It is true that if we had to do with photographs alone, however much we might look at them, we should never see them animated […]. [T]he mechanism of our ordinary knowledge is of a cinematographical kind.
Henri Bergson ( 1911 /1998, pp. 305–306)
[An argument] shall be represented by a series of such diagrams imagined to be phenakistiscopically combined (The “phénakisticope” was the first animation device capable of creating a fluid illusion of motion).
Charles Sanders Peirce (MS 292b)
Abstract
Some have suggested that images can be arguments. Images can certainly bolster the acceptability of individual premises. We worry, though, that the static nature of images prevents them from ever playing a genuinely argumentative role. To show this, we call attention to a dilemma. The conclusion of a visual argument will either be explicit or implicit. If a visual argument includes its (explicit) conclusion, then that conclusion must be demarcated from the premise(s) or otherwise the argument will beg the question. If a visual argument does not include its (implicit) conclusion, then the premises on display must license that specific conclusion and not its opposite, in accordance with some demonstrable rationale. We show how major examples from the literature fail to escape this dilemma. Drawing inspiration from the graphical logic of C. S. Peirce, we suggest instead that images can be manipulated (erased, dragged, copied, etc.) in a way that overcomes the dilemma. Diagrammatic reasoning can take one stepwise from an initial visual layout to a conclusion—thereby providing a principled rationale that bars opposite conclusions—and the visual inscription of this correct conclusion can come afterward in time—thereby distinguishing the conclusion from the premises. Even though this practical application of Peirce’s logical ideas to informal contexts requires that one make adjustments, we believe it points to a dynamic conception of visual argumentation that will prove more fertile in the long run.
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Notes
The use of photographic evidence in courtrooms, for example, amply establishes this. From a legal standpoint, the 1948 trial of People versus Doggett set a major precedent, since “[t]he 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” of oral copulation (Mouser and Philbin 1957, p. 311).
See for example the applied work on visual refutation (Lake and Pickering 1998) and contestation (McGeough et al. 2015), editorial cartoons (Edwards and Winkler 1997), visual enthymeme (Finnegan 2001), famous photographs (Hariman and Lucaites 2007), the use of visuals in charity advertising (Grancea 2015), and the reception of digitally altered images (Pfister and Woods 2016). This is not an exhaustive list.
For a similar concern, see Thomas (2014, p. 166).
As Leja notes, “[t]his natural visuality had no bearing, apparently, on Peirce’s experience of the visual arts. In contrast to other members of his social class, such as his friends William and Henry James, Peirce’s interest in art was minimal” (2000, p. 97).
What professional philosophers now take to be logic is the product of purely contingent textbook wars that took place in early 1950s. For a historical account, see Pelletier (1999).
One should not forget that, according to the medieval tradition, there is a basement beneath logic, namely “speculative grammar” or semiotics, which studies how signs convey meaning. Given that “validity presupposes meaningfulness” (Bellucci 2017, p. 1), logical inquiry cannot do without such semiotic inquiry. For a reliable portal to the best philosophical literature on that topic, see Champagne (2014).
See Arnheim (1969), Saint-Martin (1990), Messaris (1997), Mitchell (2005)—or any number of specialist journals, such as Imaginations: Journal of Cross-Cultural Image Studies, The International Journal of the Image, Philosophy of Photography, Visio: Revue internationale de sémiotique visuelle, Images: Journal for Visual Studies, Journal of Visual Communication and Image Representation, Visual Communication, Visual Communication Quarterly, Journal of Visual Literacy, Image & Text, Visual Studies, Visible Language, Journal of Visual Culture, The Visual Computer: International Journal of Computer Graphics, Antennae: The Journal of Nature in Visual Culture, International Journal of Semiotics and Visual Rhetoric, and The Journal of Visual and Critical Studies. This is not an exhaustive list.
The fallacy of circularity is not endemic to visual arguments. For a survey of why begging the question is considered fallacious, see Caravello (2018).
For a discussion of how viewers use social and cognitive inputs to carve images into parts, see Boeriis and Holsanova (2012).
For instance, one who masters the relevant cultural context might assign the following meanings to the image: the forest-dweller of Germanic folklore (likely a stand-in for Martin Zinner, a shrewd old business man) who embraces the bride (likely a stand-in for Katherine Frey, a relative of Dürer) brings with him sexual vigour on their wedding day, but the hidden side of his shield reveals him to be an agent of death (insofar as Zinner had syphilis). This reading, which has little to do with (and runs counter to?) “Reject coats of arms,” is proposed by the independent art historian Elizabeth A. Garner, who specializes in discerning “secret ciphers” in Dürer’s work (that are reminiscent of the conspiracy theories in Dan Brown’s novels).
