1. Introduction
Suppose that visual argument skeptics are correct: there are no visual arguments apart from any associated verbal content. Does it follow, then, that there is no place for images in argumentation theory or informal logic? The answer to this question, I argue, is no – at least in the case of photographic images. Instead, photographic images can fill an evidentiary role in which the image acts as a verifier, corroborator or refuter of some claim within an argument. This result is satisfying in two ways. First, it makes room for images even under the most hostile conceptions of argument for visual argumentation. Second, it forms the basis of an answer to a related question in philosophy of mathematics. In philosophy of mathematics, there is a debate about the role of diagrams in mathematical reasoning. This debate, in some respects, mimics the debate about the use of visual elements in argumentation. I show that the use of images as verifiers in argumentative contexts can inform an answer about the use of some diagrams in mathematical contexts. Diagrams can verify, corroborate or refute claims in mathematical arguments.  Hence, though this doesn’t mean that diagrams are proofs, it means that diagrams can play an evidentiary role in mathematical contexts.

As a preamble to this discussion, I describe and label several positions one can take as regards visual evidence. On one end of the spectrum one finds the proponent of visual arguments. This is the position of Leo Groarke (Groarke 1996, Groarke 2002) and David Birdsell (Birdsell and Groarke, 1996, Birdsell and Groarke 2007). The proponent takes visual arguments to be no less legitimately arguments than any verbal arguments. For example, Groarke offers a poster from the University of Amsterdam as a putative visual argument (Groarke 1996, p. 112). Regarding the argumentative status of the poster, Groarke is unequivocal. He writes, “From the point of view of logic, the poster is something more than a statement, for it visually makes the point that the University of Amsterdam’s chief adminstrators are all men, to back the intended claim that the university needs more women.” (Groarke 1996, p. 111) A proponent of visual argument, then, takes the resources needed to analyze visual arguments to include logic broadly construed. Groarke doesn’t limit the analysis and evaluation of visual argumentation to just the rhetorical powers of images; though he doesn’t neglect these either. Instead, the proponent as I envision him or her, thinks that argumentation includes visual elements in the most robust forms possible. Therefore, Argumentation Theory and Informal Logic ought to expand to account for these visual elements explicitly.

Before describing some middle ground in this spectrum, I consider the other end: the visual argument skeptics. The skeptic denies the possibility or actuality of visual arguments. David Fleming (Fleming 1996) and Ralph Johnson (Johnson 2003) are examples of visual argument skeptics. The skeptic needn’t deny the rhetorical power of images, but the skeptic does deny that the images are arguments properly so called. Johnson, for example, thinks that many of the items claimed by proponents to be visual arguments will, under scrutiny, turn out not to be arguments at all or will not be essentially visual insofar as the argumentative workload will be handled by associated verbal elements (Johnson 2003, pp.10-11).  Both Johnson and Fleming offer accounts of argument that may by fiat rule out visual arguments. “An argument is a type of discourse or text – the distillate of the practice of argumentation – in which the arguer seeks to persuade the Other(s) of the truth of a thesis by producing reasons that support it. In addition to this illative core, an argument possesses a dialectical tier in which the arguer discharges his dialectical obligations.” (Johnson 2000, p. 168) “To sum up, argument is reasoning towards a debatable conclusion.  It is a human act conducted in two parts (claim and support) and with awareness of two sides (the claim allows for and even invites opposition).”  (Fleming 1996, p. 18) Thus, Fleming argues that there is no way, on his conception of argument, for visual arguments to be anything more than “support for a linguistic claim.” (Fleming 1996, p. 19) But these visual elements are not arguments.

Between these extremes there are a variety of positions that one might take. One position is that of Anthony Blair (Blair 2004). Blair’s position as regards visual arguments seems to be reductionist, and hence, I would place it closer to the skeptic than the proponent. The logical content of visual arguments is propositional; hence, the logical analysis of visual arguments requires finding the associated verbal content of the putative visual argument. The rhetorical elements of visual arguments are, for Blair, not reducible to the verbal content (Blair 2004, p. 59). However, these elements pertain not to logic, i.e., to logical support, but to (mere) persuasive communication. The appraisal of visual arguments, then, reduces to two tasks. First, one must identify and interpret the associated verbal content. Second, one must determine the rhetorical strength of the visual appeal.  This appraisal of visual arguments, then, does not determine the logical strength of any of the inferences, or if it does, this appraisal will fail to capture the unique rhetorical influences of the visual elements.

There are surely other positions between skeptics and proponents. Yet, for present purposes, this classification is sufficient. The skeptics deny that visual arguments are arguments proper, while the proponents accept that visual arguments are simply arguments. Between these two views, one might take visual arguments to be visual attempts at persuasion without allowing visual arguments to have subtle logical forms. But what is important for my purpose is that on the skeptical side of the spectrum, the objections to visual arguments are that they are either wholly rhetorical or, if there is any logical content, it is overly simple and identifiable with some associated verbal content. I want to take this claim – that visual arguments are either wholly rhetorical or have logical content identified with or reducible to associated verbal content – seriously without also thereby marginalizing visual argumentation.

To be clear, I am not attempting to show that visual arguments are arguments in the strictest sense. Instead, I think there is a place for the consideration of the visual within argument appraisal even granting the skeptics main premises. So, what are the skeptic’s worries? Fleming worries that unadorned images lack the necessary properties of arguments (Fleming 1995, p. 15). A picture can function as evidence, but as such is not thereby a component of an argument.  Instead, the image is outside of the argument. To be a part of the argument, for Fleming, the image must be capable of asserting some claim.  And, apparently, evidence isn’t assertion.

It is tempting to take Fleming’s criticism of visual arguments as resting on an untoward distinction: pure versus mixed visual arguments. Let a pure visual argument be a putative argument that contains only visual elements essentially, i.e., it completely lacks verbal elements. A mixed visual argument, then, would be one that contains both visual and verbal elements essentially. Fleming’s criticism, then, would apply only to pure visual arguments. However, it is unclear what sense to give to “essentially” in this construction. One might take it to mean that an argument is essentially visual if and only if some visual element contains no associated verbal content. Taken this way, visual arguments are probably ruled out by fiat. This suggests that a better interpretation of visual arguments regards the mode of presentation. An argument is visual if it presents some element of an argument visually. In this way, the distinction is dissolved. It isn’t as if the proponents of visual argument are attempting to make it the case that the appraisal of visual arguments concerns ineffable and wholly visual content devoid of associated verbal elements. Instead, the proponents think that there are reasons to take the interpretation of visual elements as a yet under researched mode of argumentation. It is worth noting that all of the purported examples of visual argument given by Groarke contain verbal elements explicitly. Indeed, taken in this way, Fleming’s criticism is straw. None of the proponents seem to take images as sufficient for arguments.  Instead, images are components of arguments.

Still, Fleming’s complaint is that images don’t bear the right kind of relationships to verbal entities to be considered even a part of arguments. And this is where one can start to make room for the visual. Fleming himself goes part of the way in this regard. “So, if the visual cannot function as both claim and support (unless we make the distinction between them meaningless), and if it cannot, without language, be a claim, we are left with only one possibility: the visual can serve as support for a linguistic claim.” (Fleming 1996, p. 19) He goes on to focus on the rhetorical aspects of images. But for present purposes, we are left with the following: why isn’t the claim that the visual can serve as support for a linguistic claim enough to make room for the visual in argumentation.  I think that it is.  To see this, I next consider a scientific use of photographs.

2.  Visual Evidence in Science
The last scientifically accepted sighting of an Ivory Billed Woodpecker (IBWO) occurred in Louisiana in 1944 by Don Eckelberry. Since then, there have been numerous unsubstantiated sightings, including several apparent photographs. Sadly, by most accounts, the IBWO has become extinct. Thus it was a great surprise to read the title of a paper in Science, “Ivory Billed Woodpecker (campephilus principalis) Persists in Continental North America,” (Fitzpatrick, et al 2005, p. 1460). In the article, the claim that the IBWO persists was (mostly) supported by the analysis of a short, blurry video. Since visual evidence plays such an important role in this scientific argument, it makes a good case study for the use of visual elements in (some) scientific arguments.

The IBWO is a very large woodpecker up to 20 inches long with a wingspan of up to 31 inches. Its appearance is similar to another woodpecker that has not suffered the same fate. A pileated woodpecker (PIWO) can be up to 18 inches long with a wingspan of up to 25 inches. Both species are mostly black with various white and, in the case of males of both species, red plumage. The differences, though slight, are important. The trailing feathers on the wings of the IBWO are white while these feathers are black on a PIWO. The back of an IBWO has a white segment, while the back of a PIWO is black, etc.

The background for the argument is explained by the authors of this paper thusly. “At 15:42 Central Daylight Time on 25 April 2004, M. D. Luneau secured a brief but crucial video of a very large woodpecker perched on the trunk of a water tupelo (Nyssa aquatica), then fleeing from the approaching canoe. The woodpecker remains in the video frame for a total of 4 [seconds] as it flies rapidly away. Even at its closest point, the woodpecker occupies only a small fraction of the video. Its images are blurred and pixilated owing to rapid motion, slow shutter speed, video interlacing artifacts, and the bird’s distance beyond the video camera’s focal plane. Despite these imperfections, crucial field marks are evidence both on the original and on deinterlaced and magnified video fields. At least five diagnostic features allow us to identify the subject as an ivory-billed woodpecker.” (Fitspatrick et al. 2005, p. 1460) Aside from the technical term, “deinterlaced,” the setup is straightforward. A video frame is typically composed of two separate images that are interlaced to make up the image that we view. This interlacing can be problematic when someone wants to view a single frame of video tape. The two images are taken at fractionally different times and can therefore introduce unnecessary noise into the image. These frames can be deinterlaced by software. The deinterlaced image will be clearer than its interlaced counterpart. We are in a position, now, to analyze this argument. In its roughest form, the argument accumulates evidence in favor of the sub-conclusion that the subject of the video is an IBWO. From there we have, perhaps, an argument from sign (cf. Walton 2008, p.10) for the main conclusion that the IBWO persists.

The accumulation argument contains, at the very least, the five diagnostic features visible in the video. These include: the size of the bird, the ratio of white to black feathers at rest, the color of the feathers on the trailing edge of the bird as it flies away, the pattern of white feathers on the dorsum (back) of the bird as it flies away, and the pattern of white feathers on the bird as it is perched on a tree. Here are two possible reconstructions of this argument using the following numbered premises and conclusion.  I give two reconstruction because I don’t want to take a stand as to the proper reconstruction of an accumulation argument (i.e., whether the premises are independent or linked in some less-than-logical sense). (1) The bird on the video is too large to be a PIWO but the right size to be an IBWO. (2) The ratio of white to black feathers on the wings of the bird at rest are inconsistent with a PIWO but consistent with an IBWO. (3) The pattern of feathers on the back of the bird as it flies are inconsistent with an PIWO but consistent with an IBWO. (4) The color of the feathers on the trailing edge of the bird’s wings are inconsistent with a PIWO but consistent with an IBWO. (5) The pattern of white feathers on the back of the perched bird are inconsistent with a PIWO but consistent with an IBWO. Hence, (C), if the bird on the video is a woodpecker, then it is an IBWO rather than a PIWO.  (See Figures 1 and 2)

It is important to note that as reconstructed, the images don’t (seem to) play any role whatsoever in the argument. However, to evaluate the argument requires examining the video images. To take just one example: how do we know whether the argument from (3) to (C) is legitimate? There are at two levels of appraisal here. First, there is the evaluation of the support that (3) if true provides for (C). Second, there is the evaluation of the truth, acceptability or plausibility of (3). The image works in this second place. That is, if you want to know whether it is true that the pattern of black and white feathers on the back of the bird as it flies are inconsistent with a PIWO but consistent with an IBWO you have to look at the image. The image may verify or refute this claim, supposing it is clear enough to distinguish the relevant features.  The other premises are also verified, refuted or corroborated, to the extent that they can be, by the associated images.  I think Fleming is correct that this connection is something different from assertion. It would, perhaps, be a mistake to reconstruct the argument from (3) to (C) along the following lines (see Figure 3).

There are many issues for such a reconstruction. For example, how do we evaluate the strength of the inference from the image to (3)? Moreover, this reconstruction invites a bit more detail. The image in this reconstruction is probably operating within the context of a more subtle argument regarding the patterns of feathers on the two types of woodpeckers. Hence, one would expect there to be more detail about the patterns of feathers. Supposing that such a reconstruction were possible, it would likely be covered by some general scheme, say, argument from photographic evidence. Then, like an argument from sign (Walton 2008, p.10), we would expect a canonical form as well as a series of critical questions that allow for a standard appraisal of this argument form. Still, I don’t see how the picture would fit into the argument any better than with a simple exhortation, “see!” At which point the arguer invites the recipient of the argument to see for himself or herself the visual evidence.  Hence, it is probably better keep the evidential relation separate.

This account of visual evidence does not carry over to all so-called visual arguments. For example, it is clear that editorial cartoons don’t appeal to visual elements as verifiers of claims. So, this result is limited to cases of visual evidence such as photos, videos and x-rays.

3.  Visual Evidence in Legal Settings
Though not every visual element can be thought of as a verifier or refuter, we can see that this account of visual evidence as verification/refutation makes sense outside of science. In law, for example, photographs are regularly used as evidence. In an odd legal case from California (People v. Doggett, 1948), a couple was convicted of a crime. This isn’t by itself unusual. What is unusual is that the only evidence offered at the trial was a photograph. “In that case a husband and wife were convicted of a violation of section 288a of the California Penal Code, which makes criminal all acts of oral sexual perversion. The only evidence introduced at the trial to support a conviction was a photograph of the husband and wife in the commission of the alleged act. Supporting witnesses testified only as to the probable authenticity of the photographs without having perceived the commission of the alleged act.”  (Mouser and Philbin 1957, p. 311) There are two things to question about this use of photographs. First, what property of photographs allow them to work as evidence? Second, what are the limitations for such uses?  Regarding the first question, it is clear that photographs offer a visual representation of some objects. Moreover, although photos can be better or worse regarding focus, depth of field and the like, the representation is thought to be more or less accurate regarding the things represented, their spatial relations etc. Thus, by examining a photo one is presumed to have perceived some of the properties and relations of the things represented in the photo. As a more mundane example, consider the National Football League’s use of instant replay as a check on the calls of the referees. When a team challenges a call, the referee checks the instant replay. In cases where the referee has “indisputable visual evidence” to overturn the call, the referee changes the call. If videotape systematically distorted the properties and relations of the objects on the videotape to such a degree that the referee could not perceive the apparent properties and relations, there would be no reason to use videotape as a check. For the purposes of reviewing calls, videotape represents the properties and relations of the objects with enough accuracy to aid the referee in reviewing calls.

Something like this must be happening with photos (and videotape) in courtrooms as well. If photos were continually distorting the properties and relations of the objects represented, then the perception of the objects would not be accurate. And if the perception weren’t accurate, the use of photos would be deemed unreliable as a method for establishing facts in court. In the case of the Doggetts, the photo was apparently sufficiently compelling to warrant conviction.

Before moving on to the limits of the use of photos in court cases, I want to reconsider the actual use of photos to establish, verify or corroborate facts.  One might be tempted to think that in the case of the Doggetts, there was a rather straightforward warrant for conclusion: the photo clearly showed the Doggetts engaged in an illicit act; hence, they were engaged in that act. The supporting witnesses didn’t testify regarding the act, but only to the authenticity of the photo. So, it was the photo, along with the authentication that led to the conviction.

The problem with this account, though, is that we can’t reconstruct the case as a traditional argument.  That is, in reconstructing the prosecution’s case, the photo verifies the claim that the Doggetts engaged in the illicit act without also being a premise for that claim.  Here’s a possible reconstruction of the argument.  (1) If the Doggetts engaged in the illicit act, then they should be convicted.  (2) The Doggetts engaged in the illicit act.  So, (3) the Doggetts should be convicted.  The logic of the case is modus ponens.  Yet, there is no room for the photo in the logic of the argument.  But, we must not think that the only distinction is between logic and rhetoric here.  In this case, the rhetorical force of the photo is unimportant.  Instead, what matters is whether premise (2) is true.  The photo doesn’t support the claim logically, as logical support is about the  flow of truth values or truth-like values from a reason or set of reasons to a conclusion.  Instead, the photo merely verifies truth without offering logical support. One doesn’t infer the truth of the claim from the photo, one perceives it.  I don’t want to enter a discussion of the theory-ladenness of perception.  Instead, I distinguish the process of inferring, in which a claim garners support conditionally upon the acceptance of some other claims, from the process of perception, whereby one apprehends the truth or falsity of a claim by visual comparison.  The statement verified is different from the configuration of objects that constitute the subject of the statement.

The use of a photo in legal settings always has an associated verbal argument.  Moreover, the photo’s role in the argument will be as claimed above: corroboration, verification or refutation. The strength of this evidence will depend on many factors: clarity of the photo, for example. But it is the argumentation that gets logical criticism. The photo gets a different type of criticism altogether.

4.  Visual Mathematical Evidence
Turning now to mathematical examples, there are many mathematical results that are justified by non-deductive means. James Franklin (Franklin 1987) gives a litany of non-deductive methods. But, diagrammatic reasoning isn’t one of them. The reason, I think, is that Franklin is interested in logical rather than evidential methods – even when the logic is non-deductive or probabilistic. I don’t think there is a general logic for figurative reasoning, though there is much interesting logical work on certain diagrammatic systems. Some of this work derives from Ken Manders’s (Manders 2008) account of Euclidean Diagrams. I don’t want to discourage this kind of research. Yet, I am unconvinced that every case of figurative reasoning will be, much less should be, formalized. Instead, I want to consider a different possibility. Figurative proofs or arguments are associated with (perhaps tacit) verbal arguments. In such cases, the figurative elements operate much in the same way as photographs do in the law and in science: the figures verify, corroborate or refute specific claims. The claims, as verbal elements, are used in the actual reasoning. But the figurative elements are visual evidence for the associated claims rather than stand-alone arguments or proofs.  Consider Figure 4 below.

