The Structure of Argumentation

8/12/2019 The Structure of Argumentation

1/27

State-of-the-Art: The Structure of Argumentation

A. FRANCISCA SNOECK HENKEMANS

Department of Speech Communication, Argumentation Theory and Rhetoric

Spuistraat 134

1012 VB Amsterdam

The Netherlands

E-mail: [email protected]

ABSTRACT. In this paper, a survey is presented of the main approaches to the structure of

argumentation. The paper starts with a historical overview of the distinctions between varioustypes of argument structure. Next, the main definitions given in the various approaches are

discussed as well as the methods that are proposed to deal with doubtful cases.

KEY WORDS: argument structure, complex argumentation, complementary argumentation,

convergent reasoning, coordinatively compound argumentation, cumulative argumentation,

linked reasoning, multiple argumentation, premise structure, serial reasoning

1. INTRODUCTION

The structure of argumentation is an important issue for current approaches

to the theory and practice of argument analysis. Recurrent questions are:

How can one lay bare the structure of a complex argument? Which types

of structures should be distinguished and on what grounds?Laying out the structure of an argument is not only necessary to under-

standing how arguers defend their positions, but is also indispensable for

evaluating their argumentation. An overall judgment of the quality of a

complex argument requires not just a clear picture of individual arguments,

but also insight into the relations among these arguments.1 If it is not clear

whether or not an individual argument (or reason) is independent of other

arguments that make up the complex argument, it cannot be clear just how

damaging are the consequences of a negative evaluation of that argument.

In most approaches, at least three types of argument structure are dis-

tinguished: (1) serial reasoning (or subordinate argumentation), (2) linked

reasoning (or coordinate argumentation), and (3) convergent reasoning

(or multiple argumentation). Reasoning is serial if one of the reasonssupports the other. If reasoning is linked, each of the reasons given are

directly related to the standpoint, and the reasons work together as a unit.

When each reason separately supports the standpoint (to some degree),

the reasoning is convergent. A complex argument can combine all of these

types of argument structure.

Although at first sight there seems to be agreement on the relevant

types of distinctions between argument structures, on closer inspection,

Argumentation 14: 447473, 2000.

2000 Kluwer Academic Publishers. Printed in the Netherlands.


2/27

authors disagree with each other on a number of points. Often the sameterminology is used for distinctions that differ in crucial respects. Moreover,

the various characterizations of argument structures reflect fundamental

differences of approach to argumentation. The most important difference

is that between structural (or logical) approaches, in which attention is

paid only to the structural aspects of argument structure as they manifest

themselves in the product of the reasoning process, and functional (or dialec-

tical) approaches, in which the emphasis is on the process within which

these structures arise, and the functions the various argument structures fulfil

in this process.

Apart from differences in definitions of argumentation structures and

differences of approach, there is much discussion about the best method

of analysis, especially in doubtful cases where there is room for more thanone interpretation. For some authors, the ambiguities in the definitions

and the problems of analysis have been a reason to question the impor-

tance of the distinctions. They argue that distinguishing between the various

argument structures is often so difficult in practice that it is better not to

make these distinctions at all. This is especially true for the notoriously

problematic distinction between linked and convergent arguments.

Finally, there is also disagreement about the history of the distinctions,

in particular about the origins of the linked-convergent distinction. Since

more insight into the historical backgrounds of the distinctions between

various types of argument structure might enhance our understanding of

the current controversies, this survey begins with a historical overview.

Section 3 discusses the main definitions of linked and convergent argument

structures (or their equivalents) that are given in current approaches. Section

4 is devoted to the various methods proposed in the literature to deal with

doubtful cases.

2. HISTORICAL OVERVIEW

Attention to the analysis of argument structure first appeared in American

debate and logic textbooks in the second half of the previous century. Two

major influences are identifiable in these textbooks: classical rhetoric and

Enlightenment rhetorical theorists such as Campbell and Whately.

Although the concepts are not fully developed, and the contemporary

terminology is absent, argument structures similar to our present dayconcepts were present in nascent form in both the classical rhetorical

tradition and the 18th century Enlightenment rhetorics. The functional

approach, in which the independence or interdependence of arguments is

determined by the requirements for the burden of proof to be met by the

arguer, can be found both in the classical and the Enlightenment rhetoric.

The logical approach, in which the term argument structure refers to

relationships among premises within different inference types, is promi-

448 A. FRANCISCA SNOECK HENKEMANS


3/27

nent in the work of Enlightenment rhetoricians. They make a distinctionbetween the type of linkage between premises in a deductive argument or

proof and the way in which premises are combined in an inductive (or

moral) argument: in the latter argument the premises each separately

lend some degree of support to the conclusion (and are in that sense

independent), but they need to be combined to make the conclusion (more)

probable.

Classical rhetoric

In early Roman rhetoric, both subordinate arguments and arguments con-

sisting of a number of reasons in direct support of a (sub)standpoint were

distinguished.2 In Ciceros De Inventione, a specific type of complexargument is discussed, the epicheirema, also called thefive-part argument.

Kennedy (1994) gives the following description of the five-part argument:

it is in fact a kind of amplification of the Aristotelian syllogism and enthymeme in

which a proposition (part 1) is supported by a variety of reasons (part 2), then a second

proposition (what would be the minor premise in a syllogism) is stated (part 3), and

that is followed by a variety of reasons for believing it (part 4). The fifth part then states

the conclusion. Such an argument in Greek is sometimes called an epicheirema, liter-

ally a handful. (120)

Since part 2 and part 4 consist of reasons in support of another reason,

they can be seen as serial reasoning or subordinate argumentation. In both

cases, the support provided by the subordinate argumentation should consist

of a variety of reasons. Cicero gives the following example of support forthe minor premise Of all things nothing is better governed than the

universe:

And then [. . .] they introduce another proof, that is of the minor premise, in this way:

For the risings and the settings of the constellations keep a fixed order, and the changes

of the seasons not only proceed in the same way by a fixed law but are also adapted to

the advantage of all nature, and the alternation of night and day has never through any

variations done any harm. All these points are proof that the nature of the world is

governed by no ordinary intelligence. (De Inventione , 1. 59)

It is not clear whether these reasons are supposed to form one combined

defence (and are thus a case of linked reasoning) or whether they should

lend independent support (and are a case of convergent reasoning).

Also in the classical theory of stasis, the concepts of dependent and inde-pendent reasons seem to have been recognized, albeit it not explicitly. The

issues that had to be proven in a criminal court case differed depending

on whether the arguers position was that of the defendant or that of the

prosecutor.3 In choosing the status for his defence, according to Quintilian,

the defendant has four options:

There are four different methods which may be employed in every case, and he who is

going to plead should study them as first essentials. For, to begin with the defendant,

THE STRUCTURE OF ARGUMENTATION 449


4/27

far the strongest method of self-defence is, if possible, to deny the charge. The secondbest is when it is possible to reply that the particular act with which you are charged

was never committed. The third and most honourable is to maintain that the act was

justifiable. If none of these lines of defence are feasible, there remains the last and only

hope of safety: [. . .] we must evade the charge with the aid of some point of law,

making it appear that the action has been brought against us illegally. (Quintilian 3, 6,

8384)

Each of these ways to defend the accused is, in principle, a sufficient

defense. It is, however, also possible to combine different types of defenses.

Quintilian gives the following explanation of the reasons for using such a

multiple defense:

There are also a number who are in doubt as to a form of defence which I may

exemplify as follows: If I murdered him, I did right; but I did not murder him. What,

they ask, is the value of the first part, if the second can be proved, since they are mutuallyinconsistent, and if anyone employs both arguments, we should believe neither? This

contention is partly justified; we should employ the second alone if the fact can be

proved without a doubt. But if we have any doubts as to being able to prove the stronger

argument, we shall do well to rely on both. Different arguments move different people.

