argumentation," Peter Manicas urges a point very similar to this. He points out that when we use a premise of the form An A will in general be a B, In general, A ' s are also B's, we recognize that being A is not a sufficient condition for being B, that other provisos must be filled, but are "unclear as to precisely what [are] the

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appropriate provisos... .Were the appropriate provisos made available to us, they could then be included as part of the premisses." 7 So if we knew that {Ri, R2, ..., R„} constituted precisely the set of rebutting conditions, we could express the form of our reasoning above this way: If (not-R, and not-R2 and ... and not-RJ, then (if D, then C) D ·*· Unless (R, or R2 or ... or RJ, C. What may we say to this parsing of the reasoning? Notice that the factor making persuasive that the rebuttal clause is part of the conclusion is the claim that the rebuttals are somehow involved with one of the premises. What if this premise were suppressed or left tacit? If someone were to argue (D) Mrs. Wilson's will leaves her daughter exactly $1.00, so, presumably, (C) $1.00 is all she'll get, would we hesitate for a moment to regard (C) as the conclusion? Now suppose this person were to reformulate the argument a little more explicitly: (D) Mrs. Wilson's will leaves her daughter exactly $1.00, so, presumably, unless Mrs. Wilson was mentally incompetent at the time she made her will, (C) $1.00 is all the daughter will get. Are the conclusions of these two arguments the same, being the statement (C)? Isn't the arguer still trying to establish claim (C)? Isn't that the point of the argument? Doesn't the rebuttal clause serve to make more explicit the conditions under which the premise creates a presumption for the conclusion, rather than alter the conclusion? Should we want to represent the structure of the reasoning here, including the rebuttal, we should want something very much like the Toulmin model. In both these formulations, the premise consists of the data pertaining just to the claim and not the rebuttal. Toulmin's model gives us the same effect, since the support line goes back from the claim just to the data, not data and warrant together. But now, if we made the suppressed premise explicit, should that so alter our conception of the argument that we would now regard the entire statement Unless Mrs. Wilson was mentally incompetent at the time she made her will, (C) $1.00 is all the daughter will get as the conclusion, rather than just (C) as in the last two cases? Does this seem plausible? We can make this same point in a somewhat different way. Even if qualifying the warranting premise with "in general" conditionalizes that

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premise, the force of this conditionalization or its effect on the force of the argument is acknowledged when arguers use the modality "presumably." Toulmin sees "presumably" as meaning "the answer, unless certain exceptions hold." By using "presumably" by itself or "presumably" together with mentioning specific rebutting conditions, we qualify the conclusion, but without necessarily regarding the conclusion as a conditional statement. The issue then becomes whether the modality is part of the conclusion or not. If it is, the rebuttal might very well be regarded as part of the conclusion, but if modalities are separate elements in arguments, then "presumably" will be separate from the conclusion it qualifies. So the qualification that the conclusion holds in the light of the data and general but not universal warrant, unless certain exceptions hold, is not part of the conclusion, but a separate element in the argument. But in the last chapter, we have already argued that it is quite right to regard modalities as distinct from claims or conclusions. We expect that much of the persuasive force of this proposed parsing of the argument according to the form If not-R, then (if D, then C) D .*· Unless R, C lies in the fact that this form which arguments apparently display on this view is deductively valid. Adding "unless R" directly to the conclusion is precisely what is required to produce a deductively valid argument. Now we admit that if we are analysing a deductive argument, the unless-clause should be counted as part of the conclusion. If the argument is deductive, either it explicitly claims via a deductive modality such as "certainly" or "necessarily" that the premises necessitate the conclusion, or we concede that the argument should be evaluated as if it made such a claim explicitly. For example, it might be obvious that the premises do necessitate the conclusion or the argument might belong to a family of arguments, e.g. categorical syllogisms, which are standardly and appropriately evaluated as deductive. But to claim that the premises necessitate the conclusion is to claim that if the premises are true, the conclusion will be true also, no "ifs," "ands," or "buts." The notion of a rebuttal is distinctly anomalous, if not downright incoherent, in connection with deductive modalities. But we are here analysing inductive or non-demonstrative arguments, witness the inductive modality "presumably." When we claim that the premises give good but not conclusive evidence for the conclusion, we open up the possibility of rebutting considerations. In "Logical Form, Probability Interpretations, and the Induction/Deduction Distinction," we argued for the viability of the deductive/inductive distinction. Hence, we should be wary of any proposal which apparently leads us to view inductive or non-

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demonstrative arguments as deductive or demonstrative arguments, or to analyse inductive arguments according to a pattern motivated by deductive concerns. This might very well distort the structure of the reasoning. Can we argue that this proposed parsing according to this deductively valid form of arguments where the warranting premise is qualified by "in general" actually does distort the structure of the reasoning? I believe we can. We have already argued that when this warranting premise is not made explicit, analysing the argument according to the Toulmin model, regarding the conclusion as just the claim, not the claim qualified by the rebutting unless-clause, seems straightforward. Given this, it seems implausible that merely by making the qualified warranting premise explicit, we should be forced to reparse our argument according to the proposed pattern, counting the unless-clause as part of the conclusion. This would appear to give too much importance, too much weight to the "in general" clause introducing the premise. How could we argue that it would be giving the clause too much weight? Suppose we could find a family of inductive arguments satisfying the following conditions: (1) They are structurally parallel to the Wilson will argument we have been discussing. (2) Although there is a temptation to qualify their premises with rebuttals or to regard them as so qualified to properly represent the reasoning, such a construal is wrong. It distorts the form of the reasoning altogether, in effect analysing inductive reasoning as deductive reasoning. (3) When rebuttals are mentioned in these arguments, Toulmin's model is insightful for identifying their role. Clearly for these arguments, rebuttals are not part of the conclusion. Their being parallel to the Wilson will argument would indicate that the rebuttal in that argument is not part of the conclusion either. The fact of structural similarity and that all these arguments, including the Wilson will argument, are inductive or non-demonstrative would seem a stronger reason for regarding the rebuttal as not part of the Wilson will argument's conclusion than the presence of "in general" in the warranting premise is for regarding the rebuttal as part of the conclusion. Can we identify such a family of inductive arguments? Rebuttals and Defeasible Concepts H. L. A. Hart in "The Ascription of Responsibility and Rights" [1965] has identified one such family of inductive arguments and argued, in effect, that it is wrong to try to include rebutting material in the warranting premise. These are arguments whose conclusions involve defeasible concepts. What is a defeasible concept? The field of law is replete with many examples:

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"contract," "trespass," "guilty of the offense of φ," 8 where ' φ ' indicates some crime like murder, stealing, plagiarism, bribery, or peijury. What makes these concepts defeasible? Their defeasibility is a consequence of how one properly argues for claims involving these concepts. How would one establish that a contract existed between A and B, in other words, how would one properly argue that an alleged contract between A and Β was valid, that its provisions were enforceable? The premises of such an argument, if all explicitly stated, would presumably contain two types of statements — those describing certain pertinent facts about A and B, and those presenting certain points of contract law. The law-presenting premises would answer the question why the facts were indeed pertinent to the legal claim of contract being argued. But would it be right to insist that the law-presenting premises in a fully developed argument must present the necessary and sufficient conditions for the contract's holding, so that our reasoning ultimately displays this form: A contract exists between A and Β if and only if (C, and C2 and ... and C J C, and C2 and ... and Cn ·*· A contract exists between A and B. Hart maintains that this is wrong. It is to misrepresent, misconstrue the nature of this type of legal reasoning. The defect becomes apparent when we ask how legal reasoning for such claims as contract could be challenged. One could first challenge the truth of the factual premises. But, what is central for Hart's purposes and our purposes here, one could admit that although the points of fact and points of law presented by the premises are ordinarily sufficient to justify the conclusion, in this instance they are overridden by certain further considerations. Certain further facts hold, which constitute exceptions to the general rule. This challenge is a plea that although all the circumstances on which a claim could succeed are present, yet in the particular case, the claim or accusation should not succeed because other circumstances are present which brings the case under some recognized head of exception, the effect of which is either to defeat the claim or accusation altogether, or to 'reduce' it so that only a weaker claim can be sustained. 9

Hart maintains that any set of conditions proffered for saying that a contract holds would be liable to some exceptions, and so not constitute a genuine set of necessary and sufficient conditions. Certainly it would not constitute a complete set of sufficient conditions. This is what makes these concepts defeasible. Although the premises of an argument may establish that conditions adequate for saying that a defeasible concept applies do hold, the

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force of that argument can be undermined by showing that further defeating conditions also obtain. Against Hart, someone might maintain that these sets of adequate conditions are just sets of necessary conditions. For a true set of necessary and sufficient conditions, that the excepting circumstances do not obtain must also be included. Among the conditions substituted for the C ; 's in our schema must be statements to the effect that none of the rebuttals hold. Hart admits that this could be done. One could specify "as the necessary and sufficient conditions of contract, consent and other positive conditions and the negation of the disjunction of the various defences."10 So letting ' P ^ ' 4 P 2 ,' ..., 'P„' stand for the positive conditions which must obtain for a contract to hold and 'D,,' 'D 2 ,' ..., *Dn' be the defeating conditions, a proper definition of "contract" should look like this: A contract holds between A and Β if and only if (P, and P2 and ... and PJ and it is not the case that (D, or D 2 or ... or D m ). Alternatively, one might adopt a general blanket statement, "no defeating conditions hold," to indicate the absence of defeating conditions, rather than specifying each one individually. It would follow then that to establish properly that a contract held between A and B, one would have to show not only that P „ P2, ..., Pn all held, but also that not-D,, not-D2, ..., not-Dm also held. Arguments which present the positive conditions only are logically incomplete. A proper, developed argument for the contract's holding would look like this: A contract holds between A and Β if and only if (P, and P2 and ... and ΡJ and not-(D, or D 2 or ... or D J . (P, and P2 and ... and PJ and not-(D, or D 2 or ... or D J . A contract holds between A and B. Absent establishing not-(D, or D 2 or ... or D m ), one should properly argue A contract holds between A and Β if and only if (P, and P2 and ... and P„) and not-(D, or D 2 or ... or D J . (Ρ, and P2 and ... and P„) .*. If not-(D, or D 2 or ... or D J , then a contract holds between A and B. Here the rebuttal clause is distinctly part of the conclusion. How may we reply to this proposal about construing arguments for claims involving defeasible concepts? Is it a viable proposal? Do we have a telling objection against Hart here? We may counter this objection on at least two grounds. First, it is not obvious, at least to us, that the list of

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defeating conditions associated with a defeasible concept is always finite. Certainly it is not obvious that the defeating conditions are completely specifiable in a list of manageably small length. Even if finite, the list might be indefinitely large. Consider again Toulmin's argument illustrating rebuttals: Harry was born in Bermuda. So, presumably, unless both his parents were aliens/ he has become a naturalized American/ ... Harry is a British subject." Now clearly Harry could also lose his status as a British subject if he became a naturalized Brazilian, Norwegian, Liberian, citizen of Japan or of a host of other countries. Even if we specified all of these, would we have a complete list of the conditions under which Harry would lose his status as a British subject? Is it conceivable that the current British nationality acts had not been passed at the time of Harry's birth or that the acts then in force had been repealed by Parliament, with subsequent revocation of British nationality for all those born in Bermuda? Even if we added these conditions to our list of rebuttals, would we be guaranteed that a fertile imagination might not conceive of more? We can argue more forcefully here. We can argue that not only are situations where the list of rebuttals is indefinitely large conceivable, there actually are such situations. In The Philosophy of Science: An Introduction, Toulmin devotes significant attention to how the principle of the rectilinear propagation of light enters into scientific explanations. Toulmin sees it as a principle of inference allowing us to infer, for example, from data about the height of a wall and the angle of the sun to the length of the shadow cast by the wall. However, the rectilinear propagation principle cannot be applied in all situations. If refraction phenomena are present, we cannot infer from such data to such claims. We can use our principle confidently to argue from the height of a wall and the sun to the depth of the wall's shadow, only when there is, e.g., no glass tank of water just behind the wall, and no bonfire to produce currents of warm air and blur the shadow. It should be noticed, incidentally, that one cannot give an exhaustive list of such conditions, which does not begin with an 'e.g.' or end with the phrase 'and so on...', since the number of different kinds of situations in which refraction may occur is indefinitely large.

But where refracting phenomena occur we have rebutting conditions operative for these arguments. If Toulmin is right here, then it is not only conceivable that there be situations where an indefinite number of rebuttals may hold, but there actually are such situations. Scientific arguments are not the only arena where there may be an indefinite, or at least a practically unmanageable number of rebuttals

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associated with arguments. A s Toulmin et al point out in An Introduction to Reasoning, this is typical of everyday argumentation. Here our reasoning involves generalizations which we recognize hold typically, in general, rather than without exception. Appealing to these generalizations properly involves making certain presuppositions of a very obvious nature. "Provided the writ of Congress still runs..." "Provided the phenomena of nature still follow regular laws..." "So long as human beings remain what they now are..." 1 3 Toulmin et al comment: Naturally it would be a waste o f time and energy to bother recording these wholly general presuppositions explicitly in every actual case by writing them into the particular warrants on which our practical argumentation relies. Nor may it in fact be practicable to enumerate all these general assumptions exhaustively in advance o f encountering the very rare exceptions that bring them to light.' 4

Presuppositions and rebuttals are just two sides of the same coin. If some condition's holding is a presupposition, its not holding is a rebuttal. If there is serious doubt in the challenger's mind that some presupposition Ρ holds, she is bound to challenge the proponent by saying in effect Given that for all you have shown not-P holds, how can you be so sure of your conclusion, why do your reasons make you sure enough to accept your claim? That is, she raises the issue of not-P as a rebuttal. (We shall have more to say about locutions of this form in section six of this chapter). Conversely, if some condition is a rebuttal, its not holding is a presupposition. Arguing all things being equal presupposes that the rebuttals which would make things not equal do not hold. What would be the consequence of having to prefix a generalization with all conceivable presuppositions which must obtain and rebuttals which must fail, even when there is no plausible reason to suspect that the presuppositions fail or the rebuttals hold in a given case? In Toulmin et aVs words, it would be to produce "legal gobbledygook." 1 5 Demanding that these elements be built into the generalization is stultifying, if not practically or even theoretically impossible. Should there be reason to suspect, in a given case, that a rebuttal might hold, then it could be mentioned as a rebuttal. We are not required to mention all such rebuttals in every argument. But if the generalization we are appealing to is a qualified generalization, then to properly spell it out we would have to spell out all the qualifications—a requirement that for everyday arguments is not practical, if not downright impossible. Even if a single generalization involves only a "small" number of qualifications, the number of such conditions for all the generalizations we use is just too large.

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What do these considerations show? They show for one defeasible concept, at least, that of being a British subject, we may suspect the list of particular defeating conditions to be indefinitely long, if not infinite. We have also seen that for certain non-demonstrative arguments, the list of defeating conditions is either indefinitely or unmanageably long. Hence, we have good reason to believe that for some, if not a goodly number of defeasible concepts, the proposal to include the defeating conditions in the very definition of the concept is wnworkable, if not impossible of achievement. It is impossible, that is, if by incorporating the defeating conditions into the definition of the defeasible concept we mean incorporating clauses to the effect that each conceivable particular defeating condition does not hold. Hence we believe that many if not most defeasible concepts simply cannot be defined this way. It may be that for some defeasible concepts, there exists a finite list of defeating conditions. For these concepts, at least, the proposal of building those defeating conditions into the very definition of the concept is feasible (although we may legitimately fear that it may be quite unwieldy). But should the list of defeating conditions be indefinitely extendable, if not infinite, such a definitional construction is impossible.16 This means that our pattern for arguments whose conclusions assert categorically that some defeasible concept holds cannot properly analyse the reasoning for such conclusions, where there is an indefinite number of defeating conditions. A champion of the proposed pattern still has a way out. He or she could claim that although the list of particular defeating conditions may be infinitely long, it could be divided into a finite number of categories, heads of exception.17 For example, Hart cites six such headings for the concept of contract, admitting however that this list is incomplete. These include "defences which refer to the knowledge possessed by the defendant," "defences which refer to... the will of the defendant," "defences which may cover both knowledge and will,"18 as the first three entries. Likewise "Harry has become a naturalized American, Brazilian, Norwegian, Liberian, Japanese, ..." all fall under the single heading "Harry has become a naturalized citizen of some non-British Commonwealth country." Now in defining a defeasible concept like contract, what should constitute the various Dj's in the definition are not particular defeating conditions, like A put undue influence on Β in getting Β to enter the contract, but the general headings—Β has defense on grounds of will. Ultimately, in defining any defeasible concept, we might make do with just one supercondition—"no defeating condition holds." This maneuver could be applied, whether there was a finite or infinite list of defeating conditions. By means of such maneuvers, we could generate finitely long, putatively compete definitions of defeasible concepts. Such maneuvers, however, would not so much solve the problem as relocate it. For recall that according to our pattern, to properly argue that

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a defeasible concept holds in a given case, we must establish not only that the positive conditions in its definition all hold, but also that none of the defeating conditions hold. Now how should we go about establishing that not-D,, not-D2, ..., not-Dra when these D;'s are general headings, not particular defeating conditions? Wouldn't we have to establish that the particular defeating conditions falling under each heading do not hold? And if there are an infinite or indefinite number of such defeating conditions, can this be established within the confines of a finite argument? Given the datum that Harry had never left Bermuda, we might plausibly establish, in one fell swoop, that Harry has not become a naturalized citizen of some non-British Commonwealth country. But this information will not be available in general. Should our argument concern not Harry but Harriet, might we not have to establish for each country other than British territories that she has not become a citizen of that country, to be able to assert that she has not become a citizen of some non-British Commonwealth country? Surely, we cannot simply assert without argument that Harriet has not become a citizen of some non-British Commonwealth country, and still be arguing plausibly. This sort of statement needs evidence. Can we then correctly argue for the proposition that Harriet is a British subject? Can we, at best, point out in the second premise that she has not become a naturalized citizen of certain particular countries, and then argue just for the proposition that unless she has become a naturalized citizen of some country other than those mentioned, she is a British subject? Let's apply this in general. Suppose 'CD' is a defeasible concept for which there are an indefinite, perhaps infinite number of defeating conditions. In arguing that 'CD' applies, that is where 'CD' is a p-ary predicate and 'a,,' 'a 2 ,' ..., 'a,,' are proper referring expressions, in arguing that CDa,a2...ap is true, we must argue that no defeating condition obtains to have a correct argument, given that these defeating conditions are part of the very definition of 'CD.' Suppose we can plausibly assert, with cogent argumentative defense if necessary, that certain particular defeating conditions do not hold. We can do this, of course, for just a finite number of defeating conditions. But from the fact that we can plausibly assert that some finite number of defeating conditions do not hold, can we plausibly infer that no defeating conditions hold? Alternatively, to look at the same problem from a different angle, from the fact that D,, D 2 , ..., Dm are all defeating conditions which fail to hold can we infer that defeating condition D m+1 does not hold either? Obviously, we can make no general assertion here. Unless we know what relevant dysnanalogies there are between D,, D2 Dm on the one side and D m+1 on the other, or whether the points of similarity D m+1 shares with D,, D 2 , ..., Dm other than their being defeating

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conditions, are relevant to D m+ , not holding, we can make no judgment about the cogency of this argument by analogy. Likewise, from the fact that D„ D 2 , ..., Dm do not hold, we cannot infer that no defeating conditions hold or even that no defeating conditions hold in the various exception headings to which D,, D2, ..., Dm severally belong, unless we know that D,, D 2 , ..., Dm are sufficiently representative of all the defeating conditions or of their various subcategories. But we can certainly say nothing about this in the abstract, in general. We can only make such determinations given particular, concrete sets of defeating conditions. Hence, it is a genuine possibility that for some defeasible concept 'CD,' we simply cannot establish that no defeating conditions hold within the bounds of an argument not indefinitely long. But this means that we cannot establish in these cases that no defeating condition holds. Hence, according to our schema, we cannot properly argue that this defeasible concept applies in certain cases. At best, we could argue only that Unless some other defeating condition holds, CDa,a 2 ...a p . But this seems distinctly counterintuitive, since where P,, P 2 , ..., Pn are the positive conditions for CD's holding, one would ordinarily take the argument from P,, P 2 , ..., Pn to asserting that CD holds as properly establishing that claim, plausibly and correctly, if not conclusively. It is just plain counterintuitive to maintain that no correct arguments can be given for just CD holding, as opposed to this proposition being qualified by some unless-clause. Hence the proposal to include the specification of defeating conditions within the definition of defeasible concepts has led to a very uncomfortable result. It seems genuinely possible that in a number of cases we cannot argue that no excepting conditions hold within the bounds of a plausible, definite, finite argument. But this means that we cannot plausibly establish that claim and so cannot correctly argue that the defeasible concept actually applies in a given case. But against this proposal to include defeating conditions within the definition of a defeasible concept, we can urge not only that it leads to a counterintuitive, uncomfortable result. We said that the result was counterintuitive because we felt that an argument from the positive conditions for a defeasible concept's holding to its actually holding was plausible. And we can argue for this plausibility, contra the proposal, by arguing that the proposal to include the defeating conditions in the definition of the defeasible concept is wrong. It is wrong because it confuses and misplaces where the burden of proof lies in arguments concluding that defeasible concepts apply in particular cases. Let's return to our contract example. Suppose A wants to prove that a contract he initiated with Β is valid. As Hart points out, the positive points he must establish are that A and Β are two parties (obvious), that he made an offer to Β, Β accepted that