This is supposed to be a proof of the claim 1 + 3 + 5 + … + (2n – 1) = n². The argument that it leads to the conclusion is this. (1) 1 = 1².  (2) 1 + 3 = 2². (3) 1 + 3 + 5 = 3². (4) This can be continued for every number, n. So, (5) 1 + 3 + 5 + … + (2n – 1) = n². Claims 1 – 3 are verified by the diagram. Claim 4 is difficult to see in the given configuration; but one could say that it is an induction based on claims (1 – 3). So, (4) follows, though only inductively.

As a different case, consider an oft cited proof of the Pythagoren Theorem (Figure 5). I must confess that when I first saw this collection of diagrams, I did not see it as in any way connected to the Pythagorean Theorem.

Since that first experience, though, I have had the opportunity to discuss this proof with my daughter who was learning geometry in high school. As an experiment, I gave her the set of figures and asked what she thought. Like my first experience, she didn’t know what to make of the collection. I then gave her the collections of figures labeled Figure 6 below. The arrows represented lines of dependency. In this way, I gave her a way to read the figures. Moreover, this collection also contains the conclusion explicitly. Whether she understood the collection clearly, I cannot say. But I can say that she read through it with delight. More importantly, though, she had questions. She wanted to know what lines were a, b, and c respectively. She wanted to know whether the common notions from her geometry class were common to this collection, etc. From her questions, I constructed the following argument. Let the original triangle be a right triangle; label it T₀. Label the hypotenuse c. Label the vertical side a, and the horizontal side b. Let the squares built on the sides of a, b, and c be a², b² and c², respectively. Construct triangles T_{1 – 4} congruent to T₀. This was the setup of the argument. All of these claims are stipulated both as claims and as elements of the collection of figures. Now, manipulate the figure such that you construct a square out of a² and b² such that the missing pieces are filled in by the Triangles T’_1-4. This is stipulated. Next, construct a square using c² and the triangles T_1-4. This too is stipulated. Now, T_1-4 is equivalent to T’_1-4. This is a basic equivalency. Notice that the sides of the two squares are (a + b) units long. This is true of both cases. You can see it in the figure. Hence, the figure verifies or corroborates this claim. Finally, if you subtract the four triangles from each square, the remaining pieces are equivalent. On one side a² + b² remains, on the other it is c²: as verified by the diagram. To generalize the result, one needs a further claim: we could redo these manipulations on any right triangle.  From this, it follows that the result holds generally. This isn’t a proof because the claim regarding the reconstruction of the elements on different right triangles isn’t justified by the collection of figures. Instead, the original construction may provide evidence in the form of know-how for the reconstruction on a different right triangle. And if this is correct, then the argument could be reconstructed as follows. (1) Squares constructed out of the sum of the squares of the two sides of a right triangle and four triangles equivalent to the original triangle and the square constructed on the hypotenuse of the right triangle and four triangles equivalent to the original triangle are equivalent. (2) Since the constructed squares are equivalent, subtracting the four triangles from each square will result in equivalent areas remaining. (3) The result of such subtraction leaves (a² + b²) and c² respectively. Hence, (4) for this particular triangle (a² + b²) = c². (5) This construction can be reiterated on other right triangles. Hence, (6) (a² + b²) = c².

This is a general method for explaining putative figurative proofs: reconstruct them as arguments for which the figures function as evidence for (some of the) claims in the argument. This has the advantage that one need not construct a logic that allows for figurative elements within the syntax of well-formed formulae. Indeed, the logic of  figurative arguments will be the logic of any other natural language arguments. One may worry that the reconstruction of the figurative proofs as verbal arguments is not faithful to the actual practice involving such proofs. To the contrary, if you have tried to teach the proofs in Nelsen’s book (Nelson 1993) or the diagrammatic examples in Brown’s essay or his book (Brown 1999) to undergraduates, you probably ended up reconstructing the proofs along the lines I suggest above.

There is one caveat, however. Some of the visual proofs are immediate. That is, they aren’t mediated by intermediate steps. Once the figure is properly prepared, the conclusion is verified by looking at the diagram and not by reasoning through intermediate steps. This, however, does not undermine the method.  Rather, this simply points to the actual use of the diagram. A diagram or figure verifies a claim or claims. In the case of an immediate proof, it verifies the conclusion rather than some reason or premise.

Finally, I want to consider some objections that have been levied against diagrammatic reasoning to see whether they undermine the account I prefer. The objections are: (1) The resulting arguments aren’t proofs as the resulting arguments are defeasible. And, (2) The visual elements might be seriously misleading. Regarding (1), I simply accept the criticism. However, it doesn’t undermine my account because I grant that these aren’t proofs. Instead, I am interested in a wider variety of mathematical reasoning. The objection must surely be answered by anyone committed to the notion that reasoning that makes essential appeal to visual elements are proofs, that is not the view I defend and hence the objection misses my account.

Regarding the possibility of misleading diagrams, I can think of two sources. On the one hand, a diagram might be seriously misleading if it is poorly drawn. I liken such cases to shoddy photographs in legal or scientific contexts. I don’t find this type of difficulty unduly worrisome. For, insofar as the figures merely verify, corroborate or refute some claim that is used in an associated argument, the failure to verify in a particular case does not undermine the method. Rather, it seems like this possibility makes the reasoning that results from figurative elements much more like argumentation in other realms. Every argument is assessed on two dimensions: form and content. The poorly drawn figures affect the content of the resulting arguments but not the form.

Alternatively, there might be something conceptually wrong with diagrams generally. I think this is hinted at (though not in terms of being a problem) in Brown’s example of a “seriously misleading” figurative proof (Brown 1997, p. 178) (See Figure 7).

He begins by considering a figure constructed from four circles in a particular configuration. One can see that the configuration has the property that a fifth circle constructed so that it touches each of the original circles would itself be contained by a circumscribing square.  He then considers the same result extended to three dimensions. He claims that, “Reflecting on these pictures, it would be perfectly reasonable to jump to the ‘obvious’ conclusion that this holds in higher dimensions.” (Brown 1997, p. 178)  But the result fails in higher dimensions. I’ve argued elsewhere (Dove 2002) that this isn’t a failure of the diagram. Rather, it is a failure of an implicit premise in the proof: what holds in two and three dimension will hold at higher dimensions. This is surely false. So, it wasn’t the pictures that mislead.

5.  Conclusion
I have argued that the use of diagrams and figures in mathematics can sometimes be explained by analogy with the use of photographs in science and the law. The figurative elements verify, corroborate or refute claims in the associated arguments. Since the associated arguments are in the vernacular, as opposed to within some language that allows figurative elements to be proper components of sentences, the logic of these arguments should be mundane. The figures are used in the same way that images are used in other realms, e.g., photos in the law and in science. Hence, the use is not special and does not require one to treat these elements specially. As such, this makes more sense of the actual practice of mathematics than accounts that require occult faculties or specialized vocabularies. I find this result doubly satisfying. On the one hand, it makes room for some visual elements within argumentation theory and informal logic. Of course, this is only part of the story regarding arguments. As stated above, evidentiary uses of visual elements cannot explain the use of images in editorial cartoons, commercials and the like. On the other hand, the account of visual evidence as verifier etc., when applied to the case of diagrams in mathematics, solves a long-standing problem for mathematical practice. Namely, if diagrams aren’t a legitimate component of mathematical reasoning, why are so many mathematical texts littered with them? The answer, of course, is that they are a legitimate part of the reasoning. Their role, however, isn’t one of premise, but of evidence.

REFERENCES
Birdsell, D., & Groarke L. (1996) Toward a theory of visual argument. Argumentation & Advocacy 33, 1-10.
Birdsell, D., & Groarke L. (2007) Outlines of a theory of visual argument. Argumentation & Advocacy 43, (3-4), 103-114.
Blair, A. (2004).  The Rhetoric of Visual Arguments.  In M. Helmers & C. Hill (Eds.), Defining Visual Rhetorics (pp. 41-61). Mahwah, NJ: Lawrence Erlbaum Associates.
Brown, J. R. (1999). Philosophy of Mathematics, London and New York: Routledge.
Brown, J. R. (1997). Proofs and Pictures. Brit. Journal for Phil. Sci., 47,161-181.
Dove, I. (2002). Can Pictures Prove? Logique et Analyse, 179-180, 309-340.
Fitzpatrick, J.W., et al. (2005). Ivory-billed Woodpecker (Campephilus principalis) Persists in Continental North America. Science 3, (309, 5727), 1460 – 1462.
Fleming, D. (1996). Can Pictures Be Arguments? Argumentation and Advocacy, 33, 1, 11-22.
Franklin J. (1987). Non-Deductive Logic in Mathematics. British Journal for the Philosophy of Science 38 (1),1-18.
Groarke, L. (1996). Logic, Art and Argument.  Informal Logic 18, (2-3), 105-131.
Groarke, L. (2002).  Towards a pragma-dialectics of visual argument. In: Van Eemeren, Advances in Pragma-Dialectics.  Amsterdam: SicSat, and Newport News:Vale Press.
Johnson, R.H. (2005). Why “Visual Arguments” Aren’t Arguments. In: Hans V. Hansen, Christopher Tindale, J. Anthony Blair and Ralph H. Johnson (Eds.).  Informal Logic at 25, University of Windsor, CD-ROM.
Johnson, R. H. (2000).  Manifest Rationality: A Pragmatic Theory of Argument. Mahwah, NJ: Lawrence Erlbaum Associates.
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Walton, D., Reed, C., & Macagno, F. (2008).  Argumentation Schemes.  New York: Cambridge University Press.

There seems to be a mismatch between the classification of arguments given by Aristotle at the beginning of the Sophistical Refutations and some influential contemporary theories of argument for they do not pay much attention to a whole kind of Aristotelian arguments, namely didactical arguments.

An explanation could be that didactical arguments are implicitly included in these theories. But if you grant that didactical arguments differ from dialectical arguments in many respects and if you consider that for these theories the very notion of argument is dialectical, this interpretation of the demise of didactical arguments is not very plausible unless it results from equivocation on the word “dialectical”.
After a review of Aristotle’s classification we shall examine these theories to see if they are well suited to accommodate the kind of argument Aristotle called didactical.

1. Aristotle’s four arguments
In the Sophistical Refutations (II, 165a-b) Aristotle claims there are four kinds of διαλέγεσθαι λoγων, an expression generally translated by “argument (or reasoning) involved in a discussion”. This expression can also be interpreted simply as “dialogue” or “dialectic”, taken in the broad sense of “talking together”. Although Aristotle neither uses the word “syllogism” nor “enthymeme” it seems reasonable to agree with the translation using the word “argument” since the Philosopher stresses that these discourses have premises. And it is these premises which make the main difference between the four kinds of argument. In short:
Dialectical arguments are rooted in an endoxa, a common opinion.
Critical arguments start from premises accepted by the answerer but also granted by the arguer for his discourse aims at “showing that he [the arguer] knows”.
Eristic arguments reason from premises that appear to be generally accepted but are not so.

Finally, didactical arguments do not reason from the opinions of the answerer but from “principles appropriate to each μαθhματος”. Before commenting on this last word, it should be noted that, a few lines further, Aristotle says that dialectical, critical and eristic arguments are studied in specific books and “demonstrative” ones in the Analytics. Therefore, he holds didactical arguments to be demonstrative.

The word μαθhμα is usually translated by “branch of knowledge” or “discipline” but it also means “lecture” or “lesson”, two notions often related to an educational context. It is also close to μαθhματicoς which means “someone who studies” or “relative to a field of knowledge” and, of course, it is also germane to μαθhματicα, usually translated by “mathematics”.

Although it is demonstrative we should avoid to identify a didactical argument with what we now call a mathematical proof for the very notions of mathematics and science have changed since Aristotle. Remember, for instance, that he held sciences like optics, astronomy and music (harmony) to belong to the mathematical science even if pertaining to “more physical” parts of it (Physics, II, 2 194a). For Aristotle, what makes something “mathematical” is rather the way you consider it, namely the properties you drop in the process of abstraction and the principles you take into account, some of them being proper and some others not proper to the said science (Posterior Analytics, I, 10, 76a, 35-40). This is why one should take didactical argument to mean deductive argument based on the principles of a field of knowledge, of a discipline. It is “mathematical” in the broad sense of “systematic”.

That the four types of arguments are “open to discussion” does not entail that they are always debatable. For Aristotle’s definition of science requires that the conclusion of the arguments which are scientific to follow necessarily from their premises. And if these premises belong to the principles of a science they must be “true, primary, immediate, better known than, prior to, and causative of the conclusion” (Posterior Analytics, I, 2, 71b 20). Since their principles cannot be demonstrated but only grasped by induction – a specific act of abstraction – and their conclusion are necessary, Aristotelian scientific arguments are not “open to discussion” even if Aristotle grants that a superficial debate is always possible (Posterior Analytics, I, 10, 76b 25-30). A discussion may only occur in the case of postulates, namely demonstrable propositions supposed by the master but not by student.

2. What is left today?
I have just called to Aristotle’s categorization to stress a contrast with some contemporary views about what counts as an argument. Today, dialectical, critical and eristic argumentations are well alive and acknowledged. The three of them are even key notions in distinct fields of investigation. But what happened to didactical arguments? They seem to have disappeared. How come that several of the prominent contemporary theories of argumentation do not consider them as specific arguments or even as genuine arguments?

This could be a consequence of a fundamental theoretical orientation. The revival of argumentation studies began around the mid-twentieth century with Perelman’s and Toulmin’s reactions against the infatuation of philosophy with formal logic. Perelman made an extra step by linking closely together the notions of science, rationality, demonstration, proof, certainty, logic and mathematics, a move which allowed him to build his empire of rhetoric against the world of proof, demonstration and certainty, including natural sciences and, first and foremost, mathematics. For instance, according to him, Descartes “considered as rational only demonstrations” (starting from clear ideas) and since the nineteenth century “under the influence of logicians-mathematicians, logic has been limited to formal logic, namely the study of the means of proof used in mathematical sciences” (Perelman 1958, p. 2-3).

Inspired or not by Perelman, many streams of contemporary argumentation studies have rooted their concept of argument into a broad notion of dialectic. And some scholars take for granted that proofs and arguments are different things: a proof is not a kind of argument or a part of an argument; it is no argument at all. Hence the view that argumentation is foreign to hard sciences and, especially, to mathematical demonstration.
This view, making an oxymoron of the notion of scientific argument has been challenged from various areas since a few decades (Lakatos, 1976; Finnochiaro 1980; Gross 1990) and the exclusion of mathematics from the kingdom of argumentation has been seriously challenged recently (Rav 1999; Dove 2007, 2009; Aberdein 2005, 2009). My own call to a reappraisal of Aristotelian didactical arguments wants to be another contribution to the refutation of the dogma of a sharp distinction between scientific demonstration and argumentation.

A pragmatic approach is certainly required by any theory of argumentation based on the way people actually argue. But a systematic call to dialectic in the very definition of an argument results in an unfortunate narrowing of the field of study for it leaves out some argumentative forms, especially didactical arguments. The point is that it is possible to be an argument without being dialectical unless the very notion of dialectic is made so loose that it accommodates any argument. According to me, the fading of didactical arguments comes from a soft imperialism of dialectic.

What is meant by “dialectic”? As many old and tired words it has become vague and covers a range of different notions after an already equivocal career in the ancient times. In Aristotle, for instance, Wolf (2010, p 25-33) distinguishes three different meanings of “dialectic”. Its broadest sense is “discussion” or “conversation”: we have seen that the four kinds of arguments, including dialectical and didactical arguments, can be said dialectical in this sense. A second meaning is more specific since it refers to a regulated dialogue, typically between two participants. Paradigmatic examples are the dialectical debates at the core of Plato’s dialogues or Aristotle’s Topica. Finally, the narrowest definition is found in the Sophistical Refutations: “Dialectical arguments are those that reason from premises generally accepted, to the contradictory of a given thesis”. Dialectic is here based on the endoxa and you can notice that this definition does not contain a term referring to an arguer or an opponent.

Nowadays, dialectical argumentation is usually not identified by the status of its premises but rather by its pragmatic goal, namely arguing against a thesis. Refutation, opposition or, at least, resistance are key notions in the contemporary understanding of dialectical argumentation which comes very close to controversy.
Many contemporary theories include a dialectical requirement in the very definition of an argument: if it does not go against the view of an explicit opponent, at least it supports a view against alternatives that could be held by opponents. I shall use the expression “virtual dialectic” to qualify a dialectical opposition which is only potential, that is which does not identify an actual opponent. From a logical point of view the conclusion of any argument opposes at least its negation and this makes any argument virtually dialectical. Hence, any theory accepting virtual dialectic as a genuine kind of dialectic can claim to be dialectical. This broadening of the notion of dialectic provides a concept wide enough to cover the whole field of argumentation: since not all arguments are dialectical in a narrow sense, dialectic has to become virtual to accommodate any argument. But this broadening does not cancel the fact that didactical arguments belong to a field of knowledge where they are viewed as deductive and do not aim at a refutation. Their dialectical use is only derivative.

3. Dialectic accommodated
Pragma-dialectics claims that argumentation aims at the resolution of a difference of opinion by rational and critical means (Van Eemeren & Grootendorst, 2004). The basic disagreement may not be an open opposition: pragma-dialectics allows being an opponent without holding the contrary view. Sometimes, you argue with people who do not deny your position but only doubt. According to pragma-dialectics, such a situation can be qualified as dialectical. But it is not Aristotelian dialectic if the skeptic does not aim at a refutation of the proponent’s thesis but only waits for convincing evidence. So, you can grant to pragma-dialectics that a difference of opinion does not always amount to a genuine divergence for some doubts are challenges and some are not. However, a different opinion can be looked upon as a kind of opposition, just like resistance or inertia can be interpreted as a form of opposition. But when your interlocutor’s doubt does not challenge the rationality of your position, you do not argue against an active opponent but against someone who hesitates between several opinions. Ignorance too can be seen as a kind of opposition even if in some didactical contexts you do not argue with people who have a different opinion but with people who have no opinion at all. In such a case, as in the case of a non challenging doubt, the opposition is only potential. Pragma-dialectics will make a virtual dialectic out of a didactical situation whose specificity is not acknowledged since the interlocutor does not assume a critical position.