[. . .] one who is confident of his powers as a marksman may be content with one shaft,

whereas he who has no such confidence will do well to launch several and give fortune

a chance to come to his assistence. (Quintilian 4, 5, 1314)

The prosecutor makes use of the same issues in choosing his main argu-

ments, but he has to prove all four points in order to make his case:

The accuser [. . .] must prove that something was done, that a particular act was done,

that it was wrongly done, and that he brings his charge according to law. (Quintilian 3,

6, 85)

In view of the requirements of the burden of proof, the prosecutors main

reasons for finding the accused guilty must be regarded as interdependent,

since the success of the argument as a whole depends on the success of each

of its component parts.4

A different type of interdependency is at stake in the following fragment

from the Rhetorica ad Herennium, where the ideal order of the arguments

is discussed:

In the Proof and Refutation of arguments it is appropriate to adopt an Arrangement of

the following sort: (1) the strongest arguments should be placed at the beginning and at

the end of the pleading; (2) those of medium force, and also those that are neither useless

to the discourse nor essential to the proof, which are weak if presented separately and

individually, but become strong and plausible when conjoined with the others, should

be placed in the middle. (Rhetorica ad Herennium 3, 10, 18)

Unlike the prosecutors main arguments, some of the arguments that are

supposed to be placed in the middle are not essential to the proof according

to the author of the Rhetorica ad Herennium. The reason for their depen-

dency on other arguments is that they are too weak to stand on their own,

and they become stronger when combined with the other arguments.



5/27

Enlightenment Rhetoric

In The Philosophy of Rhetoric (1991/1776), Campbell makes a distinction

between scientific evidence and moral evidence. One of the main dif-

ferences between these two types of evidence is a difference in structure:

whereas scientific evidence consists of a set of interdependent premises

which together form one argument, moral evidence consists of a number

of independent arguments:

scientific evidence is simple, consisting of only one coherent series, every part of which

depends on the preceding, and, as it were, suspends the following: moral evidence is

generally complicated, being in reality a bundle of independent proofs. The longest

demonstration is but one uniform chain, the links whereof, taken severally, are not to

be regarded as so many arguments, and consequently when thus taken, they conclude

nothing; but taken together, and in their proper order, they form one argument, which isperfectly conclusive. (45)

Although each of the reasons given in moral reasoning is independent of

the others, with each new reason the conclusion may become more likely:

In moral reasoning, [. . .] there is often a combination of many distinct topics of argument,

no way dependent on one another. Each hath a certain portion of evidence belonging to

itself, each bestows on the conclusion a particular degree of likelihood, of all which

accumulated the credibility of the fact is compounded. (1991/1776: 45)

Campbell acknowledges that it is possible to give more than one indepen-

dent proof of the same proposition, but he believes that there is not much

point in doing this:

It is true, the same theorem may be demonstrable in different ways, and by differentmediums; but as a single demonstration, clearly understood, commands the fullest con-

viction, every other is superfluous. (1991/1776: 45)

Campbell also gives a description of the consequences that will result

from taking away one or more parts of a demonstration or of a moral

argument:

[A demonstration] may be compared to an arch, no part of which can subsist indepen-

dently of the rest. If you make any breach in it, you destroy the whole. [. . .] [Moral

reasoning] may be compared to a tower, the height whereof is but the aggregate of the

heights of the several parts reared above one another, and so may be gradually diminished,

as it was gradually raised. (1991/1776: 4546)

Whately discusses two different ways in which reasons may be combined

in order to produce a stronger argument (and thus may be considered aslinked). A first type of case consists of reasons which separately have

little or no weight, but which can lend sufficient support to a conclusion

when taken together:

The remark above made, as to the force of concurrent testimonies, even though each,

separately, might have little or none, but whose accidental agreement in a falsehood would

be extremely improbable, is not solely applicable to the Argument from Testimony, but

may be extended to many arguments of other kinds also; in which a similar calculation



6/27

of chances will enable us to draw a conclusion, sometimes even amounting to moralcertainty, from a combination of data which singly would have had little or no weight.

(1846: 74)

In inductions, according to Whately, mentioning just one instance can in

some cases suffice to justify a general conclusion. But if not, then a number

of instances are needed to support the conclusion:

In human affairs [. . .] our uncertainty respecting many of the circumstances that may

affect the result, obliges us to collect many coinciding instances to warrant even a probable

conclusion. (1846: 88)

Instead of combining a number of reasons of the same type (i.e., a number

of testimonies, signs or instances), it is also possible to produce a stronger

argument by combining different types of reasons. A second type of linkage

(implicitly) distinguished by Whately consists of a combination of dif-ferent types of reason, where the one reason is a means of showing that

specific objections against the other reason (that there are certain

exception-making circumstances to the general rule or warrant under-

lying that reason) are not valid:

the a priori Argument and Example support each other, when used in conjunction

[. . .]. A sufficient Cause being established, leaves us still at liberty to suppose that

there may have been circumstances which will prevent the effect from taking place; but

Examples subjoined show that these circumstances do not, at least always, prevent that

effect. (1846: 138)

From his discussion of issues related to the burden of proof (112), it becomes

clear that Whately also allows for the possibility of putting forward more

reasons than are required, so as a result the defense as a whole consistsof a number of independent reasons. If the arguer has the presumption,

then the burden of proof belongs with the other side and putting forward

further evidence in support of the presumption amounts to giving an

argument ex abundanti (a superfluous argument).

It is a point of great importance to decide in each case [. . .] on which side the Presumption

lies, and to which belongs the [onus probandi] Burden of Proof. For though it may often

be expedient to bring forward more proofs than can be fairly demandedof you, it is always

desirable, when this is the case, that it should be known, and that the strength of the

cause should be estimated accordingly. (1846: 112) 5

So, there is nothing against doing this, provided it is made clear to the

opponent that one is doing more than required.

The early textbooks

American textbooks on argumentation and debate that started appearing

in the 50s to a large extent reflected the traditional views on argument

structure. But there were also a number of new developments. Modern

tradition has it that Monroe Beardsley (1950) was the first to represent

the structure of argumentation by using diagrams (consisting of numbered



7/27

statements and arrows indicating support relationships). Beardsley also intro-duced part of the terminology that is still used by informal logicians to refer

to the different argument structures. He gives the following definitions:

In a convergentargument, several independent reasons support the same conclusion

[. . .] In a divergent argument, the same reason supports several conclusions [. . .] A

serial argument contains a statement that is both a conclusion anda reason for a further

conclusion (1950: 19).

Thomas claims credit as the first to distinguish between linked and con-

vergent arguments rather than as others have thought, Beardsley:

The distinction between linked and convergent inferences was not drawn by Beardsley,

not even in his fourth edition of Thinking Straight. It was introduced in the 1973 edition

of PRNL [Practical Reasoning in Natural Language]. Beardsley represented linked and

convergent inferential relationships alike, using multiple arrows for (what I call) linkedrelationships, as if all reasoning with multiple reasons were convergent (except that this

distinction did not exist in his system). The concept of linked reasoning, and the distinction

between it and convergent reasoning, needed to be added to Beardsleys system of analysis

before it could be generally applied at all (1986: 457)

As far as the terminology is concerned, this seems to be correct, but similar

distinctions between interdependent and independent reasons were already

made before 1973. One example is Mills (1968), who makes a distinction

between cases where there is one conclusion with several coordinate

reasons and cases where one has one conclusion supported by two or more

pairs of coordinate reasons. The latter type of structure is more likely to

be a case than an argument. An example of the first type of structure is:

Conclusion: Our top debaters are top scholarsReasons:

1. They are John, Mary, and Jim.

2. John has a 3.9

3. Mary has a 3.8

4. Jim has a 3.7

Mills (1968: 182183)

An example of the second type of structure, according to Mills, would be

a case on a value proposition where each pair of reasons consists of a

criterion and its application.6 Mills also introduces a diagram convention

for making the distinction between these two types of structures (1968: 183).

From his examples, it becomes clear that Mills does make a distinction

between arguments with a structure comparable to a linked argument (the

first type) and a structure which is comparable to a convergent argument(the second type, where each pair of reasons taken together constitutes an

independent reason).

