The study of schematizations is the defining objective of the Natural Logic developed by Jean-Blaise Grize, a student and subsequently a collaborator of Jean Piaget at the Research Center on Genetic Epistemology in Geneva. This logic is called “natural” as opposed to formal logic: on the one hand, it is a “logic of objects” (1996: 82) and a “logic of subjects” (Grize 1996: 96); on the other hand, it involves processes of thought that leave “traces” in natural discourse.
According to Grize, discourse is essentially argumentative, meaning that all utterances frame the world or the situation, along their subjectively relevant lines, to build a meaningful “schematization”. “Scheme” has here a totally different meaning from “argument scheme”, which would be called a “reasoned organization”, in Grize’s vocabulary, corresponding to the second-level phenomenon of sentence combination, whereas schematization is a first-level phenomenon, that of sentence production.

According to Grize’s favorite metaphor, to argue, is to “give to see” to the audience a situation as “spotlighted” by the speaker. As every speech throws some subjective lighting on the world, argumentation is inherent to speech. In Perelman’s terms, this operation consists in giving “presence” to an object (Perelman & Olbrechts-Tyteca, [1958], p. 116).

In this perspective, an argumentation is not necessarily a set of statements organized in line with the layout proposed by Toulmin. The influence of an argument and its rationality are not attached to a special kind of speech, or to the use of such and such specific “discursive techniques”, as suggested by Perelman & Olbrechts-Tyteca. Any statement, any coherent succession of statements, be it viewed as descriptive, narrative or argumentative, is indeed argumentative, insofar as it builds a point of view mapped into a meaningful schematization. Natural Logic is defined as the study of such schematizations, the cognitive counterpart of sentence construction.

This concept is adapted to a vision of arguing as story telling, as offering a coherent and detailed presentation of the world. This might be of some comfort to all students who find themselves disheartened by the difficulty of giving a dense account of extended texts or interactions in terms of argument schemes, even where these are supplemented by an extensive repertoire of figures of speech.
If persuading is defined as shifting the partner’s representations, and, accordingly, his or her behavior, then any informative statement, such as “It is 8 a.m.” is argumentative. If the addressee has to take the 7.55 train and is savoring a last coffee, thinking it is a quarter to 8, then, the information will dramatically change his vision of the immediate future. Natural Logic is also a theory of generalized persuasion, as just “focusing on the relevant aspect of reality”.

1. Schematization, a step-by-step process of meaning construction

Argumentation is traditionally defined as a combination of utterances. Natural Logic studies argumentation as a cognitive process evidenced in natural discourse, and manifested at every stage of discourse production, from the first elaboration of an idea to the combination of utterances, which is only the final stage of the argumentative process. Schematization corresponds to a representation embodied in a complex discursive unit,

Influencing the interlocutor is to try to modify his or her representations, by emphasizing some aspects of things, concealing others, proposing new ones, and all this by using appropriate schematization. (Grize 1990, p. 40)

Argumentation does not appear to be a chain of statements in a discourse. It emerges progressively at every stage of the production of the utterance, from the first operation of apprehension of content to the construction of a meaningful and therefore “reasoned” discourse. Any statement, any coherent succession of statements, whether or not it is traditionaly considered to be argumentative, narrative, or descriptive … , is indeed argumentative to the extent that it constructs a unique point of view, that is a “schematization”. This conception leads to reconsider all information as argumentation, tending to liken discursive meaning to argumentation, S. Argumentation (I); Argumentation (II).

Grize defines Natural Logic as “the study of logical-discursive operations that make it possible to construct and reconstruct a schematization” (1990, p. 65); “Its task is to account for the operations of thought allowing a speaker to construct objects and to predicate upon them at will” (1982, p. 222).
The concept of schematization defined as a “[discursive representation], oriented towards an addressee, of what the author conceives or imagines of a certain reality” (1996, p. 50), “of what it is all about” (1990, p. 29). A schematization is a discourse that focuses the listener’s attention upon a “micro-universe” given as “an accurate reflection of reality” (id., p. 36), which constructs or “structures” (id., p. 35) a synthetic, coherent, stable meaning. The purpose of schematization is “to show something to someone” (Grize 1996, p. 50; my emphasis); “to schematize […] is a semiotic act: it is to give to see” (id., p. 37; my emphasis). The object of Natural Logic is the study of the operations constructing such images.
The functioning of schematization is particularly clear in classical argumentative situations, when a discourse directly confronts a counter-discourse; the same reality is given two antagonistic descriptions:

S1 — These replacement workers, you will pay them with the strikers’ money!
S2 — Not the strikers’ money, the taxpayers’ money.

