On Defining ‘Argument’

The emphasis here is my own. I don’t think that Hamblin means to discourage one from attempting to define ‘argument’ altogether, he merely is suggesting that any attempt to define ‘argument’ in a head-on sort of way is not really worthwhile; understanding is best gained “indirectly” (perhaps by trying to avoid the articulation of necessary and sufficient conditions). On the other hand, I think a frontal, direct assault on the definition of ‘argument’ by way of trying to provide necessary and sufficient conditions is worthwhile.

See, e.g., Walton (1990), van Eemeren and Grootendorst (1984), Blair (2004), Bowles and Gilbert (1993), Goddu (1999, 2011a, b), Hitchcock (2007), Johnson (2000), Pinto (2001) and Tindale (2002).

Or at least there appears to be this ambiguity in ‘argument’. Simard-Smith and Moldovan (2011) defend the idea that ‘argument’ is univocal, and the only legitimate sense of the term is the logical sense. Whether they are right or wrong is for another time; since the disputed sense is not my subject here anyway, their project is simply irrelevant to my present concerns. Also: as an anonymous referee at Argumentation has also pointed out, an opposition between a logical sense and a practical sense would be misleading when considered from the viewpoint of dialogue logic (see, e.g., Barth and Krabbe (1982)). Dialogicians hold that crucial logical terms such as ‘argument’ and ‘validity’ can be adequately defined from a practical point of view. According to this approach, argumentation is not the mere application of pre-existing logical notions; logic itself is inherently a practical enterprise. At any rate, I will be putting the views of dialogicians such as Barth and Krabbe to the side for the purposes of this paper.

Arguments-as-objects are sometimes regarded not as sets or collections of propositions, but rather sets or collections of sentence types or sentence tokens. I will henceforth be assuming not only that propositions exist, but that arguments-as-objects just are sets of propositions, and here’s why. I can surely consider Anselm’s Ontological Argument. When I do so, however, I am not considering any set or collection of sentence tokens uttered or inscribed by Anselm—I am not in contact with them. Nor am I considering any set or collection of sentence types that those tokens were instances of—I am ignorant of Latin. I thus think it is eminently reasonable to regard arguments in the logical sense as sets or collections of propositions, the abstract semantic contents of the types of sentences once tokened by Anselm to express his Ontological Argument.

It is apropos here to register my main complaint against the definition of ‘argument’ in the logical sense that Hitchcock (2007) provides. He takes arguments-as-objects to fundamentally be sets of speech acts plus an illative relation. However, just as I am not considering any set of sentence tokens or sentence types when considering Anselm’s Ontological Argument, I doubt I am considering any of Anselm’s speech acts when considering his argument. Rather, I am grasping the propositions expressed by his assertions, etc.

One might resist here. One may try to provide a deflationary or minimalistic definition of ‘argument’ on which some mere collections of propositions would count. See, e.g., Kalish and Montague (1964), Skyrms (2000), or Bergmann et al. (1998). Addressing such views, however, is outside the scope of my current project. Rather, my paper is aimed at those argumentation theorists who at least start with the assumption that there must be a robust relation present among certain propositions in certain collections counting as arguments that makes arguments irreducible to mere collections of propositions of any sort.

The first two proposals seem to endorse the idea that arguments are discovered, the last five seem to favor some kind of constructivism. Regarding the last of the above proposals, viz., Copi’s, Walton (1990, p. 409) comments: “Claimed by whom? And regarded by whom? By the proponent of the argument, one would suppose.” Now, of course Walton is right that we must address the issue of intentions and how they figure into the logical definition of ‘argument’, but Walton’s remark is a little too cavalier. Specifically, as I argue below, ‘argument’ must not be defined in such a way that the intentions of an argument’s proponent are all-important in a way that leads to an objectionable sort of relativism that merely provides a sufficient condition, or an objectionable sort of absolutism that leads to contradiction.

There are, of course, objective, mind-independent support relations among propositions. If p then q, together with p, objectively, conclusively supports q. Most As are Bs, together with c is an A non-conclusively supports c is a B. The problem here is simply the fact that the expression ‘awful argument’ is both non-empty and semantically unlike ‘fake fur’; the former expression truly denotes a kind of argument. I will simply be assuming throughout that ‘p supports q’ means that the probability of q given p is greater than the probability of q alone. I wish to thank an anonymous referee at Argumentation for help in articulating these points more precisely.

I am indebted here to Tom Adajian. The comments he provided during a presentation of this paper at a colloquium organized by James Madison University’s Logic and Reasoning Institute were crucial in helping me formulate my worries for this version of absolutism precisely.

There may, however, be further problems in the neighborhood. As Daniel Flage has pointed out in conversation, if we are to understand arguments solely in terms of intentions of their active proponents, then we may be tempted to understand dependent notions such as deductive argument and inductive argument in terms of (something like) airtight intentions versus fairly strong intentions. But this is not plausible. An argument’s proponent may intend that some propositions conclusively support a further when they truly don’t, and an argument’s proponent may intend that some propositions support a further with a probability of .8 when they are truly conclusive. Furthermore, there may simply be no fact of the matter about what a proponent of an argument intends regarding the strength of the support relation, and it would thus turn out, absurdly, that there is no fact of the matter about whether or not some argument under consideration is deductive or inductive.

