To demonstrate comes from the Latin demonstrare “to show, to point out”. To demonstrate and to show verbs are synonymic in some contexts: “in what follows, I’ll show (= demonstrate) that…”.
In ordinary life, people engage in demonstrations of friendship, solidarity, affection… making an exhibition, a show of their sentiments, as they give proofs of love.The word demonstration, even in its most abstract uses, keeps a link with the visual and pictorial; if a proof involves touching with the finger, a demonstration shows. Argumentation has no such metaphorical backgrounds; it originates and deploys within language.
In rhetoric, besides the meaning of “proof”, the word demonstration is used with two totally different meanings.
— A demonstration is a vivid representation of an event or a state of affairs as a picture, for an audience or a reader, put in the position of witness of the represented event. This figure is also called evidence or hypotyposis (Lausberg , § 810).
—The demonstrative genre is another name for the epideictic or panegyric or laudatory genre, next to the deliberative and judicial genres (Lausberg , § 239).
Demonstration is often opposed to argumentation as belonging to two different cultures without contact and communication, the world of science vs. the world of human affairs, the world of truth vs. that of opinion. This popular opposition is often considered a definitional characteristic of argumentation. Nonetheless, its substance and actual scope, the precise relations between argumentation and demonstration, should be considered as an essential issue for the development of argumentation studies.
1. The hypothetico-deductive demonstration, ideal of proof?
In logic, a demonstration is a discourse proceeding from axioms to theorem, according to specified deduction rules. The construction of a demonstrative sequence is guided by intentionality, since it aims at a stopping point, a remarkable, detachable result, the theorem.
A proof has been formalized if it can be presented as a mathematical demonstration. Formal proof is seen as characteristic of science as pure calculus, and is sometimes considered as the ideal of proof. This vision is contrasted with science as a description of reality (geography, zoology), or as a combination of calculation, observation and experimentation (physics, chemistry).
In the sciences, a demonstration is a discourse, bearing on true propositions: (true by hypothesis; or as a result of observations or experiments carried out according to a validated protocol; or as results obtained from previous demonstrations), and leading to a new, stable, true, proposition. Such a proposition marks a step forward in the field, and is likely to guide further developments in research.
Scientific practice presupposes many non-formal linguistic, cognitive or material operations, other than demonstration. Such operations might include grasping a situation, formulating the problem, conceiving a hypothesis, defining an experience, realizing an experimental setup, manipulating the objects and instruments, selecting, observing and describing the relevant data, making quantitative measurements and the relevant calculation, checking the results, imagining new experiences, drawing conclusions, editing the results for oral communication and publication, answering the colleagues’ objections, revising the claims, etc. We might add to this all the professional argumentative situations in which researchers must apply for new funding, write or evaluate a research project or to employ a new colleague. These argumentative operations require the coordinated management of technical, mathematical and natural languages, including a variety of semiotic media, figures, tables, schemes and diagrams. Argumentation in natural language plays a key role in all these mixed activities.
2. Two distinct fields: What we know, what we do
Argumentation deals with what is to be believed. Argumentation concerns the question of proof and demonstration, but goes beyond this. The exploratory function of argumentation extends beyond its epistemic role, to practical discussion (internal or external) of what, in view of one’s current interests, would be the most sensible next move. So for example, one might ask, “should I apply for this or that position, buy this or that car, ignore or accept offers of negotiation”. And human affairs extend still further, beyond the realm of practical decisions; generally speaking, argumentative situations emerge as soon as any kind of choice is possible. Argumentative situations can thus arise in regard to antagonistic feelings, what is really worthy of admiration or love, S. Emotions. In these areas the language of proof and demonstration does not makes sense, whereas the language of argument does.
