Tag Archives: rhetoric and argumentation

Thinking about an experiment on “practical math” in normative contexts

I am trying to think about an experimental situation that would allow me to test how normative-institutional contexts impact on children quantitative reasoning. Ideally, it has to be an easy experimental task that can be tested quickly with children from different cultures. What follows is a half-baked draft. Your feedback and criticism is most welcome.

So this is the idea… Children (ages 4 to 7) are interviewed individually. During the interview, they are shown a series of very short puppet plays. After each play children are questioned about the best way to solve a problem that arose in the play. Children are required to offer quantitative answers to such problems; for example, “how much money does character A have to pay character B to get even?” or “How many blocks does character A need to add in order to complete the building?”, etc.  The narratives are different in nature. Some narratives provide a social and normative context to the problem, in the sense that they highlight certain social rules children need to take into account in order to respond appropriately to the situation. Other narratives, by way of contrast, highlight “technical” or “engineering” problems, and involve means-ends reasoning. They problems they involve are similar to the normative problems in their mathematical content, yet the narrative context is markedly different.


A1: “Negative reciprocity and reparation”. Character A has a bag with three candy bars. Character A shows the bag to character B and tells her that she loves candy bars and that she plans to eat them with her friends the next day. Character A goes to sleep. Character B steals the bars and eats them. Character A wakes up and finds character B stole the candy, and asks character B to return them. Character B says she doesn’t have the candy anymore but that she can offer character A some money to make up for the stolen candy. She opens a purse and drops some coins and bills on the table. The child is asked to choose the coins and bills character B has to hand over to character A in order to get even. They child is questioned about how she made that decision; and how she calculated how many bills and coins that character B must give character A.

A2: “Destruction and reconstruction”. The child is shown a tower formed by six big blocks. The child is told that a powerful storm and strong winds hit the building during the night and broke the three upper stories of the building. She’s then given a number of smaller blocks of different sizes and is asked to rebuild the tower so that it is as high as it was before the storm. The child is questioned the criteria she used to select the blocks and to decide how many blocks to use.

B1. “Positive reciprocity”. Character A visits character B and shows up with a present: a stack of stickers or trading cards. Each character returns to her own home. Then character B says that character A was really nice and that she would also like to give her a present to “get even”. The child is asked to help character B prepare her present. She is shown a cup and a collection of marbles and is told to fill the cup up until there are enough for A’s present. The child is also asked about how she decided how many marbles to give; i.e. to justify her decision.

B2. “Bridging the gap”. The child is shown a model of a river. On the river there is half bridge built with legos. The bridge starts on one shore and goes only half-way over the river. The child is asked to pick the lego pieces that she would need to build the other half of the bridge. The set of lego pieces the child can choose from have a different size than the ones used to build the first half of the bridge.

All four situations involve some kind of addition and subtraction of different units; they also involve compensating different dimensions of problems (values of the goods exchanged, sizes of different objects, etc.) A1 and B1 are “social” and “normative”: they involve the concept of justice; A2 and B2 are “technical”: they involve a kind of means-ends reasoning.

One possibility is to give situations A1-B1 to one group and A2-B2 to a different group. One could then compare the reasoning and argumentation of children who are given a “normative” vis- à-vis a “technical” narrative. To this end, one might use the theory of argumentation and other tools of discourse analysis. One could also do some standardized numeracy tests (perhaps those used by Opfer & Siegler, Dehaene, Piagetian conservation tests, etc.) after the main tasks in order to evaluate if each of these normative contexts has “sensitized” the child to quantities in a special way; i.e. if the children who just completed the “technical” problem perform better or worse than the children who did the “social-normative” problem.

Another possibility is to give the same children all four situations so as to compare the features of quantitative thinking in technical vs. normative contexts in the same children.

Still thinking…

The persuasive power of likes and up-votes

There’s a recent article in the New York Times about how “likes” and “up-votes” are contagious. http://www.nytimes.com/2013/08/09/science/internet-study-finds-the-persuasive-power-of-like.html

“Likes” and other user feedback systems are at the core of what is called the “Web 2.0”, a transformation of Internet culture (which is like saying, culture) that started around 2006.