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offer, that there was an issue of consideration, and perhaps a memorandum in writing.19 There are defeating conditions. If A had somehow misrepresented his side of the contract, or if Β were under the pressure of duress or undue influence, or if Β were somehow mentally incompetent at the time the contract was ratified, then the contract would be voidable, if not actually void, despite A's argument.20 Now one quick way of saying that none of the defeating conditions mentioned obtained is saying that B's consent was "true, full, and free." B, fully informed, freely willed his consent.21 But except in certain special cases, "no party attempting to enforce a contract is required to give evidence that there was 'true, full and free consent. "22 Building the defeating conditions into the definition of "contract" or any other defeasible concept by including a clause that these defeating conditions do not obtain requires that the arguer show that these defeating conditions do not obtain as part of the argument that the defeasible concept applies in a given case. This proposal then puts the burden of proof on the arguer to show that these defeating conditions do not hold and so misplaces the burden of proof. The burden of proof is on the challenger to show that some defeating conditions do hold or to raise the question of whether it is significantly possible that some hold in this case. Only then would the burden of proof shift to the proponent to show, if possible, that the defeating conditions in question did not obtain. By improperly shifting the burden of proof, this proposal distorts the structure of arguments for defeasible concepts. The claim that a defeasible concept applies in a given case can be properly argued for by showing that the positive conditions for the application of that concept hold in that case. And here the conclusion of the argument is the claim that the defeasible concept applies. Should an arguer include rebuttal qualifications in the argument, we cannot argue that these qualifications are properly part of the conclusion because of the way the proposal we have been considering construes proper reasoning for defeasible concepts, since this construal is a misconstrual. Our argument that the proposal distorts the nature of legal reasoning can be reinforced by these further considerations.23 Suppose a judge must determine whether a contract is valid. The plaintiff will present facts to show that the positive conditions of the contract are satisfied. The defendant will present facts showing that certain defeating conditions hold. In rendering a decision, the judge's job is to determine whether the plaintiff s argument in itself is correct and further whether it is defeated by the defendant's argument. Suppose the plaintiff has presented a proper argument and the judge finds it so. Suppose none of the defendant's defeating conditions avail to undercut the plaintiffs argument. Then it would be right for the judge to decide for the plaintiff. But suppose also that some other defeating condition which the defendant has not presented does obtain. Suppose also that should the defendant have presented this condition,

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the plaintiffs argument would have been undercut and the judge should have decided for the defendant. Has the judge made a wrong decision? No. The Judge's function is.. .in a case of contract to say whether there is or is not a valid contract, upon the claims and defences actually made and pleaded before him and the facts brought to his attention, and not on those which might have been made or pleaded. It is not his function to give an ideally correct legal interpretation of the facts, and if a party...through bad advice or other causes fails to make a claim or plead a defence which he might have successfully made or pleaded, the judge in deciding in such a case, upon the claims and defences actually made, that a valid contract exists has given the right decision. 24

But if the definition of "contract" contained a clause to the effect that no defeating conditions held, then it would seem that the plaintiffs argument was defective and the judge should have decided for the defendant. But this, as we have seen, is not the case, further underscoring how the proposal is at odds with actual legal procedure in reasoning. Formal legal proceedings are not the only places where defeasible concepts occur. Hart provides further examples in "The Ascription of Responsibility and Rights." Consider quasi-legal reasoning about property rights in everyday life. Suppose a watch falls out of someone's pocket.25 I infer that the watch belongs to that person, that it is his or hers. If I later learn that the person has stolen the watch, I shall abandon my decision. But does this show that my original inference was improper or that I should have inferred only "Unless the watch was stolen, it belongs to that person"? Responsibility-ascribing statements are also defeasible. Should I say, "He hit her," intending not just to describe the physical impact of his fist on her body but to ascribe liability for this action, my judgment can be overturned by various defenses—it was an accident, done in self-defense, a symptom of mental derangement.26 My judgment was based on observing certain physical facts. Should a defeating condition hold, would this show that my inference, when I made it, was improper, that such observations are not ordinarily or typically good reasons for ascribing liability? All these considerations on defeasible concepts support Toulmin's conception of rebuttals as separate elements in arguments, not part of the conclusion. If certain facts constitute good albeit not conclusive reasons for saying that a certain defeasible concept applies, then we may properly argue from those facts to the concept's applying. We may, in addition, admit by using a modality that our inference is not certain, and also admit that it can be defeated in certain circumstances. But if so, an enumeration of these circumstances should be regarded as a qualification of the argument and not a revision of the conclusion. Hence, the family of arguments to defeasible concepts or more precisely to conclusions asserting that defeasible concepts apply, satisfies the three conditions for an argument family which we set out on Page 139 above. First, such arguments are structurally parallel to the

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Wilson will argument. Arguments to defeasible concepts involve a premise that in general if certain positive conditions hold, a defeasible concept applies. They also involve a premise that these conditions do hold in a particular case. And they conclude that the defeasible concept applies in that case. In the Wilson will argument, we have a premise that in general, if a will indicates that someone is to receive a certain amount of money, that amount is the person's share in the estate. We also have a premise that Mrs. Wilson has bequeathed her daughter exactly $1.00 and we conclude that $1.00 is the daughter's share in the estate. Secondly, although many philosophers may be tempted to regard the premise connecting the positive conditions to the defeasible concept's applying as also involving rebuttals, regarding the non-occurrence of the rebuttal as part of the very meaning of the defeasible concept, such an interpretation distorts the reasoning in such arguments. But as we see it, this misconstrual is the lynch pin in construing rebuttals, should they be mentioned in these arguments in conjunction with the conclusion, as part of that conclusion. For arguments to defeasible concepts, rebuttals, if mentioned, should rather be treated as Toulmin's model suggests, as qualifying the argument. Thus, the third condition, that Toulmin's model be insightful for discerning the role of rebuttals in these arguments, is satisfied. Hence, by analogy, we have good reason to suspect that the rebuttals mentioned in the Wilson will argument should be treated on the lines of Toulmin's model, as elements separate from the conclusion. Now our concern is not with the Wilson will argument per se. We have taken that simply as a convenient illustration. The point we want to make is for arguments in general. If rebuttals appear in these arguments, they function as the Toulmin model suggests. Rebuttals in Scientific Contexts We have seen, in connection with Toulmin's discussing the principle of the rectilinear propagation of light, that his notion of rebuttals, if not the actual word, already occurs in his earlier book, The Philosophy of Science: An Introduction, published previously to The Uses of Argument. We have also seen, again in connection with this principle, that there being an indefinitely large number of rebuttals counts for Toulmin's construal of them as independent elements in argumentation. We may find even further evidence for Toulmin's view of rebuttals in The Philosophy of Science. Toulmin believes that we must sharply distinguish a scientific principle, law, theory from statements stipulating the situations in which it can be applied. Statements delimiting conditions of application concern the scope of the principle. For example, that no refraction phenomena occur is pertinent to delimiting the scope of the principle of the rectilinear propagation of light. We may apply this principle only when no refracting material interrupts the

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light coining from the source. Such situations are outside the scope of the principle. Toulmin maintains that statements indicating the scope of a principle are distinct from that principle. As Toulmin sees it, principles are inference rules and are stated quite generally. They tell us that from data of a certain kind we can make certain inferences or predictions. But it is understood that these rules apply only to certain phenomena or when certain conditions are fulfilled. Now the statement of these conditions is not part of the rule. Such statements are independent specifications of where the rule can be applied. Toulmin adds that much research effort may be devoted to discovering the precise scope of a law. Learning the scope of a law or principle, learning in what area it may be applied, is part of learning what it is to practice the science involved.27 Not counting scope specifications as part of the law has a distinct economy. Otherwise, the law itself would have to be changed or regarded as changed given fresh discoveries concerning its scope.28 This has a distinct import for understanding how laws of nature are established. If a prediction is made upon certain data using some principle, and that prediction proves false, does this discredit the principle? Not necessarily, Toulmin would reply. This may show only that the principle is being applied outside its proper scope. It is interesting in this connection to note how Toulmin here anticipates themes enunciated by Thomas Kuhn in The Structure of Scientific Revolutions [1970]. In discussing the nature of normal science, Kuhn points out that scientists may gather facts as part of articulating a paradigm. One way to articulate a paradigm is to attempt to apply it to a new area, one concerning phenomena distinct from but similar to the phenomena for which the paradigm was developed. Given the way a paradigm works for certain phenomena, just how will it work for others? This indicates that for Kuhn, paradigms have scope—they are intended to apply to a given range of phenomena, and application outside that range calls for further research. As Kuhn points out, Newton's "Principia had been designed for application chiefly to problems of celestial mechanics. How to adapt it for terrestrial applications, particularly for those of motion under constraint, was by no means clear." 29 Toulmin also anticipates Kuhn in describing the reaction of scientists to anomaly, and sees this issue as connected to scope. There will not be a perfect match between theory and observation. At times, the facts are not what the theory predicts. But such anomalies do not automatically spell the rejection of theories or paradigms. The mere recognition does not mean the paradigm is henceforth replaced, adjusted, or even qualified as not applying to the anomaly. As Kuhn sees it, one works under the current paradigm to try to solve the puzzle of the anomalous behavior. Likewise, Toulmin remarks

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Departures from the law [Snell's Law for refraction] and limitations on its scope, such as double refraction and anisotropic refraction, come to be spoken of as anomalies and thought of as things in need of explanation in a way in which ordinary refraction is not; and at the same time the statement of the law comes to be separated from statements about the scope and application of the law. 30

If statements about the scope were part of the law, would not the discovery of anomalies automatically presage a revision of the law, adding a clause removing this anomaly from the law's scope? If Toulmin's observations here give a sound representation of scientific procedure, then we have further evidence that rebuttals should be regarded as separate elements in arguments. References to scope may function analogously to the defeasibility conditions we examined above. When a law is applied, we presuppose we are applying it to phenomena lying within its scope. The phenomena's lying outside the scope constitutes a defeating condition. We saw that the temptation to construe the "unless" clause as part of the conclusion of an argument to a defeasible concept was bound up with trying to incorporate defeating conditions into the very definition of defeasible concepts. The situation seems parallel here. If scope specifications were part of the laws and principles used in making scientific predictions, then the gross form of much scientific argumentation might look like this: law or principle scope conditions satisfied

,

* >

If S, and S2 and ... and Sn, then if data D, then prediction P. D Unless not-(S, and S2 and ... and SJ, then P. In invoking the law, the scope conditions would at least be understood, and so manifest references to scope made in conjunction with the prediction would plausibly be parsed as part of the conclusion inferred. We should not infer the unqualified prediction that Ρ itself unless we knew that the scope conditions were satisfied; unless, that is, we knew that no phenomena indicating that we were outside the scope of the law or principle in this case had surfaced here. That is, asserting that the scope presuppositions are satisfied is part of arguing for the prediction P. But does this reflect scientific procedure? Aren't predictions made categorically and not qualified this way, without assurances that scope presuppositions are satisfied? Doesn't this misrepresent scientific reasoning? Scope considerations, then, are not part of the conclusion, but express independent reservations about the applicability of the law or principle. They function to qualify the inference. They function precisely as rebuttals in Toulmin's sense.

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To determine the adequacy of Toulmin's account of scientific procedure would take us beyond our scope in this study. In Toulmin's mind, it is closely allied with his instrumentalism. But it is not obvious that we must assume some form of instrumentalism to justify regarding scope considerations as separate assertions. We could appeal to scientific procedure directly. Even if Toulmin's account of scope indicators should prove wrong, this would not discredit his claim that rebuttals are independent elements in argumentation. The evidence generated by arguments involving defeasible concepts would still be in tact. But if Toulmin's account of scope considerations has merit, then we have additional evidence that his construal of rebuttals is correct. Given the various considerations which we have adduced to this point, we feel we have enough evidence to claim that rebuttals are separate elements in arguments.

6.3. ARE ONLY EXCEPTIONAL CONDITIONS REBUTTALS?

We now have resolved the first and major of the two critical issues which we raised in the introduction to this chapter for Toulmin's conception of rebuttals. It is perfectly proper to distinguish and isolate rebuttals as a distinct type of element in arguments. The second issue remains. We are agreed with Toulmin that rebuttals are excepting conditions. But Toulmin frequently speaks of rebuttals as being exceptional, as holding only in rare or unusual instances. We could put the point this way—On this conception, if a challenger attacks an argument by claiming that some rebutting condition holds, the burden of proof is on that challenger to show that the rebuttal actually does hold. No doubt, many rebuttals will be exceptional in just this way. But do we want to build being exceptional into the very definition of a rebuttal? Suppose someone argued sloppily. Suppose that person adduced some relevant reasons for a claim, but reasons whose force was undercut by some excepting condition. And suppose it was pretty obvious that the excepting condition could hold in this situation. Would we want to deny that the excepting condition was a rebuttal, just because it was not exceptional? Can such a situation arise in real life? In Logical Self Defense, Johnson and Blair report an argument of a University of Texas biochemist concerning why the city of El Paso, though one-third the size of Dallas, has only one-seventh the number of its residents in state mental hospitals. According to the biochemist, this is because El Paso's water has high lithium levels, while Dallas' water does not, lithium being a tranquilizing agent. Hasn't the biochemist overlooked other hypotheses? Couldn't larger cities be more tension filled and that account for the higher admission rate? Also, given that the nearest state mental hospital to Dallas is thirty-five miles away while the nearest hospital to El Paso is three hundred fifty miles away, what about the hypothesis that

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proximity to a state mental hospital explains the higher proportion of Dallas residents in mental hospitals?31 What, argumentatively, are these alternative competing hypotheses? Wouldn't either of them, if true, undermine the force of the biochemist's argument, whatever force it might have? Wouldn't they operate as rebuttals do? Why shouldn't we count them as rebuttals? There is one reason why we might not want to call these alternative hypotheses rebuttals. What would be the effect of incorporating these alternative hypotheses into the biochemist's argument in an unless-clause qualifying the force of the argument? First, exactly how is this person arguing? His conclusion is that the presence of lithium explains the relatively low rate of admissions to mental hospitals in El Paso. His premises are that El Paso's drinking water contains lithium while Dallas' does not, and that lithium is a tranquilizing agent. Now suppose the biochemist presented the following: El Paso's drinking water contains lithium unlike the drinking water in Dallas. Lithium is a tranquilizer. So—unless Dallas' greater size (three times the size of El Paso) or greater proximity to a state mental hospital (35 versus 350 miles) explains the higher admissions rate—the presence of lithium in the supply of drinking water causes El Paso's lower admissions rate to mental hospitals. Has the biochemist presented an argument here, or just an exposition structured like an argument? To have an argument, we must have a claim that certain statements, the premises, support another, a conclusion. To be sure, the conclusion indicator "so" appears in this passage. To be sure, if the qualifying unless-clause were not present, we would have an argument, albeit one which is logically faulty, committing the hasty conclusion fallacy. But when the claim that the premises support the conclusion is provisoed with such a strong excepting condition—"unless Dallas' greater size (three times the size of El Paso) or greater proximity to a state mental hospital (35 versus 350 miles) explains the higher admissions rate," is that illative claim still being made? Wouldn't acknowledging these undercutting circumstances take away any claimed argumentative force from this passage? Suppose our biochemist had qualified his "argument" with "unless some other hypotheses hold"? This would be an even stronger condition. Would his "argument" then be an argument? The point is that if rebuttals are a type of argumentative element, yet adding an unless-clause with excepting but not exceptional conditions transforms an argument into a non-argument, it is distinctly anomalous to regard those excepting conditions as argumentative elements. But regarding them as rebuttals is doing precisely that. Against these considerations, there is still a reason for allowing excepting but not exceptional conditions to count as rebuttals. Theoretically

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at least, our biochemist need not stop with his "argument" as presented above. Notice that the challenger's rebuttal introducing question Why do your premises make you so sure (in light of condition or counterevidence R)? does not ask the proponent simply to acknowledge excepting conditions but to give some evidence why those excepting conditions do not operate in this case, do not undercut the force of this argument. The question is intended to elicit further argument. It is intended to draw out counterrebuttals from the proponent. We shall develop this notion of counterrebuttal explicitly in section six of this chapter. Now it is conceivable that the biochemist, after qualifying his argument with these alternative hypotheses as excepting conditions, would argue further that in this particular case they do not explain El Paso's lower rate of admissions to mental hospitals. Whether the biochemist could actually argue cogently in this case is another matter. But it is certainly conceivable that someone could present an argument for which significant excepting conditions could be framed. These excepting conditions could be so significant that the burden of proof would be on the arguer to show that they did not undercut the force of the argument. Yet, the arguer might very well be able to meet this challenge. For example, consider again Toulmin's argument from Harry's being born in Bermuda to his being a British subject. Tne force of this argument would be undercut if neither of Harry's parents were British subjects. Suppose that there was significant question about the nationality of Harry's parents. But suppose also that they were both British subjects and that the arguer could readily establish that fact.32 Then acknowledging the excepting condition and presenting the relevant countering information in the context of this argument would be in line with producing cogent reasoning. We should certainly still have an argument. Notice that it would be perfectly appropriate for a challenger to point out any undercutting conditions in criticizing an argument, and to claim that if the proponent were to make a logically cogent case, he or she must qualify the force of the argument by admitting these conditions. But since these conditions qualify the force of the argument, and since it is at least possible that the proponent could counter them and so still be arguing, are they not in fact rebutting conditions? Should the fact that they are not exceptional disqualify them from being rebutting conditions? Since the model of argument on which our account of argument structure is built in fact calls for challengers to raise such rebutting questions, we believe the concept of a rebuttal should be widened to include any undercutting condition, not just those which are exceptional. There is something right in Toulmin's conception, since if someone is arguing cogently, the rebuttals to the argument will ordinarily be genuinely exceptional. But not everyone

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will be prepared to argue cogently, and we must be prepared to diagram arguments, even if they are fallacious.33 Hence, we are in basic agreement with Toulmin that rebuttals are separate elements in arguments. We differ only in specifically allowing any undercutting circumstances to count as rebuttals. Since the unless-clause indicating these conditions functions like a rebuttal to qualify the force of the argument, and we still may have an argument here, it seems perfectly proper to regard the unless-clause as a rebuttal, even though these excepting conditions are more than exceptional. How then do rebuttals fit into the structure of arguments? Toulmin represents them as connected to modalities on his model. We turn to understanding and representing their structural role in the next section.

6.4. HOW DO WE REPRESENT REBUTTALS DIAGRAMMATICALLY?

Our view of the structural role of rebuttals is implicit in the foregoing discussion. We have said that rebuttals are excepting conditions. That a rebuttal holds diminishes or undercuts the strength or force of our argument. Acknowledging rebuttals in the context of an argument, then, is to qualify the argument. It is to qualify the claim about how strongly, with what force, the premises support the conclusion. As we have seen, modalities describe the force of arguments. Rebuttals then modify or qualify modalities. In effect, they sharpen modalities. The premises support the conclusion with given strength unless.... Overtly indicating rebutting conditions, especially exceptional rebutting conditions, makes the modality more precise. Alternatively, we could regard such < modality, rebuttal > pairs as complex modalities indicating how strongly the premises support the conclusion. This indicates that Toulmin had the right insight when he called for attaching the rebuttal to the modality in argument diagrams. As modalities modify the plain illative claim that the premises support the conclusion, indicating the strength of support, so rebuttals modify modalities. The diagram perspicuously indicates their structural position in argumentation. Hence, we shall follow Toulmin in attaching rebuttals to the modality in our diagrams. We shall write out the rebuttal34 under the word "unless" to the left of the modality box, and connect the rebuttal and modality boxes by a horizontal line. Thus illustrates the positioning of a rebuttal in an argument diagram. Must an argument, then, explicitly contain a modality to contain a rebuttal? If an argument does not contain a modality, must we supply one in diagramming the argument if we want to represent the rebuttal? This is not necessary. Even if an argument makes no manifest claim about how

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© unless R

Μ

VK

© strongly its premises support its conclusion, by putting forward those premises as evidence for that conclusion, the argument does claim, at least, that the premises support it with sufficient strength to create a presumption for the conclusion, and this claim may be qualified or sharpened with rebuttals. Should there be no modality in the argument, should the rebuttal challenge in effect whether the premises give sufficient and proper information to create even a presumption for the conclusion, we may construct a rebuttal box as before, here to the left of the horizontal line indicating that the weight of various premises is taken together to support the conclusion.