In Manifest Rationality Ralph Johnson holds that an argument has two sides, two tiers. One is the illative core, the fact that an argument is made of reasons supporting a thesis. And since this is not enough to account for the practice of argumentation, a dialectical tier is required. But this dialectical component does not imply an actual opposition between the arguers. Johnson writes: “that there is an argument, in the first place means that the conclusion is at least potentially controversial” (Johnson 2000, p. 206). Here again argumentation is made dialectic by means of a virtual dialectic. And it is the dialectical tier which makes a major difference between a mathematical proof and an argument for “No mathematical proof has or needs to have a dialectical tier” (Johnson 2000, p. 232). But is it really sufficient to support the claim that a proof is not an argument? Can’t a demonstration be “at least potentially controversial”? Some of them have been notoriously controversial, at least in their early days.

Johnson adds an interesting epistemic comment about the relationship between proof, argument and epistemic level. “The proof that there is no greatest prime number is conclusive, meaning that anyone who knows anything about such matters[i] sees that the conclusion must be true for the reasons given” (Johnson 2000, p 232). In some way, this is certainly true. But on the one hand Johnson’s view also suggests that in mathematics you would argue only with someone who does not stand on a sufficient epistemic footing and, on the other hand, that opposition is not possible between peers because all are convinced by the proof. This last idea of a necessary agreement between educated people reminds us Aristotle’s thesis that scientific arguments are not open to discussion. But what happens with someone who only knows some things, not any thing, in the mathematical field and feels concerned by the question of a greatest prime number?

A dialectical treatment may not be possible here for, taken narrowly, dialectical argumentation presupposes a partial epistemic equality or symmetry between the arguers since it has to rely on common premises that may not be shared by anybody. (Remember Aristotle’s formula about them: “they commend themselves to all or the majority or to the wise – that is, to all of the wise or to the majority or to the most famous and distinguished of them.” (Topica, I, 1, 100, b 20)). So, what rational solution is left when you can’t find common premises but you still want to argue that there is no greatest prime number? The authoritative use of didactical arguments which requires granting the truth of the proof premises. In some way, this is a means to make them common and, therefore, to reduce didactical argumentation to dialectic. But it also eliminates the specific cognitive context of didactical argumentation.

Not all reasoned dialogical forms at the core of Douglas Walton’s conception of argumentation presuppose epistemic symmetry. According to him, informal logic brought a major contribution to the study of arguments by replacing them in the context of their utterance and he holds this context to be essentially conversational. He acknowledges a debt to Hamblin’s notion of a dialectical system understood as “regulated dialogue” (Hamblin 1970, p. 232), that is several participants “speaking in turn in accordance with a set of rules or conventions” (Hamblin 1970, p. 255). But are turns of speech essential to argumentation?  The Aristotelian notion of a didactical argument has no such requirement: it may happen in a situation deprived of any turn of speech and so, it is only broadly dialectical. The character Aristotle calls the “answerer” may keep silent and even anonym during all the time of the transaction. This is not unusual: it is an ideal classroom situation, especially during a mathematical demonstration.

This quasi anonymity is even typical of didactical argumentation for, leaving aside eristic arguments, it is not possible with the other Aristotelian kinds of arguments for they have to be adjusted to the other party. In a critical argument the answerer cannot be anonymous since the premises of the argument are borrowed from him. This personal adjustment may seem less salient in the case of a dialectical argument since its premises do not come from the opponent but from common opinion. But when a dialectical argument is not only virtual, the arguer knows the person or the party she is talking to and chooses her common premises accordingly.

Contrary to the model at the core of pragma-dialectics which presupposes a critical symmetry between the arguers, Walton’s approach leaves room for asymmetric epistemic situations. This is the case of information seeking dialogues. In Informal Logic/ A Pragmatic Approach Walton writes (Walton 1989, p. 7) that besides persuasion, inquiry and negotiation dialogues which are “the fundamental kinds or reasoned criticism”, there are other forms including information-seeking dialogues. Here, “one party has the goal of finding information that the other party is believed to possess”. This seems to come close to Aristotle’s didactical arguments. However there is a difference stemming from Walton’s dialogical/dialectical a priori. In an information-seeking dialogue the seeker is not the answerer but the questioner, the one who initiates the exchange. “The role of the respondent is to transmit the information by giving answers or replies that are as clear and helpful as possible” (Walton 1996, p. 126). On the contrary, a didactical argument does not require a previous question to be asked. This can be illustrated by the case of professors making demonstrations in front of students who do not ask any question. Such a context is pragmatic without being dialectical or dialogical, except in the broadest sense. Walton avoids the restrictive view limiting argument to controversy, but making any argument part of a dialectical/dialogical system keeps too restrictive for it fails to acknowledge the pragmatic peculiarities of didactical arguments.

We come more explicitly to the relation between virtual dialectic, didactical arguments and mathematical proof with Eric Krabbe (Krabbe, 2008). His view is inspired by the integrated version of pragma-dialectics and he grants that proofs can be involved in dialectical exchanges. But he does not assume that mathematical proofs are arguments. Like most people having paid attention to the practice of mathematicians, he resists the common temptation to reduce all their works and productions to proofs. A proof is only an object – often a goal – in the life of mathematics and mathematicians. Historians and mathematicians, among others Pólya (Pólya, 1945, 1954) and Lakatos (Lakatos, 1976), have already stressed that informal exchanges and dialectical argumentation is very common in mathematical research, notably during the stage that classical rhetoric dubbed the “invention” of a proof. Mathematicians are sometimes at pain finding the demonstration of a conjecture and they have to argue to go ahead. Sometimes one of them argues with himself. And when the time has come to present a proof to colleagues, argumentation may still be needed to convince them. History is full of corpses of failed or uncompleted demonstrations, convincing for a time or for no time.

Krabbe grants that mathematical proofs may have an argumentative dimension of their own, but he keeps within an a priori dialectical conception of argumentation. For instance, about the various kinds of discussions arising around proofs he writes: “they are argumentative in the sense that, given some difference or conflict, they serve to overcome the doubt of an interlocutor”. And he adds: “whenever in a proof the reasoning displays persuasive functions, the proof can[ii] be regarded as an argument” (Krabbe 2008, p. 457). Yes, it can. But persuasion is not always the result of a fight against an opposition or a doubt. If persuading amounts here to giving reasons to make someone believe something, a previous opposition or doubt may not be necessary. To have no opinion about a claim is both an opinion (a position) and a different opinion without being a doubt. You can persuade ignorant people too. And didactical arguments can do that.

Krabbe asks: “Is a formalized proof not the natural limit of dialectical depth”? Yes, but a limit touching two areas, different but close to each other and sometimes partly overlapping, the dialectical and the didactical one. Krabbe is certainly right when saying that “proof in a didactic context has not just explanatory functions, but also persuasive ones” (Krabbe 2008, p. 458). It may not be easy to disentangle one from the other, for understanding a proof is the result of both.

I neither contest what Krabbe says about dialectical situations in the practice of mathematics nor Johnson’s claim that “the conclusion of an argument is at least potentially controversial”. The assertion of the conclusion of an argument goes at least against contradictory statements but, per se, this trivial potential opposition does not require a pragmatic approach. Virtual dialectic can be seen as universal, but it lacks the pragmatic definiteness which makes an argumentation really contextual. And it has the drawback of concealing the specificity of didactical arguments or at least of a didactical use of arguments which requires neither an opposition nor an actual dialogue.

4. A thought experiment
Finally, here is an anecdote showing again that blurring the border between dialectic and didactic does not eliminate their specificities. It relies on two facts. First, that a mathematical demonstration has no definite length (We tend to forget it when talking about “the” demonstration of a theorem); second, that when you make a demonstration you sometimes “jump” from one statement to another, taking a shortcut that not everybody may follow.

During a public demonstration several voices broke the silence after a mathematician took a shortcut to reach his conclusion. One looked satisfied: “Yes. Brilliant! Very convincing.” Another complained “Wait! How do you get to the conclusion from the previous step?” And a third voice went on: “Come on! You have not proven that unbelievable conclusion.” Doubt, perhaps opposition, is creeping in with this last comment. But is the second one the expression of an opposition or a doubt? Not necessarily, it may be motivated by a lack of understanding.

Very devoted to his audience, the mathematician decided to give a single answer to everybody and began to get into the missing details. And at the same time his speech gave a proof, explained and argued. And even if the last voice, the dialectical one had not been heard, the improved support that the mathematician gave to his conclusion would still have been an argument.

NOTES
i My emphasis.
ii My emphasis.

REFERENCES
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This paper is an attempt to bring together ideas discussed in several papers that I have read in conferences of the International Society for Studies in Argumentation and the Ontario Society for Studies in Argumentation (Durán 2007, 2008 and 2010). Its main thrust is the view that the study of argumentation should include the analysis of emotional, physical and intuitive arguments as well as logical ones. However, this paper concentrates on the contribution that the psychoanalytic theory of Bi-Logic has to offer for the study of argumentation.

I begin this paper by summarizing the main aspects of my research on the propaganda of agitation developed by the Chilean daily newspaper El Mercurio of Santiago against the government of Salvador Allende (1970-1973). A fully developed account of this study appears in my 1995 book (Durán 1995), and a summary of it was published in the Proceedings of the Sixth Conference of the International Society for the Study of Argumentation (Durán 2007). In essence, El Mercurio represented the interests of powerful enemies of Allende that felt threatened by his government, from the Chilean upper classes to the United States’ government and some influential multi-national corporations. The purpose of the propaganda of El Mercurio was to undermine the Allende government by instilling fear and hatred in the middle classes and the military so that a coup d’état could be staged. This happened on September 11, 1973 followed by a military dictatorship of 16 years led by General Augusto Pinochet.

The concept of propaganda of agitation is taken from the French author Jacques Ellul (1973) who defines it as an opposition and subversive propaganda destined to undermine a government, even to overthrow it. Furthermore, according to Ellul, this form of propaganda operates within a crisis, or it tends to provoke it. Fear and hatred are generally two of its emotional objectives and springs. In contrast to propaganda of agitation, Ellul says, there is propaganda of integration, which is propaganda of conformity with a given social system. This latter form of propaganda tries to stabilize, unify and reinforce the social system. Finally, Ellul says that these forms of propaganda usually work together, in different combinations.

Two of the main themes of El Mercurio’s propaganda were at that time, “Need for Order” and “Marxist Violence”. Both were quantitatively and qualitatively very significant, and intended to portray what El Mercurio perceived as the fundamental clash in Allende’s Chile. The following image illustrates the clash. In the picture, a violent Marxist appears attacking a police officer, who represents traditional order, according to El Mercurio.

Fig. 2

However, another important theme in this propaganda was “Anguishing Portrait of the World”. This was an unusual theme for El Mercurio, a paper that represents a rather liberal rational tradition in Chile. The theme intended to relate items about crimes, accidents, natural catastrophes, fires and other non-political anguishing stories to Marxist Violence, as if both kinds of items were of the same nature, and indeed identical. Thus, a news-story about a murder, for example, could be closely related to a Marxist vicious attack. This issue is illustrated in the following image (Fig. 2) .

This page juxtaposes two completely different events that took place in subsequent nights, as if both represented the state of Chile in terms of criminal and/or Marxist violence.. The main headline reads “Horrible murder of a young girl”; there is a picture of the place where she was found (actually she was murdered and raped) in the Spanish Country Club in Santiago; and another picture of the same story shows the brother of the girl talking to journalists from El Mercurio. The other set of stories refers to violence incurred by a Marxist assault of High School for Girls No. 12.

For several months, coverage of crime became very high in El Mercurio. The next illustration shows how the newspaper attempted to describe a criminal gang as very dangerous and bloody. (Fig. 3)

The headline reads, “Two bloody assaults by the ‘Black Jackets’ in the Capital”. This gang appeared all of a sudden as a Congress election campaign started in Chile. El Mercurio presented it as a high-level criminal organization, equivalent to similar gangster organizations in the United States. The ‘Black Jackets’ was identified metaphorically with an extreme left Marxist movement on the basis of the black color of the uniforms of its members.

Fig. 3

However, the most gruesome and remarkable case of propaganda of agitation by El Mercurio was the coverage of the “Quartered Man” of Quilicura. The story appeared two weeks before the Congress election, and was covered with great intensity until then. The next page of El Mercurio illustrates this case (Fig. 4).

The headline here reads, “The body of the man found in Quilicura was quartered alive”. Quilicura is a small town in the outskirts of Santiago.

During the two weeks of coverage of the “Quartered Man” before the election, packages with human flesh were found in plastic bags in successive days. The case gave rise, as well, to news-stories about cannibalism that clearly echoed the cannibalism practiced by a group of young rugby players from Uruguay in the last two months of 1972. Their plane had crashed in the Andes, and they survived eating human flesh (Fig. 5).

Fig. 4

The next page of El Mercurio appeared the day before the election. It represents an outstanding case of juxtaposition of disturbing items. The main headline reads, “Armed Forces Take Control”. It is juxtaposed to the following news-items: El Mercurio equivocally identified Allende as saying that the government intends to advance towards dictatorship of the proletariat; the ambassador of the United States is assassinated (in Sudan); the wife of the Quartered Man is found strangled; and there is a very low-key picture about the election the next day. Now, the headline about the Armed Forces is misleading because, according to the Chilean Constitution, the Armed Forces in times of election assumed control of Public Order: the headline is clearly suggesting that the Armed Forces should take Control of the Country! (Fig.6)

Finally, the day of the election, the coalition of all the opposition parties to Allende published, as a coalition, only one political ad. The ad relates one of the cases of cannibalism covered in the past two weeks, and generally the “Quartered Man” story, explicitly to the situation of Chile in those days.

In the second part of the paper, I introduce Michael Gilbert’s theory of Multi-Modal Argumentation. In doing so, I try to show that the propaganda of agitation discussed in part one, can be described in a comprehensive and thorough way in terms of this theory. Michael Gilbert attempts an ‘opening’ of the traditional view that has conceived argumentation as based, essentially, on the logical mode. His theory proposes that we enlarge and extend the range of meaningful intellectual, academic and argumentation activities to include:  Emotions, which had been traditionally excluded, at least from Plato onwards. Physicality, that is, the domain of the body, which includes visual aspects. Moreover, the kisceral, which relates to intuition, the spiritual, the religious, the uncanny, etc.

Fig. 5

Gilbert (Gilbert, 1997, p. 75) introduces his theory in the following passage: “It has been argued in previous chapters that the traditional and dominant mode of arguing, the C-L, Critical-Logical mode, is restrictively narrow. When this mode is seen as the only legitimate form of rational argumentation, then there are profound and unreasonable limitations on actual argumentation as performed by real actors, and the limitation of methods favored by one group over another. These limitations provide both descriptive and normative reasons for rejecting the C-L mode as the sole legitimate form of argumentation. In this chapter, three new modes of argumentation, raising the number to four, are introduced. In addition to the classical logical mode (usually and egregiously identified with the “rational”), there are the emotional, visceral (physical), and kisceral (intuitive) modes.”

It is important to stress that this is not a way of reversing things, such that the logical mode would be excluded, but now, this mode can be assessed in the full flow of argumentation: it is possible thus to recognize the fundamental and substantive roles played by all the modes.

Applying now Gilbert’s theory to the analysis of El Mercurio’s propaganda, it is convenient to go one mode at a time. Thus, from the point of view of the logical mode, the first thing that stands out is a set of arguments that relate Marxists to violence, quartering and cannibalism. A plausible expression of such set is the following:
(1) All criminals (or quarterers or cannibals) are violent
All Marxists are violent
Therefore, all Marxists are criminal (or quarterers or cannibals)

Fig. 6

Any one of the implied arguments here is a second figure syllogism, and thus, invalid. These arguments can be gathered from specific pages of El Mercurio as well as from the whole propaganda. The idea was to instill fear in the population at large, especially the middle classes and the military. To start with, then, the logical mode shows the presence of invalid arguments. In any event, the invalid logical arguments as mentioned, relate to the production of fear and, in addition hatred in large sections of the Chilean people. This takes the analysis to the emotional mode. It is possible to claim that this is the predominant mode in El Mercurio’s propaganda of agitation. Another significant element, from the perspective of the logical mode, is the presence of fallacies that appeal to emotions such as appeal to fear, abusive ad hominem, loaded language, etc. In this sense, these two modes work closely connected to each other.

It is important as well to indicate the input of the physical mode, in this case in its visual dimension. This seems evident in this propaganda. The pages of the newspaper serve as the background for actual visual expressions: We see the impact of the layout of each page, the juxtaposition of items, the influence of some individual items, be they headlines or pictures.

Finally, considering the kisceral mode, I believe it is also present in the propaganda. The attempt has been to induce a profound connection between crimes, accidents, and natural catastrophes, etc., on the one hand; but also, on the other hand, the connection between them and Marxist violence.

There is, however, another interesting aspect in dealing with the logical mode. The study that I presented in part one of this paper, concentrated on propaganda of agitation. Nevertheless, the study as a whole focused, as well, on some relevant aspects of propaganda of integration. In this sense, it is important to show one specific and significant valid logical argument found in the study.

(2) The Marxists always try to destroy democracy
Allende and his people are Marxists
Therefore, Allende and his people are trying to destroy democracy

Furthermore, if Allende and his people are destroying democracy, then they should be stopped with military violence. There is a good deal of historical sense in this argument, so besides its validity, the argument could be considered sound as well.

Given the comprehensive view that is possible to gain with the application of Multi-Modal Argumentation to the study of El Mercurio’s propaganda, a further issue becomes clear. The four modes work in integration in the propaganda; they relate to each other in a way that makes the propaganda much stronger. They subtly reinforce each other. For example, the valid, and plausibly sound argument mentioned above, can provide logical credibility to the emotional, visual and kisceral argumentation. The layout of the pages and their structure contribute to make the propaganda more credible. However, the fundamental issue is to reinforce the production of fear and hatred so that the middle classes and the military can be prepared to undertake military action against Allende. For that purpose, the propaganda has provided logical grounds as well. I believe it is pertinent to say, that any individual opposing Allende would experience great anxiety, and that she or he would be able to produce invalid and valid logical arguments, and these latter arguments would provide a sense of credibility to their mere emotional reactions. This key issue will be examined in more detail below.