Just as in the classical and enlightenment tradition, for most of the earlier

textbook authors, the distinction between interdependent and independent

reasons coincides with the distinction between the structure of premises

in a deductive argument and the structure in an inductive (or non-deduc-

tive) argument.



8/27

The distinction then is that in a deductive argument the premises needto be taken together to constitute a reason, whereas in an inductive argument

a combination of reasons is needed to make the conclusion (more or less)

probable. McBurney, ONeill and Mills (1951) explain that a combination

of (inductive) analogies may strengthen the support for a conclusion:

From a series of analogies showing the success of a certain project, we argue that it

will be successful in a particular case. [. . .] Reasoning from analogy becomes increas-

ingly strong as the number of comparisons is increased, or in other words, as the analogies

are cumulated (1951: 108)

And Ray and Zavos (1966) explicitly compare deductive arguments to a

chain of links, and contrast this with the more gradual type of support

supplied by induction and arguments from circumstance:7

Deductive reasoning is often compared to a chain. The last link in the chain is depen-

dent not to some degree but totally on the connection of every other link. [. . .] Induction

and argument from circumstance can be better compared to the relation of the legs of a

table to the tabletop. Each leg, though cooperating with the others, supports the top

independent of the other legs (at least to a point). (1966: 101)

In the early textbooks, the tradition of the classical theory of stasis, in which

it depends on the requirements of proof that the arguer must meet what

the resulting structure of his argument is, is also preserved. A good example

of a textbook in which the latter approach is taken is Windes and Hastings

Argumentation and Advocacy (1965).

According to Windes and Hastings, the issues an advocate needs to prove

in order to establish the guilt of X in an embezzlement case are:

1. Certain property was misappropriated.

2. X misappropriated the property.

3. The misappropriation was fraudulent, i.e., without the consent of the owner.

4. The property was for the personal use of X (1965: 75).

In such cases, the issues taken together form one linked argument and the

advocate has to provide sufficient evidence for each of the issues:

Usually there is one over-all argument leading directly to the proposition, and the elements

of this argument are further supported by sub-arguments. The over-all argument states

the issues and the sub-arguments are contentions in support of the issues [. . .] Each

one of the issues must be established for the proposition [X is guilty of embezzlement]

to be established. If any issue is not proved, then the proposition is not proved (1965:

215216).

The task of the opponent (the negative advocate) is easier: The other party

can logically defeat the proposition by defeating one of these issues (1965:

232).

Apart from cases where the advocate needs to put forward a number

of interdependent reasons (corresponding to the issues) in order to defend

the proposition, Windes and Hastings also discuss the possibility of con-

structing an argument with independent lines of reasoning:



9/27

Another aspect of case building to note is that independent lines of reasoning may leadto the same conclusion. We may, for example, use three reasoning processes to support

the conclusion the corn crop of Dullnia is failing.

1. Dulnia is buying corn on the world market. (Reasoning from effect to cause.)

2. The testimony of an agricultural expert who visited Dullnia. (Testimonial evidence.)

3. The presence of drought and poor growing conditions this year. (Cause to effect).

In this series of arguments, rather than having a clear set of issues to be established, the

proof of the proposition depends on the number and plausibility of the component argu-

ments. In such cases, one strong one may be sufficient, but the more independent argu-

ments which lead to the same conclusion, the more probable is that conclusion. (1965:

216218)

For Windes and Hastings, two criteria seem to be relevant in determining

whether arguments are interdependent or not: (1) whether the arguments

given by the arguer form part of a clear set of issues that should be estab-lished (the burden of proof-criterion), and (2) whether the argumentation

as a whole is based on one reasoning process or whether the arguer uses

different reasoning processes (the different types of argument-criterion).

3. CURRENT APPROACHES

Since the 70s, a large number of textbooks have appeared in which it has

become customary to devote attention to analyzing the structure of argu-

ments and to ways of portraying this structure in a diagram. With the

exception of van Eemeren and Grootendorsts (1992) pragma-dialectical

textbook, all these books are written by informal logicians. It is not until

the 90s that the subject of argument structure starts receiving a more

theoretical treatment. In the journalsInformal Logic andArgumentation, the

distinctions made by informal logicians between different types of struc-

ture are discussed. Also, three monographs on argument structure appear,

each of which proposes a dialectical approach to argument structure.

Since most of the discussion has centered on problems involved in the

distinction between linked and convergent arguments, I shall restrict my

further discussion of the literature to these two types of structure.

The textbook distinctions

Thomas (1986, 1st edition 1973) was the first to use the terms linked

and convergent in describing interdependent and independent premise

support, and his way of portraying these two structures has become standard.

Although Thomas has had a large influence on all later informal logic

accounts of argument structure, his own definitions of these two types of

structures are different from those of many of the other authors. Whereas

most informal logicians continue the tradition of associating linked argu-

ments with deductive reasoning and convergent arguments with inductive



10/27

reasoning (or other types of non-deductive reasoning), Thomas deviates fromthis tradition:

The natural-logic concept of linked inference [. . .] bridges the supposed sharp line of

the traditional induction-deduction dichotomy, severely straining [. . .] the traditional theory

that induction and deduction comprise two completely different kinds of inference

[. . .] Both of these supposedly different types of reasoning receive identical diagram-

matic representations. (1986: 461)

Thomas gives the following definitions of linked and convergent rea-

soning:

When a step of reasoning involves the logical combination of two or more reasons, they

are diagrammed as linked. (1986: 58)

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. (1986: 60) 8

Both deductively valid reasoning and inductive reasoning from several

similar items of evidence are analysed as linked by Thomas. In the case

of inductive reasoning, the reason for linking the premises is not that each

reason separately does not give any support to the conclusion, but that

the support is stronger when the reasons are combined (1986: 59).

Linked arguments form one single argument, whereas convergent argu-

ments consist of separate arguments:9

A convergent argument is equivalent to separate arguments (or evidence coming from

separate areas) for the same conclusion. (1986: 61)

The closest formal approximation to the natural-logic portrayal of convergent inferencewould perhaps be two separate deductions leading to two different tokens of the same con-

clusion. (1986: 459)

For this reason, convergent arguments are less vulnerable than linked

arguments to criticism of the acceptability of their premises:

An important feature of convergent reasoning is that the support given to the conclu-

sion by each separate reason, or line of reasoning, would remain unaffected even if the

other [. . .] reason(s) were false. (1986: 61)10

Pinto and Blairs (1993) definitions closely resemble Thomas distinction

between linked and convergent arguments. They make a distinction between

a group of premises that together form one inference and independent

groups of premises which can be seen as parallel inferences to arrive at

the same conclusion:

What makes for groups of premisses which are independentof each other? The fact that

the premisses work in combination to support the conclusion constitutes them as a set

or group, and the fact that the premisses of each group are able to provide their support

without any help from premisses in any other group make them independent of each

other (1993: 77).

From their examples it becomes clear that just like in Thomas approach,



11/27

a premise group may both consist of premises that deductively entail theconclusion, and of premises that taken together make a conclusion likely

or plausible (1993: 111).

Independent groups of premises should be evaluated separately for

inference strength:

you should consider each independent group separately and try to judge how strongly

its premisses taken together are linked to the conclusion (109).

Even though independent groups of inferences (or parallel inferences)

are to be evaluated separately, they are linked up by Pinto and Blair when

diagramming their structure. This becomes clear from step three in their

diagramming method:

Step 3: Make a full diagram showing all the inferences in the reasoning. In doing so,link up any [. . .] parallel inferences (1993: 260)

Pinto and Blair do not specify what the consequences are for the overall

evaluation if one of the groups of premises provides strong support, but

the other weak. The fact that they link parallel inferences in the diagram-

matic representation, however, suggests that they think that the groups of

premises should be assessed in combination in evaluating the overall

strength of the argument.