The relation between text and image that one finds in joint arguments can be further clarified by using the taxonomy laid out in Martinec (2013, pp. 150–153).
For more on the idea that “visuals such as pictures do not argue” but “only influence or persuade—often in a manipulative way,” see Kjeldsen (2015, p. 118).
Naturally, establishing the motion of a star does not establish that a given party is enjoying political ascent. Being movable is thus a necessary but not sufficient condition.
Dove (2016, pp. 259–260) has objected that students are often able to distinguish valid and invalid syllogisms verbally, before they ever employ Venn diagrams. Although Godden (2017, p. 425) has retracted his suggestion in light of Dove’s objection, we do not think Godden should have backed down so quickly. It is true that, before inventing his improvement on Euler diagrams, Venn knew which syllogisms are valid and which are not. Venn nevertheless devised a diagrammatic notation capable of converting those intuitions into something that is publically verifiable. So, whereas medieval philosophers catalogued and memorized valid syllogistic forms, he was able to demonstrate—in a new pictorial fashion—why those rules may be considered rational.
Peirce’s choice of the label “existential,” which first appears in his letters and notes from the late 1890s, stems from this. As Roberts explains, in Existential Graphs, to “write something is to ‘aver that such a thing exists’ (MS 513), and is to claim that something having the character described exists in the universe which the sheet represents” (1973, p. 30).
Stjernfelt (2014) is mandatory reading for anyone who wonders/worries whether images can be “propositional.”
Burke (1966, p. 419) may have been overly-confident when he claimed that “the negative is a peculiarly linguistic resource.”
For more on the primitive role of conjunction in constituting atomic and compound propositions, see Champagne (2019).
It is a reasonable question whether the cut, instead of negating the assertion, divests a proposition of its assertoric force. This question has been dealt with in Bellucci and Pietarinen (2017). There is also the dual system of “entitative graphs,” where the main connective of the graph in Fig. 9 is NOR, not AND. In Existential Graphs, the sheet represents tautology, not contradiction.
One can use a truth table, a device invented by Peirce (Anellis 2004), to confirm that the diagram for ~ (P ∧ ~ Q) indeed captures the standard material conditional P → Q.
Addressing the resurgence of interest in early devices like the phenakistiscope, Carels notes that, “100 years before the GIF entered popular consciousness, Marey, Leprince, and several others, had already presented very short sequences of about a dozen photographic images” (2015, p. 34). Interestingly, spinning disks like the thaumatrope (1825) were sometimes marketed as “philosophical toys” (ibid.).
Once again, one can use a truth table to confirm that the enriched diagram for {P → [Q ∧ (Q → R)]} ∧ (Q → R) is indeed equivalent to the previous step of (P → Q) ∧ (Q → R).
The thin black arrow has been added solely for didactic purposes and is not part of the language of graphs. The intent is to show the direction of the iterative movement on the static medium of the printed page.
Informally speaking, removal by deiteration is sound, because the image remains in the context of the image that was removed.
Erasure is permitted on asserted areas, that is, on the sheet or on graphs resting on areas enclosed within an even number of cuts.
Since imagistic systems of representation can provide a well-defined relation of consequence (and thereby perfect systems of proofs and demonstration), their power is not limited to the representation of structured semantic contents or arguments. See Ma and Pietarinen (2017b, 2018) for recent studies of Peirce’s proposed calculi of graphs as systems of algebra, deep inference, and sequent calculi.
For a discussion of the role of observation in diagrammatic reasoning, see Legg and Franklin (2017).
Despite advances in computer imaging, no special effect can successfully depict a square-circle. A world-wide contest was held inviting logicians and artists to depict contradictions visually (see Beziau 2015). Tellingly, no submission succeeded. Champagne (2016a) argues that this impossibility (which he dubs “contrapiction”) is the main source of diagrammatic reasoning’s normative power, insofar as some qualities or tones simply resist being squeezed into one token. For more on the type/token/tone distinction, see Champagne (2018a, pp. 22–26).
Pietarinen points out that the notational simplicity and multimodality of logical graphs can make them beautiful. In an attempt to account for this experience of beauty, he conjectures that “logical graphs excite those Brodmann areas that are responsible for emotional experiences, whereas traditional (non-graphical) logical notations may fail to do so” (2018, p. 12). For neuroscientific investigations that used paintings as visual stimuli, see Ishizu and Zeki (2011).