One might think that in the case of certain issues concerning true beliefs and accurate scientific predictions, doubt is provisional, and that any doubt will be removed in view of scientific progress. When considering situations involving human agents, however, doubt is an essential component. In such situations, it is often impossible to completely dispel doubt, and one can legitimately ask what would have happened if …
We turn to argumentation when the data is incomplete or of poor quality and the assumptions and laws imperfectly defined; the deductions are, therefore, subject to a continuous principle of revision. As the last resort, we are referred to the question of time: an argued claim is a bet. Linked with urgency and occasion, argumentation is a time-limited process, different from the unlimited time afforded to the philosophical or scientific demonstration. There are essential differences in the modus operandi of argumentation and demonstration, their fields of application and the kind of problem they can apply to.
When operating in the field of knowledge, argumentation has an exploratory and creative function which goes beyond its demonstrative and critical function, S. Abduction. Argumentation produces hypotheses, opens up discussions and triggers the critical process of verification and revision.
Demonstration is by definition related to a domain; argumentation may combine heterogeneous evidence. Argumentation is the art of hierarchizing not only values,, but also proofs and demonstrations. If one wants to explore the possibilities and economic interests of a major environmental management works, constructing a channel between the Green and the Yellow Oceans, for example, then the technical proofs, solutions and objections offered by geologists, economists and ecologists must be articulated and confronted with those of neighbors, citizens, investors and politicians. The negotiation will take place in view of calculations and technical proofs each as unique as the others, and argumentation in natural language will have to fully exert its synthetizing function.
3. Argumentation-proof and argumentation-demonstration:
Several theories of otherwise very different orientations come together in order to oppose argumentation to demonstration. Historically, the notions of demonstration and argumentation inherited through Western tradition were developed in ancient Greece. Demonstration in science and mathematics (Archimedes, Euclid) was built without relation to argumentation in social affairs. According to Lloyd, Aristotle elucidated “the explicit concept of rigorous proof” (, p. 77) in a scientific context where four types of argument were currently used:
The first of these is arguments in the legal and political domains, the second those in early Greek cosmology and medicine, the third mathematics in pre-Aristotelian period, and the fourth deductive arguments in philosophy. The first two relate primarily, to informal, the second pair to rigorous proof. (Ibid.)
The unity of the disciplines of proof can be shown by the examination of their vocabulary:
The same vocabulary, not only of evidence, examination, judgment, but also proof, appears also outside the specifically legal or political domain, notably in a variety of contexts in early Greek speculative thought. Both cosmology and medicine, and some extended passages from the Hippocratic Corpus merit particular attention. (Id., p. 78)
In Aristotle’s work, convincing rhetorical argumentation is characterized by its differences with valid logical demonstration (and probable dialectical deduction). Since then, argumentation has been conventionally referred to logical demonstration, to argumentation-demonstration, and not to argumentation-proof such as exemplified in the practices of scientists, practitioners, historians, police investigators, etc. Argumentation is most strongly linked to these practices, in virtue of its substantial nature and its relationship to practical action. For example, the essential concept of argumentative question does not derive from a logical concept, but from the medical descriptive concept of stasis, that is a state in which physiological fluids are blocked, and, metaphorically collaborative speech and actions are suspended.
This non-operational opposition between demonstration and argumentation, which now functions as a commonplace, has been considerably restated and strengthened by the New Rhetoric, as well as by the non-referentialist positions of the theory of Argumentation within Language.
4. Demonstration against argumentation?
Demonstration and logical proof are classically opposed to argumentation on the basis of their premises and modes of inference. Things go much deeper than that, however. Natural language and discourse are inherently subjective, that is self- and we-related, focused on the “here” and “now”, S. Subjectivity. Words allow synonymy, homonymy and polysemy; their meaning is context-sensitive. Syntactic constructions must be interpreted. Discourse is figurative. Meaning and reference are negotiated and managed by relevance principles. These processes are stigmatized as being inherently “vague and elastic”; but the polymorphism of language should simultaneously be praised for its adaptability to new situations and its rule-changing capacity.