Whereas Thomas and Pinto and Blair analyze both deductive and non-

deductive arguments as linked, Goviers (1992) distinction between linked

and convergent support more or less coincides with the distinction between

deductive and non-deductive arguments, albeit that she also considersanalogies as linked:

In most deductively valid arguments, and in analogies, the support provided by the

premises is linked, not convergent. There are exceptions, as when a person offers two

separate premises, both of which deductively entail the conclusion, but this is quite rare.

There are arguments in which support is convergent and in which the premises do not

entail the conclusion nor support it by analogy [. . .] These arguments we call conduc-

tive arguments. [. . .] Some philosophers have referred to these arguments based on

separately relevant factors as good reasons arguments. The relevant factors provide reasons

for the conclusion, though they do not deductively entail it. (1992: 308309)

Linked arguments are thus deductions or analogies, and convergent argu-

ments are non-deductive (i.e. conductive) unless they consist of two

premises that each deductively entail the conclusion, but, according to

Govier, One might also insist that such a case represents several argu-

ments all with the same conclusion (1992: 356).11

As soon as a premise can be seen as separately relevant, the argument

is analyzed as convergent by Govier, even if the premises need to be taken

together to provide sufficient support to the conclusion. But analyzing an

argument as convergent has no further consequences for the evaluation: It

is not the case that each of the premises should then be separately assessed.



12/27

Govier claims that the separate premises in a convergent argument shouldalways be treated as a unit:12

There are [. . .] two basic facts to understand right now about the way in which premises

support conclusions. First, premises should be considered together in their support. Second,

they may be linked or convergent. In the latter case, it would be possible to see each

premise as providing a separate reason or separate bit of evidence, in support of the

conclusion, but the whole argument requires us to think of these separate strands together,

as the weight of support accumulates. (1992: 48)

Groarke, Tindale and Fisher (1997) and Copi and Cohen (1990) give similar

definitions as Govier of linked and convergent premises.13 Groarke, Tindale

and Fisher make the distinction in the following way:

Linked premises work together. Taken independently, they do not support the arguments

conclusion. Convergent premises do not require each other, for they support the conclu-sion independently of the arguments other premises. (1997: 35)

If all of the premises but one of a convergent argument were to be taken

away, we would have a weaker argument, but the premise would still

provide some evidence for the conclusion. None of the premises requires

one of the other premises for this to be the case (1997: 36). In other

words, the premises are independent in the sense that they are separately

relevant, that is, lend some support to a conclusion by themselves.

According to Copi and Cohen, premises depend on each other if each

premise supports the conclusion through the mediation of the other premiss

(1990: 20). If one of two interdependent premises were true, but the other

not, the conclusion would have been given no support at all (20). Two

premises support a conclusion independently if each supplies some warrantfor accepting the conclusion and would do so even in the absence of the

other premiss. (1990: 19). How independent are the arguments then in a

convergent argument, according to Copi and Cohen? Do they consider them

as separate arguments for the same conclusion, as Thomas does? This is

not the case:

Emerging practice is to say that it is one argument with two independent premisses. The

principle seems to be that the number of conclusions determines the number of arguments.

So by a single argument is meant an argument to a single conclusion, regardless of

how many premisses are adduced in its support. (1990: 1920)

However, this remark does not really clarify what exactly Copi and Cohen

mean by independent premises, since they now introduce a new crite-

rion for the singleness of an argument: the number of conclusions insteadof the probative force of the individual reasons.

Johnson and Blair (1994) use a different definition of single argument

than Copi and Cohen: they speak of a single argument if it contains one

premise set and one conclusion (1994: 37). Premises belong to one set,

if they are relevant in combination (p. 36). Convergent arguments consist

of a combination of two or more premise sets, and therefore of a combi-

nation of arguments:



13/27

When there are, in effect, two or more distinct independent grounds for a conclusion, thinkof each ground as a separate argument. (1994: 38)

Convergent arguments can typically be found in a case, which consists

(minimally) of arguments for the claim and arguments against the claim

(1994: 247). Each distinct argument for a claim is called a line of

argument. In cases where the premises constitute several independent

lines of arguments, the relevance is checked for each premise individu-

ally, but the sufficiency of these premises should be established by

considering them as a whole:

Check the premises individually for relevance. [. . .] Finally, check for sufficiency: Do

the premises, taken together, satisfy the sufficiency requirement? Do they provide enough

support for the conclusion? (1994: 269)

From this comparison of informal logical approaches to argument struc-

ture, a number of differences emerge. For Thomas, premises are

interdependent both when no premise separately lends any support to the

conclusion, whereas the combination of premises does and when each

premise separately provides some support to the conclusion, but the com-

bination of premises forms a stronger argument than each premise by

itself. Both deductive and non-deductive arguments consisting of premises

whose separate support is too weak for them to stand on their own are

analyzed as linked by Thomas. Only if each reason alone would be enough,

if true, to support the conclusion, and if the falseness of one reason would

not weaken a step of reasoning from the other to the conclusion, the rea-

soning may be regarded as convergent. Linked arguments are seen as

equivalent to one single argument, whereas convergent arguments areregarded as a combination of single arguments, which should be sepa-

rately evaluated for their strength of support. Pinto and Blair seem to employ

similar definitions of linked and convergent arguments as Thomas. They

also think independent groups of premises should be assessed separately for

their strength of support, but they are less clear as to how these separate

assessments should be used in the overall evaluation of an argument.

Other authors (such as Govier, Copi and Cohen, and Groarke, Tindale

and Fisher) employ a more restricted definition of interdependency:

Arguments are interdependent only when they are separately irrelevant to

the conclusion and relevant in combination. As soon as premises can be

seen as separately relevant (as providing some support to the conclusion),

they are considered to be independent, and thus convergent. This is alsothe case if they can only in combination lend sufficient support to the

conclusion. To the evaluation of whether the amount of support the premises

lend to the conclusion is sufficient, it makes no difference whether the

premises are independent or interdependent in these approaches: they are

always considered together in their support during the evaluation.

Johnson and Blairs position seems to be intermediate: on the one hand,

just like Thomas and Pinto and Blair, they consider convergent arguments



14/27

as separate arguments. On the other hand, they claim that the sufficiencyof support should always be assessed by checking whether the different

premises (or reasons) taken together provide sufficient support for the

conclusion. It is unclear in their approach what the consequences would

be for the evaluation of the argument as a whole if one of the lines of

argument would be flawed but one or more of the other arguments would

prove to be acceptable.15 In Johnson and Blairs view, the question of

whether an argument is single or convergent is only important for deter-

mining whether one should take the premises together in determining their

relevance, or whether each premise should in principle be relevant by

itself. The singleness or complexity of an argument does not make any

difference to the evaluation of the strength of the argument: in either case,

the premises are considered as a whole. Although Johnson and Blair observethat convergent arguments are typical of a case, in which one should

respond adequately to relevant objections, they do not devote any atten-

tion to the connection between the burden of proof and the argument

structures that result from arguers attempts to fulfil their obligations.