For an applied exploration of how diagrams can prompt discoveries in the social sciences and humanities, see Champagne (2016b).
Nothing about arbitrary strings of characters like “because” and “therefore” makes them intrinsically suited to be inference indicators. Hence, once a language-user becomes adept at recognizing the syntactic places and pragmatic roles that premises and conclusions play in a given system of meaning, these textual markers can eventually be dropped. One might take this possibility of absence to mean that the expressive needs of an argument are different—and quite less—than the expressive needs required to demonstrate logical consequence. However, such a view would overlook that (1) the textual markers needed to be present before they could be learned and eventually omitted and (2) the markers can at any time be reincorporated (in specific locations that are subject to robust standards of correctness).
The derivation of residuation has a particularly apt diagrammatic proof in Existential Graphs that requires only the observation that the space between two cuts is empty (see the graph RG1 in Ma and Pietarinen 2017a, p. 180). This makes Peirce’s transformations not only valid and sound, but also evident to reason.
The discovery of diagrammatic logic was inextricably woven to the development of modern logic and modern metatheories of logic. In fact, “the very notion of iconicity comes out of deep issues in the discussion of formal logic and different ways of representing it” (Stjernfelt 2015, p. 35).
As Tversky puts it, “maps, like many other kinds of visualizations, distort the ‘truth’ to tell a larger truth” (2011, p. 502).
It may be that verbal arguments have occupied a prominent place, not so much because “argumentation is a verbal activity” (Eemeren et al. 2004, p. 2; italics in original), but because argumentation is a sequential activity.
Some researchers (like Messaris 1997) have suggested that lack of argumentative stringency is what makes images so rhetorically effective. That may be. But, if this lack of stringency is so pronounced that it opens the door to completely opposite conclusions, then the label “argument” becomes unwarranted.
For a discussion of the potential of diagrammatic reasoning in conflict resolution, see Hoffmann (2005).
Scientific arguments are often complexes of verbal, graphical, tactile, and auditory modalities (Gross and Harmon 2013), so there is no need to lay excessive emphasis on the visual at the expense of many other facilitators of discovery, synthesis, and analysis. Richard Feynman, for example, famously claimed to “listen” to his imagination. For more on the role of sound in formal logic, see Pietarinen (2010) and Champagne (2015b). For more on the role of sound in informal logic, see Groarke (2018). For a practical exploration of gestures and body positions in regimenting elementary argumentative structures, see Champagne (2018b).
For a discussion of sequential Christian depictions as precursors to modern-day comics, see Alaniz (2014, pp. 14-15).
It is not necessary to require, atop all this, that a visual argument achieve inferential feats that no words ever could. This requirement of non-redundancy (as Grancea 2017 calls it) is too demanding. While some images exhibit unique properties that language cannot match, there is no reason why some verbal and visual arguments could not make similar points, in parallel. Even in such a redundant scenario, one can ask whether the visual argument is sustaining the passage from premise(s) to conclusion(s) visually. For an illustration of the disappointments that ensue when we insist that images must do their argumentative work non-redundantly, see Brody et al. (2000).
One change that would put the conversation on a firmer footing would be to drop folk semiotic categories like “textual” and “visual” and instead employ principled distinctions like iconicity, indexicality, and symbolicity. A sign-vehicle like “S,” for instance, is both a similarity-based icon of a(ny) serpentine figure and a conventional symbol invested with a role in a linguistic code. The idea that a sign-vehicle like S is intrinsically a letter—which is unquestioned in the folk semiotic text/image distinction—therefore occludes more than it reveals.
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Acknowledgements
We want to thank Chiara Ambrosio, Liam Dempsey, Wayne Fenske, Patrick Findler, Leo Groarke, Hans V. Hansen, Parthiphan Krishnan, Melinda Hogan, Martin Lefebvre, Puqun Li, Judy Pelham, Aud Sissel Hoel, Doran Smolkin, Byron Stoyles, as well as anonymous reviewers for this journal. Research for this work was funded in part by the Estonian Research Council (Projects PUT267, PUT1305), the Academy of Finland (Project No. 12786), and the Russian Academic Excellence Project (No. 5-100).
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Champagne, M., Pietarinen, AV. Why Images Cannot be Arguments, But Moving Ones Might. Argumentation 34, 207–236 (2020). https://doi.org/10.1007/s10503-019-09484-0
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DOI: https://doi.org/10.1007/s10503-019-09484-0