Should there be no horizontal line, as ordinarily there would not be if just one reason (either in a single statement or in several premises linked) is given for the conclusion, we can always furnish a horizontal line between reason and conclusion in a diagram to which to attach the rebuttal box. Thus to add rebuttals to

How Do We Represent Rebuttals Diagrammatically?

®

© or

P2

N/

© we simply break the downward directed arrow with a line

M' and proceed:

® unless R \f

©

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o

or

θ unless R

0 ψ

6.5. IMPLICATION OF REBUTTALS FOR THE LINKED-CONVERGENT DISTINCTION

In section four of Chapter Four, we discussed several arguments which have proved problematic in the literature. Some want to count these arguments as linked, others as convergent. The way we have drawn the linkedconvergent distinction, how we have characterized linked versus convergent argument structure, gives us a clear-cut determination of these cases. They all turn out convergent on our account, because in each argument, the several premises were each themselves independently relevant to the conclusion. We did not need to take the various premises together to see why we had a reason for the conclusion. But some intuitions pointed toward counting these arguments as linked. If each premise by itself is a weak reason for the conclusion, yet all the premises together constitute a good case, does convergent structure adequately represent their connection in this argument? Again, there are arguments we count convergent where the falsity of one premise would largely undercut, if not completely undermine, the force of the others. It's not that one premise's proving false would cause us simply to subtract its weight from the overall case the argument makes for the conclusion, the legitimate force of the argument being the weight of the remaining premises. Rather, from the fact that this premise is false, we see that the force of the others is nullified in this case. For example, in a categorical inductive generalization argument, where our conclusion is a statement of the form "All A are B" and we really mean "all," no matter

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how many instances of A's which are B's are cited in the premises, if one of those claims should prove false, if one β; which is an A is not a B, that is enough to show false that all A are B, despite the force of the other instances. Since the premises in these arguments are thus interdependent, since the force of each one in this argument depends on the truth of the others, shouldn't we regard these arguments as having linked structure? Thomas, as we saw, builds this right into a criterion for distinguishing linked from convergent arguments. An argument is convergent only if each reason would support the conclusion just as well, even if the other reasons were false. Otherwise, it is convergent. In our discussion in Chapter Four, we pointed out how intuitions based on the additive nature of some arguments, that several weak reasons could combine to give a strong, or relatively stronger argument, could be accommodated by revising the way we represent convergent arguments. By inserting a "pan" on which the independently relevant reasons can "deposit their weight" in supporting a conclusion, we can illustrate modal connection without using relevance linkage. (See Page 104.) We did not, however, address objections to our system based on Thomas' intuition that when the falsity of one reason would undercut the force of the others, we should have linked structure. By incorporating rebuttals into our system of argument diagramming, we may accommodate this intuition and still draw the linkedconvergent distinction where we have. That is, we may diagram as convergent arguments where the several premises are independently relevant to the conclusion, even though the falsity of one would undercut the force of the others, but yet satisfy intuitions to represent them as linked. Consider such an argument. Suppose the falsity of any one of its reasons serves to rebut the argument and any argument from the remaining premises to the conclusion. But we can represent that fact in an argument diagram directly through the use of rebuttals. We can place the denial of any one of the premises, or a disjunction of such denials, or a statement equivalent to such a disjunction in the rebuttal box. The falsity of one converging premise, then, can serve as a rebuttal for the entire argument. But with the category of rebuttals at hand and a method for representing them diagrammatically, we can represent this fact without resorting to linking independently relevant premises. We can represent this rebutting function for what it is, a rebutting function. Suppose an argument has η

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independently relevant premises, where the falsity of any of them would serve to undercut the force of the argument. We can represent that fact this way:

unless not—Ρ1 or not—P2 or • • •

not—Pn

or

Μ 0

This diagram certainly indicates that the falsity of any premise would not merely subtract that one piece of evidence from the argument, but would undermine its entire force. Yet the diagram does this without resorting to linked structure. Each reason does provide some evidence, no matter how small, for the conclusion. Each is independently relevant to the conclusion, and our diagram shows this. The claim that we have a case for the conclusion is based not on the weight of each severally, but added together, and our diagram shows this through its horizontal line under PI, P2, ..., Pn. That the falsity of any one of these undercuts the argument is indicated through the rebuttal box. Hence, as with other intuitions which seemed to conflict with our way of distinguishing linked and convergent structure, we can accommodate these intuitions without redoing the boundaries of that distinction. Notice that judging that the falsity of one premise would undercut the force of the others is distinct from and additional to judging that several premises have been put forward to support a conclusion and that each serves to give a distinct, independently relevant reason for that conclusion. The latter is especially a structural issue. The former involves some evaluation. Suppose a proponent simply presents several independent reasons to support a conclusion. He does not acknowledge that the falsity of one rebuts the argument, even though this is true in this case. To diagram his argument

Counterrebuttals

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properly on our view, we need only recognize its convergent structure. We do not have to make the additional evaluative judgment about the interdependence of the premises, as Thomas would require for a correct diagram on his approach. We do not have to enter into evaluative considerations to complete our structural analysis. As we saw in Chapter Four, this was a benefit of our approach, keeping modal and relevance considerations distinct. And notice also that recognizing that the falsity of one premise would undercut the force of the whole argument is a modal issue, different from recognizing that the premises present various pieces of evidence to support the conclusion. Hence, on our approach we can diagram such convergent arguments straightforwardly, while having the resources to explain the intuitions of those who would see them linked because of the interconnection of their premises. Such persons are perceiving that the falsity of such premises would serve to rebut the argument, and we can represent what they perceive. We submit, then, that these considerations answer objections based on Thomas' intuitions.

6.6. COUNTERREBUTTALS

As we have pointed out in section one of this chapter, our challenger asks the third ground adequacy question not just to make the proponent aware of rebuttals but to get an answer to the objections they pose. Should the proponent simply incorporate the rebuttals into his argument, he would not be answering the challenger's question directly or head on. When asking "Why in the light of R do your premises make you so sure?", the challenger's purpose is not primarily to get the proponent to qualify his argument, but to provide some further argumentation for why he is so sure. How may our proponent reply? Notice that the challenger is not claiming that the rebutting condition actually holds, but is simply raising the issue. 35 At most in her role as rational challenger, she is claiming that the rebutting condition is a live possibility. That is, it is not simply logically possible, but something worth worrying about, something which, in Toulmin's words, "has a right to be considered," demands "our attention." 36 The most straightforward answer would be to assert that the rebutting condition does not hold, and to back up that assertion, if need be, with argument. For example, consider the following dialectical exchange:

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Rebuttals — What is Their Place in Argumentation ?

PROPONENT: CHALLENGER: PROPONENT: CHALLENGER:

PROPONENT:

Mrs. Wilson has disinherited her daughter. HOW do you know that? Her will leaves the daughter exactly $1.00. How do you know Mrs. Wilson wasn't mentally incompetent when she made her will? (Given for all you have shown that Mrs. Wilson was mentally incompetent when she made her will, why does that reason make you sure enough to accept your claim?) But Mrs. Wilson was mentally competent when she made her will.

By answering the challenger's rebuttal, the respondent has presented further information supporting his original claim. He has asserted a further premise. But such premises have a different function from either presenting evidence bearing directly on the conclusion or explaining why certain premises are relevant to the conclusion. Consider the argument Mrs. Wilson was mentally competent at the time she made her will. So Mrs. Wilson has disinherited her daughter. That argument is distinctly odd. What does the premise have to do with the conclusion? Why is it relevant? It does not obviously give evidence for the conclusion. The other premise in the dialectical exchange, "Mrs. Wilson's will leaves her daughter exactly $1.00," does not so much show this premise relevant as otiose. The fact that the will leaves the daughter only $1.00 justifies saying the daughter is disinherited and hardly needs any explanation of its relevance. Hence the premise that Mrs. Wilson was mentally competent neither explains the relevance of the other premise, nor is its relevance explained by that premise. Linking the two statements would be inappropriate, as would be convergent structure. The proponent is not simply giving another piece of evidence for the conclusion here, else the above argument would not be so odd. What then is the function of this premise? It functions to show that a possible rebuttal is non-operative, to rule out the possibility of this rebuttal operating in this case. Given this further evidence, this possibility is no longer something to worry about. We call such premises counterrebuttals. By answering the third ground adequacy question, they have a distinct function and thus enter into arguments in a structurally distinct way. There is another way this third ground adequacy question may be answered, another way rebuttals may be countered. A rebuttal constitutes evidence, at least potential evidence, against the claim being argued. Raising

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163

the rebuttal as a genuine possibility casts the claim in doubt, even given the argument for it. But this does not mean that invariably if the rebuttal holds, so does the denial of the conclusion. There could be some further condition, in effect a rebuttal of the rebuttal, such that if it, together with the rebuttal and the original premises all held, we would have a presumptively strong case for the conclusion. The proponent may then concede "R" but indicate that its rebutting force is undercut by "S." For example, our dialectical exchange might proceed this way: PROPONENT: CHALLENGER: PROPONENT: CHALLENGER:

PROPONENT:

Mrs. Wilson has disinherited her daughter. How do you know that? Her will leaves the daughter exactly $1.00. HOW do you know she hasn't drawn up a supervening will invalidating the old? (Given for all that you have shown she has drawn up a supervening will, how can you be so sure?) Oh, she has drawn up a supervening will, but it is invalid.

Our proponent does not actually have to concede that the rebuttal holds to make this type of reply. Simply asserting that a condition holds which undercuts the force of the rebuttal, whether or not it holds, is sufficient. Consider the following example, adapted from an argument Thomas considers in Practical Reasoning in Natural Language?1 PROPONENT: CHALLENGER: PROPONENT: CHALLENGER: PROPONENT:

I should remodel my home. Why do you believe that? The house has painful psychological associations for me. But how do you know that remodelling the house would remove the painful psychological associations? Even if my house retained its painful psychological associations, I could always resell it, perhaps at a profit.

In his last response, the proponent is not conceding that the house will retain its painful psychological associations, but is claiming that an additional condition holds which would undercut the force of this rebuttal. We don't have to worry about it, even if it does hold. Our diagrams can display the unique role of counterrebuttals quite perspicuously. Since counterrebuttals support conclusions by ruling out possible rebuttals, by claiming either that they do not hold or that they do not undercut the argument in this case, there should be downward directed arrows from the encircled numbers representing these premises to the rebuttal box. Typically the representation of an argument with rebuttal and counterrebuttal would look like this:

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Rebuttals — What is Their Place in Argumentation?

© The arrow from the counterrebuttal premise does ultimately point to the conclusion. But it points to it through the rebuttal box to indicate that the rebuttal is non-operative in this case.38 Where the counterrebuttal concedes R but undercuts its force with some other statement S, these two statements constitute the counterrebuttal and so should be linked. So far, we have entertained arguments where there is at most one rebuttal and counterrebuttal. But certainly our challenger could have several rebuttals in mind and present them either all at once or one by one, as the proponent answers each with a counterrebuttal. Furthermore, the proponent might present several premises to counter some rebuttal, and leave another rebuttal uncountered. We can easily extend our diagrams to represent these further features perspicuously. If there are several rebuttals, we label them "Rl," "R2," .... We then label each downward directed arrow from a counterrebutting premise "CRn," when "n" numbers the rebuttal the premise counters. An argument diagram with several rebuttals and counterrebuttals might very well look like this:

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Comparison with Other Authors

Ο Toulmin does not include counterrebuttals in his model of arguments. However, he does recognize that premises may function as counterrebuttals. That both Harry's parents were aliens serves to rebut the argument concluding that he is a British subject from the fact that he was born in Bermuda. The datum that his parents were not aliens serves as a counterrebuttal.39 It may be unusual to find rebuttals and counterrebuttals when analysing argumentative texts. However, as we shall develop in the next section in comparing our position with Jack Meiland's, these categories are essential in developing cogent arguments and in argument evaluation. In properly developed arguments of any complexity, we should expect to find rebuttals and counterrebuttals. These elements in argument analysis clearly pay their way at that level.

6.7. COMPARISON WITH OTHER AUTHORS

At the end of the last section, we admitted that rebuttals and counterrebuttals seemed to be rather rarified elements in arguments. These elements might not appear in many argumentative texts. However, we have argued that rebuttals and counterrebuttals are genuine elements in arguments. In this section, we would like to supplement our argument by discussing how these elements appear in the work of various other authors on argument analysis. We shall first show that both rebuttals and counterrebuttals are involved in the formal dialectic Rescher presents in Dialectics. We shall then review how these elements are recognized in several basic texts. Rebuttals, Counterrebuttals, and Formal Dialectic As we pointed out in the introduction to this chapter, our comparison of the basic dialectical questions with formal dialectic in Chapter Two indicated

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that we may correlate two basic moves in formal dialectic with the third ground adequacy question, the rebuttal introducing question. These moves are provisoed denial and weak distinction. Now that we have both the concepts of rebuttal and counterrebuttal at hand and have argued for their legitimacy, we can see more clearly how such elements appear in formal dialectic. Let us recall certain basic features of a formal disputation. The proponent begins with a categorical assertion, "P is the case," "I assert that P , " "!P." One of the challenger's possible responses is a cautious denial, "Why P , " "For all you have shown, not-P," " f ~ P . " T o this the proponent must reply by defending P, giving some evidence, Q, for it. In formal dialectic, this response has a prescribed form, "P/Q & !Q," "P standardly holds, given that Q and Q is the case." Now to this, the challenger may reply with a weak distinction, "But ~ P holds, given Q & R, and Q & R holds for all you have shown," " ~P/(Q & R ) & |(Q & R ) · " But R here is clearly a rebuttal. This very move of weak distinction injects the notion of rebuttals into formal dialectic. In fact, we could say that the issue of rebuttals arises in formal disputation primarily at this point. Although Q may generally establish a presumption for P, should R also hold that presumption is undercut. The challenger is in effect asking "Given that for all you have shown rebuttal R holds in addition to your premise Q, why does Q make you sure enough to accept P?" That is, the challenger is asking the third ground adequacy question. Conversely, in asking certain forms of the third ground adequacy question, Given that for all you have shown R holds, how can you be so sure (that P)? why do your reasons ( Q ) make you sure enough to accept your claim (that P)? the challenger is raising the possibility that R holds, not claiming that it does. It is simply understood in asking the question that should R hold, we should have distinct grounds for doubting the conclusion P, or at least for doubting that Ρ has been established with the strength claimed, even if the proffered premise held, i.e. " ~P/(Q & R ) " is frequently understood. Recall that the challenge " ~P/(Q & R ) & t ( Q & R ) " is called a weak distinction because the challenger does not claim that Q & R holds, but only raises that as a possibility. The proponent has said nothing to rule this out. Since it is the possibility of R's holding which upsets the force of Q to establish P, it is straightforward to see that these forms of the third ground adequacy question are in effect ways of making the weak distinction move. Hence, to raise the issue of a rebuttal is to make a weak distinction and to make a weak distinction is to raise the issue of a rebuttal. Thus the challenger's move of weak distinction in formal disputation significantly corroborates the

Comparison with Other Authors

167

centrality of the third ground adequacy question and the legitimacy of rebuttals as argument elements. The proponent has three countermoves to a weak distinction open to him. In categorical counterassertion, he asserts that (Q & R) does not hold, "! ~ ( Q & R)." In provisoed counterassertion, he claims that Q & R does not hold given S and S does hold, " ~ ( Q & R)/S & !S."40 But in both cases, this is to reply with the first type of counterrebuttal we examined in the last section. Since the proponent is committed to Q, his asserting ~ (Q & R) amounts to asserting ~ R . In making these countermoves, the proponent then is saying that we need not worry about R, because R does not hold. In categorical counterassertion, he simply offers the counterrebuttal that R does not hold. In provisoed counterassertion, he is offering that counterrebuttal together with argumentation for it. But the other type of counterrebuttal, in effect rebutting the rebuttal, also occurs in formal disputation. To claim that there is such a further rebutting condition is to make the countermove of drawing a strong distinction to the challenger's weak distinction.41 To the challenger's ~P/(Q & R) & t(Q & R), the respondent answers with P/(Q & R & S) & !(Q & R & S). Hence in formal disputation, the proponent replies to the question of rebuttals with counterrebuttals. To the proponent's categorical assertion !P, the challenger may also reply with a provisoed denial, ~P/Q & fQ. In Chapter Two, we pointed out that this move of provisoed denial is also in effect a way of asking the third ground adequacy question. Q constitutes an objection to P. Any argument for Ρ must either meet that objection or acknowledge Q as a rebuttal,42 qualifying the force of the argument. The proponent has the same modes of attack, categorical counterassertion, provisoed counterassertion, or strong distinction open to him to reply to this objection. Q then functions as a rebuttal to P. The provisoed denial in effect asks, "Given that for all you have shown Q holds, how can you be sure enough to accept P?" Hence, this mode of attack and these moves in response basically present rebuttals and counterrebuttals from another angle. That provisoed denial is one of the three principal forms of challenge in formal disputation yet further corroborates the legitimacy and centrality of the third ground adequacy question as a basic dialectical question and the rebuttals that question introduces. That the proponent's counterrebuttal-introducing countermoves are sanctioned in formal disputation in turn corroborates the legitimacy of counterrebuttals as a category of argumentative elements. Formal dialectic, then, gives us additional evidence for including rebuttals and counterrebuttals as categories of argument analysis.

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Rebuttals — What is Their Place in Argumentation?

Approaches of Various Texts Several authors of basic college texts have recognized the need for taking counterevidence, counterconsiderations into account in argumentation. In Reasoning, Michael Scriven presents a conception of argument analysis which calls at one point for considering arguments alternative to the one we are analysing and evaluating. Some of the alternative arguments may actually provide stronger cases for the conclusion our argument supports. But in other cases, the argument "points in exactly the opposite direction."43 Surely, then, we would expect such counterarguments to raise rebuttals to our main argument. As our considerations on formal dialectic make plain, rebuttals are reasons against the claim being argued, reasons for ~ P , where the main conclusion is P. The premises of such counterarguments then may plausibly function as rebuttals. In terms of structural analysis, Scriven proposes analysing the counterargument separately from the main argument under consideration. He says, "You must set it off as a separate little tree on the side, leading to an implied conclusion which you usually have to add; then you can draw a line back to the main trunk from that implied conclusion."44 I, for one, find this directive unclear. By saying that the counterargument gets its separate diagram on the side, I should expect our representation very schematically to look like this:

Here, diagram for main argument and subargument are not connected at all. How should they be connected? Furthermore, is ~ Ρ the implicit conclusion to which the counterargument is supposed to lead? To begin to answer these questions, let's consider the argument Scriven analyses: One of the most attractive lines of argument that the Democrats have used in order to justify support for a Democratic candidate for President in 1976 is the unfortunate affair of Watergate. But what guarantee do we have that such an event would not have occurred under a Democratic administration? Looking back over the track record of Democratic

Comparison with Other Authors

169

administrations of the past, it is easy to point to example after example of corruption, of political misjudgment, of impropriety and technical breach of the law. This, like other arguments that they have produced, can't really be regarded as having any real significance... 45

Scriven says this example is a fragment of an argument whose main conclusion is "that we should vote for a non-Democrat [i.e. Republican] for President in 1976. Yet Scriven says, "And the conclusion to which the little tree [diagram] leads is, 'The Democrats are unlikely to be any better with respect to Watergate-type occurrences.'" 47 Now this is clearly not the conclusion of the counterargument. How does the counterargument "lead to" this statement or how should it be represented as leading to this statement? Looking at the counterargument in the context of the entire quoted passage gives us some indication of what Scriven means here. Not only is this counterargument considered, it is attacked. Its "rebuttal" of the main argument is countered by the considerations in the second and third sentences. Scriven gives little indication of how these counterrebutting considerations could be represented as rebutting or refuting the counterargument, how they should be added to the overall argument diagram, nor does he indicate how this complex of information should be represented as leading to his alleged implicit conclusion, again namely "The Democrats are unlikely to be any better with respect to Watergate-type occurrences." Scriven does indicate that this statement (and as conclusion presumably the whole counterargument leading to it) should be incorporated into the main argument this way: With the addition of the obviously plausible assumption that either the Democrats or the Republicans are going to win, one can conclude, "Voting Republican should not be ruled out because of Watergate-type considerations," and that conclusion can be fed directly into the conclusion of the main argument, that one should vote Republican. 48

How might all this look on a diagram? Although the conclusion of the counterargument is clear, its premise, obviously, needs reconstruction. But the following seems fair: The unfortunate affair of Watergate shows the Republicans (non-Democrats) distinctly inferior to the Democrats in their ability to govern. Let "W" abbreviate this statement, let "non-D" abbreviate the conclusion of the main argument (we should vote for a non-Democrat), and let "D" abbreviate the conclusion of the counterargument. Let's abbreviate the implicit conclusion Scriven sees the counterargument leading to by "not-B." Letting "E" and "V" abbreviate the two additional statements Scriven supplies, "Either Democrats or Republicans will win," "Voting Republican

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Rebuttals — What is Their Place in Argumentation?

should not be ruled out...," we can schematically represent the situation as Scriven envisages it this way:

Notice that this is only a schematic representation. In particular, it is still unclear how the material attacking the counterargument relates to that argument structurally. Nor is it clear how all this relates to not-B. Furthermore, notice that to get all this material worked into the diagram on Scriven's view involves a good deal of reconstruction. It should be interesting to compare Scriven's approach to this passage with ours. Some reconstruction will be necessary, but it is less extensive than Scriven's. Let's first work up the passage for diagramming. Since the initial sentence indicates the rebutting considerations, let's explicitly cast it in the form of an unless-clause. ^ REASONS FOR non-D ^ So, ^ non-D ^ , unless the unfortunate affair of Watergate shows we should support a Democratic candidate for President in 1976. But

171

Comparison with Other Authors ^

we have no guarantee that such an event would

not have occurred under a Democratic administration.