So far, I have tried to show that the propaganda of agitation by El Mercurio against the government of Allende in Chile entails a combination of all four modes of Michael Gilbert’s theory of Multi-Modal Argumentation, and that the predominant one is the emotional mode. In the next part of the paper, I attempt to develop a Bi-Logical interpretation of El Mercurio’s propaganda with especial focus on emotional arguments.

Bi-Logic is a psychoanalytic theory introduced by the psychoanalyst Ignacio Matte-Blanco with the publication of his main book The Unconscious as Infinite Sets. An Essay in Bi-Logic (Matte-Blanco, 1975). The essential issue in this theory is the assumption that there are two different logics operating in the mind. In order to understand Bi-Logic, it is necessary to be aware of set theory and the concept of relation, and specifically one of the properties of relations, called symmetrical/asymmetrical. A relation is called symmetrical when the relation can be reversed and asymmetrical when it cannot. Thus, a=b is a symmetrical relation for the relation is maintained if we reverse it and say b=a; whereas a relation is called asymmetrical if it cannot be reversed, such as in the case of a>b. In essence, Matte-Blanco believes that, based on those two issues, it is possible to systematize Freud’s proto-logical ideas on the unconscious. For, according to Matte-Blanco, in the unconscious there is no respect for asymmetrical relations and then all relations tend to be treated as symmetrical. In this sense, he says that the unconscious is regulated by what he calls the Principle of Symmetry (PS).

In his attempt to reformulate the Freudian unconscious, Matte-Blanco deduces a set of consequences that derive from the PS.
1)  If the PS is applied then the part becomes identical to the whole. The reason for this identification is that if ‘p’ is part of the whole ‘W’, then applying the PS, ‘W’ is part of ‘p’. This takes us to identify part ‘p’ and whole ‘W’. Moreover, the same would happen to each part of this whole with the consequence that all the parts of a whole are identical to the whole and to each other.
2) If the PS is applied then the members of a set are identical to the set and to each other. Similarly to the above explanation, if ‘m’ is a member of the set ‘S’, then applying the PS,  ‘S’ is a member of  ‘m’. The same would happen to each member of the set and thus, they would be identical to each other and the set. The same can be said of subsets as related to sets.
3) If the PS is applied then there are no negations. For if the set of affirmative propositions is a subset of the set of propositions, and then applying the PS, the set of propositions is a subset of the set of affirmative propositions. The same would apply to the subset of negative propositions with the consequence that this set would be identical to the set of affirmative propositions.
4) If the PS is applied then there are no contradictions. The reason relates closely to the previous consequence of the application of the PS: since the affirmative and negative propositions are identical to each other, there cannot be contradictions.

Now, if we take seriously the (possible) existence of a PS and its consequences as described above, then certainly, we would be in the realm of another ‘logic’. Consider the following argument: The body is contained within the heart because it is clear that the heart is contained within the body. This logic is called by Matte-Blanco “symmetrical” logic. It refers to the sequence of propositions that results from applying the PS to a given piece of quite acceptable traditional logic. Notice, therefore, that symmetrical logic appears in the propositional sequences of traditional logic whenever the PS makes itself present in its midst. In essence, then, this logic assumes traditional logic as operating all the time. On the other hand, it should be said that traditional logic assumes that symmetrical logic is operating all the time. Another important point about Bi-Logic here is that our thinking processes are  combinations of traditional logic and symmetrical logic, in different proportions, depending on the level of depth of the appearance of symmetry. Thus, in a mathematical theorem, the level of traditional logic is very high and the level of symmetry very low, whereas in a psychotic piece of reasoning, such as the above example of the heart and body relation, the opposite happens. In reality, our thinking processes are classified as happening between two polar extremes: pure traditional logic and pure symmetry, both of them, of course, impossible to achieve.  Therefore, there are many levels of symmetrical depth. Matte-Blanco discusses this idea in detail and systematically in his book Thinking, Feeling and Being (1988). In synthesis, he shows that, due to the proportions in which asymmetrical and symmetrical logic combine, it is possible to distinguish a series of strata or zones in the mind. He concludes that there are five basic strata or zones: a first zone in which asymmetrical logic predominates; a second one in which both logics appear in similar proportion;  a third one in which the set is identified with its members; a fourth zone in which two or more sets are identified with each other; and finally, he refers to a fifth strata in which all sets tend to be identified with one another.

Matte-Blanco explores as well the way in which emotions relate to thinking, and he concludes that emotional thinking is bi-logical, with a stronger predominance of symmetrical logic. I come back now to Michael Gilbert’s theory of Multi-Modal Argumentation, in order to develop a Bi-Logical interpretation of emotional argumentation found in the propaganda of El Mercurio. Emotional arguments may be characterized as arguments in which emotions arise in a meaningful way, that is, emotions become the most important aspect of the argument. However, according to Matte-Blanco, when emotions appear, they involve a type of thinking which is symmetrical. The emotional state developed when being in love, for example, takes the person in love to think that the loved one is the most beautiful or handsome person in the world, and tends to attribute to him or her all the positive qualities that could be thought about. Evidently, asymmetrical thinking takes a lesser role here.

Now, which exactly is the nature of the emotional argumentation found in the propaganda of agitation of El Mercurio? I said that the assumption is that El Mercurio’s propaganda, seen in its overall and comprehensive multi-modal shape, had the purpose of developing fear and hatred, especially in the middle classes and the military so that a coup d’état could be in place to overthrow Allende. The way in which these emotions were developed is highly subtle and sophisticated, for the whole campaign involved a set of invalid and valid logical arguments, fallacies of appeal to emotions, visual appeals in the layout of the pages, and kisceral connections. In synthesis, all of the above centered on the following emotional issues: the Marxists closely relate to crime, quartering and cannibalism. In that way, they destroy the very fabric of a society, and then the traditional sense of order is undermined. They do it, so that they can replace democracy with a Communist dictatorial system. There is in these highly charged emotional issues, an assemblage of points that are not at a clear level of asymmetrical understanding. I mean, it is logically acceptable to say that Marxists try to overthrow capitalist democratic regimes; it may be debatable, but there are historical and political precedents to assert that claim. Thus, it is only reasonable that people may develop fear, and indeed hatred, against the Marxists. These emotions possibly belong to the second strata mentioned above, one in which there seems to be a sort of balance between asymmetry and symmetry. However, the association of Marxists with crime is logically indefensible, and more problematic is the connection between Marxists and quartering and /or cannibalism. The emotions here correspond to deeper strata of the mind, where very little sense of asymmetry could be found. Most probably, in these strata the anxieties are so strong and terrifying, that people may fall in states of sheer panic.

In my 1995 book (Durán, 1995), I discussed this topic as well from a traditional psychoanalytic perspective, using ideas derived from the clinical work of the Melanie Klein School. I cannot discuss this approach in any detail here, but I would like at least, to mention a few things about it. According to Matte-Blanco, some significant correlations can be made between the strata discussed above and clinical findings of other psychoanalytic schools. One of these correlations relates to intense fears of destruction of the body, of being torn apart, of cannibalistic impulses, etc. that are encountered in clinical practice, especially in Kleinian analysis. Moreover, some analysts of this school who have done clinical work with groups as opposed to individual therapy, claim that when the group fails, disintegrates, or is in danger, the above fears tend to increase. Indeed the Chilean society, in the Allende years, was in a serious critical state where people felt in great danger. Therefore, the fears that I have mentioned above were running rampant as well as strengthened by the propaganda of agitation of El Mercurio. Finally, those fears happened at the third and fourth strata of symmetrical depth given the confusion of sets entailed.

In the final part of this paper, I attempt to develop a way of evaluating the propaganda of agitation of El Mercurio. Indeed, it is possible to focus upon the logical arguments and decide on their validity and on the truth of the premises, if they are formal arguments, and/or on the nature of the informal fallacies that they may contain. Certainly, El Mercurio’s propaganda campaign would seem to be faulty in terms of an assessment in the logical mode, but this may be reductionist, for the propaganda of El Mercurio centers on the emotional mode as discussed above. Therefore, criteria for evaluation of emotional arguments need to be ascertained, and this is not something that has been done in the field of Multi-Modal Argumentation. One plausible approach to the evaluation of propaganda and emotional arguments is focusing upon their success.

Of course, many people would be prepared to say that El Mercurio’s propaganda of agitation against the government of Salvador Allende was successful, in that it contributed to mobilize the middle classes and the military in order to oust Allende. Indeed, these social sectors were mobilized because their way of life was in serious danger. Therefore, El Mercurio, as their representative, was right in its propaganda of agitation, since it was meant to defend them against a potential traditional Communist dictatorship. The criterion implied here is that in the defense of a way of life, it is right to use deep emotional arguments against the aggressors.

However, this criterion seems to be missing an ethical clearance, so to speak. At this point, I would like to introduce an idea contributed by my colleague Leo Groarke from University of Windsor in Canada. In an e-mail exchange concerning the evaluation of emotional arguments, Groarke suggested that, “I argue that a plausible account of argument in informal contexts cannot reduce acceptability to ‘acceptable as true’, and that we need a broader notion of acceptability that recognizes moral and emotional elements of acceptability.” Of course, the same idea would apply to the other two non-logical modes of argumentation in Gilbert’s theory, but in the present paper, the issue relates only to the emotional mode. Applying this idea to the evaluation of El Mercurio’s propaganda against Allende, a plausible interpretation can lead to the conclusion that for the upper classes, the middle classes and the military, the coup d’état was both, emotionally and ethically acceptable. Now, for the people who suffered the coup and the ensuing military repression of the Pinochet regime, the coup was both, emotionally and ethically unacceptable. Thus, so far, it is possible to claim that the coup was emotionally and ethically acceptable for some and not acceptable for others. However, is there a way of superseding the relativism of this conclusion? In order to examine this question, I believe it is necessary to inquire into the nature of the views of each side involved in the conflict.

Taking a rather common sense and ordinary experience in liberal-democratic societies, people have a chance to develop strong positive emotions about their lives. Thus, they will fight very hard against attempts to undermine the system, and then they would be prepared, most probably, to support a coup against a government who threatens to undermine the society. People are deeply attached to the liberal-democratic system in emotional and ethical terms.

However, what happens to the people who are undermining the social system? They seem to have emotional and ethical reasons as well in their attempts to replace it with another system, even if this is dictatorial. After all, these people have been excluded from the real and symbolic goods produced by the overall society. Therefore, they have not been able to develop the strong positive feelings that the upper and middle classes have developed. Their struggle is for access to share in the wealth of the society. Therefore, for them the coup is not emotionally and ethically acceptable.

Thus, it seems that it is not possible to come out of the relativism of the claim that the coup, and the propaganda against Allende, was emotionally and ethically acceptable for one part of the society and not for another. In concluding the paper, it is clear that more research needs to be undertaken for the development of a thorough way of emotional and ethical evaluation of propaganda.

REFERENCES
Durán, C. (1995).  Propaganda de Agitación en el Período Agosto 1972-Marzo 1973.  Santiago: Ediciones Chile América-CESOC.
Durán C. (2007) Analysis of arguments in political propaganda: the case of the Chilean press 1970-1973. In F.H. van Eemeren, B.J. Garssen, J.A. Blair and C.A. Willard, (Eds.). Proceedings of the Sixth Conference of the International Society for the Study of Argumentation (pp. 359-366), Amsterdam: SicSat.
Durán, C. (2008). Bi-Logic and Multi-Modal Argumentation. In H.V. Hansen, C.W. Tindale, J.A. Blair, R.F. Johnson and D.M. Godden (Eds). Dissensus and the Search for Common Ground: Proceedings of OSSA 07, CD-ROM (pp. 1-9). Windsor, ON: OSSA.
Durán, C. (2009). Revisiting Emotional Arguments in the Context of Western Culture. In J. Ritola (Ed.). Argument Cultures: Proceedings of OSSA 09, CD-ROM (pp. 1-10), Windsor, ON: OSSA.
Ellul, J. (1973).  Propaganda. The Formation of Men’s Attitudes. New York: Vintage Books (Random House).
Gilbert, M. (1997).  Coalescent Argumentation. Mahwah, New Jersey: Lawrence Erlbaum Associates.
Matte-Blanco, I. (1975).  The Unconscious as Infinite Sets. An essay in bi-logic. London: Duckworth.
Matte-Blanco I. (1988).  Thinking, Feeling, and Being. London and New York: Routledge.

1. The analytical status of the notion of ‘strategic maneuvering’
The notion of strategic maneuvering, introduced by van Eemeren and Houtlosser, is basically an analytic concept enabling a more refined, accurate and comprehensive account of ‘argumentative reality’ than can be achieved by means of the existing, purely dialectical tools of canonical, standard pragma-dialectics (van Eemeren & Houtlosser, 1999b, 2000, 2002a, 2000b; van Eemeren, 2010). With the help of the notion of strategic maneuvering it becomes possible to reconstruct argumentative discourse as it occurs in practice in such a way that not only the dialectical dimension pertaining to its reasonableness is taken into account, but also the rhetorical dimension pertaining to its effectiveness (van Eemeren, 2010). In sum, in the extended pragma-dialectical approach incorporating the theory of strategic maneuvering the standard analysis of argumentative discourse is systematically enriched with the use of rhetorical insight.

The extended pragma-dialectical argumentation theory in which classical and modern rhetorical insights are integrated in the existing pragma-dialectical tools for reconstruction – i.e. resolution-oriented reconstruction – offers in the first place analytical instruments for analysing and evaluating argumentative discourse. It is not an empirical model of the various ways in which ordinary arguers try to achieve effective persuasion within the boundaries of dialectical rationality.[i]

Argumentative discourse can only be critically evaluated in a theoretically justified way if the discourse has first been adequately analysed. Starting from the pragma-dialectical point of departure, the analysis of argumentative discourse can be envisioned as a methodical reconstruction of the process of resolving the difference of opinion contained in the discourse. Using the extended theory taking account of strategic maneuvering as an analytical instrument for analysis and evaluation is to lead to an analytical overview attuned to enabling a sound critical evaluation. The ideal model of a critical discussion can serve as a heuristic instrument for reconstructing argumentative discourse in such a way that it becomes clear which function the various speech acts performed in the discourse fulfil and which commitments they create.

In a reconstruction of a discourse as a manifestation of a critical discussion it is assumed that the arguers aim to resolve their dispute on the merits. At the same time, however, it may be assumed that they will be intent on having their own standpoints accepted. This means that on the one hand they have to observe the dialectical obligations that have to do with the argumentative procedures that further an abstract ideal of reasonableness in critical discussion while on the other hand they have aims and considerations that are to be understood rhetorically in terms of effectiveness (also referred to as persuasiveness). Attempting to resolve a difference of opinion and at the same time trying to do so in one’s own favor creates a potential tension between pursuing dialectical objectives and rhetorical, persuasive aims. It is precisely this potential tension that gives rise to what van Eemeren and Houtlosser have coined strategic maneuvering, which is aimed at making the strongest possible case while at the same time avoiding moves that are clearly unreasonable.

In argumentative discourse, whether it takes place orally or in writing, it is generally not the arguer’s sole aim to win the discussion, but also to conduct the discussion in a way that is considered reasonable […] In their efforts to reconcile the simultaneous pursuit of these two different aims, which may at times even seem to go against each other, the arguers make use of what we have termed strategic maneuvering. This strategic maneuvering is directed at diminishing the potential tension between pursuing at the same time a ‘dialectical’ as well as a ‘rhetorical’ aim (van Eemeren & Houtlosser, 2002b: 135).

In a great many cases, the maneuvering, whether it is successful or not, is in perfect agreement with the rules for critical discussion and may count as acting reasonably. As a rule, strategic maneuvering is at least aimed at avoiding an open violation of these critical standards. Even arguers who momentarily let the aim of getting their own position accepted prevail will strongly attempt to keep up the appearance of being committed to the critical ideal of reasonableness (van Eemeren & Houtlosser, 2002: 16).

Much more could be said about this view of strategic maneuvering, but this short overview (and the references that are given) may suffice to show that one could easily be misled by interpreting the analytical model involved as an empirical-psychological one, as a model that aims to describe the argumentative behavior of ordinary arguers and their intentional, persuasive goals in ordinary real-life discussions. As said before, the analytical model for dealing with strategic maneuvering is definitely not an empirical model. One of the consequences of the specific analytical character of the model is that it cannot simply be put to a critical empirical test, at least not in a strict sense: empirical data are not able to falsify this model, nor are they able to confirm it – unless one is willing to add certain psychological or sociological assumptions to the model which are empirical by their very nature. But this does not mean that, seen from an empirical point of view, this model is useless: even if the model cannot be empirically tested in a strict sense, it is easy to see that it can function as a source for the derivation of theoretically motivated hypotheses about the argumentative behavior and persuasive goals of arguers in ordinary argumentative practice. And that is precisely the way in which this model will be used in this paper.

2. Three predictions
Three rather straightforward and plausible predictions can be derived from the notion of strategic maneuvering if this concept is interpreted empirically:
(1) Ordinary arguers are, at least to a certain extent, aware of their dialectical obligations; they know, at least at a pre-theoretical level, which contributions to the discussion are in accordance with the rules for critical discussion and are thus to be regarded as reasonable, and which contributions have to be considered as violations of these dialectical rules, in other words: which moves are fallacious and thus unreasonable. If ordinary arguers would lack such specific knowledge of the boundaries of the dialectical framework, there would be no reason at all for them to maneuver in a strategic sense – in that case they could go all out for rhetorical effectiveness, pursuing only and exclusively their own personal persuasive aims without taking into account the obligations dictated by the dialectical framework.
(2) Ordinary arguers assume that the other party in the discussion commit themselves to the same kind of dialectical obligations as they themselves do. If these jointly shared expectations (the protagonist knows… (…) and the protagonist knows that the antagonist knows… (…)) would not be in force in ordinary discussions, there would again be no reason for them to maneuver strategically. Expressed differently, ordinary arguers assume their interlocutors to apply similar norms and criteria for the evaluation of the reasonableness of discussion contributions as they themselves do, and regard ‘overt’ fallacies equally unreasonable as they do.
(3) Ordinary arguers assume – and assume that their interlocutors assume – that discussion contributions that violate the norms incorporated in the rules for critical discussion are unreasonable and that interlocutors who violate these commonly shared rules can be held accountable for being unreasonable. Consequently, the notion of ‘reasonableness’ is not only perceived by ordinary arguers in a merely (“descriptively”) normative sense, but also (and for the most part) in a prescriptive sense. Again, if this condition would not be met, there would be no reason for the discussion parties to maneuver strategically.