Although at first sight the definitions given by van Eemeren and

Grootendorst (1992) seem to resemble the definitions provided by Thomas,

Johnson and Blair and Pinto and Blair, there is an important difference: both

the equivalent of a linked argument (coordinatively compoundargumenta-

tion) and the equivalent of a convergent argument (multiple argumentation)

are seen as forms of complex argumentation consisting of a number of single

argumentations:

Analytically, complex argumentation can always be broken down into single argumen-

tations. (1992: 73)

The distinction between coordinative and multiple argumentation is there-

fore not that coordinative argumentation describes the relations between

premises within one single argument and that multiple argumentation

consists of a combination of single arguments, but that the relations between

the single arguments that constitute these two types of complex argument

are different. In multiple argumentation, the constituent single argumen-

tations are, in principle, alternative defenses of the same standpoint (1992:

73). In coordinatively compound argumentation, unlike in multiple argu-

mentation, all the component single argumentations are, in principle,

necessary for a conclusive defense of the standpoint (1992: 77).In pragma-dialectics, unlike in most informal logical approaches, coor-

dinatively compound argumentation always consists of a combination of

(independently relevant) arguments, that nonetheless need to be taken

together for reasons of sufficiency. Coordinatively compound argumenta-

tion is therefore comparable to the concept of a convergent argument in

the definitions given by Govier, Groarke, Tindale and Fisher and Copi

and Cohen. The premise structure of a single argument is not dealt with



15/27

by van Eemeren and Grootendorst in the context of argument structure.Premise structure is seen as an issue of a different hierarchical nature than

argument structure. Each separate argument in a coordinatively compound

argumentation can be analyzed as a single argument, consisting of two

premises, one of which is usually left unexpressed.16

Van Eemeren and Grootendorst give the following two examples to

explain the difference between the two structures. Example (1) is an example

of a multiple argument; example (2) of a coordinative argument:

(1) Postal deliveries in Holland are not perfect. You cannot be sure that a letter will be

delivered the next day, that it will be delivered to the right address and that it will

be delivered early in the morning. (1992: 73)

(2) Postal deliveries in Holland are perfect. You can be sure that a letter will be deliv-

ered the next day, that it will be delivered to the right address, and that it will be

delivered early in the morning. (1992: 77)

In example (1), each of the single argumentations is in principle sufficient

to defend the standpoint. What would be the reason for an arguer to produce

multiple argumentation if one single argument might have sufficed? Van

Eemeren and Grootendorst mention the following possible reasons:

It is possible that the speaker tries to cater for various kinds of doubt about his stand-

point, pertaining to different aspects. [. . .] Multiple argumentation can also be used for

rhetorical reasons: the profusion of arguments makes the defense appear stronger. The

speaker gives the impression of having taken account of every possible objection to his

standpoint. [. . .] Because acceptance is liable to gradations, in producing a multiplicity

of arguments the speaker may gradually overcome the last remaining morsel of doubt

in the listener. It may also simply be that after one argument the speaker advances

another quite different sort of argument in the hope that it will be more successful.(1992: 74)

In example (2), the three argumentations that support the standpoint that

postal deliveries in Holland are perfect are interdependent: Only if they are

taken together, they are deemed to provide sufficient grounds for accepting

the standpoint. If [any] of the single argumentations proves to be unac-

ceptable, the entire coordinatively compound argumentation falls apart

(1992: 77).

The main reason given by van Eemeren and Grootendorst for putting

forward a coordinative argument is :

in many cases, it is not possible to remove all the antagonists doubts by means of one

argument. When defending his standpoint, the protagonist then has to advance two or more

connected arguments that, only when taken together, are supposed to constitute a well-rounded and conclusive defence. (1992: 77)

Each individual argument (or reason) in a coordinative argumentation gives

some partial support to the standpoint, but the degree of support per

argument may vary:

Although the term coordinative may suggest that the argumentation consists of a series

of arguments that are equally important, this need not be so. It is, for instance quite possible



16/27

for one argument to account for, say, 60% of the cogency of the argumentation, the nextfor 10%, and the third for 20%.

Apart from the fact that the concept of argument structure applies to

combinations of single arguments in van Eemeren and Grootendorsts

approach, a second difference with the informal logicians approach is

that they explicitly connect argument structures with the dialectical situa-

tion: it depends on the antagonists doubts and the way the arguer attempts

to deal with these doubts what the resulting structure of his argument will

be. In this respect, the pragma-dialectical approach can be seen as a con-

tinuation of the functional aproach of the theory of stasis and debate.

Theoretical approaches

In the 1990s, three monographs on argument structure appeared: Freemans

(1991) Dialectics and the Macrostructure of Arguments, Snoeck

Henkemans (1992)Analysing Complex Argumentation and Waltons (1996)

Argument Structure; A Pragmatic Theory. What these three approaches have

in common are, first, dissatisfaction with the unclear and ambiguous way

in which the concepts of independent and interdependent arguments have

been defined in the literature, second, the aims of arriving at more precise

definitions and giving a functional justification of structural distinctions

by means of a dialectical approach. Whereas Freeman and Snoeck

Henkemans each propose a dialectical model of argument structure, Waltons

contribution mainly consists in a critical discussion of the existing defini-

tions and tests for deciding whether an argument is linked or convergent.He supports the dialectical approaches to argument structure, and introduces

a new system of diagramming argument structure.

Freemans (1991) thesis is that argument structures should be analyzed

as the results of argumentative processes, i.e. of challenger-respondent

dialogues.17 His approach to argument structure is to a large extent based

on the procedural model introduced in Toulmins The Uses of Argument

(1958). In Freemans view, a theory of argument structure should provide

a clear-cut demarcation of argument structures. Such a theory should provide

a rationale for distinguishing different types of argumentative elements and

structural configurations (1991: 37).

In his endeavor to provide such a rationale, Freeman takes the basic

dialectical situation as a starting-point: a respondent develops an argumentin response to the questions of a challenger. The situation is dialectical,

and not merely dialogical, if the challengers questions are aimed at criti-

cally testing the claim and if the whole interactive process is clearly

regimented.

In the basic dialectical situation, the challenger can ask three types of

basic dialectical or argument generating questions: acceptability ques-

tions, relevance questions and ground adequacy questions. Each of these



17/27

questions calls for a specific elaboration of the argument by the respon-dent and results in a different type of argument structure.18

Linked and convergent argument structures (as well as other types of

argument structure) are analyzed as answers to different types of dialec-

tical questions: a linked structure is the result of the respondents answer

by means of a relevance explaining premiss (9394) to the question

of relevance (Why is that reason relevant to the claim?). A convergent

structure results from the arguer giving more evidence for the conclusion

in response to a ground adequacy question (Can you give me another

reason?) (95). Then, the result of the exchange is an argument with premises

that are each independently relevant to the conclusion.

For Freeman, linked structure is exclusively connected with the question

of relevance: premisses are linked when we need to take them togetheror they are intended to be taken together to see why we have a relevant

reason for the conclusion (1991: 94) According to Freeman, the source

of confusion in the definitions of linked structure in most textbooks is the

lack of clarity as to whether the arguments are linked because each of the

premisses by itself is irrelevant to the conclusion, or because each of the

premisses by itself provides insufficientsupport for it. In addition to the

normal concept of a linked argument, Freeman introduces a second type

of linkage, modal linkage. Freeman introduces a special notation for this

type of linkage. In this way, he thinks, we have a perspicuous way of

accomodating some intuitions of those who want to link, while still keeping

modality and relevance issues distinct (1991: 104). In modal linkage,

each premise constitutes a separate reason for the conclusion, but the pre-

misses only in combination lend sufficient support to the conclusion. Snoeck

Henkemans (1994) points out that it is questionable whether Freeman has

indeed succeeded in achieving his aim of clarifying the distinction between

linked and convergent arguments:

This solution merely adds to the confusion concerning the concepts of linked and con-

vergent structure: an argument can now be (modally) linked and convergent at the same

time. Another problem is that Freeman ignores the possibility that a convergent argument

consists of premisses that are not only separately relevant but also have sufficient weight

by themselves: in his approach, all convergent arguments are modally linked. Instead

of clarifying the distinction between linked and convergent arguments, his solution amounts

in fact to drawing a distinction between two types of linked argument. (1994: 320321)

Snoeck Henkemans (1992) gives a pragma-dialectical analysis of multiple

and coordinative argumentation as resulting from different types of defen-sive moves aimed at removing different forms of criticism. This analysis

can be seen as an elaboration of van Eemeren and Grootendorsts (1984)

pragma-dialectical discussion procedure, in which different types of argu-

mentation are regarded as functional means to further the resolution of a

difference of opinion. Snoeck Henkemans (9293) develops a model in

which rules are given for responding to criticism. The type of criticism

and the way an arguer chooses to deal with this criticism determines the



18/27

form of complex argumentation that will arise in a discussion. When anarguers attempt to get his standpoint accepted on the basis of an argument

meets with criticism, the arguer can use various types of argumentative

strategies to make his standpoint acceptable as yet. He can advance more

arguments to anwer the criticism, he can attempt to counter the criticism

with new arguments, or he can withdraw the original argument and under-

take a new attempt at defending the standpoint.

