On the Norms of Visual Argument: A Case for Normative Non-revisionism

Abstract

Visual arguments can seem to require unique, autonomous evaluative norms, since their content seems irreducible to, and incommensurable with, that of verbal arguments. Yet, assertions of the ineffability of the visual, or of visual-verbal incommensurability, seem to preclude counting putatively irreducible visual content as functioning argumentatively. By distinguishing two notions of content, informational and argumentative, I contend that arguments differing in informational content can have equivalent argumentative content, allowing the same argumentative norms to be rightly applied in their evaluation.

Appendices

Appendix 1: A Proof that There are Visual Arguments

1.1 Proof

P1    Categorical syllogisms are arguments.

P2    Categorical syllogisms can be expressed by Venn diagrams.

P3    Venn diagrams are visual images.

∴C    Some visual images express arguments.

1.2 Reply to an Anticipated Objection

To those inclined to respond that images can only express, rather than be arguments, consider the analogous argument:

P1    Categorical syllogisms are arguments.

P2    Categorical syllogisms can be expressed by sets of sentences.

∴C    Some sets of sentences express arguments.

Consequently, in whatever sense sentences can be syllogistic arguments, so too can images.

1.3 Discussion

There is considerable debate about whether mathematical diagrams constitute proofs (i.e., arguments of a kind) or whether they are merely ancillary to proofs which, properly conceived, are ordered sequences of sentences or formulae where the initial items on the list are given as axioms or premises, the remainder of which are theorems derived by rules of inference from items higher up on the list, and where the last item in the sequence is the conclusion (Barwise and Etchemendy 1996; Brown 1997, 2008; Dove 2002). The work of Shin (1996) and Hammer and Danner (1996) demonstrates that Venn diagrams can be operationalized as a logical system, understood as “a mathematical model [either semantic or proof theoretic] of some pretheoretic notion of consequence and an existing (or possible) inferential practice that honors it” (Barwise and Hammer 1996: 51). That is, the basic diagrammatic elements of Venn diagrams can be provided with a syntax, semantics, and system of derivation rules such that Venn diagrams can be rigorously and unambiguously interpreted as expressively equivalent to sequences of lines in a syllogistic proof. If successful, this conclusively demonstrates that Venn diagrams are arguments if syllogisms are. Mumma (2010) provides a similarly rigorous interpretation of the diagrams in Euclid’s Elements, in an effort to establish that they too function demonstratively, rather than merely instrumentally as heuristic or illustrative devices. See also Dove (2013: 8–9) for a visual, diagrammatic refutation of the transitivity of the quantifier “most,” and (9–14) for a diagrammatic map that provides a Heawood counter-model to Kempe’s four-color theorem about the minimum number of different colors required to shade any planar map such that no bordering regions will have the same color.

The point here, I take it, is not that such a rigorous interpretive system is a requirement for something’s being an argument. Rather, the point is that whatever standards of meaningfulness we require in order that something rightly be interpreted as an argument, those conditions can be met by images when they are supplied with an appropriate context of use. More generally then, as Groarke (2014) argues, meaning is a function of use, and images, when used in the right sorts of ways, can take on meaning such that they can function argumentatively (cf. Lake and Pickering 1998; Barceló-Aspeitia 2012; Tseronis 2013). And most importantly, the meaningfulness and argumentative function of images is to be explained in exactly the same way as the meaningfulness and argumentative function of words. When embedded in an appropriate system and practice of use, images become linguistic elements just as phonemes and graphemes do.

Appendix 2: On the Nature of Argument Modality

Section 3.2.2 characterizes the modality of an argument as its presentational manner, such that modes are distinguished not on the basis of content but according to the manner in which some content is presented. Blair (2015: 218; emphasis added) adopts a similar idea whereby the modal categorization of an argument designates “the manner in which the argument is expressed or communicated.” By contrast, Groarke (2015: 140, 143; emphasis added) proposes an account that “define[s] modes in terms of the ingredients (the ‘material’, the ‘stuff’) an arguer uses and arranges when they engage in an act of arguing,” such that “[t]o see if an act of arguing is an instance of a particular mode it is enough to check whether it is built from ingredients that define the mode.”

Given its centrality in theories of multi-modal argumentation, there is a pressing need to articulate a workable and agreeable concept of an argumentative mode. Of the two views just considered, despite their difference in focus on adverbial qualities of argumentative acts (presentational manners) versus noun-categories of argument components (material ingredients), the views are similar in that each directs us to consider by what means the arguer is arguing when determining the mode of argument. I recommend an account that permits the distinction of function, content, and mode. Functionally speaking, arguments are all built from the same stuff. Arguments are composed not of images, nor even of words, but of claims and reasons (Godden 2015b: 237). As Blair (2015: 232) writes: “Arguments are not themselves verbal or visual.” Whatever reasons are built out of, it is a condition of their being a reason that they be able to function as such. Thus, the modality of a reason cannot interfere with its functionality as a reason; similarly with claims. Further, in order to retain the possibility that the same argumentative content (whether claim or reason) might occur in a variety of different modes, I suggest that there is an advantage in identifying reasons and claims by their content. Rather than a noun-category, the modality of a claim or reason could then be either an adjectival property of the artifact (i.e., its manner of presentation), or an adverbial property of the presentational act. This would allow claims and reasons to be identified by their content and categorized by their mode in a way consistent with Groarke’s (2015: 135ff.) key component tables.