Thanks to Daniel Flage for this point as well.

Blair (2004, p. 141) states, “[…] I propose that we conceive a set of one or more propositions to be an argument […] just when all but one of them constitute a reason for the remaining one.” He then goes on to remark (p. 143):

Someone will notice that by this definition there cannot be an argument with no support. It is important to distinguish between an argument and some person’s (or persons’) argument. Someone’s argument consists of a proposition and the consideration which that person takes to support it or offers as support for it (taking and offering are importantly different). A person's argument can contain premises that are irrelevant as support for their conclusion. Indeed, all the “reasons” a person takes or offers as support for a proposition can be completely irrelevant to it. We still correctly speak of that person's “argument.” But if the offered support is completely irrelevant to the conclusion, then that person’s argument – what he or she the “proposed” or “offered” or “understood” to be an argument – is in fact not an argument. […] Such a person presumably thinks he has an argument, but he is mistaken.

This strikes me as incorrect. There may be genuine, full-fledged arguments of which there is simply no mind-independent support among the relevant propositions. Tim’s “lasagna” argument is meant to illustrate this. ‘A person’s argument’ and ‘argument’ should, by my lights, be regarded as synonymous. I do, however, hear the ambiguity in ‘reason’ that Blair notes: ‘someone’s reason’ may not pick out a real reason. The upshot is that premises may wrongly be regarded as reasons, but that does not entail that such propositions cannot be constitutive of genuine arguments. ‘Reason’ seems to entail nonzero probabilistic support, while ‘someone’s reason’ does not.

Related to these points: Bowles and Gilbert (1993) accept a definition of ‘argument’ on which it’s a necessary condition that the probability attributable to the conclusion given the premises be greater than .5. See Goddu (2011(a)) for a forceful and compelling rebuttal.

While arguments come into existence fairly easily on my view, merely possible, fictional, or hypothetical agents are not agents, and so sets of propositions entertained inferentially by merely possible, fictional, or hypothetical people are not arguments. There must be an actual agent that has at some time or other in our world entertained some set of propositions inferentially for there to exist an argument. We may merely imagine or merely pretend someone has entertained a set of propositions inferentially when no actual person, including those doing the imagining or pretending, has in fact believed there to be a support relation present in the relevant set. To entertain a set of propositions inferentially, on my view, is to believe there exists objective, a mind-independent support relation among them, whether such a relation exists or not. Genuine arguments may, of course, be easily imported into a fiction or a thought experiment, just as a fiction or thought experiment may involve Napoleon or Einstein. And we are, of course, very often inspired to create or discover genuine arguments by reflecting on the events described in fictions or thought experiments, or by authoring them ourselves. But such a creation or discovery would be an event distinct from any event we’d merely imagine or merely pretend to occur.

Granted, the “identity conditions” they provide are not explicitly time-indexed, but unless we understand a time-indexing to be implicitly built into them, it seems we could hardly make sense of the passage just quoted.

Goddu (2011b, p. 6) expresses worries for Simard-Smith and Moldovan (2011) that are relevantly similar to some of the ones I’ve expressed here. He asks:

[On their view] arguments contain propositions as constituents. What kind of abstract objects are they? Did the content of Anselm’s argument come into existence because of Anselm or not? Can the content go out of existence? Certainly the content can stop being expressed, and in that sense, stop being instantiated, but is that the same as going out of existence?

And:

Anselm intends a specific conclusion to be inferred from a specific set of premise propositions. But suppose this intention is never expressed on paper or recorded. I have the same intention over the same propositions 800 years later. Did the argument exist in the intervening 800 years or not?

On the view I am defending, propositions ought to be understood as entities that are abstract and eternal. (But this does not necessarily entail that they are atemporal nor even aspatial; they may exist at all times, and they may exist in some spatial way that is fundamentally different from concreta. Moreover, the eternality of propositions is not essential to my view, nor is their necessary existence. Some propositions, at least for all I have said here, may be contingently existing, abstract artifacts). So, if by ‘content of Anselm’s argument’, Goddu means the propositions Anselm chose to regard inferentially 800 years ago, then the content of the argument never came into existence in the first place, nor will it ever cease to exist. The argument, however, i.e., the propositions-so-entertained, came into existence 800 years ago when Anselm chose to regard them inferentially. That entity has existed in all the intervening years, and will forever exist.

Goddu (2011a) argues that one would be mistaken if one were to take arguments-as-objects to be the following sort of product: a group of propositions, one produced by the activity of arguing. Whether I agree or disagree with him depends on what is meant by ‘group’. I say that a set becomes an argument when entertained with support relations in mind, so in a sense there exists a set that at first is not an argument, but then it becomes one due to something one of us does. But that’s not to say that we perform some act of bringing propositions together (that we thereby “group” them) by engaging in argumentation; all sets of propositions are already in existence prior to our consideration of them. What we are responsible for is choosing to entertain some such sets with support relations in mind. When that happens, a set that was not an argument becomes one given something we’ve done. So, in that sense, an argument is a product of our activity.