3. Prediction 1
3.1. Method prediction 1
During the past years we collected a mass of empirical data that are relevant for testing the first claim. In 1995, we started a comprehensive empirical project entitled Conceptions of Reasonableness that was completed in 2008 (for a detailed overview, see van Eemeren, Garssen & Meuffels, 2009). The aim of this project was to determine empirically which norms ordinary arguers use (or claim to use) when evaluating argumentative discourse, and to what extent these norms are in agreement with the critical theoretical norms of the pragma-dialectical theory of argumentation. Expressed differently: the aim of this ten-year project was to investigate and to test the conventional validity of the pragma-dialectical discussion rules: can it be expected that in actual discussion the rules are intersubjectively approved by the parties involved in a difference of opinion? The problem validity of the pragma-dialectical rules (are the rules instrumental in resolving a difference of opinion?) is primarily a theoretical issue. In contradistinction, the conventional validity of these rules can only be established by means of empirical research.

We carried out some 50 independent experiments, investigating the (un)reasonableness of 24 different types of fallacies. The setup of the experiments, the design of which we will report here, was in all cases the same: a repeated measurement design, combined with a multiple message design. That means that a variety of discussion fragments, short dialogues between two interlocutors A and B, were presented to the participants. (1) is an example of such a discussion fragment in which the abusive variant of the ad hominem fallacy is committed, (2) an example of the circumstantial variant, and (3) an example of the tu quoque-variant.

(1) (abusive variant; direct attack)
A:  I think a Ford simply drives better; it shoots across the road.
B:  How would you know? You don’t know the first thing about cars.

(2) (circumstantial variant; indirect attack)
A:  In my view, the best company for improving the dikes is Stelcom Ltd; they are the only contractor in the Netherlands that can handle such an enormous job.
B:  Do you really think that we shall believe you? Surely, it is no coincidence that you recommend this company: It is owned by your  father-in-law.

(3) (tu quoque-variant; you too variant)
A:  I believe the way in which you processed your data statistically is not entirely correct; you should have expressed the figures in percentages.
B:  You’re not being serious! Your own statistics are not up to the mark either.

For baseline and comparison purposes, the participants also had to judge the (un)reasonableness of fragments in which no violation of a pragma-dialectical rule was committed:

(4) (no violation of the freedom rule)
A: I believe my scientific integrity to be impeccable; my research has always been honest and sound.
B: Do you really want us to believe you? You have already been caught twice tampering with your research results.

In all cases in the discussion fragments non-loaded topics were discussed, and in all cases paradigmatic, clear-cut cases of the fallacies were constructed. All fragments were put in a certain context. For instance, fragment (1) was presented in a domestic discussion context, fragment (2) in a political context, and fragment (3) and (4) in the context of a scientific debate. The participants were invariably asked to judge the reasonableness of the last contribution to the discussion, i.e. the contribution of B in the examples above. The participants had to indicate their judgment on a 7-point Likert scale, ranging from very unreasonable (=1) to very reasonable (=7).

3.2. Results prediction 1
First, we tested the conventional validity of the rule for the confrontation stage (the Freedom Rule) by investigating the (un)reasonableness of the three variants of the ad hominem fallacy, various variants of the argumentum ad baculum, the argumentum ad misericordiam, and the fallacy of declaring a standpoint taboo or sacrosanct (see Table 1 a + b).

Table 1a

Table 1: Overview of average reasonableness score for fallacious discussion contributions and the non-fallacious counterparts; effect size (ES) for the difference between the (un)reasonableness of fallacious and non-fallacious discussion contributions, per argumentation stage – (1=very unreasonable; 4=neither unreasonable, nor reasonable; 7= very reasonable)

Second, we tested the validity of the rule for the opening stage (the Burden of Proof Rule) by investigating the (un)reasonableness of, among others, the fallacy of shifting the burden of proof and the fallacy of evading the burden of proof in a non-mixed and in a mixed dispute. Third, we tested one of the pragma-dialectical rules for the argumentation stage (in this case rule number 8, the Argument Scheme Rule) by investigating the (un)reasonableness of the argumentum ad consequentiam, the argumentum ad populum, slippery slope and false analogy. And last, we tested the conventional validity of the rule for the final stage in a critical discussion (the concluding stage), by investigating the (un)reasonableness of the argumentum ad ignorantiam.

From the data presented in Table 1(a + b) it is clear that – with the notable exception of the logical variant of the argumentum ad consequentiam – the participants in our experiments made a clear distinction between the unreasonableness of discussion moves that, according to pragma-dialectical standards, involve a fallacy and those that are not fallacious: fallacious discussion moves are considered unreasonable by ordinary arguers, while non-fallacious moves are judged as reasonable.[ii] These results can be taken as a strong support for our first prediction: ordinary arguers are to a large extent aware of what the dialectical obligations in an argumentative discussion entail.[iii]

Table 1b

4.Prediction 2
Methodological considerations
In contrast with the mass of empirical data we have collected in order to test the conventional validity of the pragma-dialectical discussion rules, only one single experiment is conducted in which we tested our second prediction that could be derived from the extended model incorporating strategic maneuvering. This prediction pertains to the reciprocal social expectations of discussion parties regarding the commitment to dialectical discussion rules: ordinary arguers assume that the other party in the discussion commit themselves to the same kind of dialectical obligations as they themselves do. As for testing this second prediction (and, by the way, also the third prediction), we will make use again of the empirical results obtained in the project Conceptions of Reasonableness.

In the project Conceptions of Reasonableness the three variants of the ad hominem-fallacy are investigated frequently, not only in the Netherlands but also in countries abroad (see Table 2). As a consequence, we have now insights into (1) the stability of the reasonableness data for the three types of fallacy, (2) the ordinal reasonableness relations of the three types of fallacy, and (3) the absolute reasonableness assessments of the three types of fallacy. Based upon these insights, different specific predictions can be inferred for experiment 2 (and also for experiment 3). First, from the consistent results shown in Table 2 it is clear that the ordinal relations between the rated reasonableness of the three types of ad hominem-fallacy in the original main investigation and in the replications of this investigation are identical: the direct attack is invariably judged as the least reasonable move, next the circumstantial variant, and lastly the tu quoque-variant. Second, the tu quoque variant tends to be judged as a reasonable move, provided we abstract from the specific contexts in which this fallacy was offered to the participants. Third, in line with the results reported in Table 1 it is evident that invariably those non-fallacious, reasonable discussions contributions are (in a statistically significant sense) considered as more reasonable than the fallacious moves in which an argumentum ad hominem is committed.

Table 2

Table 2: Average reasonableness score for three types of ad hominem-fallacy (direct attack (=dir), indirect attack (=ind), tu quoque-variant (=tu)) and for non-fallacious reasonable argumentation, per replication (standard deviation: between brackets)*  *(1=very unreasonable; 4=neither unreasonable, nor reasonable; 7= very reasonable)

In our investigation of prediction 2 we exposed our participants to instantiations of the three types of ad hominem-fallacy and instantiations of non-fallacious moves, and we requested them to rate the (un)reasonableness of these discussion fragments (i.e. the last contribution) according to their own insights and judgment – as was the case in all our experiments conducted within the framework of the project Conceptions of Reasonableness; in addition to that, they had to rate similar fallacious and non-fallacious fragments, but this time with the instruction to indicate how reasonable or unreasonable they think and expect that relevant others would judge these fragments. Prediction 2 can be considered to be confirmed if the three above mentioned stable patterns of Table 2 show up again, not only in the condition in which the participants have to rate the fragments according to their own insight but equally well in the condition in which they have to make an estimation of the judgment of relevant others. Any difference between both conditions as a (statistical) main effect (or an interaction between ‘condition’ and ‘type of fallacy’) would be disastrous for the confirmation of prediction 2.

4.1. Method prediction 2
In order to test prediction 2, 48 discussion fragments were constructed: short dialogues between two discussants (called A and B) in which the antagonist B violated 36 times the pragma-dialectical rule for the confrontation stage by means of one of the three variants of the argumentum ad hominem. In 12 discussion fragments no discussion rule was violated; in those fragments B adduced only non-fallacious, reasonable argumentation.

Two versions were constructed: version ‘Self’ and version ‘Other’, both consisting of 24 discussion fragments; the fragments in each version were randomly drawn from the whole set of 48 fragments and subsequently quasi-randomly assigned to one of the two versions, such that both versions contained precisely the same number of instantiations of the same type of fallacy. Consequently, both in the version Self and in the version Other the direct attack, the indirect attack and the tu quoque-variant are each represented by 6 instantiations. The design in this experiment can thus characteristically be regarded as a multiple message design (examples of concrete messages presented to the participants are shown in Section 3).

56 pupils of the fourth and fifth year of secondary school (most of them 16 and 17 years old respectively) participated in the experiment; none of them had ever had any specific argumentation teaching. After each discussion fragment in the version Self the question that is asked is “How reasonable or unreasonable do you (yourself) think B’s reaction is?”, and in the version Other the question that is asked is “How reasonable or unreasonable do you think relevant others would judge B’s reaction?” (relevant others were in the instruction described as friends or relatives). In both versions they could indicate their judgment on a 7-point scale, ranging from 1 ‘very unreasonable’ (=1) to ‘very reasonable’ (=7). The order of presentation of the two versions was randomized over the subjects; half of the participants had first to fill in the version Self and subsequently the version Other, the other half of the participants received the reversed order (as there were no statistical significant differences between the two orders, we will abstract from this variable). As all the participants were exposed to all levels of both the independent variable ‘version’ and the independent variable ‘fallacy/no fallacy’, the chosen design can also be described as a repeated measurement design.

4.2. Results prediction 2
The data in Table 3 were analyzed by means of a multivariate analysis of variance (‘mixed model’ approach for repeated measurements, with ‘subject’ and ‘instantiation’ as random factors and the variables ‘version’ and ‘type of fallacy’ as fixed factors; the random factor ‘instantiation’ is nested within the interaction of the fixed factors ‘version’ and ‘type of fallacy’, whereas the random factor ‘subject’ is fully crossed with the random factor ‘instantiation’ and the fixed factors ‘version’ and ‘type of fallacy’; the statistical consequence of this rather complicated design is that – instead of ordinary F-ratio’s – quasi F-ratio’s have to be computed, while the degrees of freedom have to be approximated).

From the data in Table 3 it is evident that the well known ordinal pattern in reasonableness relations between the three types of ad hominem fallacies crop up again in this experiment, regardless of the type of condition (version). No matter whether the participants have to base their reasonableness ratings on their own judgment or whether they have to estimate the verdict regarding the unreasonableness of the three variants of the ad hominem fallacy of relevant others, the direct attack is invariably judged as the most unreasonable move, next the indirect attack and subsequently the tu quoque-variant. And precisely as was the case in the investigations presented in Table 2, again the tu quoque-variant tends to be considered as a reasonable discussion move.

Table 3

Table 3: Average reasonableness score for three types of ad hominem fallacy and for non-fallacious reasonable argumentation, per version (N=56)*
*(1=very unreasonable; 4=neither unreasonable, nor reasonable; 7= very reasonable)

So far as the differences in reasonableness between non-fallacious reasonable argumentation on the one side and fallacious argumentation on the other side are concerned, there are no statistically significant differences between the version Self and the version Other. In both conditions reasonable argumentation is regarded (in an absolute sense) as reasonable, while in both conditions the direct attack and the indirect attack are considered as significantly less reasonable than non-fallacious argumentation (contrast direct attack vs. reasonable argumentation F(1,42)=84.46; p<0.001; ES=0.31; contrast indirect attack vs. reasonable argumentation F(1,28)=12.51; p<0.001; ES=0.07). However, both in the condition Self and in the condition Other our subjects do not discriminate between the (un)reasonableness of the tu quoque-variant and the (un)reasonableness of reasonable argumentation: F (1, 23) =2.60; n.s.).

At least as important for the confirmation of prediction 2 is our finding that there is no statistical significant (main) effect of the independent variable ‘condition’ in case of the three relevant contrasts between (1) the direct attack and reasonable argumentation: F(1,32)=3.81; n.s., (2) the indirect attack and reasonable argumentation: F(1,25)=.35; n.s., and the tu quoque-variant and reasonable argumentation: F(1,25)=.24; n.s., nor a statistically significant interaction between the independent variables ‘condition’ and ‘fallacy/no fallacy’ (direct attack: F(1,25)=.41; n.s.; indirect attack: F(1,27)=1.72; n.s.; tu quoque-variant: F(1,23)=1.17; n.s.).

All these results point in the same direction: ordinary arguers expect others to judge the (un)reasonableness of fallacious and non-fallacious discussion contributions in a similar way as they themselves do.

5. Prediction 3
5.1. Method prediction 3
For testing prediction 3 (ordinary arguers assume – and assume that their interlocutors assume – that discussants who violate the commonly shared rules for critical discussion are unreasonable and can be reproached for being unreasonable; consequently, the notion of ‘reasonableness’ is by ordinary arguers not only used in a mere (“descriptive”) normative sense, but also and for the most part in a prescriptive sense) we will make use again of our consistent findings in the project Conceptions of Reasonableness: once again the three variants of the ad hominem fallacy were presented to the participants, but this time the discussion fragments did not have to be judged on reasonableness but they had to be rated according to the extent that the antagonist is violating a norm in his (last) contribution to the discussion.

59 subjects (18-19 years old pupils) participated in this experiment. Similar discussion fragments were presented to them as in the previous experiment. In 12 of the 48 fragments the fallacy of the direct attack was committed, in 12 fragments the indirect attack, in 12 fragments the tu quoque-variant and in the remaining 12 fragments reasonable argumentation was used. This time the reaction of antagonist B had to be judged on a 7-point, scale ranging from ‘absolutely violating a norm’ (=1) to ‘not at all norm-violating’ (=7). The design of this experiment is the same as in the previous experiment: a repeated measurement design, combined with a multiple message design.

5.2. Results prediction 3
In Table 4 the results are reported.

Table 4

Table 4: Average scores for the extent of norm violation for three types of ad hominem fallacy and for non-fallacious reasonable argumentation (N=59)*
*(1=absolutely violating a norm; 7= not at all norm-violating)

The familiar patterns, derived from Table 2, are again present in Table 4: the direct attack is judged as the most norm-violating move, next the indirect attack, and finally the tu quoque-variant; this last variant is considered as a discussion move that tends to be the qualified as ‘no norm violating’. As expected, the non-fallacious discussion contributions are rated as moves that can be regarded as non-norm-violating.Each of the three ad hominem fallacies is judged in a statistically significant sense as more rule violating compared with non-fallacious reasonable argumentation. This holds even in the case of the tu quoque variant (direct attack: F(1,72)=65.73; p<0.000; ES=.27; indirect attack: F(1,58)=31.80; p<0.000; ES=.13; tu quoque variant: F(1,28)=6.03; p<0.02; ES=.04). Nor surprisingly in light of the data in Table 2, there are big differences between the three types of fallacies regarding the extent to which they are regarded as norm-violating (F (2, 57) =15.03; p<0.000; ES= .11). According to the judgment of our participants, in case of the direct attack norms are much more violated compared with the other two types of fallacy (F(1,57)=23.41; p<0.001); the indirect attack in turn is considered as a more norm-violating move than the tu quoque variant (F(1,57)=5.92; p<0.02).

In sum, discussion moves that are considered as unreasonable by our participants (moves that are also unreasonable in a theoretical sense according to the pragma-dialectical standards) are judged as norm-violating, while moves that are assessed as reasonable by our participants (moves that are also reasonable in a theoretical sense) are considered as not norm-violating.

6. Conclusion
The paradigmatic division between dialectical and rhetorical approaches to argumentative discourse can be bridged by introducing the theoretical concept of strategic maneuvering, as proposed in the extended pragma-dialectical theory of argumentation. This makes it possible to integrate rhetorical insights into a dialectical framework of analysis. Strategic maneuvering refers to the deliberate efforts arguers make to reconcile their aiming for rhetorical effectiveness with maintaining dialectical standards of reasonableness. If one interprets this analytical model in an empirical sense, three rather vital claims can be derived. We have shown in this article that these claims are strongly supported by the results of our experiments. (1) Ordinary arguers are, at least to a certain extent, aware of their dialectical obligations; they know, at least at a pre-theoretical level, which contributions to the discussion are in accordance with the rules for critical discussion and are thus to be regarded as reasonable, and which contributions have to be considered as violations of these dialectical rules, in other words: which moves are fallacious and thus unreasonable. (2) Ordinary arguers assume that the other party in the discussion commit themselves to the same kind of dialectical obligations as they themselves do. (3) Ordinary arguers assume – and assume that their interlocutors assume – that discussion contributions that violate the norms incorporated in the rules for critical discussion are unreasonable and that interlocutors who violate these commonly shared rules can be held accountable for being unreasonable.