^

( 2 ) ^ Looking back over the track record of Democratic administrations of the past, it is easy to point to example after example of corruption, ^ misjudgment, > ζ ) ^

^

^

of impropriety ^

technical breach of the law. ^

of political and

This, like other

arguments that they have produced, can't really be regarded as having any real significance... We do not assign a number to the last sentence, since we see it as summarizing the effect of the counterrebutting argument, rather than entering into the argument itself. It is background properly speaking. We may now diagram the argument this way:

Θ Ο

On Scriven's approach, the statement indicating the counterargument had to be reconstructed as an argument. On our approach, we only needed to recast it as a rebuttal. Otherwise, we only had to recast the rhetorical question in the form of the assertion it obviously makes in this context. Notice that we could straightforwardly work in the counterrebutting material. Nor did we have to add any intermediate premises or conclusions. But our diagram is faithful to Scriven's intuition that attacks on a counterar-

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Rebuttals — What is Their Place in Argumentation?

gument may be incorporated into the main argument for a conclusion and may be represented diagrammatically. But conversely the fact that we could obviously correlate what Scriven perceived as a counterargument with what we perceive as a rebuttal, that on both accounts these rebutting considerations can be countered, and that all this should be incorporated into argument diagrams shows that Scriven is aware of both rebuttals and counterrebuttals, and regards them as having a legitimate place in argumentation. By considering counterarguments, Scriven opens up the possibility that rebuttals will not be simply raised in the course of an argument, but actually argued for. Up to this point, we have not considered defended rebuttals because rebuttals on our model are introduced by challengers. Challengers do not make assertions, but raise questions. In an argument, premises and conclusion are asserted. So it would seem that should a challenger put forward some argument for a rebuttal, she would be making assertions and so overstepping her role in the dialectical exchange. Yet, may there not be argumentative texts where our arguer counters some defended rebuttal? Might not some reasoning that this rebuttal is worth worrying about, that it does pose a genuine threat appear in the context of the argument? Might this not raise further issues for an account of argument structure? Scriven's talk of counterarguments certainly suggests that there are such argumentative texts. We shall consider this issue specifically in section three of the next chapter. Scriven considers another type of argument which on the surface appears to involve rebutting considerations. This is a " 'balance of considerations' argument where we say that 1 , 2 , and 3 suggest the conclusion 5, 'despite' 4 (which points the other way)."49 Govier, in A Practical Study of Argument, also considers such arguments, describing them as involving counterconsiderations, points which count against the conclusion of the argument.50 As examples, she cites Although (1) he is fat, (2) he is still a very agile dancer. Notwithstanding the fact that (1) we think of science as impersonal, it is (2) ultimately motivated by the deep personal curiosity and concern for truth.51 Scriven recommends diagramming arguments involving such couterconsiderations this way:52

0_©

• ©_©,

©

Comparison with Other Authors

173

Govier recommends diagramming counterconsiderations as converging on the conclusion, but with wavy rather than straight-lined arrows. 53

Although counterconsiderations share with rebuttals the fact that they count against the conclusion of the argument, counterconsiderations do not function as rebuttals in the overall economy of the arguments in which they appear. As Govier points out, "counterconsiderations do not really weaken the case. "54 Nor does the arguer claim that they weaken the case, that the conclusion follows (with a certain force) unless these counterconsiderations hold. Rather, the claim is that the positive considerations favoring the conclusion completely outweigh these negative considerations. Even though true, we may set aside any reservations they engender. (Notice that arguers admit counterconsiderations as true, as opposed to rebuttals which are frequently mooted as just possible.) Hence, counterconsiderations, if they are elements in arguments, are distinct from rebuttals. However, I question whether counterconsiderations should be counted as elements of arguments. They serve neither to enter into nor to refine, at least in a logical sense, the case the arguer is making for the conclusion. In fact, it is not obvious, at least in some cases, that there is any claim that the counterconsiderations constitute evidence against some statement. Consider Govier's first example. To be sure, as Govier points out, it suggests that there is a contrast between (1) and (2),55 but does it claim that (1) is a reason against (2)? Govier argues that Acknowledging counterconsiderations is very important. It makes explicit the fact that there are pros and cons to questions and that the arguer is an honest person who will admit this. It shows clearly that he takes his " p r o ' factors to outweigh the "cons" in significance, and makes obvious to the audience the fact that this judgment is required if his conclusion is to be accepted. 5 4

I ask—Is the point here mainly rhetorical or logical? Rhetorically, it may be quite important to show your audience your awareness of counterconsiderations, your sensitivity to these issues. It may be very effective to make manifest that the positive reasons you have for your conclusion outweigh these negative considerations. But this does not show that these considerations enter into your argument itself. Hence, one may acknowledge counterconsiderations in the context of an argument without making them part of the argument. They are background material, albeit rhetorically crucial background material.

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Hence, I find Scriven's and Govier's proposals for including counterconsiderations in argument diagrams to be misleading. They represent as a part of an argument what is actually background. Even apart from these consideration, there is something misleading in both modes of representation. Even though (4) is preceded by a minus sign, Scriven represents the whole complex pointing toward (5). This suggests that (4) somehow supports (5). Again, an arrow standardly represents positive support. Negative support, being a reason against, is not some funny kind of positive support, as a wavy arrow is a funny kind of arrow. Hence, I submit that counterconsiderations, though distinct from rebuttals, do not constitute some additional category of argumentative element. One author who has clearly recognized the need for including rebuttals and counterrebuttals in cogent argumentation (although he does not use this terminology) is Jack W. Meiland. In his primer for beginning college students, College Thinking: How to Get the Best Out of College [1981], Meiland devotes several chapters to argumentation, including a pattern for organizing the argumentative essay which clearly calls for including rebuttals and counterrebuttals. Even his very definition of argumentation makes implicit reference to rebuttals: The fimdamenlal idea behind all argumentation is this: a possible reason that survives serious objections is a good reason for accepting the belief in question. To evaluate a reason, one tests it with objections; and if the objections prove to be ineffective against the reason, then one is justified in regarding the reason as a good reason. 57

In discussing how to criticize arguments, Meiland directs students to frame specific possibilities which might count against premises or inferences. For example, against the premise that A person who does not follow his own advice believes that the advice is bad,58 we may conceive the possibility that the person does not follow his own advice because he suffers from weakness of will, not because he believes the advice bad. 59 Anyone who wants to maintain this premise should argue against this possibility. In the economy of the argument, it functions as a rebuttal. Again, one may criticize the argument 1. No one can be considered educated unless he has an understanding of the structure of language. 2. The purpose of college is to educate students. 3. Therefore, all college students should be required to take a foreign language.60 by raising the possibility that a "student can learn the structure of language by studying English."61 Here, we can easily imagine attaching this

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possibility in an unless-clause to the "therefore" in the argument. But, Meiland continues, That is not the end of the matter, of course, because the author of the argument can reply to this objection. The author can, for instance, claim that the study of English does not yield this understanding of the structure of language. 62

But what is this reply, if not a counterrebuttal? In organizing the argumentative essay, Meiland directs his readers first to state and clarify the issue, next to take a stand, and then to present one single argument for that stand. Immediately after giving that argument, one should present an objection to it, i.e. the arguer should consider one or more rebuttals to the inference from premises to conclusion. Again, Meiland sees this as central to the task of argumentative inquiry. In constructing an argument, we seek not just reasons for some claim but good reasons. And we discover whether a reason is good by confronting it with objections. After presenting the objections, one's next task is to reply to them, if a reply is possible. It is interesting to note here that Meiland allows that not only may such replies deny an objection, they may rather admit that the objection is true—or that there is some element of truth in it—but that further considerations hold which render it not a serious objection to the argument. For example, one may argue that college students should study a foreign language in college because such study will let them read in the original great works of literature written in that language. To this one may object that four semesters of language study will not give sufficient proficiency to read such literature. But to this one may reply that although in themselves four semesters of language study are not sufficient for proficiency, gaining such proficiency is an easy step once such basic language training is in place.63 This does not deny the objection or rebuttal, but attempts to neutralize its undercutting force by presenting some further information. After presenting and replying to one objection, an arguer may consider another objection or present another argument for the original claim. He should then subject this next argument to the test of objections and replies. At some point, the arguer must go on to consider objections against the original claim or position, rather than objections against arguments for that position. But this is simply to consider rebuttals to a claim rather than rebuttals to an argumentative move. For can any argument present a successful overall case for its conclusion without replying to these objections to its main claim? So Meiland, in effect, recognizes both kinds of rebuttals we have identified. It is interesting to note that whereas Scriven suggests in effect that some rebuttals will be defended, that we need to consider arguments which reply to or counter defended rebuttals, Meiland actually calls for defending

176

Rebuttals — What is Their Place in Argumentation?

objections to arguments. To the argument that the U.N.is useless because it has failed to prevent conflict, we may object by pointing out specific other missions in which the U.N. has been involved and arguing for their value.64 Again, we could object to the premise that the U.N. has not been able to prevent conflict by claiming that it has prevented conflict in some instances. "To make this objection strong enough to be worthy of being taken seriously, we would have to provide evidence showing that this is not merely a possibility but a fact."65 We shall return to this argument and consider how to represent its structure in the next chapter. Finally, one writer who recognizes rebuttals—though he also does not use that term—and whose diagramming of certain rebuttals is strikingly similar to ours is Stephen N. Thomas. In the chapter on practical decision making in Practical Reasoning in Natural Language, Thomas presents a procedure for "making decisions logically."66 He sees this as an extension of the method of making decisions by comparing the various pros and cons for each possible alternative course of action. In Thomas'procedure, one not only considers pros and cons, but also considers "further reasons that support or oppose the originally-considered pros and cons themselves, as well as other reasons which attack the soundness of these further reasons, or the validity of preceding reasoning."67 Thomas counsels his readers when making a serious decision to first of all gather up all the reasons, pro and con, each alternative. These reasons should be presented in the form of argument diagrams. But instead of constructing for each alternative X a pair of diagrams — one presenting all the pro reasons converging on the conclusion "I should do X," the other presenting all the con reasons converging on "I should not do X" — Thomas advocates combining these two diagrams into one. Here the conclusion is the claim "I should do X." All the pro reasons are represented converging on this statement with solid arrows indicating support, while con reasons also converge on the conclusion, with dashed arrows indicating opposition. Keuoa doing X

for

R e u o a ffZ for dotal X

R e u o n f l ngniiut doing χ

\

'

Reason 02 against doing X

/

I should do X.

From our perspective, by urging the reader to combine pro and con reasons into one convergent diagram, Thomas is treating pro reasons as premises and con reasons as rebuttals. Con reasons are objections to the claim that I should do X. Whatever pro reasons we may give must be

Comparison with Other Authors

177

weighed against the con reasons. Unless they are neutralized, these con reasons should qualify how strong a case we feel the pro reasons make for the conclusion. The con reasons, in effect, are rebuttals. We then should represent the situation this way:

Reuon #1 ifalnRrt doing X Reuon §2 against doing X

Thomas points out that his "way of representing the situation makes it easier to survey the pros and cons in their entirety and assess their combined weight or force later."68 But in representing con reasons as rebuttals, we are further emphasizing that their combined weight is to count against (be subtracted from) whatever combined weight the positive reasons possess for supporting the conclusion. With our rebuttal notation, we are not picturing objections to the course of action as if they were some kind of funny reasons, which Thomas' dashed arrow procedure may suggest. Our diagram reminds the reader of their very different function in argumentation. We feel this contrast becomes especially advantageous when we go on to consider objections to the premises of an argument. For example, Thomas points out that we might question the premise, "Doing X would please George," given the information that George has "often expressed indifference to whether or not X was done."69 On Thomas' system, this could be incorporated into a decision diagram this way:

178

Rebuttals — What is Their Place in Argumentation?

Note how Thomas is getting the main argument and argument involving the objection mixed or amalgamated into one in this diagram. It seems to us that the following is a far clearer way of representing the structure: unless R

© I d> ο Τ ©

Thomas' diagramming notation for considerations against the validity of steps of reasoning as opposed to considerations against other reasons or claims is strikingly like our notation for rebuttals. Against the inferential step from Doing X would please George Pleasing George is desirable to I should do X Thomas frames the attacking consideration, For me to please George by doing X would be, under the circumstances, inappropriate or liable to cause difficulties.™

Comparison with Other Authors

179

Such considerations clearly are rebuttals. Thomas diagrams the argument this way: 71 Doing X would plea·· George.

Pleasing George *

i· desirable.

For m e to p l e u e George b y d o i n g X would b e . under the i n a p p r o p r i a t e or l i a b l e to cause difficulties.

s/ 1 a h o u l d do X.

Again, at points, Thomas considers cases where what we identify as rebuttals are defended, in the course of constructing the decision diagram. This further highlights the need to consider such arguments, which we shall address in the next chapter. We feel we have now demonstrated our point in this section. What in effect are rebuttals (and counterrebuttals) are recognized by a number of authors. Especially in criticizing arguments or developing arguments with maximal cogency, such considerations are crucial. All this provides further evidence for the genuineness of counting rebuttals as a type of argumentative element. At this point, we have distinguished conclusions, premises, modalities, and rebuttals as distinct types of elements in arguments. We have indicated how modalities and rebuttals may function in arguments and how this may be represented diagrammatically. We have also indicated that the premises and conclusion of an argument may appear in any of four patterns: divergent, serial, convergent, and linked. We have in addition indicated how premises may serve as counterrebuttals. Are there any other aspects of argument structure we must consider to get a complete picture of how the elements in an argument fit together? That is the topic of the next chapter.

180

Rebuttals — What is Their Place in Argumentation?

Notes 1. Toulmin, [1958], p. 101. 2. Toulmin et al, [1984], p. 96. 3. Toulmin, [1958], p. 102, italics mine. 4. Toulmin et al, [1984], p. 95, italics in original. 5. Toulmin et al, [1984], p. 95. 6. In [1984], Toulmin et al again proceed to emphasize the functional differences between warrants and rebuttals. In arguments, we may appeal to principles holding generally but not universally. Applying these principles creates presumptions for certain conclusions. But these presumptions can be set aside in unusual circumstances. Such exceptional circumstances are rebutting conditions. 7. Manicas, [1966], p . 85, italics in original omitted. 8. Hart, [1965], p. 153. 9. Hart, [1965], p. 154. 10. Hart, [1965], p. 158n. 11. Toulmin, [1958], p. 102. 12. Toulmin, [1960], p. 58, italics mine. 13. Toulmin et al, [1984], p. 100. 14. Toulmin et al, p. 100. 15. Toulmin et al, [1984], p. 101. 16. If, in fact, there are defeasible concepts with just a finite list of particular defeating conditions, where the proposed pattern is theoretically workable, applying the pattern leads to a further problem. For here some defeasible concepts will be definable according to the proposal, while others will not. So it would seem that the proper reasoning for some conclusions involving defeasible concepts would be structurally quite different than for others. Yet do ordinary arguments for such conclusions present these structural differences? Is this difference of conceived structure contrived by the interpretation? 17. Hart, [1965], p. 154. 18. Hart, [1965], pp. 155-56. 19. Hart, [1965], p. 154. 20. Hart, [1965], pp. 155-56. 21. Hart, [1965], p. 157. 22. Hart, [1965], p . 158, italics mine. 23. See Hart, [1965], p. 162. 24. Hart, [1965], p . 162. 25. Hart discusses this example in [1965], p . 166. 26. Hart, [1965], p. 170. 27. Toulmin, [1960], p. 31. 28. Toulmin, [1960], p . 31. 29. Kuhn, [1970], p. 31. 30. Toulmin, [I960], p. 79. 31. This argument is reported in [1977], pp. 86-87. Johnson and Blair credit it as coming originally from 7tme. 32. Compare Toulmin, [1958], p. 102. 33. In [1984], Toulmin et al make some remarks which corroborate our view. If the exceptions are so frequent that we must continually make allowances for them, we should "take care to make the character of the possible rebuttals explicit." (P. 99, italics mine.) Here Toulmin et al are still referring to these conditions as rebutting conditions. 34. As we shall develop shortly, there can be several, not just one, rebuttal to an argumentative move. In other words, the rebuttal may consist of several rebutting conditions.

Notes

181

35. In the terminology of van Eemeren and Grootendorst, the rebuttal is an expressed opinion, a subject of argumentation, and not a standpoint, an explicit, externalized commitment, positive or negative, to an expressed opinion. (See [1984], p. 5, p. 10.) 36. Toulmin, [1958], p. 18. We shall develop even more explicitly what the challenger is asserting here when we examine rebuttals in the light of formal dialectic in the next section. 37. Compare [1986], p. 321. 38. As arguments with a rebuttal need not also explicitly include a modality, so arguments with both a rebuttal and counterrebuttal need not explicitly involve any modalities. 39. Toulmin, [1958], p. 102. 40. Rescher presents both these moves in [1977], p. 15. 41. Rescher, [1977], p. 15. 42. We shall discuss rebuttals to claims in Chapter 7.2. 43. Scirven, [1976], p. 162. 44. Scriven, [1976], p. 161. 45. Scriven, [1976], p. 161. 46. Scriven, [1976], p. 161. 47. Scriven, [1976], p. 162. 48. Scriven, [1976], p. 162. 49. Scriven, [1976], p. 42. 50. Govier, [1985], p. 152. 51. Govier, [1985], pp. 152, 153. 52. Scriven, [1976], p. 42. 53. Govier, [1985], p. 152. 54. Govier, [1985], p. 154. 55. Govier, [1985], p. 152. 56. Govier, [1985], p. 153. 57. Meiland, [1981], p. 26, italics in original. 58. Meiland, [1981], p. 33. 59. Meiland, [1981], p. 34. 60. Meiland, [1981], p. 36. 61. Meiland, [1981], p. 36. 62. Meiland, [1981], p. 36. 63. See Meiland, [1981], pp. 53-57. 64. Meiland, [1981], p. 40. 65. Meiland, [1981], p. 40. 66. Thomas, [1986], p. 303. 67. Thomas, [1986], p. 304. We should remember that when Thomas uses "validity," he means not only deductive validity, but a spectrum of degrees of support, with deductive validity as the highest degree possible. 68. Thomas, [1986], p. 306. 69. Thomas, [1986], p. 309. 70. Thomas, [1986], pp. 327-28. 71. Thomas, [1986], p. 328. In [1986], the vertical arrow appears dashed (and slanted). We expect the dashed representation is a misprint, since the premises are certainly reasons for doing X. Thomas characterizes his method for representing validity-attacking considerations this way: "A consideration of this sort can be represented by adding a vertical line to the righthand end of a horizontal line, and using a dashed arrow drawn horizontally to the vertical arrow being attacked, to show that it is the validity of the inference, and not the truth of the other reason, that is being attacked." ([1986], p. 327.)