If the antagonist has criticized the argument for reasons of sufficiency,

the protagonist can attempt to remove the criticism by supplementing his

argument with another argument. This can be done in two ways. The pro-

tagonist can add one or more arguments that in combination with the

argument given earlier should suffice to convince the antagonist of the

acceptability of the standpoint (direct defense). The protagonist can alsorefute the counterargument that has been used by the antagonist against

the original argument (indirect defense). Both types of defense result in

coordinative argumentation, but in the direct defense case the argumenta-

tion is called cumulative and in the indirect defense case it is called

complementary.19 In both cases, the arguments that are put forward must

be combined, because the arguer can only convince the opponent of the

acceptability of the standpoint if he succeeds in removing the opponents

doubt, or criticism regarding the sufficiency of the argumentation.

In multiple argumentation, the only connection between the arguments

is that they are all advanced as a defense of the same standpoint. In a

completely externalized discussion, a protagonist who finds that he is not

capable of dealing with the antagonists criticism, may withdraw his

argument and undertake a new attempt to defend the standpoint. The

argumentation is then multiple in the sense that more than one attempt to

defend the standpoint has been undertaken, but the final result is in fact a

single argument. In an implicit discussion this is different. In anticipation

of a possible non-acceptance of his argument, the protagonist may advance

a new argument. Each of these arguments is a separate attempt to defend

the standpoint, and is motivated by the (potential) failure of a previous

attempt.

In his approach to argument structure, Walton (1996: xiv) proclaims to

use methods similar to Freeman (1991) and Snoeck Henkemans (1992), and

to take a pragma-dialectical approach, although some of his solutions will

be different. His main goals are to develop more refined guidelines foridentifying linked and convergent arguments and to rescue and refine the

technique of argument diagramming. Walton discusses numerous examples

of linked and convergent arguments and develops a classification and ter-

minology of the different tests used in the literature to determine whether

an argument is linked or convergent.

Walton discusses the following five tests (for simplicity, he applies

them only to two premise arguments):



19/27

1. Falsity/No Support Test: If one premise is false, the conclusion is not given any support.2. Suspension/Insufficient Proof Test: If one premise is suspended (not proved, not known

to be true) the conclusion is not given enough support to prove it.

3. Falsity/Insufficient Proof Test: If one premise is false, the conclusion is not given

enough support to prove it.

4. Suspension/No Support Test: If one premise is suspended (not proved, not known to

be true), the conclusion is not given any support.

5. Degree of Support Test: reasons are dependent when together they make the overall

strength of the argument much greater than they would considered separately (1996:

119120, 127).

Whereas the first four tests are based on the idea of whether the conclu-

sion is given enough or any support to prove it and are thus absolutistic,

all-or-nothing kinds of tests (121), the Degree of Support Test is a matter

of degrees.20

In order to determine which of these tests should best be used, Walton

thinks one should consider the purpose of distinguishing between these

structures, the evaluation of argumentation:

The critic needs to know whether it is necessary to refute both the [. . .] premises, or if

it is enough to find fault with just the one, in order for the whole argument to fall down.

[. . .] From this point of view, the pragma-dialectical viewpoint represented by the van

Eemeren and Grootendorst conception of the linked-convergent distinction is basically the

right one, because it is centrally concerned with the question of whether a set of premises

is sufficient for a conclusion, where sufficient means adequate to resolve the other partys

doubts in a context of a critical discussion. (1996: 175)

Walton adopts afunctional interpretation of the linked-convergent distinc-

tion, meaning that it relates to how the premises of an argument function

together in supporting the conclusion in a context of dialogue (1996:

177). Seen from this perspective, the fact that there are many cases where

it is hard to determine whether an argument is linked or convergent are

not an indication that the linked-convergent distinction is vague or inco-

herent: it is possible to see why, in many cases, it is difficult or even

impossible to determine categorically whether the argument is linked or

convergent. The reason: there just isnt enough evidence given to enable

us to determine how the argument is being used in the given context

(178).

Waltons conclusion is that the Suspension/Insufficient Proof Test is

the best test in the sense that it is congenial to our pragmatic theory of

argument because of its frankly dialectical conception of an argument as

a dialectical exchange. According to Walton, this test is used by pragma-dialecticians such as van Eemeren and Grootendorst and Snoeck

Henkemans. Applying this test is problematic, however, since it is extremely

difficult in practice to determine whether or not the support for a conclu-

sion is sufficient (180181). Moreover, the fact that this text contextualizes

the distinction between coordinative and multiple argumentation may be

positive in itself, but it also makes the test more difficult to apply in cases

where this contextual background is not available. In such cases, according



20/27

to Walton, the Degree of Support Test is most useful to determine whetherthe argument can best be analyzed as linked or as convergent (1996:

179181).

Finally, Walton also proposes a new method of diagramming linked and

convergent arguments, the graph method:

The most important thing is to see that, by changing from the old notation to the graph

method, we are freed from always being forced to model an argument as either linked

or convergent. It is for this reason that the recommendation is made here that we should

move from the existing method of argument diagramming to the new method of

reasoning graphs (1996: 187).21

4. METHODS IN THE ANALYSIS OF DOUBTFUL CASES

According to Snoeck Henkemans, (1992: 43), the problem of making a

choice between a linked or a convergent analysis of an argument, is not

simply caused by a lack of clarity in the definitions, but also by the lack

of information concerning clues in the verbal presentation. Van Eemeren

and Grootendorst (1992: 7585) are an exception: they mention a number

of words and expressions that can be indicative of coordinatively compound

and multiple argumentation. Examples of indicators of multiple argumen-

tation are: quite apart from, and then I havent even mentioned the fact

that, and needless to add that. Indicators of coordinatively compound

argumentation are: in addition to the fact, when it is also remembered

that, as well as the fact that.

Snoeck Henkemans (1992) adds three types of clues to van Eemerenand Grootendorsts indicators of argumentative structure: pragmatic clues

in the way the arguer has presented the standpoint, dialogical clues in his

references to criticism, and dialectical clues following from the assump-

tion that he observes the procedural norms for a critical discussion,

specifically those norms that are related to the burden of proof. 22 Among

the pragmatic clues are expressions by means of which the arguer indi-

cates the force of his standpoint, and the quantifying elements in the

propositional content of the standpoint: they influence the burden of proof.

Among the dialogical clues are the arguers acknowledgements and refu-

tations of counterarguments. Among the dialectical clues are the procedural

norms pertaining to a critical discussion. One of them concerns the require-

ments an arguer should meet if his argumentation is to defend theacceptability, or unacceptability, of a speech act; the other concerns the

requirements he should meet to justify the use of a particular argumenta-

tion scheme. These two types of requirement enable the analyst to determine

whether, in order to lend sufficient support to the standpoint, the argu-

ments that are advanced should be taken together, or whether they should

be taken to stand by themselves.

In cases where there is doubt as to whether an argument should be



21/27

analyzed as linked or convergent, informal logicians generally instruct theanalyst to apply the types of tests that have been classified by Walton (1996).

Groarke, Tindale and Fisher (1997) are an example:

If you have difficulty deciding whether you should join one premise P to another, ask

whether the support it provides for the conclusion depends on some other premise(s) (1997:

36)

Problems in deciding on the right structure of an argument are generally

attributed to a lack of clarity in the definitions, and the absence of clear

and decisive tests. According to Walton, when diagramming arguments,

there are many cases where there is room for more than one interpretation.23

This leads to a pedagogical problem in argumentation courses, which is

compounded by the use of short contextual examples as arguments, con-joined with the use of a test that appears to be precise, decisive, and

non-contextual (1996: 108). In a functional approach in which it depends

crucially on the context of dialogue how the structure of a given argument

should be analyzed, one should be prepared to accept that there will be cases

where there is not enough contextual evidence to enable a well-founded

decision (1996: 178). Apart from contextual evidence (evidence concerning

the type of dialogue, the stage of the dialogue and the burden of proof),

the analyst can make use of structural evidence (evidence of the type of

reasoning (deductive, practical) being used) and textual evidence (indi-

cator words, such as My one reason for believing is this, and my other

reason is that and This reason, taken along with my other reason [. . .]

shows that my conclusion is true), which give clues as to how the argument

is structured. Once all these types of evidence have been collected, therelevant test can be applied as a fourth resource that may help in the iden-

tification of the argument.