NOTES
[i] For our use of the terms effectiveness and persuasiveness and our use of the terms rationality and reasonableness, see van Eemeren, 2010: 39 and 29, respectively.
[ii] With the exception of the logical variant of the ad consequentiam fallacy, all differences in reasonableness between a particular fallacy and its non-fallacious counterpart are statistically significant – ordinary arguers not very often regard the reductio ad absurdum as a type of sound argumentation, just as they hardly see that the fallacy that copies this sound argumentation (namely the logical variant of the argumentum ad consequentiam) is an obvious fallacy. In some cases in Table 1 no effect size is reported – in those cases ES could not be computed, due to the specific characteristics of the chosen design. Moreover, from the data presented in Table 1 (and equally in Table 2) one may not infer that fallacies such as the tu quoque-variant are regarded as reasonable moves. In Table 1 we abstracted from the specific discussion context in which the fallacies were offered to the participants, but in a scientific discussion context the tu quoque fallacy is invariably judged as an unreasonable move.
[iii] Notice that there is an enormous range in the judged unreasonableness of the various fallacies: the physical variant of the argumentum ad baculum, for example, is regarded as an absolute unreasonable move, while the tu quoque variant of the ad hominem fallacy tends to be considered as a reasonable move (provided we abstract from the specific discussion contexts in which this fallacy was presented). Such data make sense: threatening the other party in the discussion with brute physical violence is the example par excellence of irrational, unreasonable behavior, while committing a tu quoque fallacy has at least in some discussion contexts the appearance of being reasonable. Serious participants in a conversation may be expected to show some consistency between their (past and present) words and deeds.

REFERENCES
Eemeren, F.H. van (2010). Strategic Maneuvering in Argumentative Discourse. Extending the Pragma-Dialectical Theory of Argumentation. Amsterdam/Philadelphia: John Benjamins.
Eemeren, F.H. van, Garssen, B., & Meuffels, B. (2009). Fallacies and Judgments of Reasonableness. Empirical Research Concerning the Pragma-Dialectical Discussion Rules. Springer: Dordrecht.
Eemeren, F.H. van, & Houtlosser, P. (1999). Strategic manoeuvring in argumentative discussions. Discourse Studies, 1(4), 479-497.
Eemeren, F.H. van, & Houtlosser, P. (2002a). And always the twain shall meet. In F.H. van Eemeren & P. Houtlosser (Eds.), Dialectic and Rhetoric: The Warp and Woof of Argumentation Analysis (pp. 3-11). Dordrecht: Kluwer.
Eemeren, F.H. van, & Houtlosser, P. (2002b). Strategic maneuvering: Maintaining a delicate balance. In F.H. van Eemeren & P. Houtlosser (Eds.), Dialectic and Rhetoric: The Warp and Woof of Argumentation Analysis (pp. 131-159). Dordrecht: Kluwer.

Long lists of topoi fill the manuals of classical rhetorical theory. There are topoi for the person and topoi for the act. There are topoi for encomia and topoi for the defence. Such lists are teaching devices designed to teach students particular aspects of the art of rhetoric. The lists are numerous, each author producing his own list. Within the realm of rhetoric topoi are a repeated theme, and the discussion usually concerns which topoi best suit each particular circumstance. The topoi for argumentation are taught in the two rhetorical exercises called “refutation” and “confirmation”. This paper will focus on six topoi from these rhetorical exercises suggesting that they are better for teaching argumentation to students than some modern approaches to argumentation.

First the term topos and its relationship to argumentation theory should be explained. A topos in Greek is literally a “place” for finding arguments. The “place” is often understood metaphorically as a “place” in the mind, and topoi can refer to many different kinds of mental places. Sara Rubinelli has made a distinction among the different kinds of strategies in classical rhetoric covered by the term topos. The term can be an indicator of the subject matter the orators might take into consideration for pleading their causes. Topos can also designate a certain argument scheme that focuses on the process of inference, such as the argument from the contrary. According to Latin rhetoricians, locus communis designates a ready-made argument that can be re-used by other speakers (2006, pp. 253-272).

Michael Leff looks back at his forty years of studying rhetorical invention in a recent article where he concludes that the topoi are an ambiguous and multi-faceted concept, sometimes referring to modes of inference, sometimes to aspects of the subject, sometimes to the attitudes of an audience, sometimes to types of issues and sometimes to headings for rhetorical material. Leff points to Boethius and the difference between the dialectical and the rhetorical tradition as an explanation for the many meanings of topos. The subject matter of dialectics is theses, i.e., an abstract question without connection to any particular circumstance. The subject matter of rhetoric is hypotheses, questions concerning particular circumstances. Dialectic is interested in argumentation as such; rhetorical theory is concerned with arguments on specific topics for specific audiences (2006, p. 205).

Modern approaches to argumentation usually follow the dialectic tradition and study argumentation divorced from the context.  In Garssen’s view, the classical concept of topos in rhetoric and dialectic corresponds to argument schemes.  The function of argument schemes is to designate different principles of support that link the argument to the standpoint. Pragma-dialectical argumentation theory classifies argument schemes in three main categories: symptomatic argumentation of the “token” type, comparison argumentation of the “resemblance” type and instrumental argumentation of the “consequence” type (2001, p. 82, 91). Critical discourse analysis also views topos as argument schemes. Wodak has, for example, a table of strategies of justification and relativisation with lists of argumentation schemes including topos of ignorance, topos of comparison, topos of difference, and topos of illustrative example. (Wodak, 1999, pp. 36-42).  It should be pointed out that the argument schemes in these modern approaches to argumentation are analytic results from argumentative texts. They were not designed for teaching argumentation.  It is questionable whether learning long lists of argumentative nomenclature do actually help students develop their own argumentation.

One difference between the dialectical tradition, including the above mentioned modern approaches, and the rhetorical tradition, is that the former tends to view the argumentative topoi as a product of an analytical examination, while the latter views them as a process for finding arguments in particular contexts. The Italian humanist Giambattista Vico lamented already three hundred years ago that:
“In our days …. Philosophical criticism alone is honoured. The art of ‘topics’ is utterly disregarded … This is harmful, since the invention of arguments is by nature prior to the judgment of their validity … so in teaching, invention should be given priority over philosophical criticism” (Vico, 1709/1990, p. 14).  Crosswhite laments that what was true in 1709 is still true today. Criticism and analysis are usually treated as the whole of invention. “Invention is rarely explored as being in some way prior to analysis and criticism” (Crosswhite, 2008, p. 176).

This problem is well known to Quintilian. When he comes to the “places” of arguments, he corrects other rhetoricians: “I do not use this term in its usual acceptance, namely commonplaces, directed against luxury, adultery and the like, but in the sense of the secret places where arguments reside, and from which they must be drawn forth. For just as all kinds of produce are not provided by every country, and as you will not succeed in finding a particular bird or beast, if you are ignorant of the localities where it has its usual haunts or birthplace, … so not every kind of argument can be derived from every circumstance, and consequently our search requires discrimination” (Inst. V.10.21). Leff comments that from Quintilian’s perspective, topics are not theoretical principles. “They are precepts that have potential application to accrual cases, and their most important function is as a training device.” Proper use of the topics helps to develop a capacity for arguing in precisely those situations where theory offers the least guidance. The theoretical tradition therefore does not help if one wants to find the function of topoi. In recent years Leff consequently has paid more attention to the rhetorical handbook tradition, such as the progymnasmata (2006, pp. 208-209).

1. The Progymnasmata
The progymnasmata are a set of preliminary rhetorical exercises designed to teach students the art of rhetoric. A gymnasma is an exercise and the word refers to physical exercises as well as mental exercises, the plural gymnasmata refers to a set of exercises. Isocrates comments that just as we need exercises to train the body, we also need exercises to train the mind, Antidosis 180-185.  The progymnasmata originated in Hellenistic times and came to dominate the early stages of Roman rhetorical training and had a tremendous influence on rhetorical teaching in the renaissance. The main versions of progymnasmata come from Theon (first century CE), Hermogenes (second century CE) and Aphthonius (fourth century CE), see the translations by Kennedy (2003). The progymnasmata have been used throughout the schools of western civilisation and Gert Ueding even calls them the “Lehrplan Europas”.

The Aphthonian set of fourteen exercises has had the most influence. Manfred Kraus has found more than 400 different editions of Aphthonius in European renaissance. The set starts with easy exercises like retelling a fable and telling a story. Next come the chreia and maxim which develop a theme with a set of topoi. More advanced exercises are the encomion, comparison, characterization, description and thesis, which all prepare the students for the declamation at which the students take a stand on particular argumentative issues. The teaching idea behind the progymnasmata is described by Fleming (2003, pp. 105-120).

Progression in learning through the use of topoi is the central ideas behind the progymnasmata. The students are taught a topical way of thinking about rhetoric. The topoi come in many forms in the progymnasmata. When composing narratives, students should consider the six attributes of narrative; the person who acted, the thing done, the time at which, the place in which, the manner how and the cause for which it was done (Aphthonius 2.23-3.2). Theon (78.16) calls them the stoicheia or basic elements of the narrative. To learn how to compose a narrative the student should make sure that all these attributes were covered. When he would write a chreia he would have to develop the meaning of an utterance or action with a set of topoi; first, a praise of the person who uttered the saying or performed the action, then a paraphrase of the meaning in his own words, then a reason, an argument from the contrary, a comparison, an example, a testimony from reputable people and a brief conclusion. These topoi are called kefalaia, “headings” for developing a subject.

The basic training in argumentation occurs in the combined exercises “refutation” and “confirmation”, number five and six in the series. The exercises presuppose that the students know how to tell a story from different perspectives and how to use topoi like the contrary, example, analogy and witness from other persons. Students typically refute and confirm the meaning of a narrative. This means that the students first must interpret the meaning of the narrative, typically a mythological story, analyze it and then write a small text as the basis for an oral performance in the class room. The process is hence both analysis and composition. To accomplish this task the students are given a set of six topoi that will guide them through the learning process. These topoi are ‘the clear’, ‘the persuasive’, ‘the possible’, ‘the logical’, ‘the appropriate’ and ‘the advantageous’. Each of these topoi is accompanied by its opposite so that the student will look both for the clear and the unclear, for the persuasive and the unpersuasive, for the possible and the impossible, the logical and the illogical, the appropriate and the inappropriate, the advantageous and the disadvantageous. This way the students are taught the practise of two-sided arguments.

2. The clear
The first topos is ‘the clear’ and ‘the unclear’. Using this topos the students start their interpretative process by clarifying the issue. If the subject studied was a narrative, maybe a mythological story, the interpretation of the meaning of the story would be the first part of the process. In the rhetorical perspective, stories are ways of describing human activity from a certain perspective. To analyse the perspective chosen by the narrator, the student could use the topoi from the previous exercise ‘narrative’: the person, the act, the time, the place, the means and the reason for the human activity. Such topoi would be pertinent in juridical cases where the background of the proposed crime would be given in the narratio of the speech. If these narrative topoi were used as questions to the text and the answer was satisfactory, then the narrative could be described as clear. Theon comments that the narration becomes clear from two sources: from the subjects that are described and from the style of the description of the subjects (2003, pp.29-30). Lack of clarity comes in many forms. A statement would be unclear if the wording does not express the meaning behind the words. In rhetorical theory clarity is a virtue of style as well as a topos for argumentation. In the rhetorical view of argumentation the linguistic expression is intimately connected with the argumentative content. So for example, Kraus argues that the rhetorical figure contrarium is also an argument (2007, pp. 3-19). Form and content cannot be separated. Muddled thinking cannot be expressed in a clear style.

When a student would use the topos ‘the clear’ he would try to determine the argumentative content behind the linguistic expression. The interpretation of arguments and the reconstruction of argumentation is a complicated process, some of the problems involved are described by van Rees (2001, pp. 165- 199). Under this topos, could also be listed such sub-topoi as the determination of the actual wording of the source criticised. Was the source quoted correctly? Was the translation correct from the original language? Under “clarity” we could also include interpretations of words and definition of terms.

The topos also has its opposite ‘the unclear’. Expressions that are ambiguous and obscure are a sign of unclear thoughts. Looking for unclearness in the linguistic form teaches the students the need for a good language, as to spelling, choice of words and stylistic level.

3. The persuasive
The second topos is ‘the persuasive’ and ‘the unpersuasive’. There is an analytical move from text to context in this process.  Once the student has made a preliminary interpretation of the meaning of the statement, customarily contained in a story, he is advised to consider the audience for whom this statement would be persuasive. For whom would this be credible? Who would believe this story? The Greek term to pithanon, used by Aphthonius, is the same word as Aristotle uses in his famous definition of rhetoric, “Let rhetoric be defined as an ability in each particular case to see the available means of persuasion” (Rhet. 1.2.1). Aristotle also comments that “the persuasive is persuasive in reference to someone” (Rhet. 1.2.11). The argument is not a good argument unless it persuades the intended audience.

The centrality of the audience is also emphasized in modern versions of argumentation. In the New Rhetoric by Perelman and Olbrechts-Tyteca the premises of the audience are the starting point for argumentation. The pragma-dialectical understanding of argumentation also includes a reference to an audience when it defines argumentation as “convincing a reasonable critic of the acceptability of a standpoint” (van Eemeren, 2004, p. 1).

Subtopics to the topos ‘the persuasive’ would be different kinds of analysis of the audience.  Perelman and Olbrechts-Tyteca call the premises held by the universal audience premises relating to reality and divide them into facts, truths and presumptions. The premises relating to that which is preferable to particular audiences can be divided into values, value hierarchies and loci, a preference for one abstraction rather than another. Other kinds of analyses of the audience would be opinion polls, interviews and surveys.

This emphasis on the audience in rhetorical theory draws a line between what is true and what is persuasive. Quintilian comments that some people criticise him for suggesting “that a statement which is wholly in our favour should be plausible, when as a matter of fact it is true”. It is not enough that a statement is true, it must also be credible since “There are many things which are true, but scarcely credible, just as there are many things which are plausible though false” (Inst. IV.2.34). To make sure that the narrative will be credible to the audience he recommends that the speaker should: 1) take care to say nothing contrary to nature; 2) assign reasons and motives for the facts on which the inquiry turns; 3) make the characters of the actors in keeping with the facts we desire to be believed; 4) do the same with place and time and the like (Inst. IV.2.52). These points could serve as subtopics to determine whether a narrative is credible or incredible.

Form and content cannot be separated in rhetorical theory. Res and verba are intimately connected. As students are looking for what is persuasive in the narrative analysed they should also remember that credibility or persuasiveness is the third virtue of style for the narration. And they are well advised to remember this lesson when they prepare their own composition.

As noted above, the point with the topos ‘persuasive’ is not the factual veracity of the statement; correspondence with extra-linguistic reality is beyond the purview of most rhetorical theories. This second topos is also not the same as the probable; probability theory belongs to the field of statistics. But that which happens often is likely to happen again. People are often the same in different circumstances. History tends to repeat itself. Looking for that which is common, usual, customary is therefore one way of finding that which is persuasive. It is reasonable to look for similarities in behaviour patterns.

4. The possible
The third topos is ‘the possible’ and ‘the impossible’. The previous topos ‘the persuasive’ emphasised the audience and their frames of reference; now ‘the possible’ emphasises the physical world and its limitations. In Greek the topos is to dynaton, that which can be done. Using this topos the student asks whether the statement is possible. Can it be done? Are there obstacles that would make the proposed action impossible to accomplish in the future or to have been performed in the past? In a juridical context, where so much of classical rhetorical theory comes from, the prosecutor and the defence would argue whether the action could have been done considering the circumstances of the persons involved, the time, the place, the manner and the reason for the action, usually called the motive.

When the action proposed is in the future, a political issue in rhetorical theory, the deliberation would consider different obstacles to the proposal. Are there sufficient resources, economic or material? Are there other factors at work that would hinder the accomplishment? Are there legal complications? Quintilian remarks that the third consideration for deliberative oratory [besides honour and expediency] is to dynaton or possible. “The practicality of the matter under discussion is either certain or uncertain. In the latter case this will be the chief, if not the only point for consideration” (Inst. III.8.16). The topos of the possible could also be used today when teaching students argumentation. Possibility is still an issue and we could use the various connotations of the words “optimist” and “pessimist”. The optimist would see the various possibilities in a case and might see himself as a possibility thinker. The pessimist would see the obstacles and the difficulties, and he would probably call himself a realist.

5. The logical
The fourth topos is the logical and the illogical. Using this pair of topoi the student would look at the mode of reasoning in the argumentation. The Greek term for the topos is to anakolouthon which literally means “that which does not follow”. The wording suggests that the parts of the argument should follow from one another, that the reasoning should be coherent. As an argumentative topos “that which does not follow” scrutinizes the relationship between the terms in the reasoning. The focus is especially the implied premises from which the reasoning does not follow. The topos helps to make the implied premises explicit, a basic step in an analysis of argumentation. In formal logic non sequitur, the Latin translation of to anakolouthon, is an argument in which the conclusion does not follow from the premises. The non sequitur concerns the formal validity of the reasoning. In this type of argument the conclusion can be either true or false, but the argument is fallacious because there is a disconnection between the premise and the conclusion. All formal fallacies are special cases of non sequitur.

When a student would use this topos he would look for fallacies in the argumentation. The topos can be used both for analysing argumentation from someone else and for preparing the student’s own argumentation. When the student has scrutinized the coherence of the argumentation he wishes to put forward, he has probably found some fallacies and some logical inconsistencies. When the student has corrected the fallacious reasoning, he should have a watertight argument. This process of looking for fallacies is the process of using the topos of the logical. Fallacies are central to the pragma-dialectical school. It is interesting to note that formal validity is not the primary concern but comes as number four out of six topoi in the progymnasmata.

The coherence in thought corresponds to coherence in style. An anacoluthon is a grammatical term for when a sentence abruptly changes from one structure to another. The sentence is not completed as it started when the introductory elements of a sentence lack a proper object or complement. This is a grammatical error and should usually be avoided, but since rhetorical style is adapted to the particular situation, strict adherence to rules is not always recommended. In rhetoric an anacolouthon is therefore regarded as a conscious choice of style, a rhetorical figure that shows excitement, confusion, or laziness. 

6. The appropriate
The fifth topos is ‘the appropriate’ and ‘the inappropriate’. These terms emphasize the importance of the rhetorical situation. Behind these terms we find the Greek to prepon “that which is fitting”. Lausberg comments that to prepon relates both to outward circumstances and moral fitness (1998, p. 1055). It is the virtue of the parts in fitting themselves harmoniously together as a whole. The verb is used for what seems right to the eye in the situation. In Latin the corresponding terms are aptum and decorum. Other English translations would be ‘the suitable’, ‘the seemly’, ‘the proper’, or ‘the decent’. The form and the content are two sides of the coin in rhetorical theory and therefore the rhetorical concept of prepon has an inner dimension relating to the components of the speech that should be in accordance with one another and an external prepon which concerns the relationship between the speech and the social circumstances of the speech. Quintilian treats both levels of aptum extensively (Inst XI.1.1-93). “For all ornament derives its effect not from its own qualities so much as from the circumstances in which it is applied, and the occasion chosen for saying anything is at least as important a consideration as what is actually said (Inst. XI.1.7).