Chapter 7

Further Considerations on Argument Structure

In the last section of the previous chapter, we pointed out that several authors have indicated, implicitly or explicitly, that some arguments may include refutation of other arguments. These other arguments are aimed at rebutting some claim or some argumentative move in the main argument. We also indicated that such arguments raise structural issues which our model may not yet be prepared to accommodate. On our model, the moves which the proponent and challenger in a basic dialectical situation may make are strictly circumscribed. The challenger may only ask questions. She does not put forward or defend theses of her own. She may raise the issue of rebuttals, but she does not claim categorically that these rebuttals hold. Given for all you have shown R holds, how can you be so sure of your conclusion? This does not assert that R holds, nor does it even assert categorically that R is a possibility the proponent must worry about to argue responsibly. It simply raises the issue of R as a rebuttal. It would seem, however, that if there were an argument for R presented in the dialectical exchange, the challenger would put forward that argument. But since, in an argument, premises and conclusion are asserted, this would presuppose that the challenger be allowed to make assertions. That there is argumentation where defended rebuttals are countered strongly suggests, then, that our model of the basic dialectical situation must be enriched to allow the challenger to put forward arguments for rebuttals, and thus, under some circumstances at least, to make assertions. This also raises the issue of how to represent the structure of such argumentation diagrammatically. Even without the considerations of the last chapter, we could raise the issue of whether our model of the basic dialectical situation is rich enough to generate any argument. Not only is the challenger limited to asking questions, the respondent may only make assertions. He does not ask questions of the challenger. Suppose these restrictions were relaxed. Suppose challengers were allowed, at least at certain points in an exchange, to make assertions, and respondents to ask questions, at least under certain conditions. With such moves available, could the participants in a dialectical exchange generate arguments with structural features which could not be

184

Further Considerations on Argument Structure

generated with our circumscribed model? Could we properly diagram such arguments with our system as presently developed? Such considerations would show that our account of argument structure is not yet complete. We may attack this question of completeness from another angle. We may ask whether any current textbook discussions of diagramming use further diagramming procedures beyond those we have presented, and whether these further procedures are necessary to represent properly the structure of the arguments they diagram. If so, then our diagramming procedure needs to be extended, and we might expect our motivating model needs to be enriched also. Looking at the restrictions on our model and looking at actual textbook diagramming procedures are two approaches to the question of whether our account of argument structure is complete and if not, how it must be extended. We shall consider each approach in turn in the third, fourth, and fifth sections of this chapter. That our system must be further developed is our main contention. First, however, there are some preliminary issues, points of clarification, which we must square away.

7.1. MIXED STRUCTURE

As should be obvious, our challenger need not ask just one of the basic dialectical questions in a given situation. Each time the proponent answers, the challenger may ask a further question, concerning the answer just given or concerning some previous answer. And each time it is her turn to ask a question, the challenger may ask a different basic dialectical question. The resulting arguments, then, will have a mixture of the structures these various questions generate. We can easily imagine such structural combinations, and texts in informal logic are replete with many examples of arguments having mixed structure. We should note here that as there may be a number of arrows in an argument diagram, so there may be a number of different modalities of various strengths and a number of occasions on which questions of rebuttal are raised and premises given in counterrebuttal. The diagrams of such arguments will be quite complex, but the arguments themselves will be complex. The complexity of the diagram just reflects the complexity of the argument being diagrammed. Such complexity, however, should make us acutely aware of a significant theoretical issue: Just when do we have one argument and when do we have more than one? Our dialectical model presupposes that one argument grows through a series of challenge and response exchanges. It presupposes that the proponent's later responses extend an argument already begun, rather than constitute a new, numerically distinct argument. This brings us to the question of argument individuation, which we address in the first section of Chapter Eight. However, as long as we agree that arguments can be developed by this dialectical procedure, so that successive questions

Mixed Structure

185

extend an argument already begun rather than generate new arguments, we must be prepared to countenance complex arguments, sometimes arguments of great complexity. The following argument, adapted from Aristotle's Nicomachean Ethics, illustrates the complexity we can deal with at our current point of development:1 Q

^

It is very characteristic of friendship that friends

live together. ^

Now that ( 2 )

^

One cannot live with

many people and divide oneself up among them ^ plain, because

^

time together ^

is

Living together requires spending

and

^

difficult to have enough time. ^

With large numbers, it is Further

© < A

person's friends must be friends of one another, if they are all to spend their days together; ^

and ( ό ) ^

It is

a hard business for this to be fulfilled with a large number. ^

Q

^

It is found difficult, too, to rejoice

and to grieve in an intimate way with many people, for ( δ ) ^

^

It may happen that one has at once to be

happy with one friend and mourn with another. ^ Hence, apparently, unless one is both very flexible and has a large circle of acquaintances which by good fortune are unusually compatible and undemanding,

^

impossible to be a great friend to many people. ^ ^

It is

But CIS)

Even if one is very flexible, there is no guarantee that

he shall remain so, ^ and C C D < Even if he has the good fortune to have a large number of acquaintances which are very compatible and undemanding, there is no guarantee that these acquaintances will remain compatible, ^ years. ^

for

CS)

^

People change

Presumably, then,

COD

^

over

the

It is well not

Further Considerations on Argument Structure to seek to have as many friends as possible, but as many as are enough for the purpose of living together.

Ο presumably

ΊΓ ©

^

Rebuttals to Claims

187

7.2. REBUTTALS TO CLAIMS

Our account of rebuttals allows that we may entertain rebuttals not only to inferential moves from premises to conclusions, but also to claims themselves, be they premises or conclusions. A challenger may pose an objection not only to an argumentative move, but to a statement asserted in the argument. Both Meiland and Thomas draw a distinction between objections to claims, reasons against reasons (and conclusions), and objections against arguments, reasons against the validity of other reasons. Yet we count both types of objections as rebuttals. We should defend, then, why we have just one category of argumentative element here, rather than two. Furthermore from the perspective of the Toulmin model, it may seem odd to speak of rebuttals to claims rather than rebuttals to arguments, moves from premises to claims. For Toulmin, rebuttals attach to and so qualify or modify modalities, which indicate the strength or force warrants in particular confer on claims. We have one principal reason for counting objections to claims as rebuttals in addition to objections to arguments. We see both sharing the same function in the overall economy of an argument. If a challenger raises a plausible, significant objection to an argumentative move, then the force of that move is qualified if not altogether undercut until and unless the proponent successfully replies to that objection. To continue that argument without replying to the objection would ordinarily leave the argument qualified. But to challenge a statement, be it either the main conclusion of the argument or some premise, is to ask bothfor an argument for that claim and that whatever argument be proffered speak to that objection. As with objections to inferential moves, any argument for the claim would be somehow qualified if it did not met the objection. Hence the issue of rebuttals can arise right at the beginning of arguing for some assertion, even before the proponent has given any reasons to support his conclusion directly. In effect, the challenger poses an objection, rebuttal to any argument the proponent may offer, unless, of course, that rebuttal can be set aside. This is recognized explicitly in formal dialectic through the move of provisoed denial. We can readily identify the rebuttals in such attacks. PROPONENT:

The Senator is sure to be nominated for President next

year. CHALLENGER:

HOW do you know he doesn't have sexual peccadillos which will come to light?

The opponent's challenge can be obviously recast in the form of our rebuttal introducing third ground adequacy question, patterned after provisoed denial:

188

Further Considerations on Argument Structure

CHALLENGER:

Given that for all you have shown the Senator does have sexual peccadillos which will come to light, how can you be so sure?

Representing objections to claims as rebuttals in addition to objections to inferential moves has a distinct advantage. It lets us readily analyse arguments instancing a distinctive type of argument strategy without adding any further structural machinery. In considering questions of fact, there may be several distinct viable possibilities as to what event occurred or what might explain a certain event. Similarly, in considering questions of policy, there may be several distinct courses of action open for serious consideration. One way of supporting a particular alternative — for arguing that one event and not some possible alternative happened, that one causal hypothesis is the best explanation, that one particular policy deserves endorsement — is to argue against its alternatives. In Logical Self Defense, Johnson and Blair call this strategy attacking alternative positions.2 In formal disputation, we may see such arguments arising as responses to provisoed denials. Instead of the challenger asking "Why C(laim)?" as her first question, she asserts " ~ C/A and that A holds for all you have shown." Here "A" may stand for several different alternatives to be considered. In effect she is asking the third ground adequacy questionGiven for all you have shown at least one of alternative(s) A,, A2, ..., \ holds, how can you be so sure, how do you know that C, the alternative you are supporting? The dialectical question shows these alternatives serving the role of rebuttals in the argument, the answer serving to supply one or more counterrebuttals. In an argument using this strategy exclusively, all the premises would be either counterrebuttals or statements supporting counterrebuttals. But our machinery for argument structure is already equipped to handle arguments with this strategy, which is really a special case of arguments involving rebuttals and counterrebuttals. Given this, that such arguments are important enough to merit identification as a distinctive strategy underscores the importance of rebuttals and counterrebuttals as elements of argumentative analysis.

7.3. ARGUMENTS COUNTERING DEFENDED REBUTTALS

The Need to Expand Our Concept of a Basic Dialectical

Stiutation

In the last section of Chapter Six, we pointed out that both Scriven and Meiland indicate the need for considering arguments which include defended rebuttals, arguments which incorporate somehow arguments for rebuttals directed against some claim or inferential step in the main argument. We

Arguments Countering Defended Rebuttals

189

have pointed out that at present, our dialectical model does not seem to generate such arguments. This is because the subargument for the rebuttal would be presented by the challenger. This would require the challenger to assert claims rather than just to ask questions, which is proscribed by her challenger role. But that challengers would, on occasion, want to defend the rebuttals they raise, or be required to defend their rebuttals, is a good reason for thinking that our rules governing the type of contributions proponent and challenger may make in a dialectical exchange are drawn too strictly. Why would a challenger want to defend a rebuttal? Why might it be incumbent on her, from a logical point of view, to give such argumentation? Our challenger might be quite concerned to show that the rebuttal was at least plausible, that it was worthy of enough consideration to be countered. Jack Meiland presents specific examples in College Thinking. Here is one adapted to our dialectical format: PROPONENT: CHALLENGER: PROPONENT: CHALLENGER:

Liberal arts colleges should require at least intermediatelevel proficiency in a foreign language. Why do you say that? Studying a foreign language broadens a student's mind by teaching other perspectives and cultures. But don't other subjects, history being a prime example, provide a much more effective way to learn about other cultures?3

Is this objection, as it stands, very strong? As Meiland points out, it amounts to little more than an unsupported claim. The author must say something to show us that history is a much more effective way to learn about other cultures. Without this, the statement gives us no reason for doubting the argument. 4

Might not our challenger want to defend her objection to show that we do have genuine grounds for doubting the argument? Even if she did not, wouldn't it be appropriate for our respondent to ask the challenger at this point why she thinks other subjects do or might provide a more effective way to learn about other cultures? Isn't the prohibition on the respondent's asking questions artificial at this point? Conversely, isn't the burden of proof on the challenger to assert some reason for her objection, rebuttal? Shouldn't she be allowed to add After all, in history we may proceed directly to studying other cultures, their perspectives and world views, without devoting the significant amount of time to the mechanics — grammar, syntax, and vocabulary — that learning a foreign language requires.

190

Further Considerations on Argument Structure

Especially if the challenger believes she has a solid objection against the claim the respondent is arguing, solid because she can support her objection with reasons, shouldn't she be allowed to present her argument? Some might counter that to prevent her doing so is to vitiate the concept of argument! In "Interactive Argumentation: Ideal and Real" [1987], Richard Hirsch claims In the ideal, argumentation will be characterized as attempted refutation.... When testing a claim a counterclaim is presented backed up by a set of premises. This counterclaim is conceived of as being at least incompatible with the initial claim and, therefore, if a better case can be presented for the counterclaim, then the initial claim is refuted. j

Meiland presents a further consideration showing the importance of defending objections, of conceiving it possible for challengers to defend their rebuttals, in his rationale for developing arguments. When arguing, we want not just to give reasons for some claim but to give good reasons. We test to see whether an argument offers good reasons by bringing objections against the argument and seeing whether they can be met and how successfully. Hence we may need to show that the objections considered are strong objections and this means we need to present reasons indicating why those objections might hold. Let us agree then that in a dialectical situation, when the challenger has introduced some rebuttal through asking the third ground adequacy question, the proponent may respond not only by offering some counterrebuttal but by himself challenging the challenger to defend that rebuttal, or at least the claim that the rebuttal is plausible enough to constitute a threat to his argument meriting consideration. To this question, the challenger may then respond by presenting an argument for her rebuttal. The challenger's asking the third ground adequacy question raises the possibility of switching the proponent and challenger roles in a dialectical exchange. Once the challenger asks this question, the proponent has the option of switching the roles. He now asks the questions, seeking to draw out the most cogent argument possible from the challenger for her rebuttal; the challenger responds with assertions. This role reversal continues until either the challenger completes her argument, resigns her attempt to defend the rebuttal or its plausibility in the face of the proponent's challenges, or until the proponent himself asks the third ground adequacy question and the challenger exercises the option to re-reverse the roles. Diagramming Arguments Calling for Defended Rebuttals As a proponent may very well want to ask a challenger to defend a rebuttal in the argumentative process of a dialectical exchange, so in composing an argument as product, an arguer may want to indicate that a rebuttal is questionable. In fact, indicating such questionability may be a sufficient

Arguments Countering Defended Rebuttals

191

counterrebuttal. A rebuttal might be conceivable, a number of persons might entertain it, but when thinking critically about the issue, there may be little reason to regard the rebuttal as a serious threat to the argument. For example, Intensive sex education, together with making clean needles available free to drug addicts, may curb the spread of the AIDS epidemic, for AIDS is transmitted by sexual intercourse or injection directly into the blood stream, e.g. by contaminated needles. Unless, that is, AIDS may be transmitted through casual contact. But what evidence is there that AIDS is spread through casual contact? Here the arguer entertains a popular suspicion about how AIDS is transmitted, a suspicion that would function as a rebuttal to his premise. But he counters this by asking for evidence for the suspicion. Until there are some grounds for the suspicion, until there is some evidence for it, it does not constitute a significant objection to the premise, one the arguer need worry about. By calling it into question, the arguer undercuts, counters its ability to undercut the argument. In effect, the arguer is countering this rebuttal with a cautious denial. "For all that has been shown, ~ R . " "Why R?" That is, in the symbolism of formal dialectic, " f ~ R . " It is certainly quite conceivable that the arguer might want to counter the rebuttal R with a provisoed denial, ~R/S & |S. These questions clearly call for argument, even though none may appear in the argumentative passage. The arguer may be content that merely calling the rebuttal into question counters it. How may such questions be incorporated into argument diagrams to show their counterrebutting function? We propose that the most perspicuous way is to represent them in counterrebutting position, and to avail ourselves of the symbolism of formal dialectic to make manifest their connection with the rebuttal. This entails that besides writing out some indication of each rebuttal in the rebuttal box, we should label each rebuttal R, R,, R2, .... We can then readily represent the cautious or provisoed denials of whatever rebuttals are so denied in the argumentative passage. Thus numbering the component statements in order in our above example, and labelling the one rebuttal with "R," we have

192

Further Considerations on Argument

Structure

θ I unlen It: AIDS brtn emitted through casual contact

1

I ο Similarly, should the arguer reply to R with a provisoed denial, questioning whether R holds (or is a plausible alternative) because for all we know S does, we have < S > T - 0

1UÜCBB R' AIDS transmitted through caiual contact

>u

Θ I Ο Of course, an arguer may question rebuttals to inferential moves just as well as rebuttals to premises. The only difference here is the positioning of the rebuttal box. In general, then, we can have arguments questioning rebuttals looking like this for simple questions (cautious denials),

Arguments Countering Defended

Rebuttals

193

T~R

I unless

R

vk

0 and mutatis mutandis for provisoed denials. Diagramming Arguments with Defended

Rebuttals

So far, we have considered the structure of arguments where the proponent deems his questioning of a rebuttal sufficient to counter it. But proponents in composing arguments as products may very well want to consider defended rebuttals, to present arguments defending these rebuttals in the course of developing their main overall argument. Analysing the structure of such arguments raises four questions: How are arguments defending rebuttals to be identified? How are they to be represented diagrammatically? How are these counterarguments integrated into the main argument? How should this integration be represented? We shall consider each question in turn. In the dialectical process of generating an argument, challengers defend rebuttals. In composing arguments as products, a single arguer may mark such counterarguments explicitly with phrases such as "We may object that..." or "An objection to this argument (position) is that...." How, then, may we incorporate these arguments for rebuttals, reasons for objections into our argument diagrams? Such reasoning, in effect, constitutes a separate argument which we may diagram alongside the main argument. 6 Nothing that we have seen so far suggests that the reasoning for the rebuttal, as an argument, involves any structural novelty beyond the argument patterns we have examined so far. However, for maximum diagrammatic perspicuity, we should indicate that this argument has a different status from the main argument. The proponent has not simply

194

Further Considerations on Argument Structure

ended one argument and gone on to another. His purpose is ultimately to counter the objection contained in this argument. To indicate its status, then, we use dashed rather than solid arrows. 7 Thus, if one argues8 Mrs. Wilson has disinherited her daughter because her will leaves the daughter only $1.00; unless, of course, she wasn't mentally competent at the time she made her will. But, one may object, wasn't Mrs. Wilson mentally incompetent at the time she made her will? After all, when she drew up the will, she had been suffering from Alzheimer's disease for many years, her condition becoming steadily worse we can diagram the argument this way:

unices menially incompetent when m a k i n g will

We have numbered the component statements in order of their appearance. The " = R" in the circle enclosing "3" indicates that this statement has been entertained as a rebuttal in the main argument. How does the supporting material for the rebuttal function in the overall economy of the main argument? How is this counterargument a part of the main argument? How is it integrated into that argument? To answer this question we must ask how arguers may reply to the objections these defended rebuttals pose. As rebuttals typically call for counterrebuttals, so these objections call for replies. As we have seen, there are two ways to counter a rebuttal: We may either deny that the rebuttal holds or claim that some further condition also holds which undercuts the force of the rebuttal. These again are stances open to someone seeking to reply to a defended rebuttal. But notice that in the light of the challenger's argument, the proponent's simple denial that the rebuttal holds is not an adequate or appropriate reply. The challenger has presented an argument and it is incumbent on the proponent to respond to that argument. Even defending the denial of the rebuttal with argument, giving an argument for this counterrebuttal, may fail to respond directly to the challenger's argument. Although this approach may even satisfy a rational judge, for the proponent's argument for the counterrebuttal may be a better argument than the challenger's case for the rebuttal, we still do not have a reply directed at the challenger's argument. What is called for is a critical attack on that

Arguments Countering Defended

Rebuttals

195

argument. The purpose is to defeat whatever presumption the opponent's argument creates for the rebuttal. Now such an attacking argument may also be an argument against the rebuttal, an argument to show that this rebuttal does not hold. By pointing out defects in the objecting argument, w e may be able to construct a case, and claim we are constructing a case, against the rebuttal. In particular, by pointing out that the premises of the objecting argument are false, that to the contrary certain incompatible statements are true, one may give a case for the denial of the rebuttal. Consider the following argument, adapted in part from Meiland: I maintain that the U . N . should be disbanded because it has been unable in general to prevent conflict and war around the world. One might object that the U . N . has been able to prevent certain conflicts. 9 For U . N . peace keeping forces ended the border fighting between Tyra and Sidonia, U . N . negotiators brought about a cease fire in the Volta War, and they have prevented armed conflict in the Equatorian crisis. I reply that the U . N . has not been able to prevent even particular conflicts, certainly not these. For fighting ended between Tyra and Sidonia because the troops ran out of ammunition; internal political problems ended the Volta War; and pressure from allies contained the Equatorian crisis. The objection presents three premises to support the claim that the U . N . has been able to prevent certain conflicts. Each of these premises, imputing successful agency to the U.N. in resolving some conflict, is an interpretation, rather than a straight description of fact. 10 Each, then, may involve an element of controversiality and none is defended in the objection. The arguer attacks each in turn by presenting a contrary interpretation, claiming that each converges to support the denial of the claim that the U . N . has been able to prevent certain conflicts. The arguer replies to the objecting argument by denying each of its premises in an argument supporting the denial of its conclusion. The structure of the argument looks like this:

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Further Considerations on Argument Structure

οφρ j

ο

I

i j ψ ^

nnnnlleeiiii UN ha α been able

.

to prereat certain

S=R )

particular c o n f l i c t ·

Ο We have an appropriate reply to the objection because each point made to support the rebuttal is countered in turn. This is made perspicuous in our diagram by indicating which premise for the rebuttal each basic counterrebutting premise attacks. The arguer's attack need not establish or give evidence directly that the rebuttal does not hold, however. The arguer need not accept the burden of proof for showing the rebuttal false. To argue that certain reasoning for a conclusion is not logically cogent is not to argue that the conclusion is false. We thus have a third type of counterrebuttal here. Instead of claiming that the rebuttal is false or indicating that its force is undercut by some further condition holding, the proponent attacks the argument for the rebuttal. This means that the rebuttal itself may very well not pose a serious objection to the main argument. If the challenger herself had to provide an argument to show that the rebuttal posed an objection worthy of consideration, and that argument is not cogent, how much of an objection is her rebuttal? In all of these cases, then, the intent is to counter the force of the rebuttal as an objection to the main argument. Of course, a proponent may reply to the challenger's argument by not contesting it, perhaps even conceding the rebuttal in the light of the argument, but contending that some further condition underlies the force of the rebuttal. Here there is a reply to the objecting argument, although it does not take the form of an attacking argument. This is appropriate, for the supporting argument may have sufficient weight to establish a presumption for this rebuttal. For example, here is a second adaptation of Meiland's U.N. argument:

Arguments Countering Defended

Rebuttals

197

I maintain that the U . N . should be disbanded because it has been unable to prevent conflict and war around the world. One might object to this argument that the U . N . has other valuable missions besides conflict resolution and peace keeping. For the U.N. is involved in other missions, such as refugee relief. Surely these activities are valuable, for they relieve genuine human suffering and remind the world community of human vulnerability and the need to show compassion. Now I admit that the U . N . engages in other valuable activities, but the raison d'etre of the U . N . is prevention of war and conflict. That is, if it fails in this mission, it fails. I stand by my argument." Here the arguer's reply in the last paragraph concedes the defended rebuttal, but counters it with a further claim intended to undercut its rebutting effect. Numbering component statements in the order in which they occur, we represent the structure of the argument this way:

unlnn UN hAB othfT valuable ralmrinn«

So far, none of these replies to defended rebuttals have introduced much which is new to our account of argument structure or its diagramming. The only modification has been to add certain information to how statements are indicated in the diagram, making it more perspicuous how certain counterrebutting premises were related to the objecting argument. But both types of reply we have examined so far are special instances of our two basic types of counterrebuttals, denying a rebuttal or alleging that some further condition holds which undercuts it. However, we have indicated that in attacking an objecting argument without attacking or denying its conclusion, simply attacking its cogency, we have a third type of counter-

198

Further Considerations on Argument Structure

rebuttal. Does this introduce new structural considerations? How might the cogency of such objecting arguments be attacked? In his attack, the arguer may charge directly that the argument fails either because of the premises' being unacceptable, their lacking relevance to the conclusion, or their having inadequate weight. Alternatively, he may attack the argument by presenting a logical analogy intended to manifest the argument's fallaciousness. One might argue that refutations by logical analogy are special instances of showing the premises irrelevant to the conclusion. However, such arguments have very interesting structural features which a simple charge of irrelevant reason need not have. We shall consider direct attacks first, and then refutations by logical analogy. In directly attacking the cogency of an objecting argument, our proponent will typically either contradict or question a premise, point out that a particular premise is irrelevant to the conclusion, or question the adequacy of the premises to support the conclusion. The latter could take the form of a question — Is this all the evidence there is?12 — or of a rebuttal to the objecting argument — a rebuttal which the proponent not only moots but asserts. In each case, the intent is to show the objecting argument not cogent and thus to undercut its force, and thus the force of the rebuttal it supports to compromise or undercut the force of the main argument. What would arguments involving such attacks look like? Let's return to the Wilson will argument (See Page 194). The objecting argument claims that Mrs. Wilson was mentally incompetent at the time she drew up her will, because at that time she had been suffering from Alzheimer's disease for many years. But suppose the proponent replies that Mrs. Wilson made her will eleven years ago, before the onset of Alzheimer's disease. Although this may suggest that Mrs. Wilson was mentally competent at the time she made her will, the denial of the rebuttal, it does not claim that outright. It certainly does contradict the premise given to support this rebuttal. Its force is just to show that no reliable evidence has been given for the rebuttal. It is put forward then to knock out the argument for the rebuttal, and so to neutralize its rebutting force. We might say that its knocking out the objecting argument constitutes a counterrebuttal. How should we represent this diagrammatically? This counterrebuttal is an integral part of the overall main argument. Since it indicates that the objecting argument is not cogent, it incorporates that argument via the denial of its cogency into the main argument. We may represent that the objecting argument is not cogent by enclosing it in a box and crossing out the box, viz:

Arguments Countering Defended Rebuttals

199

That the assertion contradicting the premise gives a reason for this denial of cogency may be represented just as any statement's giving a reason for another may be represented. For greater perspicuity, however, we may explicitly indicate that the replying statement in effect denies the premise.

I

This whole complex then may be entered into the diagram for the main argument in counterrebuttal position. Since in this type of reply, the objecting argument is actually incorporated into the main argument, there is no need to represent it separately on the side.

200

Further Considerations on Argument Structure

Θ >* unleai mentally Incompetent w h e n m a k i n g will \ f

Ο How might a proponent attack an objection on the ground of relevance? Let's consider an instance adapted from a classic example of the fallacy of irrelevant reason in Johnson and Blair's Logical Self Defense:13 I maintain that Kellogg's Corn Flakes should be banned, because this cereal contains high levels of preservatives dangerous to human health. Now some may object that Cora Flakes is good, nutritious food. After all, don't we put milk on our Corn Flakes when we eat them? But what does putting milk on your Corn Flakes have to do with the Corn Flakes being nutritious? (i.e. Milk doesn't have anything to do with Corn Flakes' being nutritious. Milk is irrelevant to the nutritional value of Corn Flakes.) The argument for the rebuttal which constitutes the objection is directly attacked on the ground of relevance. Notice that here the respondent does not claim outright that Corn Flakes is not a good, nutritious food, although this may certainly be suggested and seems in accord with his intentions. But we need not supply such a statement to diagram the argument. We can see the counterrebuttal as the claim that the challenger's premise is irrelevant

Arguments Countering Defended Rebuttals

201

to her conclusion, and so her argument is not cogent. Diagrammatically, we may represent the reasoning parallel to the previous argument:

>u

unless Corn Flakes is good nutritious food

(4) is the statement that we do put milk on our Corn Flakes, the obvious, intended answer to the rhetorical question asked in the second paragraph. Again, for perspicuity, we indicate what statement (5) is in relation to the objecting argument it attacks. We have last to consider replies which attack the ground adequacy, the weight of the objection. The structure of a reply which attacks an objection on the basis of giving too little information would be parallel to the two replies we have just examined. However, a reply which advanced a rebuttal to the objecting argument would involve a further structural feature which we have not yet seen. Consider: The Democrats will win the next election because the Republicans have made a number of mistakes in office, and after this many years people are just plain tired of them. One may object that the Democrats are totally fragmented. After all, six candidates are running and none has anything close to a majority.

202

Further Considerations on Argument Structure But it is far too early in the electoral process for this to be meaningful.

This reply asserts a rebuttal to the objecting argument. Six candidates running with none emerging from the pack may be a prima facie good reason for saying the party is fragmented, but not so early in the election process. Although the arguer may not want to claim outright that the Democrats are actually not fragmented, the outright denial of the rebuttal, he certainly claims that we have no good reason to accept this view. Hence the force of the rebuttal is undercut. We can diagram the argument by first representing the reply as a rebuttal to the objecting argument.

unless

Θ—ι—Θ

6

But since that reply is asserted, and since this assertion constitutes the evidence indicating the objecting argument is not cogent, we incorporate all this into the main argument, in a manner parallel to our previous two cases:

See Figure Next Page Hence, by extending our diagramming machinery, we can represent the structure of arguments involving counterrebuttals which directly attack the cogency of an objecting argument for a rebuttal. Above we have also indicated that the counterrebutting reply can take the form of a refutation by logical analogy. Not only do such refutations involve interesting structural features, they may be offered as arguments in their own right, independently of an attempt to reply to an objecting argument. Hence, they merit consideration on their own right.

Rotations

by Logical

203

Analogy

Θ 1 unless β

1

0

©

i unless Democrats are fragmented

Ο 7.4. REFUTATIONS BY LOGICAL ANALOGY

In his Introduction to Logic, Irving Copi characterizes a refuting analogy as "an argument of exactly the same form or pattern as the given argument, but whose premisses are known to be true and whose conclusion is known to be false." 14 This characterizes refutations by logical analogy for deductive arguments. The refuting analogy has exactly the same form but is invalid. So the original argument is invalid. Copi indicates that we may also have refutations by logical analogy for inductive, non-demonstrative arguments. His definition would obviously have to be modified, since correctness for non-demonstrative arguments is not simply a matter of form. But Copi does not characterize, except by example, what is involved in a refuting analogy for an inductive argument. Yet such arguments present very interesting macrostructural features. Consider: Mrs. Perry's own conclusion is that the insanity was not faked but that he [the psychiatrist, Harry Stack Sullivan] had in fact committed a criminal act, a conclusion she defends by pointing to his unmistakable empathy for youthful offenders as well as for psychotics. Using the

204

Further Considerations on Argument Structure same logic, however, one might also conclude that he was black and female: he was the first social scientist to champion field research on the effects of discrimination on black youth, and a rock of respectful support for intellectually gifted women like Clara Thompson, Ruth Benedict, Hortense Powdermaker, Karen Homey, Frieda Fromm-Reichmann, Margaret Bourke-White, and Katherine Dunham. —Barbara Lerner, Review of HELEN SWICK PERRY, Psychiatrist of America: The Life of Harry Stack Sullivan. Commentary, (August 1982).15

Mrs. Perry's argument is under attack. How has she reasoned? We may accept that Harry Stack Sullivan committed a criminal act while insane, because he had an unmistakable empathy for youthful offenders as well as for psychotics.

How does Barbara Lemer attack this argument from (2) to (1)? She identifies, albeit implicitly, the material inference rule apparently used in passing from (2) to (1) and shows that this rule is unreliable. She does this by in effect constructing two arguments employing this inference rule, each of which has a true premise and false conclusion. How do we get from (2) to (1)? It seems that the principle of this inference, its warrant, could be expressed this way: Given that X has an (unmistakable) empathy for members of class C, we may take it that X is a member of class C or has the defining attributes of class C. As Ms Lerner points out, we may use this inference rule to argue: (3) Sullivan was black because (5) he was the first social scientist to champion field research on the effects of discrimination on black youth. (4) Sullivan was a woman because (6) he was a rock of support for [certain] intellectually gifted women.

Refiitations by Logical Analogy

205

Ms Lerner vouches for premises (5) and (6). She takes it that (3) and (4) are known false. This is to show that the inference rule behind these two arguments is fallacious. Notice that Ms Lerner is in effect claiming that because we can argue fallaciously from (5) to (3) and (6) to (4), Mrs. Perry's argument from (2) to (1) is refuted. The fallaciousness of certain arguments as a whole is evidence for the fallaciousness of another argument. We might then represent the macrostructure of her reasoning this way (at least its manifest macrostructure):16

But this leaves out something indicated by the phrase, "using the same logic." Our diagram does not show that all three arguments use the same (material) inference rule. Yet this is the key, together with recognizing the patent fallaciousness of the two analogous arguments, to seeing that we have a refutation by logical analogy here. Hence, we propose indicating that all three arguments use the same inference rule right in the diagram. Since Toulmin has already made "warrant" current in discussion of macrostructure and since warrants are inference rules — material inference rules at least — let us refer to the inference rule by "W." Let us attach "W" to the arrow on the right hand side, to indicate that it is the principle behind that inferential move. Our diagram then looks like this:

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Further Considerations on Argument Structure

Ms Lerner is arguing that because we can argue from (5) to (3) via W and from (6) to (4) via W, the argument from (2) to (1) via W is fallacious and should be rejected. Our diagram represents the structure of this argument. We may also have refutations by logical analogy where instead of presenting an analogous argument, the arguer presents one or more statements which constitute a counterexample to the material inference rule. For example, This argument asserts that 18-year-olds, being old enough to fight, are old enough to vote.... Army mules and police dogs are used to fight: nobody is interested in giving them the right to vote. This argument rests on a false analogy. —Richard M. Weaver, "A Responsible Rhetoric." The Intercollegiate Review, Winter 1976-77.17 What inference rule does Weaver perceive the argument he is refuting to be using? We may phrase it this way. W:

From the fact that X is a living being that can be used in a military fight [X can fight], we may take it that X should have the right to vote.

Refutations by Logical Analogy

207

Although the third and fourth statements in themselves do not constitute an argument, they do constitute a counterexample to W. By asserting them in this context, Weaver argues that the voting argument is fallacious. We may display the structure this way:

We link (3) and (4), since we need to take the two statements together to see that we have a counterexample to W. In this way, then, we may diagram refutations by logical analogy of arguments which proceed by material inference rules. This may obviously be extended to arguments with formal inference rules. We simply let W stand for the inference rule in the deductive argument being refuted. One might object that our diagramming procedure violates one of our desiderata for argument diagramming, since we have to supply the material inference rule. In general, to understand what W stands for, we have to phrase this warrant in our own words. Neither the argument being attacked nor the refuting analogy states this principle explicitly. Why then should we explicitly require supplying it to diagram a refutation by analogy? Does that compromise our principle that we should not need to supply elements to complete our argument diagrams, that we should be able to diagram arguments as manifestly stated? I believe we have already met this objection in justifying why we should explicitly display the warrant. Remember that the phrase "using the same logic" introduced our first refuting analogy. Copi points out that in addition such phrases as "the same argument proves," "this is about as

208

Further Considerations on Argument Structure

logical as arguing that," "I could use the same reasoning to claim that," "the same methodology would lead to the conclusion that"18 signal refutations by logical analogy. In all these cases, I believe we need to ask why the refuting argument uses the same logic, is the same argument, reasoning, or methodology, or is as logical as the argument allegedly being refuted. And in each case, the answer is that the original argument and the refuting analogy use the same warrant, or the refuting analogy is a counterexample to the original warrant. If someone gives a premise to support some conclusion, especially if he marks this with a logical indicator, we do not need to supply a warrant to see how this argument hangs together. On the other hand, to appreciate how refutations by logical analogy hang together, it is certainly helpful to make the warrant being attacked explicit. Certainly, should we evaluate a refutation by analogy, we should want to judge whether the arguer putting forward this refutation had correctly or fairly abstracted the warrant from the argument he is allegedly refuting. So far, the refutations by logical analogy that we have seen do not refute arguments presented to defend rebuttals. The goal of the arguments we have presented has simply been to show some argument not cogent. But we can certainly imagine such refutations put forward to counter arguments defending rebuttals. As we said above, refutations by logical analogy may in effect be ways of charging irrelevant reason, or ways of sustaining such a charge. It is in the light of inference rules that we see premises relevant to conclusions. Should then the principle of an inference be shown unreliable, that would be significant prima facie evidence that the premises of that inference were not relevant to its conclusion. Let us then reconsider our argument involving charge of irrelevant reason. (See Page 200.) Instead of simply charging irrelevant reason via the rhetorical questions "What does putting milk on your Corn Flakes have to do with the Corn Flakes being nutritious?" one could counter the rebutting argument We put milk on our Corn Flakes when we eat them, so Corn Flakes is good, nutritious food by replying By the same reasoning, we could argue that a heap of sawdust with a golden ring on it is valuable. Here, we have abstracted the following warrant from the rebutting argument: W:

Given that X has Y on it and Y has value, we may take it that X itself has value.

Refutations by Logical Analogy

209

Clearly then, where HS refers to a heap of sawdust which has a golden ring GR on it, we have (a) HS has GR on it. (b) GR is valuable. as premises even though unstated. Hence, letting "5" number the statement "A heap of sawdust with a golden ring on it is valuable," the structure of the entire argument looks like this:

unless Corn. F l a k e s is g o o d , n u t r i t i o u s food

So refutations by logical analogy may function as counterrebuttals, showing arguments defending rebuttals not to be cogent. Conversely, refutations by logical analogy are not the only arguments which simply refute given arguments, where the arguments being refuted are not put forward to defend rebuttals. Consider again Scriven's

210

Further Considerations on Argument Structure

argument which suggested the issue of defended rebuttals presented in Chapter Six. (See Page 168) Simply given the passage presented there, and construing the first sentence One of the most attractive lines of argument that the Democrats have used in order to justify support for a Democratic candidate for President in 1976 is the unfortunate affair of Watergate. as presenting an argument, we have in this passage just an argument which attacks another argument. In the passage itself, we do not see that the conclusion of the attacked argument functions as a rebuttal. The arguer here charges the Democrats' argument with hasty conclusion. We may diagram the attacking argument this way:

That there are arguments which simply refute other arguments also indicates that the rules governing exchanges in basic dialectical situations need to be expanded further. In attacking an argument, one is basically playing the challenger role. But one is playing it in a distinctly different way from what we have seen so far. Up to this point, the challenges have all been constructive. The challenger's intent was to draw out the best possible argument from the proponent. Even when herself arguing to defend

Refutations by Logical Analogy

211

rebuttals, the challenger's aim is to show the proponent that the rebuttal is serious enough to merit countering. But here, where the challenger attacks the argument, her aim is "destructive." We may assume the proponent has completed his argument and the challenger's aim now is to show it not logically cogent. But surely we should want to allow challengers to do this in the course of a dialectical exchange. In the attempt to resolve some issue through rational argument or inquiry, we should expect the proponent to reach a point where his argument is completed. He has nothing further to add. Is his argument a good one? Surely if not, we should allow the challenger to show it, i.e. to propound an argument showing the weaknesses and faults of the proponent's argument. That is, we should allow the challenger to put forward an argument of her own, to in effect switch roles with the proponent. We may then see argumentative passages, arguments as products, which serve simply to attack other arguments as generated through such dialectical exchanges or those portions of dialectical exchanges where the challenger argues against the proponent's argument. The arguer composing the attacking argument should be identified with the challenger of the overall exchange, albeit the challenger allowed to play the proponent's role. The attacks we have considered, in the last section and in this, have been attacks on arguments. This, obviously, is one way of attempting to undercut whatever presumption those arguments create for their conclusions, and so to bring those conclusions into question. Just questioning a statement may undercut whatever presumption it has. Offering rebuttals, obviously, is another way to undercut that presumption. Rebuttals are reasons against the claim the proponent is defending. Our comparison of the basic dialectical questions with formal disputation makes this perspicuous. Whether a rebuttal appears in a provisoed denial, i.e. being the "Q" in " ~ P / Q & tQ" or in a weak distinction, i.e. being the "R" in " ~P/(Q & R) & f(Q & R)," a rebuttal is evidence for " ~ P " against the proponent's "P." Thus we can see rebuttals as part of an effort to support a counterclaim. Seeking to refute a claim by arguing for a counterclaim Hirsch calls "the constructive method of refutation." 19 But, as Perelman and Olbrechts-Tyteca point out in The New Rhetoric, there is another way to bring a statement into question. Besides "showing that the so-called fact is simply the conclusion of an argument which, by its very nature, is not compelling," 20 an interlocutor may "endeavor to justify his [questioning] attitude...by showing the incompatibility of the statement in question with other facts and attacking it for its inconsistency with the coherence of reality."21 What would this second mode of attack involve? It might very well involve supposing this "fact" to be true and deriving from that supposition together with other admitted facts an outright contradiction. This is the "destructive method which consists of showing that the initial claim implies something absurd or has undesirable consequences and is therefore

212

Further Considerations on Argument Structure

absurd and undesirable itself."22 Such an argument would involve the strategy of reductio ad absurdum, something we have not yet examined. But such arguments have been investigated in the literature. In particular, Stephen Thomas in Practical Reasoning in Natural Language indicates how to diagram arguments involving the reductio and related strategies. This calls for a distinct extension of the diagramming system developed thus far. In the introduction to this chapter, we said that we would examine not only limitations on our account of argument structure imposed by the rules for exchanges in basic dialectical situations, but also proposals in the textbook literature to diagram certain arguments which apparently exceed what our current diagramming procedure can do. It is now time to examine those diagramming procedures. How and why must the diagramming technique be extended? Can these extensions be motivated dialectically? Do they indicate any other circumstances where the proponent and challenger roles may switch? We answer these questions in the next section. We shall consider first the structure of these arguments and their diagrammatic representation. Then we shall see whether such arguments can be generated in a basic dialectical situation.