Some authors propose a special policy for problematic cases. The policy

which both Thomas (1986) and Nolt (1984: 32) propose for doubtful cases

is to start with a linked interpretation. To Nolt, the main reason for

advocating this policy is that it is the most charitable: he thinks that in

borderline cases an argument is usually strongest if it is regarded as linked.

Thomas realizes that there may be situations where the policy might not

be to the advantage of the arguer:

Probably, you will want to separate reasons, and diagram reasoning as convergent, anytime

you suspect that one of the lines of reasoning is bad, while the other line of reasoning

is good (1986: 65)

Thomas justifies his approach by saying that it is in accordance with his

Principle of Charity: When unclarity exists, analyze reasoning in whatever

way it gives the greatest strength (1986: 89). Snoeck Henkemans (1992)

objects to this solution because she thinks that the analysis and the evalu-

ation of an argument are mixed up in this policy.24 The question of whether

the arguers reasons are good or bad, only becomes relevant when the



22/27

argumentation is evaluated. In deciding on whether the argumentation isbest analyzed as convergent or as linked, a different issue is at stake:

The decision on whether to analyze the argumentation as linked or as convergent only

depends on the degree of support which the premisses, either separately or jointly, lend

to the standpoint, and should not be confused with an assessment of the acceptability of

the premisses (1992: 42)

Van Eemeren and Grootendorst (1992: 8182) propose a policy, called the

strategy of maximally argumentative analysis, which is the converse of

Nolts and Thomas policy. In cases that cannot be decided on pragmatic

grounds, they advise to start by analysing the argumentation as multiple (i.e.

convergent). They motivate this strategy as follows:

By way of this strategy, all single argumentations are being given the greatest possiblecredit [. . .] analyzing the structure as multiple can, at the same time, be called more

and less charitable than analyzing it as coordinative. It is more charitable, because in

multiple argumentation each individual argument is supposed to have its own, indepen-

dent argumentative force and, in addition, dropping one unacceptable argument does

not automatically undermine the whole argumentation. It is less charitable, because in

multiple argumentation, in principle, all the individual arguments must be separately

conclusive. More important than charity, however, is from a dialectical perspective that

the quality of each and every individual argument shall be examined critically (1992:

8181)

5. CONCLUSION

Two approaches to argument structure, the functional approach of theclassical theory of stasis (and of the debate tradition) and the logical

approach of identifying argument structure with different inference types,

have continued to exist until present. Dialectical approaches to complex

argumentation can be seen as a continuation of the tradition of viewing

argument structures as the result of an arguers attempts to deal adequately

with an opponents objections in a context of dialogue. Just as in clas-

sical status theory, it depends on the requirements the arguer should meet

to provide sufficient support for his standpoint (and thus on the dialogical

context) whether or not these arguments should be taken together, or seen

as separate, alternative defenses. In contrast with all informal logical

approaches (and with Freemans dialectical approach), argument structures

in pragma-dialectics are always analyzed as combinations of single argu-

ments. As a result, a large category of linked arguments dealt with by

informal logicians, i.e. those linked arguments that are equivalent to one

single argument, falls outside the scope of the pragma-dialectical treat-

ment of argument structures.

In informal logic, the logical tradition is still predominant. Informal

logicians are either concerned with describing different types of premise

structure within one (deductive or non-deductive) inference, or with dis-



23/27

tinguishing between arguments with one inference and arguments consistingof a number of inferences, that is, with the distinction between single and

complex argumentation.

The definitions given in informal logic of the key concepts, linked and

convergent arguments, differ considerably. The guidelines that are given for

evaluating linked and convergent arguments also vary from author to author.

Authors who give a narrow definition of linked arguments, regarding only

premises as interdependent that need to be taken together in order to be

relevant, generally advise to always consider all the premises together when

evaluating the argument, regardless of the structure of the argument. In

this interpretation of argument structure, part of the rationale for making the

distinction between interdependent and independent arguments is lost. There

also seems to be a general (though unsupported) belief among informallogicians that structures consisting of combinations of separate arguments

are extremely rare, and therefore not worth any serious attention. This belief

in itself may be traced back to the logical tradition where presenting more

than one independent proof is, generally speaking, superfluous. In the

context of our everyday discussions, however, one can rarely be sure that

a defense that should be conclusive will really convince our opponent and

one is often at the same time addressing several opponents with different

views. Presenting a number of arguments which would, if acceptable, each

provide sufficient support to the conclusion, may then often be the only

realistic option.

NOTES

1 A complex argument is an argument that consists of a number of single arguments for

a conclusion. A single or individual argument is the equivalent of a reason.2 The Aristotelian sorites can also be analysed as a serial argument in support of the

major premise.3 In his study of classical status theory, Braet (1984: 55) points out that classical rhetori-

cians seem to have had some idea of the difference in burden of proof for the defendant

and the prosecutor, but that they did not devote any systematic attention to this difference.

The emphasis was always on the defendant. Quintilian is an exception.4 The same difference in obligations for the defendant and the prosecutor is found at the

sublevels of the argumentation. Cicero (De Inventione 2, 3233) points out that the prose-

cutor cannot just prove that the accused had a motive for his crime unless he also proves

that the character of the defendant is consistent with his having such a motive (and vice versa).

The defendant should show that the accused has never committed any offence, and thisargument will be strengthened if it can be shown that when he had an opportunity of doing

a dishonest deed with impunity he had no desire to do so (Cicero, De Inventione 2, 35).5 In refuting an opponents argument though, one should be careful not to adduce much more

than is sufficient to prove ones conlusion, according to Whately, since otherwise ones

opponents may become distrustful (1846: 165).6 Mills gives the following example: Installment buying is harmful if it encourages people

to live beyond their means, and it does so; it is harmful if it causes inflation, and it does

so, etc. (1968: 183)



24/27

7 Ray and Zavos (1966: 99) give the following definition of an argument from circumstance:[It] is an argument in which a number of particulars are brought to bear on some point. It

is usually used to prove the occurrence of some past event.8 According to Thomas, a more important criterion for the independency of premises is

that the falseness of one reason would not weaken the step from the other to the conclu-

sion than that each of them individually supports the conclusion: It is possible to have a

correct convergent diagram in which the result of combining the separated reasons would

(if this were done) be a stronger argument than either reason provides alone, as long as the

negation or falsity of the various separated reasons would not decrease the support given

by the other(s) to the conclusion. (1986: 62)9 Yanal (1991: 139) gives a similar analysis of the distinction between dependent and

interdependent reasons: What [. . .] is the difference between dependent and independent

reasons? [. . .] Dependent reasons form one argument; independent reasons form multiple

arguments.10 The idea that convergent arguments are less vulnerable than linked arguments is all myth

according to Conway (1991: 155): Even when premises clearly work together, we knowperfectly well that the falsity of one need not necessitate rejecting the entire argument.

With any sort of argument, when we find that one of the premises are false, we dismiss

the unacceptable premises and evaluate the support on the basis of those that remain. We

do not need a notion of convergent support to enable us to do this. Conway concludes that

we can very well do without the notion of convergence (156).11 It is not clear to which category inductive generalizations belong in Goviers classifica-

tion.12 According to Conway (1991: 148149), if individual relevance is the criterion for

convergence, the distinction does not correspond to our intuitions about the separateness

of premises. Moreover, an argument being convergent on this criterion cannot serve as an

instruction to evaluate each line of support separately or to evaluate the degree of support

of the premises for the conclusion in any other particular way. Conway concludes: if there

is any evaluative importance to the linked/convergent distinction, understood in this way, it

is not in the area of the degree of support premises give to a conclusion (149).13 Similar definitions of linked and convergent arguments as Goviers are also given by

Kelley (1988: 687), albeit that he uses the terms additive and nonadditive premises.