Considerations of aptum lead the student to consider social and cultural conventions. In rhetorical theory considerations of the rhetorical situation have been a major point of interest since Bitzer’s groundbreaking article (Bitzer, 1968). Does the context of the argument have a place in a modern theory of argumentation? On this issue it is interesting to note that the definition of a fallacy has changed in the pragma-dialectical school. According to the standard definition of a fallacy, accepted until recently, a fallacy was considered to be “an argument that seems valid but is not”. This classic definition restricts the concept of fallaciousness to patterns of reasoning and formal validity, and neglects the fact that many fallacies are not included. Therefore a broader definition was adopted: “deficient moves in argumentative discourse,” (van Eemeren, 2001, p. 135).  In his more recent writings van Eemeren, together with Houtlosser, has attempted to bridge the gap between dialectical and rhetorical views on argumentation by the concept of strategic manoeuvring, which is an attempt to find the most expedient choice of arguments to seek successful persuasion (van Eemeren, 1999). Strategic manoeuvring also leads him to redefine fallacies as “violations of critical discussion rules that come about as derailments of strategic manoeuvring” (van Eemeren, 2006, p. 387). This is a clear example of taking the rhetorical situation into consideration in argumentation.

Quintilian comments on speakers who break the social and cultural conventions of aptum. They use offensive and distasteful language, upset the hearers by the wrong level of style and use the wrong type of emotions. “An impudent, disorderly or angry tone is always unseemly, no matter whom it is who assumes it”. Vices of a meaner type are “grovelling flattery, affected buffoonery, immodesty in dealing with things or words that are unseemly or obscene, and disregard of authority on all and every occasion” (Inst. XI. 1.29-30).

Are considerations of social and cultural conventions legitimate concerns in a theory of argumentation? For a rhetorical theory of argumentation, which is concerned, not with abstract argumentation schemes, but with specific argumentation addressed to particular audiences, the rhetorical situation is the central concern. Politeness and offensiveness therefore should be concerns for a rhetorical theory of argumentation.

Students using the topos “the appropriate” would look for aspects of the case they are analysing that would be in accordance with social and cultural norms. The topos would also help the student to find elements in the analysed story, or in the position put forward by the other side, that would be inappropriate or offensive. Having analysed the rhetorical situation of someone else, the student would be ready to consider his own rhetorical situation as he performs the analysis he has prepared. What are the expectations in the class room? What norms apply? And what norms are governing the public discourse outside the class room? Political correctness is a prevailing issue even today and should therefore be taken into account in a theory of argumentation..

7. The advantageous
The sixth topos is ‘the advantageous’ and ‘the disadvantageous’. Using this topos the student asks who benefits from the proposed action. The Greek to sympheron refers to the goal of the argumentation in deliberative rhetoric. The political speaker seeks to present his proposal as advantageous to the audience. This advantage could be long or short range, and could concern a particular group or the common good. The advantage could be material or concerned with honour and prestige. Aristotle comments that “the end of the deliberative speaker is the expedient, to sympheron, or the harmful”. The political speaker recommends the expedient and dissuades the audience from doing what is harmful. “All other considerations, such as justice, and injustice, honour and disgrace, are included as accessory in reference to this” (Rhet 1.3.5).

The Latin translation of the term is utilitas. The term ‘utility’ in English, together with words like ‘expedience’, ‘interest’, ‘benefit’, ‘gain’ and ‘profit’, would be variations of this topos.  When a student would use this topos, he would engage in a simple form of what we would call ideological critique. Behind every story and statement we can suspect that there is some kind of interest hidden. Using the topos ‘advantage’ the student would ask for the real motive and who would gain by the suggested action.

8. Hermogenes’ example 
Hermogenes gives an example of how a student could use the six topoi in refutation:
“You will refute by argument from what is unclear, implausible, impossible; from the inconsistent, also called the contrary; from what is inappropriate, and from what is not advantageous. From what is unclear; for example, “The time when Narcissus lived is unclear.” From the implausible, “It was implausible that Arion would have wanted to sing when in trouble.” From the impossible; for example, “It was impossible for Arion to have been saved by a dolphin.” From the inconsistent, also called the contrary, “To want to destroy the democracy would be contrary to wanting to save it.” From the inappropriate, “It was inappropriate for Apollo, a god, to have sexual intercourse with a mortal woman.” From what is not advantageous, when we say that nothing is gained from hearing these things,” (2003, p. 179).

9. Argumentation with the topoi
Hermogenes’ example shows how the argumentative topoi can function like an argument machine. The student could always say that the position he would refute is unclear, unpersuasive, impossible, illogical, inappropriate and disadvantageous. And when he would confirm his own position, he could always say that it is clear, persuasive, possible, logical, appropriate and advantageous. The problem for such a simplistic view of these topoi is that the rhetorical situation of the progymnasmata is not taken into account.  Refutation and confirmation are class room exercises designed to teach two sided arguments. In the class room there would be other students prepared to speak on the same issue, but from the opposing point of view. In such a circumstance it is not enough to state that the issue is clear to yourself, you have to convince the opposing party of the clarity of your position. It is not enough to blame the other side for muddled thinking, you must also on the spur of the moment, in the class room, with the other students as a critical audience show the lack of clarity you claim to be able to find in the argumentation from the opposing side.

This is a sophistic approach to argumentation known to the ancient Greeks as antilogic and to Romans as controversia. The most influential representative of Sophistic education was Protagoras, who began his textbook Antilogiae with the famous dictum that “on every issue there are two arguments (logoi) opposed to each other on everything” (Sprague, 1972, p.4). This concept was the core of Sophistic pedagogy, and Marrou notes that it was “astonishing in its practical effectiveness” (1956, p. 51). Cicero summarizes the use of controversia in the Hellenistic Academy as follows: “…the only object of the Academics’ discussions is by arguing both sides of a question to draw out and fashion something which is either true or which comes as close as possible to the truth,” Academica 2.8.  Mendelson has shown how Quintilian makes this form of argumentation his own pedagogy of argument.  Quintilian exemplifies the method in his own writing when he constantly brings in opposing viewpoints and weighs pro’s and con’s against each other on every issue (2001, pp. 279-282.) The purpose of the rhetorical training was facilitas, the resourcefulness and spontaneity acquired from continual interaction with other discourse.  To be able to speak on both sides of the issue, in utramque partem, is at the heart of rhetorical education. This is where the progymnasmata come in. The learning outcome for these exercises is that the students would be able to perform speeches and argumentation on the spot. They should have acquired this ability so that they had the competence ingrained in them.

10. A good topical system
Karl Wallace, nestor in the Speech community, in an important article published in 1972 pondered the problem of topoi and rhetorical invention. Wallace comments that Perelman’s work has limited application if we aim to construct a system of topics that is teachable to unsophisticated learners. He specifies certain parameters for a good topical system. Such a system of topoi should be both inventive and analytic. It should aid the communicator to find materials and arguments as well as helping the listener and critic to understand and evaluate messages. It should serve as an instrument of recall and recollection as well as stimulate inquiry by revealing sources of ignorance. It should prompt ideas by appealing to meanings that have become symbolized in the language of speaker, writer, and audience. A good topical system should have the power to call up appropriate linguistic structures, as well as subject matter. How broad should such a topical system be? Wallace concludes that it must be sufficiently general to cut across a number of subject matters. Members of the national committee on the nature of rhetorical invention wanted something truly “generative”, something that would be so powerful and far-reaching that it would breed not one system of topics, but many: Something that would have the power of modifying and correcting topics from one generation to another.

The simple proposal of this paper is that the six argumentative topoi in the progymnasmata, the clear, the persuasive, the possible, the logical, the appropriate and the advantageous, fulfil these requirements for a good topical system. The list is relatively short and it cuts across a number of subject matters. The list is truly generative and breeds many systems of topics. The six topoi combine stylistic form and argumentative content. There is a progression in the series that concerns the inventive process of gathering content. The six topoi can also function as the basic outline for the disposition for a short argumentative text.  And they also teach the students the art of arguing on both sides of an issue, in utramque partem. Therefore the argumentative topoi for refutation and confirmation are better for teaching argumentation to students than the modern approaches to argumentation.

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This paper makes a proposal about the structure and representation of practical reasoning in political discourse. We provide an overview of the arguments that were used in a particular public debate on the fairness of bankers claiming and receiving bonuses in the present context of economic crisis and discuss the structure of those arguments. We adopt an instrumentalist approach to practical reasoning, which regards all reasons for action as means-end reasons. We argue that an instrumentalist approach is supported by the particular logic of political discourse: various types of action that are defended in political discourse are supposed to be means towards the realization of political goals, seen as states of affairs or modes of social organization informed by a normative commitment to various moral-political values (justice, equality, freedom).

We start from a distinction made in philosophy between two types of practical reasoning, “prudential” and “moral” (Gauthier 1963). Prudential arguments take the agent’s desires (wants, needs, interests) as premises: if the agent desires a certain outcome, then a certain course of action is recommended; if he doesn’t desire the outcome, the he has no reason to do the action. Moral arguments do not seem to have this conditional (hypothetical) structure, they present an action as necessary in itself, regardless of the agent’s desires or interests, regardless of any further goal that is desired, regardless of circumstances. Prudential reasoning corresponds to Kant’s hypothetical imperative, while moral reasoning corresponds to his categorical imperative. This might suggest that the structure of moral arguments is significantly different from that of prudential arguments.
The view we will defend here is that the two types of arguments have the same means-goal underlying structure, involving the same type of premises, but with significant differences in the agent’s relationship towards the goal (which he may or may not desire) and in the nature of the reasons that support or inform the goal (internal or external reasons). We suggest that, together with an adequate understanding of the Speaker-oriented (as opposed to Subject or Agent-oriented) nature of deontic modality, the distinction between internal (motivating) and external (normative) reasons for action is crucial to understanding the structure of practical reasoning, including practical reasoning in the political field. Our more general concern is to arrive at a conception of practical reasoning that can be used in the analysis and evaluation of political discourse and its characteristic genres (deliberation, debate) – see Fairclough and Fairclough (forthcoming) – within a version of Critical Discourse Analysis (Fairclough 2003, 2010).

1. Practical reasoning: a cognitive-motivational account
According to Audi’s (2006) cognitive-motivational account, practical reasoning is a process by which agents infer judgments favouring action from premises expressing motivation and (instrumental) cognition (Audi 2006, p. 104). Audi’s account is Kantian in that practical reasoning can take duties (principles, norms), not only desires, as major premises. Thus, judgments of duty (i.e. reason) can also motivate action, not just desires. By contrast, on a Humean view of practical reasoning, defended by Blackburn (1998), all action is motivated by a combination of belief and desire, but desires are ultimately basic. It is our beliefs and our concerns (our emotional, evaluative attitudes towards those things we care about) that together issue in action, and everything we do can be traced back to some concern we have. For the Humean, it is concerns (or desires) that are the ultimate motivators of action, while reason is merely instrumental to desire and cannot motivate by itself.

Walton’s (2007) account distinguishes between instrumental and normative (value-based) practical reasoning; the latter involves arguing in favour of a certain action from a desirable goal (major premise), supported by a value premise, and from a means-goal (minor) premise. Values support goals by showing why goals are desirable. Walton’s discussion brings in the concept of goal into focus: the major, motivational premise (“I want φ”, in Audi’s account) is represented as “My goal is to bring about A” by Walton (2007, p. 32). In saying that “friendship requires that I see my friend before he leaves London”, I am indicating which value (“friendship”) informs my goal of seeing him before he leaves London and makes this goal desirable (Walton 2007, p. 34). Walton’s treatment of value-based practical reasoning as means-goal reasoning seems to encompass both prudential and moral reasoning, and this is a line we want to adopt and develop here. However, it seems (as in the example above) that goals are always viewed as desirable from the viewpoint of the agent, which is a position we will try to argue against.

2. Internal and external reasons
Walton’s structure of practical reasoning can account very well for prudential reasoning: given what I want (based on my values) and given that doing A will help me achieve what I want, I should do A. But it does not seem to account equally well for moral reasoning, as moral reasoning makes no reference to what the agent wants, or to ends in which his wants are fulfilled. To put it differently, while in prudential arguments the major premise makes reference to the agent’s desires, wants, interests, to what, following Searle (2010), we will call “desire-dependent reasons”, in moral arguments the major premise makes reference to moral values, duties, obligations, norms, to “desire-independent reasons”. An obligation I am under or a promise I made can be in conflict with my current desires and inclinations. In moral reasoning we say in fact this: whether you want to or not, you ought to do A. Walton’s example above, involving what friendship requires, is in fact a moral argument, in which the goal is not as much desired as recognized as something the agent has to do, whatever his present inclinations.

For a Humean, all reasons are “desire-dependent” and, to a large extent, we do follow Blackburn’s (1998) Humean account, which sees the variety of reasons that motivate action as concerns, as things we care about. In other words, unless something matters to us, we will not be moved to action by our beliefs alone. Along the same lines, we suggest, a sense of duty or a promise could not motivate us to act unless doing our duty or fulfilling a promise were something that we were concerned about. If they are to effectively motivate an agent’s action, all “external” reasons should ultimately give rise to a desire or concern to act on that reason.
From this point onwards, however, we part company with the Humeans and follow Searle’s (2010, p. 128) account of how human institutional reality (e.g., promises, laws, norms, etc.) “locks into human rationality” by providing external reasons for action. Although these external reasons must be internalized in order to motivate action, it is recognition of such external reasons as facts that may subsequently become the ground of a concern or desire to act accordingly. Thus, the desire derives from the recognition of the external reason and is therefore not basic. We often recognize the binding force of a duty or a promise and either internalize it as motivation to act or fail to do so. We may fail to be motivated by our duties or promises, even while continuing to recognize that we have a reason to act in the prescribed way.

3. Our proposal for the structure and representation of practical reasoning
Practical arguments take premises expressing goals, values, means-goal relations and, we suggest, circumstances, i.e. the context of action. Our proposal is to view goals as (possible) future states of affairs (a variation on the semantic concept of possible worlds), which the agent may or may not desire. In the latter case, the goal is generated by reasons independent of the agent’s desires, “external” or normative reasons such as duties, obligations, moral values, norms. The agent may not actually desire the goal but, in the arguer’s view, he ought to desire it. Similarly, the agent may not actually care about a particular value or duty but, in the arguer’s view, he ought to care. Because what the agent desires may be different from what the arguer thinks he ought to desire, we suggest looking at practical argument as a speech act involving three participants: a Speaker (Arguer), an Audience and an Agent.

On the one hand, we are trying to capture the fundamental Humean insight that all action is underlain by what we care about (‘concerns’). This is why we see both goals and circumstances as being informed by our concerns: the goals we set ourselves are underlain by what we value or care about, but the circumstances (facts) that we reason from are also selected as relevant to the claim and presented under a certain value-laden description in relation to our concerns. This is most obvious in the case where we are arguing from a description of the relevant facts which we see as a ‘problem’, and arguing for a course of action as ‘solution’ to that problem. Something may be a problem for one agent but not for another, whose concerns are different.

On the other hand, we want to incorporate Searle’s externalism regarding reasons such as promises, which we also extend to duties, norms and moral values. We are of course acknowledging that only internal reasons such as desires, or external reasons that we internalize, and want to act in accordance with, can effectively motivate intentional action. But human social, institutional reality provides people with “desire-independent” reasons for action and people therefore have a reason to act accordingly even when they do not want to act on them or choose to ignore them. This is the gist of Searle’s critique of the internalist (Millgram 2001, Williams 2001) position that sees all human motivation as underlain by desire (Searle 2010, pp. 127-132). Recognizing the specificity of the social world as a world of man-made institutions (commitments, contracts, laws, norms) that one is bound by even when one chooses to act otherwise underlies in fact the very possibility of normative critique.

The gist of our proposal is the following. We are detaching the Goal premise from any necessary connection with actual desire or concern: goals are states of affairs that we can actually desire but they can also be normative states of affairs that we ought to bring about even if we don’t particularly desire them. Judgments that an agent ought to do something are based either on what the Speaker believes the Agent to desire or value, on motivating reasons, or on what the Speaker believes the Agent ought to desire or value, on normative reasons (or on both). The structure is the same for both prudential and moral reasoning, involving goal and value premises which, in the Speaker’s view, actually do or ought to motivate the Agent, as well as means-goal relations and circumstantial premises informed by relevant desire-dependent or desire-independent reasons. In our view, moral reasoning is also of an instrumental (means-goal) type, but the goal is not just some desired state of affairs, but a normative goal that the Agent ought to desire, even if he does not, such as a state of affairs in which promises are kept or obligations are fulfilled. Such a goal would be generated by a Value premise that the Agent ought to be concerned about, in the Speaker’s view. If the Agent comes to internalize this concern as motivation to act, then he will act to bring about the goal, but even if he doesn’t, it would be still possible to say that he had a reason (an external reason) to act in that way, although he chose not to. The difference between the two types of argument is captured in the following two diagrams (Figure 1 and Figure 2), where arrows indicate a relation of support or justification:

In our view, the specificity of moral reasoning (including moral-political argumentation) derives from the recognition of external reasons for action as basic. External reasons in the political field vary from promises made by politicians in electoral campaigns, which they are then expected to act upon, to moral-political values (justice, equality, freedom) recognized as legitimate and binding and enshrined in laws. But they may also be constraints on agents’ action in the sense of power or coercion – obviously, not all external reasons are moral. Recognition of the power of the state or the law, or simply of the authority or power of some individual agent, as external reasons, together with instrumental beliefs (if I fail to obey the law, unpleasant consequences might follow for me), are reasons that shape agents’ action. As we argue in Fairclough and Fairclough (forthcoming), these reasons lie at the interface between agents and structures and show how agency and structure interact and shape each other.