7.5. ARGUMENTS INVOLVING SUPPOSITIONS

Let's consider a specific example of a reductio ad absurdum argument, adapted from Wellman's consideration in Challenge and Response of James' lost-soul experiment: Consider the theory that whether an action is right or wrong depends entirely upon the amount of happiness or unhappiness it brings into existence. Suppose this theory is true. What is the consequence? We can imagine that I could bring about a world in which millions would be kept permanently happy simply by consigning a certain lost soul on the far-off edge of things to a life of lonely torture. On this theory, that action would be right. But it is clearly not right. It is an act of injustice. Hence making the rightness or wrongness of an action depend on the amount of happiness it brings about is an inadequate and inaccurate moral theory.23 One salient feature of this text is its supposing or assuming something true for the sake of argument. James is not committed to the utilitarian theory. He does not present it as true. He does not ask his readers to accept this theory and then see it as evidence for some further claim. Rather, he asks his readers to entertain the utilitarian theory in order to see its consequences. Following Alec Fisher in The Logic of Real Arguments, we call

Arguments Involving Suppositions

213

such statements suppositions,24 "The essential thing about a supposition is that it is not presented as being true — it is not asserted — it is put forward so that we may consider its implications.1,25 This characterization of "supposition" points to how arguments involving suppositions are structured. We are interested in drawing out certain implications from our suppositions, in arguing to those implications. In arguments involving suppositions, the fact that we may argue from one statement to another, that we may derive certain consequences from a certain statement, is offered to support the conclusion. A reason for the conclusion is a whole argument itself, rather than a statement. Frequently, reductio ad absurdum arguments are used to support negations. Such arguments will show that from some supposition that Ρ we can reason to some absurdity and from that fact, the existence of that argument, together with the absurdity of the consequence, will conclude that not-P. A related and somewhat simpler strategy, conditional proof, may be used to support conditional statements. That we may argue from supposition "P" to consequence "Q" is given to support "If P, then Q." In neither the reductio nor conditional strategies are we simply moving from a statement supported by various premises to a conclusion drawn from that statement, as we would in arguments involving serial structure. Rather, instead of presenting just statements directly supporting a conclusion, our grounds include a whole argument. This is why these arguments involve new structural configurations. We have not yet considered argumentation which presents whole arguments as reasons, and we must extend our diagramming technique to picture the structure of such arguments properly. To see how this is done, let's first consider a specific example of conditional strategy, since such strategy is simpler than the reductio. I claim that if John gets the raise, then he'll get married. Why? Suppose John does get the raise. Then he'll have enough income to support a wife properly, i.e. to get married. But we all know that John wants to get married. And if John wants to do something and has the income to do it, he will. So it follows on this assumption that John will get married. Here the arguer assumes the antecedent of the claim he seeks to establish, and argues from that assumption together with other premises to the consequent. The argument itself is offered as the reason for accepting the conditional. How should this reasoning be diagrammed? Assigning (1), (2), (3), ... to the component assertions, including assigning (2) to the supposition that John does get the raise, we see that the final conclusion of this reasoning is (1) and the argument from (2) to (6) constitutes what is offered in its support. We may diagram the argument this way:

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Further Considerations on Argument Structure

Since it is the argument from (2) to (6), that we may properly reason from (2) to (6), which is offered as evidence for (1), we enclose that argument in a box with an arrow drawn to (1). This represents that it is the entire argument, rather than its particular component statements, which constitutes the reason for (1). We represent the fact that (2) is granted only provisionally, for the sake of the argument, and not asserted categorically, as (4) and (5) — and (1) — are, by using a dashed circle to enclose (2). Since (3) depends on (2) as does (6) ultimately, they are not categorically asserted either. The arguer is not committed to their being true but to their following, in some appropriate sense, from (2). Hence, the dashed circle here appropriately reflects their status. The distinctive features of this strategy, then, are reflected in our diagram. The idea of enclosing in a box an entire argument involving a suppositional premise and given to support some conclusion was contributed by Thomas in Practical Reasoning in Natural Language.76 This idea is certainly reminiscent of various devices used in certain systems for constructing formal derivations. Most notably, it resembles Kalish and Montague's boxing of subordinate derivations when proceeding by conditional or indirect derivation.27 The box seals off the subordinate derivation and identifies it as what establishes a certain statement in a given derivation. Similarly, in Fitch-style derivations, the vertical line indicating the scope or extent of a subordinate derivation identifies the entire argument as a reason for a certain statement.28 By enclosing the entire suppositional subargument in a box in our diagrams, we make perspicuous that entire arguments can be reasons for a statement. Previously, reasons have been statements, and those statements have been represented in our diagrams by numbers completely enclosed in circles. By drawing arrows from those

Arguments Involving Suppositions

215

encircled numbers to others, we signal that the statements they represent are reasons for the statements represented by those other encircled numbers. Analogously, we now show that entire arguments may be reasons by completely enclosing them in boxes and drawing arrows from those boxes to certain encircled numbers. In reductio ad absurdum strategy, our conclusion follows not just from the fact that we can argue from one statement to another, but from that together with the assertion that the claim reasoned to is false or otherwise unacceptable. Consider the lost-soul argument again. (See Page 212.) The arguer here assumes for the sake of argument the contradictory of the claim he seeks to establish, namely that the rightness of an action does not depend entirely on the amount of happiness or unhappiness it brings into existence. He then reasons to a statement he can argue is false, i.e. condemning a certain lost soul to a life of lonely torture is right. He points out the falsity of the statement, gives a justifying reason for regarding it false, i.e. such a condemnation is unjust, and concludes that the original supposition, the statement assumed for the sake of the argument, is false. Diagrams of reductio arguments are very similar to those of arguments involving conditional argument strategy.29 The structural diagram of the argument from our provisional assumption to the recognized falsity is boxed, the box being linked to the encircled number representing the statement asserting the falsity of the conclusion derived from the provisional assumption. The provisional assumption is indicated with a dashed circle, as are statements dependent on it. As with other diagrams, perspicuity may be increased by appropriate annotations indicating the relation of various statements to others. Hence, the diagram of our lost-soul argument looks like this:

dearly

216

Further Considerations on Argument Structure

We should consider certain structural configurations which, at first glance, might seem difficult to integrate with our boxing notation. Suppose we had a conditional argument properly diagrammed this way: /

1

ίν

Ν

)

*

I

r L

2

>

;

>f »

Λ*t

* V

>*

Θ But suppose this argument is a subargument of a larger argument. Suppose in this larger argument that supposition (1) diverges to support an additional statement (6). How should we represent this structure? The diagram :ί* l. »t:

1 I CO ι

(Jj

r \

-

t

ί> *ί /

/

:

\t

Θ

O

Arguments Involving

217

Suppositions

does represent the structure, since it shows that (1) supports (6) and that (6) is a derived supposition. But the box was supposed to seal off the argument supporting (5). Having an arrow penetrating the wall of that box seems anomalous. Leaving (6) within the box s • 1 :

A

i 6 8

·

2 J

\* χ /

;\ 4A. f

0 >f

does not seem quite appropriate either. That we may reason from (1) to (6) is not put forward to justify (5). Perhaps in this case, the most perspicuous way to represent the structure is to repeat (1), having it appear both inside and outside the box:

218

Further Cotisiderations on Argument Structure

't 1ι ι·

Ϊ 2

Ο

y

ί 1 ί

: 4

I

χ ( 6 } r

Θ This shows that it is the argument from (1) to (4) which justifies (5), that none of (1), (2), (4), or (6) are asserted, and that (1) supports (6). Should the inference from (1) to (6) be incorporated in some further suppositional subargument of our main argument, we need have no problem diagramming the argument on that account. We would then have more than one boxed argument in the diagram. For example, we might have the following configuration:

Arguments Involving Suppositions

219

Likewise, should an asserted premise, e.g. (3) in our example, diverge to support some further statement, the representation of that subargument outside the box would be most perspicuous. Suppose (3) was itself supported. How should we represent this diagrammatically? This prospect opens up several distinct structural possibilities which should be treated differently for maximum perspicuity. Should the supporting statement(s) occur within the "scope" of the supposition, i.e. should such statements occur in the argumentative text after whatever expression flags (1) as the initial supposition but before that supposition is discharged, then representing such statements and their support in the box would be most perspicuous. For example, if (3) is immediately following by some statement intended to support (3), call it (3'), (3') clearly appears in the context of the suppositional argument. It appears before (4) and certainly before (5), where our supposition of (1) is discharged. So (3') is genuinely part of the argument presented to support (5) and should be represented in that box.

Further Considerations on Argument Structure

220

Θ 1

/ Ν

i% 1 β: ν *

/

ί

\

(21 —

©

f

\ »*

λ·

χ

!\ ct /! V

\

Θ On the other hand, should the premise(s) giving evidence for the asserted premise appear outside the scope of the supposition, e.g. should (3) be supported by a statement (6) appearing after (5), it would be most perspicuous to represent that support outside the box.

©i

Θ

Arguments Involving Suppositions

221

Should a supporting statement occur in the scope of the supposition and diverge to support other statements, it would be most perspicuous to represent that statement both inside and outside the box.

V

Dialectical Motivation for Arguments Involving Suppositions — A First Approach Can arguments involving suppositions be motivated dialectically? Can we see them generated by the exchange in a basic dialectical situation? One might be tempted to answer "Yes," provided that we allow our proponent to answer the challenger with a whole argument. For the whole argument from supposition to derived conclusion, the argument boxed in the diagram, is offered in answer to the challenge "Why?" As divergent structure arises in the special case where several askings of "Why?" are answered with the same statement, so this structure arises when a whole argument is offered in response to "Why?" As long as we allow our respondent to answer with an entire argument, we need no further modification in our understanding of a basic dialectical situation or its constituting rules. But these arguments from suppositions are themselves argumentative^ structured. This answer so far shows how they may be inserted into dialectical situations. But apparently they are inserted as units. Can we understand how their internal structure is generated in a dialectical situation? Someone presenting this answer might continue this way: Consider the arguments from provisional suppositions, the arguments represented within boxes in our diagrams. Certainly the structures of these arguments may be motivated dialectically, generated by our basic dialectical questions. We

222

Further Considerations on Argument Structure

have already seen how to do this. Now these arguments have an important structural feature. They incorporate no further arguments from provisional assumptions within their scope. To represent their structures, we need construct no boxes within the boxes in which they appear. We may call these arguments "base level" arguments because of this. Now as long as our basic dialectical questions and our rules for procedure in dialectical exchanges are rich enough to generate the structures of arguments not involving provisional assumptions, the structures of base level arguments will be generated by these basic dialectical questions. But we have yet to find arguments not involving these provisional assumption strategies which our basic dialectical questions fail to motivate. So it appears we can motivate the structure of base level arguments dialectically. Now although arguments from provisional assumptions within arguments from provisional assumptions, argumentation whose structure is represented with nested boxes, is conceivable, in any argument there will always be a base level. As anyone familiar with constructing formal derivations with rules involving subproof formulations knows, no matter how complex the argument, no matter how many subproofs are nested within other subproofs, there will ultimately be subproofs not involving other subproofs. We cannot have boxes within boxes ad infinitum. We have just established that we can motivate the structure of the base level arguments dialectically. Since we can understand the respondent as offering these arguments in response to "Why?," the next level arguments are dialectically motivated. But those arguments in turn answer the question "Why?" And since the nesting is finite, at some point we shall see how a subargument containing this whole nest of subarguments answers "Why?" asked in the dialectical exchange generating the main argument. Thus, one could argue that the main argument as a whole, together with its subarguments, is dialectically motivated. But to this argument we may pose a serious objection. It makes the dialectical motivation of arguments involving suppositional strategies piecemeal. We cannot have one series of questions to generate the entire argument together with its subarguments. We cannot see the argument as a whole developing through a continuing interchange of questions and answers. Although we can imagine the subarguments, independently of the context of the overall argument, generated by a dialectical interchange between proponent and challenger, and then this already generated argument introduced as a whole to answer the challenger's "Why?," we cannot imagine the entire larger argument, including the subargument(s), as successively generated by dialectical questions. On the other hand, we can imagine arguments with direct strategy growing in a basic dialectical situation through the successive questions and answers of a challenger and proponent. We should like to see the subarguments generated at the appropriate place in the main argument. After all, these subarguments are

Arguments Involving

Suppositions

223

structured entities. The simple question "Why?" does not begin to draw out their structure. Should the same statement answer "Why?" on two different occasions, we have an adequate motivation of divergent structure. But should "Why?" be answered with an argument, we have as yet no motivation of its structure within the particular dialectical exchange where it is offered as an answer. How, then, can we say that the main argument as a whole is dialectically motivated? Dialectical Motivation for Integrated Approach

Arguments

Involving

Suppositions

— An

Can we see arguments involving reasoning from suppositions as motivated through one dialectical exchange? As we currently understand dialectical situations, there appears to be a further serious obstacle besides what our considerations above would suggest. In dialectical situations, arguments are generated retrospectively. The proponent advances some claim. The challenger asks for justification. Once the proponent answers, the challenger can ask further questions. The movement of the argument is "back" from claims to their justification, from conclusions to their supporting premises. In terms of our diagrams, we are moving upwards. But when the proponent offers an argument from a supposition, the argument is prospective, from premise(s), in particular the premise supposed true for the sake of the argument, to some target conclusion. Diagrammatically, we are moving downwards. The point of presenting the argument is to show how we can "move" from supposition to conclusion. How can this prospective reasoning be represented through a retrospective dialectical exchange? Does this mean that we cannot see arguments involving reasoning from conditional assumptions as motivated through a single dialectical exchange? It does not mean this, provided we extend the rules and thus the possible moves the participants may make in a dialectical situation. The trick is again to allow role-reversal, to allow the proponent to ask questions and the challenger to answer with assertions, under specific circumstances. Interestingly enough, in Aristotle's conception of dialectics in the Topics, the proponent is the questioner, seeking to guide, direct, force, or otherwise move the opponent to make certain answers.30 The business of the questioner is so to develop the argument as to make the answerer utter the most implausible of the necessary consequences of his thesis; while that of the answerer is to make it appear that it is not he who is responsible for the impossibility or paradox, but only his thesis, for one may, no doubt, distinguish between the mistake of taking up a wrong thesis to start with, and that of not maintaining it properly, when once taken up. 3 1

This quote contains the key for seeing how reductio ad absurdum arguments can be generated in a basic dialectical exchange. In using this

224

Further Considerations on Argument Structure

strategy, our proponent wants to show some proposition false or unacceptable by showing that it leads to false or unacceptably implausible consequences. Should the challenger agree to suppose this proposition true, she would be making an assertion, albeit in a provisional or conditional way.32 She would certainly not be asking a question. Should the proponent by asking questions draw out from the challenger certain (not necessarily deductive) consequences of the thesis, or consequences of the thesis when taken together with other statements, and by asking further questions draw out additional consequences until his target absurdity was reached, we then would see how the argument from provisional assumption to absurd consequence could be generated in a dialectical exchange. As before, we have a question-and-answer interchange. Only here, the proponent asks the questions and the challenger answers. Clearly, this picture will work also for conditional strategy. Here the respondent asks the challenger to suppose the antecedent of some conditional true. His questions then lead her to the consequent.33 Although such exchanges will generate arguments from suppositions to target conclusions, it seems that in practice they would generate much more. For if the proponent simply asked the challenger what followed from a given supposition, she could give all sorts of answers, not necessarily the one which will advance the discussion towards his intended target. He might have to ask many times what follows from the supposition before he gets his intended answer, or at least one which is usable. For the argument under construction, the other answers would be extraneous. They do not enter into the reasoning. Fortunately, we can easily rectify this situation and Aristotle again gives us the key: "The right way to answer [is] to admit or to refuse to admit what has been asked. "M That is, instead of the proponent asking "What follows from supposition S?," which admits of many replies, he asks "May we conclude to C (from supposition S)?" He has asked a question which admits of two answers, "Yes" or "No." By requiring the proponent to phrase his questions in this form and the challenger to answer with either "Yes" or "No," we keep the proponent in control of his argument and avoid entertaining the possibility that our interlocutors may grope through a series of wasteful digressions to advance from one point to the next. We now have a way of generating arguments from provisional assumptions through one protracted dialectical exchange. How does this work? In response to one of the challenger's questions asking for further argumentation,35 we now allow the proponent to answer not with a categorical assertion but with a supposition. That is, in response to "Why?," the proponent may answer with "Suppose P," for some statement P. We require the challenger to entertain this supposition. After all, her goal is to draw out the best developed argument possible from the proponent. Hence, should the proponent want to reason from a supposition, she needs to agree

Arguments Involving

Suppositions

225

to let the argument take that course, to entertain that supposition. We cannot have the humorous situation of the schoolmaster who began "Suppose y is the number of eggs..." only to be challenged with "But Sir, please Sir, suppose y isn't the number of eggs?"36 But, as we pointed out above, in signalling her willingness to entertain this supposition, the challenger is not asking a question but rather, at least for the sake of the argument, making an assertion. The proponent's "Suppose..." is the signal that the roles of questioner and answerer are now reversed. The proponent's questioning is strictly circumscribed, as we have indicated. All his questions are of the form, "May we conclude to Q (from Ρ [and R and S and ...])?" (We shall develop the significance of the conjuncts shortly.) Two patterns now emerge. As we noted above, the challenger is basically restricted to answering "Yes" or "No." In the first pattern she always answers "Yes" to the proponent's questions. Thus, by successively asking "May we conclude to ?" the proponent leads the challenger to some target statement Q. The next step varies, depending on whether we have conditional proof or reductio strategy. With conditional proof strategy, it remains only to point out that we now have the conditional statement. Given this argument, we may now assert the conditional. Schematically, the pattern looks like this: PROPONENT: CHALLENGER: PROPONENT:

Suppose P. OK (assertion of Ρ for sake of argument) May we conclude to R (from P)?

CHALLENGER:

Yes (i.e., R)

PROPONENT:

May we conclude to Q (from

CHALLENGER:

Yes (i.e., Q)

PROPONENT:

So, on supposition that P, we have it that Q, i.e. I assert that If P, then Q.

)?

The proponent's "I assert that" signals that the subargument has been completed, and that we are now returned to the main argument (or the next most deeply nested subargument, if we have subarguments within subarguments.) With reductio strategy, the target statement Q is some false or unacceptable proposition. But the form of the argument requires that this be asserted explicitly. On this first pattern, then, where the challenger is uniformly agreeable, the end of the exchange looks like this:

PROPONENT:

May we conclude to Q?

CHALLENGER:

Yes

226

Further Considerations on Argument Structure

PROPONENT:

But Q is false, Will you grant me that?

CHALLENGER:

Y e s , I agree.

PROPONENT:

SO I assert that not-P.

Again, the "I assert that" signals the end of this phase of the argument. On the second pattern, the challenger is not uniformly agreeable. On at least one occasion, she responds "No" to the proponent's "May we conclude that." When she does so, she is also allowed, indeed required, to ask a question indicating why she will not, at this point, take the proponent's next step. Her question will be one of the basic dialectical questions. Since she is challenging the move, the argumentative step, from one statement to the next,37 she will be typically asking why the premise statement is relevant to the conclusion or why we can be sure of the conclusion in the light of some possible rebuttal. The challenger also might demand another reason for the conclusion, especially if the statement concluded to was a conjunction, and the reasoning from the supposition so far supported only one conjunct. Any of these three basic dialectical questions are proper and appropriate here. The question signals that material not dependent on the initial supposition is to be introduced into the subargument at this point. This was reflected in our diagrams, where we have seen the initial supposition or a statement dependent on the initial supposition, indicated by the dashed circle, linked to material asserted categorically, indicated by the unbroken circle. Schematically, we can represent this second pattern of exchange up to this point as follows: PROPONENT: CHALLENGER: PROPONENT:

Suppose P. OK M a y w e c o n c l u d e to •

PROPONENT: CHALLENGER: PROPONENT: CHALLENGER:

M a y w e c o n c l u d e to S? Yes M a y w e c o n c l u d e to T? NO — W h y is S relevant to T ?

?

•

For all your have shown, rebuttal R holds. In the light of that, why does S make you so sure that T? You've got to give me another reason for T. Give me that first! PROPONENT: A(nswer). Will you grant me that A? Our challenger may be willing to grant that A. In this case, the subargument can continue on its merry way, perhaps without further interruption,38 and the proponent can reach his final summation statement.