At a general level, it should be noted, firstly, that there is no reason to favor elementary logical demonstration over other scientific activities, of which it is, unquestionably a distinguished member. Secondly, oppositions make sense only if the opposed domains are comparable. Experimentation, mathematics, computerization, have taken the techno-sciences worlds apart, and it does not make much sense to compare a paper in a scientific journal publishing cutting edge research with a column in a newspaper.
4.1 The New Rhetoric
Perelman & Olbrechts-Tyteca’s Treatise has constructed a powerful, autonomous concept of argument by rejecting emotions out of the field of argument on the one hand, and by setting argumentation against demonstration on the other. The purpose of the Treatise is to circumscribe an autonomous discursive domain, where speech develops cut off from demonstration and emotion. In the very words of the Treatise, the couple argumentation / demonstration functions as an “antithetical pair” (Perelman & Olbrechts-Tyteca , p. 422.), whose terms are the subject of a genuine “breaking of connecting links” or “dissociation” (id. p. 411 sq.). Systematically, the Treatise opposes argumentation to demonstration, as can be checked on every occurrence of the word demonstration mentioned in the index. This strategy, constitutes one of the building blocks of the Treatise.
The fundamental question of the difference of languages between argumentation and demonstration, is not addressed. In the Treatise, the form of demonstration opposed to argumentation is taken in a particular discipline, formal logic, which would be prototypical of demonstration as the inaccessible ideal of argumentation. This hardened and simplified image of demonstration promotes the antagonism argumentation / demonstration. This results in the exclusion of anything concerning sciences from the Treatise:
We seek here to construct such a theory [of argumentation] by analyzing the methods of proof used in the human sciences, law and philosophy. We shall examine arguments put forwards by advertisers in their newspapers, politicians in speeches, lawyers in pleadings, judges in decisions, and philosophers in treatises (, p. 10)
No reference is made to any kind of scientific activity. Argumentation addresses human affairs only, and demonstration concerns mathematics and science. exclusively. The gap between “the two cultures” (Snow, 1961) is thus effective at the very foundation of argumentation as a discipline.
4.2 The Argumentation within Language theory
This theory considers that argumentative orientation is an essential characteristic of the semantic level of language, and concludes to the impossibility of developing argumentation as good reasons in discourse and interaction. Consider the following passage:
It has often been remarked that discourses concerning everyday life cannot achieve “demonstrations” in the logical sense of the word. Aristotle already noted that, by opposing to the necessary demonstration of the syllogism the incomplete and only probable argumentation of the enthymeme. Perelman, Grize, Eggs insisted on this idea. At first I thought I was merely following this tradition, my only originality being to refer to the nature of language the necessity of substituting argumentation for demonstration. I thought that the words of language were the cause or the sign of the fundamentally rhetorical, or, as we said, the “argumentative”, character of discourse. But I am now led to say much more. Not only do words not allow demonstration, but likewise they do not allow that degraded form of demonstration that would be argumentation. Argumentation is only a dream of discourse, and our theory should rather be called « the theory of non-argumentation” (Ducrot 1993, p. 234).
As Ducrot’s structuralist framework reduces the order of speech to that of language (Saussurian langue), it is quite coherent to deny any principle of intelligibility to argumentation in discourse.
5. Arguing the non-demonstrative character of argumentation
The refutation of the possibly demonstrative nature of ordinary discourse is threatened by skeptical paradoxes and exposed to self-refutation. It is difficult to argue about the argumentative or non-argumentative character of natural language discourse, whilst using natural language discourse.
Interaction studies have taught us a great deal about what everyday life discourses can achieve. Brief, local reasoning is accomplished in sequences in which language combines with action to achieve operational conclusions. We define, categorize, articulate causes and effects, and make analogies, which are all more or less insufficient, but which are all susceptible to criticism and rectification. Sometimes, these result in the satisfaction of all parties concerned.