We also suggest placing such external reasons (institutional facts such as promises or norms) in the Circumstantial premise in the second diagram: they are facts that speakers argue from in saying that agents ought to be concerned with their realization. In the case of promises or norms and laws, the fact that the agent made a promise or is bound by a law or moral norm typically override any other possible consideration of what the context is or might require. When we say, for instance that, regardless of circumstances, the Agent ought to do A because he promised, we regard the fact that the Agent made a promise as the only relevant fact.

4. A moral justification of inequality: trickle-down economics and the common good
In what follows we will look at a public debate organized by St Paul’s Institute and hosted by St Paul’s Cathedral (2009) in London on October 20, 2009 (transcript available at http://www.stpauls.co.uk/Learning-Education/St-Pauls-Institute/2009-Programme-Money-Integrity-and-Wellbeing). The discussion focused on the responsibility of banks in the current crisis. Among the panellists were Vince Cable, then Liberal-Democrat Deputy Leader; Brian Griffith, Vice-Chairman of Goldman Sachs International, and Adair Turner, Chair of the Financial Services Authority. One of the questions was: should bankers be made to pay for the bailout, rather than keeping their profits and bonuses? This is how the Vice-Chairman of Goldman Sachs answered this question:
“When it comes to the question of bankers paying for the bailout, I think at a personal level some have paid very expensively…. I think it is very easy to construct a short-term perception of what the common good is. Let’s assume, for example, we all said we’re not going to have big bonuses… I believe you would then find that leading City firms could easily hive off operations to Switzerland, to the Far East…. I believe that we should be thinking about the medium term common good, not the short-term common good, and in thinking about the medium-term common good… at least one cluster of industries we have is the financial sector. We should be proud of that in London, and we should not therefore be ashamed of offering compensation in an internationally competitive market which ensures the business is here and employs British people.”

In his closing remarks, on markets and morality, Lord Griffiths also said the following:
“… I grew up in Wales, in a mining community… I can say I really understand inequality personally. If I felt that the present situation of rising unemployment, … of almost despair … was a permanent feature of our society, frankly I would find it very difficult to defend the City. But what I’ve tried to say is … I think that we have to tolerate the inequality as a way to achieving greater prosperity and opportunity for all”.

Lord Griffith’s interventions were widely reported in the press. The following day, most major newspapers such as The Guardian carried headlines like the following: “Public must learn to ‘tolerate the inequality’ of bonuses, says Goldman Sachs vice-chairman…” (Hopkins 2009). Not surprisingly, there was public outrage. Over the next 48 hours, there were 313 comments on the Guardian website alone (see the Comments thread at http://www.guardian.co.uk/business/2009/oct/21/executive-pay-bonuses-goldmansachs with a record number (48) being deleted by moderators for offensive language. What did Guardian readers think about the views of the Vice-Chairman of Goldman Sachs? Many recognized Griffith’s argument as a defence of “trickle-down” economics and “growth”, although neither were explicitly mentioned, and argued that “trickle-down” has never worked:
MorrisZap 21 Oct 2009, 2:18PM. Griffiths said the British public should “tolerate the inequality as a way to achieve greater prosperity for all”. Trickle-down never worked. It was always a scam for a bunch of (…) greedy, incompetent, lying bastards, to justify their outrageous salaries which they try to avoid paying tax on in any case…

BuddyBaker 21 Oct 2009, 2:26PM. Don’t these people ever ask themselves why we need our economies to keep growing? I suppose they think in phrases like “a rising tide lifts all boats” and trickle-down economics. But after all these years of GDP growth, is the average person in Britain really much better off than 30 years ago? I say thee nay. Instead we’ve just seen rising inequality, and a few people have become stupidly rich…. You can’t have infinite growth. I don’t even understand why you’d want infinite growth.

MichaelZ 21 Oct 2009, 3:45PM. So hold on a minute, we have a recession that completely discredits trickle-down economics, and is only averted from getting even worse by granting tax payers’ money to the very institutions that caused the crash – and Griffith argues for more trickle-down economics. Just how out-of-touch with reality are these people?… We’ve “tolerated” inequality for a good few decades now, and is Britain any more prosperous?… The working people saw “wealth” built on debt (effectively Monopoly money) and an utterly insane period of house price inflation…

Several readers were outraged at what they perceived as blackmail and urged each other to call the bankers’ bluff, encourage them to move abroad:
Ebert 21 Oct 2009, 2:24PM. Griffiths said that many banks would relocate abroad if the government cracked down on bonus culture… The morality of the blackmailer – so let’s call his bluff.

Alebob 21 Oct 2009, 2:17PM. … Let him relocate abroad. In fact let’s charter a ship and get rid of them all.

Goto100 21 Oct 2009, 2:39PM. … You organize the ship. I’ll organize the submarine and the torpedo.

Let us focus first on the argument in favour of inequality: people should tolerate inequality for the sake of future prosperity and opportunity for all, a goal allegedly underlain by a concern for the “medium-term common good”. The common good is offered as a normative premise (“we should be thinking about the medium-term common good, not the short-term common good”), as a concern that agents ought to have. Thus, given what people (as agents) presumably want and ought to want, a future of prosperity and opportunity for all, together with a commitment to the medium-term common good (as external normative reason that ought to motivate action), and given that, in a free market economy, allowing for inequality will help achieve this goal, inequalities in pay ought to be accepted by everyone.
Griffith spoke about “prosperity and opportunity for all”. His argument was apparently motivated by a concern for everyone’s interests. Given that the action advocated allegedly benefits everyone, and is thus universalizable, in a Kantian sense, the argument is in fact intended as a moral argument. It says that people ought to be concerned with the medium-term common good and a future that benefits everyone, i.e., they ought to have these concerns even if they didn’t particularly want to. The action would be the right one regardless of desires, because of the legitimate underlying value. The argument is therefore presented as a moral justification of inequality: inequality is necessary because it serves the common good, understood as what is good for everyone.

Figure 3 represents Griffith’s argument. There are two claims in fact, both underlain by the same value and goal (and for the sake of economy we represent them together): the claim that the right action is to allow for highly unequal pay for bankers (where the implicit Agents are presumably banks and politicians) and the claim that people (as Agents) ought to tolerate this action. The argument is also supported a Cost-Benefit premise: unless the actions in question are performed and accepted, banks will move abroad, will stop producing revenue for Britain, will not employ British people, etc. The Costs will therefore outweigh the Benefits. The circumstances that are selected as relevant for the claim constitute the ‘problem’ that the action is intended to solve: “rising unemployment”, “despair”, the broader context of “crisis”.

What does “trickle-down” economics say? According to political philosophers, it says that “inequality is justified because it promotes economic growth, thereby benefitting even the poorest members of society”. Given that people are motivated by economic incentives, trying to equalize and excessively redistribute resources will cause the most hard-working people to lose the incentives to produce. A better way of helping the poor is to promote economic growth. “Even if their share of the overall pie remains the same, perhaps even if it gets smaller, the pie will be growing at such a rate that the absolute size of their piece will be growing”. Instead of “minding the gap” between the rich and the poor (relative inequality), we should be concerned with improving the position of the worst off members of society in absolute terms (Swift 2006, p. 110). We should therefore be concerned with growth, not (re)distribution, and growth is made possible by inequality.

However, even if it is granted that “trickle-down” might make sense as a description of how people would behave if incentives were removed and everyone were paid the same, it is an incoherent concept when regarded as a justification of inequality (Swift 2006, p. 125). On the one hand, the assumption underlying it is, quite overtly, that people are motivated by selfish interest: if you don’t pay me a lot more to do this particular job, I will not do it and the entire system will collapse, thus damaging the interests of the worst off. Yet “trickle-down” is justified by those who advocate it because it allegedly maximizes benefits for the worst off: inequality at the top will allegedly benefit the most disadvantaged members of society. This double motivation (self-interest or other people’s interest?) makes “trickle-down” economics ultimately incoherent: I can be perfectly justified in paying a lot of money to those who are holding my child hostage, but it does not mean that the final distribution of money, after I’ve paid them off, is justified or fair (Swift 2006, p. 125-127). We may say that a good prudential argument (based on everyone’s desires and interests and on a cost-benefit analysis) is not necessarily a good moral argument as well: it is not fair that the blackmailers should get the money.

In their comments, Guardian readers rejected the “trickle-down” defence of inequality in several distinct ways. First, they rejected it on the basis of empirical evidence: people have always “tolerated inequality” and this has now resulted in worldwide recession. Secondly, people rejected the concept of growth and the assumption that growth will benefit everyone (Aleksandrow: “Greater prosperity for all??!! All who??!!”). In other words, it is wrong to sacrifice some people’s interests to those of others for the sake of an overall increase in prosperity, even if there is such an increase in overall growth. Thirdly, people rejected the concept on various ethical grounds: demanding incentive payments in order to do a job that will benefit the others is a form of “blackmail”. Most significantly, they rejected Griffith’s argument by invoking various conceptions of justice: it is not fair that bankers should get these unequal rewards, they certainly do not deserve them, and even if they are entitled to them according to rules they have themselves written, these rules are themselves wrong.

However, Griffith’s argument was clearly advanced as a moral argument, underlain by a normative concern for the common good, which supposedly will generate a future of prosperity and opportunity for all involved. Yet why, we may ask, is there a need to “tolerate” an arrangement which is right anyway because it serves the common good? A closer look at the structure of Griffith’s argument will show why exactly the “trickle-down” defence of inequality is incoherent and could never serve as a justification of inequality. This is because, we argue, the argument, as stated, is a rationalization: the reasons that are being offered are not the real reasons. The common good is not in fact the underlying value, although it claims to be, and the goal is not that of prosperity and opportunity for each and every citizen. The real, unstated value that underlies the argument is self-interest and it is related to the unstated goal of economic growth. Given what is in the bankers’ interests and given that in the process of serving those interests some positive side-effects will “trickle down” as by-products (benefits) of the logic of perpetual growth, and given the costs to the system of refusing to pay them, they ought to be paid a huge amount. The argument cannot be a moral argument but at most a prudential one analogous to an argument which says: it is in your interest (because of the potential costs) to pay off the blackmailers. Then it will make sense to also say that you have to “tolerate” this arrangement in order to avoid undesirable costs. But it will also be obvious that the interests of the two parties involved do not really have much in common, there is no “common good” that they both share.

To conclude, there could be a justification of inequality (inequality is functionally necessary, a necessary evil), but it cannot be a moral justification. Its best approximation is the argument from blackmail, which is in fact how many Guardian readers interpreted it. As for the “common good”, it is in fact represented by an aggregate conception of growth and some “trickle-down” of wealth as an alleged benefit of inequality. We represent this structure as follows (Figure 4):

5. Justice as fairness, justice as desert. Political values as desire-independent, external reasons for action
We have argued that Lord Griffith’s argument is not a moral argument although it is dressed up as one, as it invokes the common good as an alleged value premise. The comments thread however involved genuine moral argumentation: people did not argue from their own desirable goals but from moral-political values they thought everyone ought to be concerned with. Many posts focused on the idea that bankers do not deserve the high pay they get: they do not produce anything useful, their so-called talents are worthless and they are being rewarded for failure:
LeavesNoWitnesses 21 Oct 2009, 2:38PM. What an arrogant swine! Can he please explain how do banks serve the economy by sucking money out of it when most of the economy is in ruins? Why should we reward these idiots in charge of financial institutions that do not produce anything of value to the society? I’m really lost here. Furious, just furious.

AlanMoore 21 Oct 2009, 2:16PM. Idiot. It might be considered an investment to the general good if these bastards actually generated any wealth – or did anything useful. But they don’t, all they do is distort markets for short-term benefit…

Samboy 21 Oct 2009, 2:21PM. What these greedy snout-in-the-trough bankers utterly fail to grasp is that the obscene bonus culture which was in place before the collapse of the financial sector rewarded long term failure not success. Where’s my f*cking bonus for being part of the investment group which provided 1 trillion pounds worth of capital to ensure that Goldman Sachs could continue to trade?

Another conception of justice that was implicit in many of the posts was “justice as fairness”, with particular emphasis on equality as political value:
deano30 21 Oct 2009, 2:36PM. Foolish tosser – a society is never the richer if its good fortune is based on rampant inequality. It is a flawed and fractured place which is just about to fall apart at the seams.

Harrymanback 21 Oct 2009, 2:15PM. … [O]ne rather large hole in his argument… is the mountain of evidence that shows that happy societies are those that have low inequality, not those that are rich.

Equality and fairness were also defended in the sense of equal treatment of similar situations. If the bankers want to keep the profits, they must swallow up the losses and repay their debts first. In other words you cannot demand one rule for yourself and another one for everyone else.
farandolae 21 Oct 2009, 2:38PM … so we face unemployment, massively reduced pensions, big cuts in public services and some of the people who put us in this mess get an average of GBP 450,000+ on top of their salary. Seems fair.

The Paladin 21 Oct 2009, 9:39PM. That’s fine… You want to keep paying, I’ll let you collapse when you don’t bloody listen. Fair dos.

jacko121 21 Oct 2009, 11:40PM. … if you are not ashamed at paying your staff then you should not be ashamed at repaying your debt to the tax payers first.

Several comments addressed justice in the sense of equal treatment by means of analogies:
patelvijay 21 Oct 2009, 2:14PM. Banks must learn to “tolerate the fairness” of collapse when they mess up.

2LSE 22 Oct 2009, 9:22AM. Err … didn’t the French aristocracy also think that the peasants should tolerate inequality???

Here, we shall draw on political philosophy in order to clarify an important distinction. It is a distinction between a concept of justice and various conceptions of justice (Swift 2006, pp. 11-12). The concept of justice means giving people what is due to them (thus, justice is tied to duty and to rights, not to what is “desirable”). There are however various particular conceptions of justice, different ways of filling out the basic logic of the concept: Rawls’s conception of justice as fairness, Nozick’s conception of justice as entitlement and the popular conception of justice as desert.

In this thread, people argued from a conception of justice which rules out privileging certain people at the expense of others, or putting some alleged aggregate conception of growth above the rights and interests of individual people. The allegedly desirable goal of “growth” was challenged from the perspective of the goal of a just or fair society. Basically, people argued against Griffith’s allegedly moral argument by constructing their own moral arguments with similar structure but different underlying values and goals. Instead of the goal of growth, people argued from the normative goal of a just of fair society (in Swift’s terms, from a concept of justice, as a state of affairs in which everyone gets what is due to them, whether according to desert or a more egalitarian conception, such as Rawls’s “justice as fairness” – Rawls 1971, 1993, 2001). The popular conception of justice as desert, for example, says that talented, hard-working or successful individuals deserve more rewards than untalented, idle or unsuccessful ones. We can represent the arguments from justice-as-fairness and justice-as-desert as follows, in Figure 5:

If we argue from the goal of justice and the specific value of desert, coupled with the factual premises that bankers have in fact failed, that their work involves no special talent or difficulty, as well as the institutional fact of a conception of justice-as-desert as a socially recognized, normatively binding commitment, we are led to the claim that they should not receive bonuses. The reasoning is analogous for justice as fairness (which we discuss in detail in our forthcoming book). The moral claim that is made is based on goal, means-goal, value and circumstantial premises, like any prudential claim, only differently understood. The goal is not one that some people happen to desire because it satisfies their own concerns, but one in which nobody’s particular desires or concerns are privileged over anyone else’s, i.e. a society that gives everyone what is due to them. Likewise, the value premise says that agents ought to be concerned with justice-as-desert or justice-as-fairness, while some conception of justice is viewed as a publicly recognized and normatively binding commitment, part of an explicit or tacit contract with the citizens, as an institutional fact that politicians and the state are expected to act upon even when there seems to be little political will to do so.

6. Conclusion
We have represented arguments focusing on justice issues in a similar way to prudential arguments, as involving the same type of premises, including goal and means-goal premises, i.e. an instrumental structure. An argument in favour of a particular type of political action is intended to contribute to the realization of a particular vision about what society should be like (political goal), grounded in a normative concern for certain moral-political values (rights, obligations, shared norms), regarded as institutional facts.

We agree with the Humean view that what underlies action are beliefs and concerns (Blackburn 1998), e.g., a desire for my wellbeing as well as for the wellbeing of others, and these are internal reasons. Recognition of external reasons has to be accompanied by a desire to act accordingly in order to lead to action, so desire-dependent reasons underlie all action. However, while all action springs from beliefs and desire-dependent reasons, an argument for action can take desire-independent reasons as premises, and these may subsequently be internalized by agents as concerns and motivate action. In acknowledging this, we have moved beyond the Humean conception and adopted Searle’s view of the irreducible nature of certain external reasons, such as those we create by entering into contracts with other people, making promises, being part of human society and abiding by its rules, norms and laws. It is recognition of such reasons that can lead to the formation of a desire to observe their binding force, but the concern or desire derives from the reason we recognize, and not vice-versa (Searle 2010, p. 131). In the arguments we looked at, people argued from pre-existing norms and obligations (from an implicit “social contract”) whose binding nature ought to be recognized and internalized as motivation by politicians and by the state in deciding on a course of action. Even when politicians apparently fail to care about this social contract, and thus fail to act from a commitment to social justice, they ought to do so: they have a reason to do so, and one that they themselves have created by accepting a mandate of political representation.

Our conclusion is that we can preserve the same schema for both prudential and moral practical reasoning if (a) we understand Goals properly, as states of affairs, thus detaching them from any intrinsic connection with desire; and (b) if we understand the specific nature of the social world, as a world of man-made institutions, which generate external, desire-independent reasons for action. In the moral arguments we have discussed, the goal was a mode of social organization that is just, that gives everyone what is due to them, irrespective of anyone’s particular desires. With regard to external reasons, we have seen that they are irreducible to internal reasons but can ground people’s internal motivations, such as a desire to act so that a promise made is actually fulfilled, or a socially shared norm or contract is observed and abided by rather than ignored. An institutional obligation to be fair and impartial can only motivate people through the mediation of a concern for or desire to be fair and impartial, but it is recognition of such an independent obligation as an institutional fact that grounds (whenever it does) the concern that can subsequently lead to action. External reasons that ought to motivate but fail to do so (e.g., social contracts that are broken, publicly recognized values and norms that are disregarded) are a good starting point for social critique.

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