2. Operations constructing a schematization

Natural Logic postulates the existence of “primitive notions”, of a pre-linguistic nature (Grize 1996, p. 82), linked with the culture and the activities of the speakers. These pre-notions are the place of “cultural pre-constructions”, i.e., received ideas and current, accepted ways of doing things. The language “semantizes” these primitive notions turning them into “objects of thought” associated with words (Grize 1996, 83).
Schematization operations are anchored in these “primitive notions” (id., p. 67) and are constructed by a series of operations; “primitive notions” are actually noted by words between brackets. The following sequence is formed of the primitive image and fuzzy notions /fuzzy/ and /image/:

It’s unfortunate that the edge of the image is blurry, and it needs to be corrected. (Ibid.)

This construction follows these steps:

(a) The process of discourse construction begins with the selection of relevant primitive notions, to produce the objects of discourse; here “image, edge of the image” as well as the predicative pair “to be blurred, not to be blurred”. The objects thus schematized will evolve with the development of the discourse, S. Object of discourse.
(b) Then, the operation of characterization produces “contents of judgments” that is predications, and these are accompanied by modalizations, carried out on the objects of discourse. Here, the content of judgment is, “that the edge of the image be quite blurry”.
(c) A subject then asserts (positively or negatively) the preddication, and produces a statement, “it is unfortunate that the edge of the image is quite blurry”.
(d) Operations of configuration then connect several utterances and so build a discursive chain, “a reasoned organization”. The preceding statement for example, is connected to another statement, “this must be corrected”, which is produced according to the same mechanism:
It’s unfortunate that the edge of the image is blurry, and it needs to be corrected.

These different linguistic-cognitive operations can be likened to the vision of language and mind developed by the philosophy of traditional logic, S. Logic.

(a) Apprehension of content by the mind;
(b) Predication, constituting unasserted propositions;
(c) Judgment, expressed in an assertion, which can be true or false;
(d) Concatenation of judgments, i.e. discourse construction.

The aim of this approach is to emphasize that all operations relevant to the genesis of the utterance have an argumentative import. Argumentation is as much a sentence construction process as a sentence connection process.

3. Shoring

The concept of shoring developed in Natural Logic is defined as,

a discursive function consisting, for a given segment of speech (whose dimension can vary from a simple statement to a group of statements having a certain functional homogeneity), to accredit, to make more likely, to reinforce, etc. the content asserted in another segment of the same discourse. (Apothéloz & Miéville 1989, p. 70)

This concept corresponds to the classical problematic of argumentation as a composition of statements, a statement-argument supporting a statement-conclusion. To refer to the same phenomenon, Natural Logic also uses the expression “reasoned organizations”:

Many statements are made merely to support, to shore up the information given. This is part of the general process of argumentation, and allows us to envisage more or less extensive blocks of discursive sequences as reasoned organizations. (Grize 1990, p. 120)

The study of reasoned organizations is an instrument for the study of representations, defined as “a network of articulated contents” (id. p. 119-120). It should be emphasized that, for Natural Logic, the reasoning process is not limited to the combination of utterances but includes the whole dynamic process of structuring the utterance, whether it will function as argument or conclusion in a reasoned organization.

4. Schematization and communication

Schematizations refer to a particular communication situation. They are the product of “the activity of speech [which] is used to construct objects of thought” (1990, p. 22); these objects being part of a dialogue where they are used “as shared references for interlocutors” (ibid.). The communication situation envisioned is intended to be “essentially dialogical in nature” (1990, p. 21), but it is actually analogous to that of rhetorical address. It never considers the possible interactions between the respective schematizations of the participants.

By [dialogal] I don’t mean the interweaving of two discourses, but the production of a speech between two parties, a speaker [orator] … addressing a listener. Admittedly, in most texts, the listener remains virtual. This, however, does not alter the basic problem: the speaker constructs the speech according to his or her representations of the listener, simply, if the listener is present, he or she can actually say, “I do not agree” or, “I do not understand”. But if the listener is absent, the speaker must indeed anticipate his or her refusals and misunderstandings. (1982, p. 30)

Persuasion is given up, “the speaker can only propose a schematization to his or her audience, without actually ‘transmitting’ it” (ibid.).

5. “Logic of Contents” (Grize) and “Substantial Logic” (Toulmin)

Grize defines his Natural Logic in relation to formal logic:

Alongside a logic of form, a formal logic, it is possible to envision a “logic of contents”, that is, a logic taking into account the processes of thought, the development and interconnection of these contents. Formal logic based on propositions accounts for the relations between concepts, while Natural Logic proposes to highlight the construction and interconnection of the notions. (Grize 1996, p. 80)

This “logic of contents” might remind us of Toulmin’s “substantial logic”, S. Layout. But, unlike Toulmin, who characterizes argumentation as an arrangement of statements without discussing their internal structure, Grize considers that argumentation begins with the basic operation producing the statement itself.