By means of some conventions and adjustments, more sophisticated reasoning episodes can be developed in ordinary language. If the syllogism constitutes an example of a necessary demonstration, since the syllogism consists of a sequence of utterances in natural language, words allow at least syllogistic demonstration. All the same, figures and calculus are not entirely foreign to natural language, which also allows for some correct geometrical conclusions, so that the tenon exactly fits the mortise. Not only a logic, but also an everyday geometry, arithmetic, physics… underpin linguistic practices, and no metaphysical lack stops them from concluding properly, as shown by the following little calculation:
The Abbé du Chaila is one of the essential architects of the repression of the Protestants of the Cevennes, in Southern France. His murder is the origin of the Camisards’ war, in the 18th century.
The date of birth of the future abbot of Chaila remains a mystery, due to the disappearance of parish registers. It should be at the beginning of the year 1648. Indeed, François’s parents, Balthazar de Langlade and Francoise d’Apchier, were married on the 9th of April 1643 and had successively eight boys and two girls in ten years, at a rate of a child a year. François being the fifth child of the family was thus born in 1648, the four previous brothers being born in 1644, 1645, 1646 and 1647.
Robert Poujol, [The Abbé du Chaila (1648-1702)], 2001.
Any assertion about the demonstrative character of argumentation in general is hard to assess, regardless of the prestige of the authority supporting it. Arguments from natural signs, case-by-case arguments cannot be treated as an appeal to authority or arguments by analogy. Ordinary argumentative discourse might combine entirely heterogeneous types of arguments and fields of evidence, including rather technical and scientific episodes. One might argue correctly in natural language; sometimes, some truth emerges from judicial and historical debates when properly framed and managed; and argumentation plays a role in science acquisition.
6. Argumentation in science education
Other connections have to be found between argumentation and scientific activities. The great rule followed by Quine to construct his formal logic shows the way:
This course is prompted by an inclination to work directly with ordinary language until there is a clear gain in departing from it. (1980, p. x).
Mutatis mutandis, we will say that the teaching and learning of scientific method are necessarily anchored in natural language and everyday argumentation, and that they depart from them only when they find a decisive gain in doing so. This leads to a focus on argumentation as an instrument for knowledge acquisition.
Demonstrative-scientific proof can be considered, on the one hand, as a finished product, impeccably exposed in published papers and textbooks; and, on the other hand, as a process, which can leave room for dialogue, arguments and rectification and progression. Argumentation being on the side of the process, its claims are in the making. It might therefore be an interesting option to orient the arguer’s capacity towards the exploration of scientific domains, monitored by competent advisers.
Finally, we must consider the question as to whether there is a break or a continuity between argumentation and demonstration. This is certainly a very important philosophical and epistemological issue, yet it is quite different from the empirical issue as to how best to construct scientific capacities. The teacher might consider that the gap is a fact (Duval 1992-1993, 1995) and choose to break with ordinary language and practices, as did teachers of “modern mathematics” in the seventies in France. They might otherwise try to use everyday capacities to build knowledge. Gap and continuity are pedagogical choices and constructs.
Science acquisition, scientific “enculturation” and education are key situations for the development of argumentation studies (Erduran & Jiménez-Aleixandre 2007). The humanities remain largely trapped in a conception of argumentation based on logocentric discourses, in which all and everything can be claimed. From this conception, a comfortable antagonism has been developed, with “logical demonstration” serving as a convenient antagonist. The repositioning of argumentation as a complex, combinatorial activity which seeks to manage heterogeneous evidence in possibly complex material contexts enables us to distance ourselves from this traditional logocentric vision. Discussions between two mechanics disagreeing on how to repair a failing engine, or two students disagreeing on the shape of the beams coming out of the lens are as prototypical of what is an argumentative situation as an ideological debate where the language is perpetually referred to itself.
The research program on argumentation in science education emerged in the late 1990s and early 2000s. It now represents a key field of development for argumentation in the near future (Baker 1996, De Vries, Lund, Baker 2002; Buty & Plantin 2009; Erduran & Jiménez-Aleixandre 2008).
 Poujol R. L’ Abbé du Chaila (1648-1702). Montpellier: Les Presses du Languedoc, 2001. P. 31.