A couple of years ago I wrote a book on argumentation (still unpublished) in which I claimed that likes, user feedback, and user ratings are the new form of argumentation. That is, the argument that if many people find something good then that must be good is the main topos of the current era; a purely quantitative form of argumentation. I quote from the article:

“Hype can work,” said one of the researchers, Sinan K. Aral, a professor of information technology and marketing at the Massachusetts Institute of Technology, “and feed on itself as well.”


The first person reading the comment was 32 percent more likely to give it an up vote if it had been already given a fake positive score. There was no change in the likelihood of subsequent negative votes. Over time, the comments with the artificial initial up vote ended with scores 25 percent higher than those in the control group.

“That is a significant change,” Dr. Aral said. “We saw how these very small signals of social influence snowballed into behaviors like herding.”


Corinne Iten on Anscombre and Ducrot’s Radical Argumentativism

I’ve just read a neat article that summarizes and discusses one of my favorite argumentation theories, namely Anscombre and Ducrot’s (Iten, 2000). The article recounts the historical evolution of A. & D.’s Argumentation Theory (AT).

Let’s start with an example of my own: “August inflation was barely 2%” vs. “August inflation was as high as 2%.” As A. & D. remark in their first publications, both utterances have the same informational (i.e. truth-conditional) content, yet they cannot be used as arguments in favor of the same set of conclusions. Another example: “there’s a little wine left” vs. “there’s little wine left” (conclusions: “we don’t need to buy more wine” in the former case, “let’s go buy a new bottle” in the latter). Same information, opposite argumentative orientations. To explain such phenomena, in their early works A. & D. postulated an integrated pragmatics (pragmatique intégrée). “They call it a ‘pragmatics’ because it is concerned with the sort of meaning that can’t be captured in terms of traditional truth-conditional semantics,” says Iten.

She reviews several of A. & D.’s most famous analyses, such as their treatment of “but” as an “argumentative operator” that connects two utterances with opposite argumentative orientation. My example: “I am enjoying your visit very much, but it’s late and I have to work tomorrow”. Not only do both clauses have opposite orientations; it can also be claimed that the second argument has greater argumentative strength than the first. Or you can take the utterance: “Peter is quite helpful. He didn’t do the dishes but he cleared the table.” According to A & D (1983: 107, as explained by Iten), the but in this sentence “is scalar in nature”, i.e. it not only indicates that the two clauses support contradictory conclusions (or have opposite argumentative orientations) but it also indicates that “Peter has cleared the table” is a stronger argument for “Peter is quite helpful” than “Peter didn’t do the dishes” is for “Peter isn’t helpful”.

Another example Iten brings up is the argumentative operator “nearly”: An utterance containing “nearly” usually has the same argumentative orientation as a corresponding utterance without “nearly”. (“He nearly hit that fence” or “He hit that fence” both warrant the conclusion “he’s a bad driver”). Iten says: “This could be a banal observation if it wasn’t for the fact that, from the point of view of informational content, ‘nearly X’ is equivalent to ‘not X’. This is made even more interesting by the fact that the argumentative orientation of an utterance containing barely (…) is the opposite of that of the same utterance without barely (…), in spite of the fact that ‘barely X’ is informationally equivalent to ‘X’.”

As part of their 1983 formulation, A. & D. also claim that “an act of arguing… is an illocutionary act, which is part of the meaning of every utterance”, a claim that blurs the distinction between the pragmatic and semantic domains.

Iten then discusses the latest formulation of the theory, which relies on the Aristotelian concept of topos or “argumentative commonplace.” “A topos is an argumentative rule shared by a given community.” “This argumentative rule is used to license the move from an argument to a conclusion.” It is an important feature of topoi that they are scalar in nature. For instance, if a topos states that when it’s hot it’s pleasurable to go to the beach, then the hotter it is, the more pleasurable it is to go to the beach (or eat ice-cream, or turn on the air-conditioner, etc.) The general form of a topos is “The more/less object O possesses property P, the more/less object O’ possesses property P’.”