Fishers (1988: 19) definition of independent arguments is somewhat different, since he

analyzes independent reasons as reasons that are intended by the author to lend conclusive

support to the conclusion by themselves: reasons may be presented as independently justi-

fying a conclusion so that if you accept one of the reasons the author expects you to

accept the conclusion. Nolts (1984) criterion for independence is ambiguous: on the one

hand he seems to consider arguments as interdependent if they form one inference, and

independent if they each constitute a separate inference; on the other hand he recommends

combining inferences to produce a single inference in cases where such a combined infer-

ence would make a stronger case (1984: 32). In this respect, his approach is more like Thomas

approach.14 Vorobej (1995b) gives similar defintions as Govier (1992) and Copi and Cohen (1990),

but also introduces a third category of premise structure: the hybridargument. In conver-

gent arguments, according to Vorobej, each premise, in isolation, is relevant to or provides

a reason in support of the conclusion (289). If a set of premises is relevant to the conclu-

sion, whereas no subset of the premise set is relevant to the conclusion, an argument is

linked (290). In hybrid arguments, the relation between the premises is asymmetric. One

premise (or premise set) is relevant on its own and another premise (or premise set) is not

relevant to the conclusion on its own. The latter premise (or premise set) supplements the

other premise (set): taken together, the premises provide a better argument for the conclu-

sion than the one relevant premise (or premise set) alone (292).15 According to Conway (1991: 149), there are many authors who are unclear as to how

the evaluation of convergent arguments should take place: Remarkably, most who claim



25/27

that the linked/convergent distinction is important for evaluation say nothing about how toevaluate convergent arguments.16 Even though each coordinative argument is analysed as composed of a number of single

argumentations that each consist of two premises, one of which has been left unexpressed,

in reconstructing a coordinative argument, one combinedunexpressed premise is made explicit.

This is done to make it clear that it is only in combination that the arguments are supposed

to lend sufficient support to the standpoint. For instance, in an example of a coordinative

argument that is provided by van Eemeren and Grootendorst (1992: 89), two single arguments

are given for the standpoint that The Telegraph is a good newspaper: 1. The Telegraph

contains facts, news and background information; 2. The Telegraph is a common-sense

newspaper. In the diagram of this argument the following unexpressed premise is made

explicit: A newspaper that combines quality with wisdom is good.17 The basic ideas of Freemans approach were already introduced earlier, in an article in

Informal Logic (1985) and in his textbook Thinking Logically (1988).18 Freeman thinks that there is independent confirmation for the fact that these questions

are central to any argumentative exchange, since they pertain to the three criteria for argumentappraisal distinguished by most informal logicians, they parallel Grices (1975) conversational

maxims and are also represented in Reschers (1977) challenging moves of formal disputa-

tion.19 The terms cumulative and complementary stem from an unpublished manuscript of

Pinto and Blair. In this manuscript, they distinguish between three types of interdepen-

dency: linked premiss sets, cumulative premiss sets and complementary premiss sets.

Snoeck Henkemans (1992: 94) analyzes linked premiss sets (which consist of a minor and

a major premise) as single arguments. Explicitizing an unexpressed premise in response to

an arguers reaction is, according to her, only adequate in cases where there is a problem

concerning the comprehensibility, not the acceptability of the argument. Since all forms of

complex argumentation are seen by her as attempts to remove an opponents doubt or

criticism, and thus to resolve a problem concerning the acceptability of a given argument,

making explicit the unexpressed premise cannot result in complex argumentation. Cumulative

and complementary arguments are regarded by Snoeck Henkemans as two different ways

answering criticism of the sufficiency of one of the other arguments: if the attempt to

answer criticism consists of adding another argument that supports the standpoint directly,

the coordinative argumentation is cumulative. If it consists of a refutation of a counter-

argument, the coordinative argumentation is complementary (1992: 174). These two types

of support are reminiscent of Whatelys (1846: 88, 138) ways of combining arguments.20 In the discussion of the informal logical distinction between linked and convergent

arguments, the tests that are used to identify linked and convergent reasoning are often subject

of discussion. According to Vorobej (1994), most authors propose isolation tests for linked

arguments (tests that require the analyst to find out whether the premises are relevant in

isolation, or whether they provide less support in isolation than taken together). The problem

with those tests is that (in a weak form) they yield the result that any argument with a

single irrelevant, superfluous premise is linked, and they do not classify all deductively

valid arguments as linked. The latter is the case because many deductively valid arguments

contain no premises which are independently irrelevant to the conclusion (149). Vorobejs

own alternative is to use an elimination test, which says that an argument is linked if the type

of (positive) support which its premises offer its conclusion would be weakened upon

elimination of at least one of its premises (1994: 151). On this test, every deductively valid

argument (with two exceptions) is linked, all analogical arguments are linked, and all argu-

ments positively corroborating hypotheses. The test classifies as convergent all conductive

arguments and inductive generalizations. Isolation-relevance tests are comparable to Waltons

Suspension/No Support Test and the Elimination test is similar to Waltons Degree of Support

Test. Vorobej acknowledges that his Elimination test cannot do justice to the idea that in a

linked argument all the premises must be considered together if we are to recognize a per-

suasive case for accepting the conclusion and that convergent arguments are equivalent



26/27

to, and ought to be treated as more than one single argument (156). However, he believessuch ideas are of questionable value insofar as they tend to generate accounts of the

linked/convergent distinction which seriously run the risk of undermining the significance

of that very distinction (157). This is because, according to Vorobej, convergent arguments

consisting of multiple arguments are extremely rare. (1994: 157).21 Apart from the fact that I fail to see the advantage of not having to make a decision

between a linked or a convergent diagram, I do not think this is correct. Walton explains

that with the graph method, linked arguments all get the same number, while convergent

diagrams receive different numbers (1996: 187).22 A difference between the indicators of multiple and coordinative argumentation mentioned

by van Eemeren and Grootendorst (1992) and the clues offered by Snoeck Henkemans, is

that the first type of clues indicate how the author intends the text to be understood, whereas

the second type of clues are clues about how reasons offered in support of a conclusion support

the argument according to the most charitable analysis.23 Both Walton (1996) and Snoeck Henkemans (1992) mention a similar type of argument

of which it may be difficult to establish in practice whether it is linked or convergent.Walton calls this type of argument evidence-accumulating(132-133), Snoeck Henkemans

cumulative coordinative argumentation. According to Snoeck Henkemans (1992: 175), it

is predictable that multiple argumentation will be particularly difficult to distinguish from

cumulative argumentation, because it is not always clear whether the arguer may be assumed

to anticipate that he will have to withdraw some of his arguments, or whether he may be

assumed to believe that the arguments he has advanced strengthen each other.24 According to Vorobej (1994: 153), classifying arguments as either linked or convergent

inevitably involves adopting an evaluative point of view during the analysis. The objection

might therefore be raised that there is little point invoking a distinction between linked

and convergent arguments as an aid to argument evaluation if the distinction can be drawn

only afterengaging in that very process of evaluation. But Vorobej thinks this objection is

not sound. Appraising an argument requires several stages. Therefore, the fact that some

distinction is drawn by employing evaluative concepts and adopting an evaluative point of

view does not preclude that distinction from serving a useful purpose in the evaluative

enterprise (153).25 Vorobej makes a similar observation. He claims that determining whether an argument

is linked or convergent requires appraising the actual degree of logical support provided by

(various combinations of) the premises. Although this means that the linked/convergent

distinction does not operate purely at the descriptive level, the process of evaluation is not

over once the structure of the argument has been decided on, and the way one sho

The Structure of Argumentation

Documents

Transcript of The Structure of Argumentation