Arguments Involving Suppositions CHALLENGER:

Yes, i.e. A.

PROPONENT:

SO, e t c .

227

On the other hand, the challenger may not be willing to grant that A. She may demand justification for that claim. In this case, the roles of questioner and answerer are switched back to their original holders. Argumentation for A then will continue until the challenger signals her satisfaction, "OK, I'll grant that A" (assuming, of course, that the proponent can successfully establish A). Since all of this arguing occurs within the scope of the supposition, the diagram showing its structure is included in the box enclosing the entire suppositional argument, as in the first diagram on Page 220. Dialectically motivating those arguments whose diagrams call for some statement to appear twice, once inside and once outside the box enclosing the suppositional argument, is straightforward. Surely once the challenger has granted a supposition P, the proponent may not only ask whether we may conclude to some statement Q but whether we may also conclude to R. He might draw this second supposition right away, as a sort of aside in his argument. Alternatively, he might return to supposition Ρ after developing and concluding one suppositional argument, asking the challenger to consider (i.e. suppose) Ρ again, and then pursuing the additional consequence R. In either case, the diagram would display features of the figure on Page 218. To motivate arguments where a statement asserted categorically within the scope of a supposition is defended outside the scope of that supposition (See the second diagram on Page 220), we must allow the challenger to subsequently question assertions which she has granted in the immediate context of a suppositional argument. We must allow her to grant claims within the context of a suppositional argument and then go back and question them. But this seems quite reasonable. While engaged in developing a suppositional argument, one legitimate priority for the challenger would be to see just where the proponent was taking this supposition, just what consequences he would derive from it. As long as each inferential move was relevant and adequate, she might want to postpone until later seeking justification for any categorical assertions which seem questionable. She might then grant a categorical claim with mental reservations, intending to question it after the suppositional argument was concluded. But if this is permissible, she may question this claim just as she may question any claim which the proponent puts forward. Finally, just as in a divergent argument, the proponent may put forward the same statement to answer the challenger's asking "Why?" on several occasions, so the proponent may put forward a statement asserted

228

Further Considerations on Argument Structure

categorically within a suppositional argument to support some claim made outside the scope of that argument. (See diagram on Page 221.) Hence, we submit that the suppositional arguments whose structure we have been considering in this section can be dialectically motivated. Thus, we can see how subarguments in argumentation using conditional argument or reductio ad absurdum strategy can be generated through dialectical exchanges. The motivation is part of a single dialectical exchange generating the entire argument. We have thus extended our dialectical motivation to arguments involving these suppositional strategies. This preserves our dialectical understanding of argument structure. Differences in argument structure are motivated by the different basic dialectical questions the challenger may ask, and the different modes of response — categorical assertion, supposition, question — which a proponent may use. Consideration of these special strategies has required us only to widen our conception of a basic dialectical situation. We can readily provide a dialectical rationale for these structures and so preserve a dialectical understanding of argumentation.

NOTES 1. We have added the reason for statement (2), contained in (3) and (4), the rebuttal following "apparently," and the counterrebuttals (10) and (11), together with their defense (12). Compare our [1988], p. 196. 2. See Johnson and Blair, [1977], pp. 175-76. 3. Meiland, [1981], p . 84. 4 . Meiland, [1981], pp. 84-85. 5. Hirsch, [1987], p. 434. 6. This was our procedure in [1985], where we credit the idea as suggested by Scriven in [1976], 7. As we have seen in Chapter Six, dashed arrows appear in Thomas, [1976], pp. 306ff to indicate reasons against a claim or position. Although our use is different, it is certainly reminiscent of T h o m a s ' . 8. Perhaps to be completely accurate, we should say that we have an argument fragment in this passage, or put the word "argues" in scare quotes. Does a claim of support so highly qualified as the claim we have here actually constitute a claim of support? 9. Meiland, [1981], p . 40. 10. For the description/interpretation distinction and the contrasting issues in evaluating descriptions and interpretations, see our [1988], pp. 36-48. For this distinction, we are ultimately indebted to Sproule, [1980], 11. Meiland, [1981], p . 40. 12. That is, this is all the evidence that is given and it is not enough. 13. [1977], p . 13. 14. Copi, [1986], p. 422. 15. Quoted in Copi, [1986], p. 425. 16. We shall discuss the significance of enclosing the arguments from (5) to (3) and (6) to (4) in boxes in the next section. 17. Example in Copi, [1986], p. 424. 18. Copi, [1986], p. 423.

Notes

229

19. Hirsch, [1987], p. 434. 20. Perelman and Olbrechts-Tyteca, [[1969], p. 68. 21. Perelman and Olbrechts-Tyteca, [1969], p. 68. 22. Hirsch, [1987], p. 434. 23. Wellman, [1971], p. 34. 24. See [1988], pp. 82-83. On p. 83, Fisher argues very persuasively for calling these entertained statements suppositions rather than assumptions. An arguer may assume certain statements implicitly. He will not state them explicitly in the course of the argument, although they do enter into his reasoning. Unlike suppositions, however, he would be prepared to grant these assumptions as true, to commit himself to them. 25. Fisher, [1988], p. 83. 26. See [1986], pp. 215-22. Instead of using dashed circles to indicate the special status of premises assumed for the sake of argument and statements drawn as consequences from them, Thomas advocates drawing the top line of the box just over the suppositional premises. Thus Thomas would diagram our example this way:

0 1

Θ

0 - 0 1 © ~Ί

We prefer our method, for the entire argument is being offered to support the conditional conclusion, and the suppositional character of statements assumed for the sake of argument is clearly indicated by the dashed circles. Notice that on our view, we can represent perspicuously the provisional nature not only of the suppositional premises but also of conclusions drawn from them. What is the status of (6) in the above diagram? In [1988], Fisher presents another alternative way of representing the structure of arguments involving suppositions. See pp. 85-90. Fisher advocates "flagging" unasserted statements, be they initial suppositions or implications drawn from such suppositions, by a superscript "u" prefixed to the representation of the statement. The initial supposition will also be flagged by "(Suppose)," viz: (Suppose)

"R

i "C ([1988], p. 87.] Fisher advocates representing a conditional argument where several intermediate conclusions are drawn from the initial supposition this way: (Suppose)

U

1

I "2 u3

1 If 1 then 4

u

4

Notes

230

([1988], p. 89) I find such a representation not perspicuous, for it suggests that it is the move from (3) to (4), rather than the whole argument from (1) to (4), which constitutes the reason or justification for "If 1 then 4." Boxing the argument from (1) to (4) brings out this point perspicuously. 27. See Kalish and Montague, [1964], pp. 13-2S, in particular p. 18. 28. See Leblanc and Wisdom, [1976], pp. 77, 82. 29. As is obvious and well known, reductio arguments can be reduced to conditional strategy arguments. We can regard the boxed argument as supporting "If C, then F." This may then be linked with "not-F" to support "not-C."

*r|UB*Bt

titα C

ti ux> imputt IlM&Mdr

In [1986], this is how Thomas actually diagrams reductio arguments. But when such arguments are actually presented, the conditional, "If C, then F," may not be stated explicitly. Our diagramming procedure allows for representing just what is manifestly stated in these arguments. 30. And in [1987], Blair and Johnson acknowledge that their conception of "dialectical" borrows heavily from that in the Topics. See p. 45. 31. Aristotle, [1984], p. 268 (159* 18-23). 32. One may question whether this formulation, that the challenger makes an assertion, is correct or accurate in the light of Prof. Alec Fisher's comments in [1989]. When someone grants a supposition for the sake of argument, is he making an assertion? Is this speech act one of asserting? We could obviously ask these questions also about granting what follows from a supposition. In [1989], Fisher argues trenchantly that suppositions are not assertions, that they constitute a distinct type of speech act. To say "Suppose the Van Gogh museum is in Amsterdam" is not to assert that the Van Gogh museum is in Amsterdam. One has not presented the constituent proposition as being true. One rather "is asking us to consider the proposition with a view to drawing out its implications." ([1989], p. 402, italics in original omitted.) One who asks us to suppose Ρ need not believe that Ρ (and will not, of course, in the case of a reductio argument), whereas in asserting P, one is committed to P. One may grant all this and still ask whether it touches our formulation. Clearly to say "Suppose P" is not to assert P. In a monologically presented argument, "Suppose P" does not amount to asserting P. But we are here concerned with dialectical situations. Should one interlocutor in a dialectical exchange ask the other to suppose P, he also is not asserting P. But should the other interlocutor grant this supposition, what sort of speech act would her granting be? True, she need not believe P. But for the sake of the argument, has she not agreed to behave as if Ρ were true? She cannot simply dismiss or even question this assumption, and still be faithful to the rules of the dialectical exchange. Cannot we say then that she is committed, albeit suppositionally, to Ρ for at least part of the course of the argument? Albeit for the sake of the argument, hasn't she asserted that P? Would it be anomalous to characterize her speech act as one of "suppositional assertion"? As in assertion simpliciter, one is committed to the truth of a proposition, so in suppositional assertion, one is committed to treating a proposition as if it were true for the sake of the argument. In the framework of that argument, one is committed to Ρ and has incurred the consequences of that commitment, i.e. commitment to the consequences of P, just as by asserting Pone is committed to it and its consequences. Although one need not believe P, since this is suppositional assertion, granting Ρ for the sake of argument has enough in common with assertion to license our speaking of suppositional

Notes

231

assertions. Consequently, we regard describing the challenger's responses to the proponent's questions as assertions as not being an inappropriate description. 33. Clearly, we could tell a parallel story for separation by case arguments, and indeed for any argument involving a provisionally assumed premise and reasoning to some target conclusion. 34. Aristotle, [1984], p. 268 (159b 3-4). 35. I.e., either the plain question "Why?" or any of the basic dialectical questions except the second ground adequacy question, which asks for a modality rather than a statement functioning as a premise. 36. This is quoted on the cover of Geach's [1976], there attributed to a certain Littlewood, a Cambridge mathematician. 37. The one exception is challenging the proponent's penultimate step in a reductio argument, where "not-Q" is asserted against the derived "Q." But here again, of course, the challenger is allowed to question "not-Q." 38. Thus when the challenger doubts the cogency of an inferential move in drawing out the consequences of a supposition, she may raise the relevance question or the first or third ground adequacy questions. We may also permit her to ask "How sure do those reason(s) make you of your conclusion?" (i.e. the second ground adequacy question), when she gives a "Yes" answer agreeing to accept some inferred statement.

Chapter 8

Adequacy Considerations

Underlying our account of the macrostructure of arguments has been an assumption on how to count arguments, on what can legitimately be called one argument. As we pointed out at the beginning of Chapter Seven, this view of argument individuation is not accepted unanimously. Our first item of business in this chapter, then, will be to present our view on how arguments are individuated and to defend it against possible criticisms. Secondly, in Chapter Two, we presented desiderata for an argument diagramming technique and for a theory of argument structure. How well does our account satisfy these desiderata? In the second section of this chapter, we shall address each desideratum in turn.

8.1. INDIVIDUATION OF ARGUMENTS

Problems with argument individuation arise principally with two types of structure: serial and convergent. In both, the diagrammatic representation calls for several arrows. When arguing according to the pattern

do we have one argument or two? Is the move from (3) to (2) a separate argument from the move from (2) to (1)? Likewise, in a convergent pattern

234

Adequacy

Considerations

© Θ \/ ο do we have one two-premise argument for the conclusion (1), or do we have two, separate one-premise arguments? In speaking of serial and convergent arguments, we are already committed to a position on this issue. We see these arguments as unities, as one single argument, not as series or sets of numerically distinct arguments. To say that an argument has serial structure means that within this one argument, we can see one reason supporting another and that supporting a third (and ...). Likewise to say that an argument has convergent structure means that within this one argument we can identify several premises independently supporting the conclusion. We may raise the question of argument individuation also with arguments involving counterrebuttals and with divergent argument structure. Typically, a counterrebutting premise will lend its weight to supporting the conclusion together with one or more directly supporting premises and perhaps several other counterrebutting premises as well. Do each of these premises constitute a separate argument for the conclusion? Why should we see a divergent argument as one argument rather than two (or more) which share the same premise? From our perspective, there seems little at stake theoretically in whether we count so-called divergent arguments as one or several.1 Here we are arguing to several conclusions, all supported by the same premise. Should that premise be stated only once in an argumentative text, the standard divergent diagram would seem to reflect perspicuously the structure of that text. But does it really make much difference whether we represent the structure of the reasoning this way

Individuation of Arguments

235

or this?

Ο

ο

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Hence we shall set aside divergent arguments at this point. The issue of argument individuation becomes acute for those arguments portrayed as containing subarguments all supporting some main point. Our assumption throughout this study is that serial and convergent arguments, and arguments involving counterrebuttals, are all unities. We may regard argumentative texts displaying these structures as presenting single arguments. This is reflected in our dialectical model by our understanding the challenger's successive questions as generating a single argument, not a series of discrete arguments. How may we justify this assumption? Let us assume that convergent arguments are properly or canonically diagrammed according to the second pattern

rather than the first ©

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Adequacy Considerations

Also, instead of incorporating counterrebuttals into our argument diagrams by drawing arrows from them to the rebuttal box, we shall simply draw a straight line from the counterrebuttal down to and touching the rebuttal box. For example, instead of diagramming an argument with two premises directly supporting a conclusion and one counterrebuttal in this manner:

we shall diagram it this way:

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We understand both diagrams to be saying the same thing, but take the second as our canonical representation. As the canonical scheme for convergent arguments incorporates several arrows into one, so our canonical diagram for arguments involving counterrebuttals incorporates the arrows from the directly supporting premises and the counterrebuttals into one arrow pointing to the conclusion. As we pointed out in Chapter Four when introducing this alternative way of representing convergent arguments (See Page 96), it suggests that the various separate, independent reasons combine to form just one case for the conclusion. We may have several reasons constituting one argument. Our analogous modification of diagrams for arguments with counterrebuttals makes the same point. If these are

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Individuation of Arguments

genuinely single arguments, then, our canonical representation dispenses with the misleading suggestions made by the multiple arrows of the standard diagramming procedure. Arguments, we claim, are simple or compound. A simple argument involves exactly one arrowhead, i.e. exactly one claim that a conclusion is supported by some one or more premises. Should a simple argument involve several premises, they may either converge on the conclusion or be linked. In both

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we have exactly one arrowhead, and so a simple structure. Should the arrow be modified by a modality and/or rebuttals, the argument is still simple, for we have just one arrow. Likewise, should the argument include counterrebuttals, we still have just one arrow, and so a simple case. The counterrebuttals strengthen the one case we are making for our one conclusion. One conclusion, one case, one argument. Simple arguments are single arguments. By adopting our alternative representation of convergent arguments and arguments with counterrebuttals as canonical, we make perspicuous rather than obscure their unity. Are arguments with serial structure single arguments? Should we have several arrowheads, should we be diagramming serial structure, we have several simple arguments. But compound arguments may be built up from simple. Let's draw an analogy here between arguments and functions. We may construct functions from others by means of functional composition. Where Χ, Υ, Ζ are sets and g,f are functions such that g maps X into Y and / m a p s Y into Z, we may define a f u n c t i o n / Ο g, mapping X into Z, such that for χ e X, (f Ο g)(x)

=f(g(x)).

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Considerations

But fOg is just as much a single function as / and g are. We may regard it as a set of ordered pairs, a subset of Χ X Z, just as g a n d / a r e sets of ordered pairs, subsets of Χ Χ Y and Υ Χ Ζ respectively. We may say, "Let h = f O g," which we could not do i f / O g were not a function. Now where X > Y and Y j . , Ζ represent that g maps X into Y and / maps Y into Z, we may r e p r e s e n t / Ο g as X

g:

'

-FT-* Ζ J:

Y

Similarly, cannot we think of the move, inference, argument from a set of premises to a conclusion as in some sense an operation? If one move conveys us from premise A to conclusion Β and another move conveys us from Β as a premise to conclusion C, cannot we compose these moves to give us an argument from A to C? Isn't that exactly what happens in a serial argument which proceeds, "A, therefore B, therefore C"?

Does not this argument have a unity? Cannot we distinguish in it basic premises from main point or final conclusion? We may draw another analogy. Just as various operations of compounding, truth-functional or otherwise, can be used to build compound statements from simple or simpler statements, the result being one statement, so by the "operation" of composing arguments, we build compound arguments from simple or simpler arguments. Yet a compound argument is still one argument, one piece of argumentation. So in a serial argument, we have one argument, but a compound argument composed of at least two simple arguments. If these considerations are not sufficient to convince us that a serial argument is one, albeit compound argumentative unit, let us look at several types of arguments involving serial structure. Consider sorites. Here, in traditional categorical logic, from two premises we derive a conclusion, from that together with another premise, we derive a further conclusion,

Individuation of Arguments

239

and so on until we derive the final conclusion of the argument. Consider this example from Lewis Carroll:2 (1) Babies are illogical. (2) Nobody is despised who can manage a crocodile. (3) Illogical persons are despised. Therefore Babies cannot manage crocodiles. Clearly one could reason to the conclusion by seeing that (1) and (3) imply (a) Babies are despised, and that (a) and (2) imply the conclusion. One might very well develop the argument this way. We diagram it as

The diagram includes serial structure, but does this mean that we have more than one argument here? By developing the original argument, have we destroyed its unity? Although the logical form (i.e. the microstructure) will in general be far more sophisticated, will not a number of mathematical proofs have analogous macrostructure? In proving a theorem, a mathematician will first deduce one consequence from the available axioms, postulates, definitions, and previously proved theorems. From that conclusion, again together with other available statements, the mathematician derives a further consequence. This continues until he demonstrates the desired conclusion. Clearly, cannot we speak of the proof of this theorem? Does not this proof constitute a single argument with a unity? Do we simply have a sequence of proofs here? Although we may identify each step as a subargument or subproof, by speaking of the proof of this theorem, we indicate that we regard these individual steps as constituting one overall compound argument. Sorites and mathematical proofs are deductive arguments. But we may apply these considerations to non-deductive arguments also. The mathematician could introduce each successive consequence in his proof by " " But then why if each successive step in a sequence of non-demonstrative reasoning is introduced by "therefore" or some other conclusion

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Adequacy Considerations

indicator should we deny that the reasoning constitutes a single argument? And why should the situation be changed if we have premise indicators or even no indicators? Hence, we rest our case that serial arguments constitute single, unified, argumentative units. Are arguments with convergent structure single arguments? Although our proposal for a canonical way of diagramming convergent arguments combines what in effect are several arrows into one and so presents the image of a single argument, this proposal is open to attack. We expect that some philosophers would claim that the proposal simply misrepresents the structure of so-called convergent arguments. Rather than combining the arrows into one to highlight the unity of such arguments, we should keep the arrows separate to highlight that we have not one, but several, separate arguments here. Such claims appear in a recent exchange initiated by John Hoaglund's article, "Reasons and Premises in Informal Logic" [1988-89], Hoaglund points out that from a standard perspective informed by formal logic, arguments with false premises are regarded as fallacious. For that reason alone, we would regard an argument as failing to establish its point. But convergent arguments may have false premises and yet still establish their conclusions. For consider an argument displaying this structure:

Ο

0

0

Suppose statements (1) and (2) are both true and provide weighty evidence for (4), evidence sufficient to carry the day. Suppose, on the other hand, that statement (3) is false. Now although we may urge that the presence of (3) in this argument is a flaw, that the argument would be better off without it, that the arguer should have quit while he was ahead, this does not mean that the argument is fallacious, that it does not establish its conclusion. The moral Hoaglund wants to draw "is that we use 'premise' for 'support statement', not as 'statement necessary to establish a conclusion'." 3 However, Hoaglund indicates that the formal logician has a way to avoid this moral. Taking the case of a convergent argument with two premises, one providing strong and the other weak support for the conclusion, he [the formal logician] urges that we have not one but two distinct arguments. One of them is strong and the other weak. This preserves the sense of 'premise' that makes premises essential to a conclusion, and that of

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241

'argument' whereby any argument with a false premise is ipso facto unsound. 4

Hoaglund's rejoinder is that this proposal "makes two arguments of what was advanced as one. "5 But the debate does not stop here. In "Reasons and Premises" [1989], Peter Facione responds that we must sharply distinguish between premises and reasons. Premises link together to constitute a reason for a claim or conclusion. Should one premise prove false, the entire reason fails. But one may offer other reasons, i.e. other premise complexes to support the same claim. Each reason signifies a separate argument for the conclusion. "An argument is a claim with its supporting reason."6 So on this account, should the reasoning in an argumentative text display this structure

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