With the introduction of topoi, A. & D. will no longer try to analyze the meaning of utterances in terms of “presupposed contents” (as in the earlier versions of their theory). Rather, the meaning of linguistic predicates is defined by the topoi associated with them, and by the network of possible conclusions they enable. The meaning of a predicate like work, for example, is given by a bundle of topoi involving gradations of work. Some topoi that could be part of the meaning of work are:

  • The more work, the more success.
  • The less work, the more relaxation.
  • The more work, the more fatigue.
  • The less work, the more happiness.

“Gradations of work are linked, via different topoi, with a series of other gradations, e.g. of success, relaxation, fatigue and happiness. These gradations, in turn, are themselves linked to different gradations still. For instance, gradations of happiness could be linked with gradations of health, appetite, etc. This network of gradations, linked via an infinite number of topoi, is what A & D (1989: 81) mean by a topical field.”

With this emphasis on topical fields, Iten claims, we arrive at a completely non-truth-conditional semantic theory. “In their own words, A & D (1989: 77/79) move from a position of considering “argumentation as a component of meaning” to one of “radical argumentativism”. This is a position where “the argumentative function of language, and with it argumentative meaning, is primary and the informative function of language secondary. In that sort of an account, any informational (or truth-conditional) meaning would be derived from an underlying argumentative meaning.”

While in its earlier stages AT acknowledged (to some degree) the distinction between semantics and pragmatics, in its later formulations it abandoned this distinction completely. Iten is right in concluding that, in its current state, Anscombre and Ducrot’s theory non-cognitive, non-truth-conditional, and reduces all linguistic phenomena to a semantic-pragmatic level of analysis.

The latest version of D. & A. also includes their beautiful (in my opinion) concept of polyphony. “The idea is that the (usually unique) speaker (locuteur) doing the uttering stages a dialogue inside her own monologue between different points of view (énonciateurs).” The most obvious examples of polyphony in our speech and verbal thinking are: direct and indirect reported speech, ironical utterances, utterances containing but and negative utterances.

Finally, Iten dwells in the extreme consequences of radical argumentativism for linguistic theory, namely: all linguistic meaning can be captured in purely argumentative terms; the meaning of every utterance can be described in terms of a collection of topoi, which constitute different points of view; and there is nothing about language as such that is informative, i.e. language is not cut out to be used to describe states of affairs.

Although Iten might be French, her criticism of A. & D. is too American in my opinion, and also a little unfair. Iten favors a cognitive paradigm according to which the human brain is a computer that takes in information from the outer world (“input”), processes it by applying computational rules, and produces output. The information is encoded in the head of the speaker as representations that can be true or false, that is, that can match or not match the facts of the world. This cognitive paradigm provides Iten with a yardstick for assessing the virtues of A. & D.’s theory, which does not fare well when subjected to such standards: it doesn’t explain how language represents the world; it doesn’t connect input with output; and it doesn’t predict arguments’ conclusions based on their premises.

Yet the merits of A. & D.’s theory lie elsewhere. A. & D. teach us to look at language in a new way. They provide us with tools to understand utterances as actions. One takes positions, defends certain points of view, creates assumptions, and commits to certain conclusions. All these argumentative movements take place on a stage-like mental space, and are carried out by a plurality of characters or actors that A. & D. call enunciators. I like this approach very much, among other reasons because it fits my own emphasis on the sense of justice that animates all argumentation. That’s why A. & D. (unbeknownst to them) also appeal to quasi-legal terminology, such as saying that a certain topos “licenses” the speaker to derive a certain conclusion, etc. In other words: the movement from premises to conclusions cannot be understood in computational terms; it has to be appreciated on the level of free, human action.

Rhetoric of possession

So writes my friend Philippe Rochat (2009):

I would argue that much of the possession game is to seduce others, or at least gain recognition from those we select to maintain social closeness with, gaining reputation and social ascendance over them. Possessions, the ways we possess and how we display or carry them, are instrumental in our constant attempt at controlling what people see of us. We incorporate all of our possessions as part of “Me,” in William Jame’s sense, “Me” as a conceptual and constructed notion of self that is projected into the public eye for evaluation.

Another way to say the same: we arrange our possessions with rhetorical sagacity and with an audience in mind.  

See: Rochat, P. (2009). Others in Mind: Social Origins of Self-Consciousness. New York: Cambridge University Press, p. 147.