Human Arenas

, Volume 1, Issue 1, pp 97–111 | Cite as

From the Logic of the Child to a Natural Logic: Perspectives as Knowledge

  • Alaric Kohler


The notion of perspective is often used in Human Sciences, and some authors such as Bruner (1996) refers explicitly to a perspectivist epistemology. Yet, the general idea of such epistemology is to consider that several perspectives on the same object or phenomena can produce more relevant knowledge than one only. Yet, such epistemology is rarely theorized, which raises interesting questions: What is a perspective? Can we describe a particular perspective on something? Answering such question requires more than a philosophical standpoint or credo, none less than an empirical epistemology. Piaget and his team approached such questions empirically in Genetic Epistemology, starting from the study of actual thinking. However, formal logic of his time was not fitted for providing description of the construction of meaning. Grize later theorized and extended unconventional uses of logic within a logic of action representing the thinking of actors within irreversible time without abstracting it from particular situations and contents. Grize’s logic is about singularity—a concrete operational logic—and yet about semiotics, about meaning making. In this sense, Natural Logic may provide researchers studying knowledge with an instrument for including perspectives and points of view. As such, it can contribute to a theory of knowledge taking into account the diversity of points of view and the process of meaning making, based on a perspectivist epistemology.


Perspectivism Genetic epistemology Natural logic Socio-cognitive approach Coordination of points of view 


A perspectivist epistemology assumes that several perspectives on the same object or phenomena can produce more relevant knowledge than one only (Kohler, Lordelo, and Carriere 2017). Yet, perspectives may enter in debate one with another, provide complementary knowledge, or seem immeasurable one to another. Coordinating perspectives for a better understanding of the object of study raises a question: What is a perspective? Can we describe a particular perspective on something?

The aim of this paper is to contribute to these challenging questions with a proposal, which is to consider a particular perspective as a form of knowledge. This proposal requires an empirical approach of epistemology, such as initiated by Piaget, in which perspectives can be described, compared, and discussed. In order to contribute to an empirical perspectivist epistemology, I will provide theoretical elements based on Genetic Epistemology and an example of description of two different perspectives in physics education. The example provides an empirical illustration of a situation in which knowledge—the knowledge-to-be-learned in a classroom—precisely consists in adopting a specific perspective on the school task.

Hence, this paper tackles the work to be done for moving perspectivism from an epistemological stance (Bruner 1996) to an empirical investigation about knowledge for which perspectivism is no longer a philosophical credo making a specific type of scientific research possible, but an empirical science for a psychology of points of view. The next challenge is notably to establish a methodology for investigating perspectives, and to describe the various possibilities of coordinations of perspectives.

The Legacy of Genetic Epistemology

Studying Actual Thinking with Logic

The practice of empirical epistemology is not new. Genetic Epistemology aimed at understanding the development of knowledge through research on the child’s development. To do so, Inhelder and Piaget (1955) adapted the formal logic available at the time to represent concrete and formal operations. The theory relates knowledge (as operations and representations) to its origins in the actions of the subject (Piaget 1967; Piaget 1971). For instance, it shows how mudane actions such as walking back and forth in a garden at a young age (Piaget 1937/1967) opens the possibility, years later, of performing operations in complex systems of formal logic.

The logical part of Piaget’s work has been abundantly criticized (Smith 1992; Atkinson 1983/2006), both by logicians considering his logic unconventional, and by psychologists for adopting logic as the ultimate level of thinking. Many of the critiques, however, are based on misunderstanding of Piaget’s theory, as Papert (1963) has explained. Most misunderstandings are about the aim of Genetic Epistemology, often understood as a study of specific children in a Developmental Psychology, or as a reduction of learning processes to Logic. Yet, the aim of Genetic Epistemology is quite simply to find some sort of answer to the question “ how is human knowledge possible?” To clarify this point, Piaget distinguishes the epistemic subject he decides to focus on, with the psychological subject. Genetic Epistemology focuses on the epistemic subject, i.e., a human capable of knowledge, since its object is the possibility of knowledge, and not the actual knowledge of particular people. This distinction clarifies some methodological issues, such as the number of participants to clinical interviews. It also specifies the importance of the chronology in the apparition of cognitive abilities as having an ordinal relevance, rather than an age-related relevance as it is for instance presented by Johnson-Laird (2006). Clarifying these misunderstandings dismisses many objections addressing Genetic Epistemology as a theory of the development of the person, or as a model for learning. Genetic Epsitemology is rather an empirical theory of the development of human knowledge (Piaget 1968). Yet, it is relevant to Psychology for its interest in the thinking of the child as it operates, rather than in reference to a pre-build model of rationality. Provocatively, I would argue that the Psychology based on Piaget’s empirical epistemology, i.e., the science of the psychological subject based on his science of the epistemic subject, is still to be made.

Describing the method used in Genetic Epistemology to study the formation of concepts, Inhelder (1962) outlines two precautions: preconceived notions or points of view should not be imposed on the child when asking questions and the child’s answers should not be taken for directly intelligible. These two foundaments of the critical interview method of Inhelder and Piaget led them to “bend” logic to represent the children’s actual thinking processes, rather than to assimilate children’s response to formal rules of logic (Papert 1963). While it is specifically what contributed to the discredit of Genetic Epistemology in Logic and Philosophy, it laid the foundation for a situated approach of rationality, which was left aside by the information processing metaphor in cognitive science (Weil-Barais 1993), and is recently the focus of a growing interest (see for instance: Eemeren et al. 2009).

The Limits of Formal Logic for Representing Human Rationality

Developing an empirical research on perspective poses methodological challenges. The logical languages and tools used in Genetic Epistemology failed for the purpose of representing the logic of human thinking, according to Piaget’s collaborator, the logician Jean-Blaise Grize. Doubts about formal logic already appear in Piaget’s books, yet discretely. For instance: “Finally, it is not impossible that the class is not more a ultimate psychological reality than the set theory is the last word about mathematics foundations” (Piaget 1968, p. 196, translated by the author1). Later, Piaget recognizes the limits of formal logic more explicitly:

We have been attempting to point out areas in which psychological experimentation is indispensable to shed light on certain epistemological problems, but even on its own grounds there are a number of reasons why formalization can never be sufficient by itself. I should like to discuss three of these reasons.

The first reason is that there are many different logics, and not just a single logic. This means that no single logic is strong enough to support the total construction of human knowledge. (...)

The second reason is found in Gödel’s theorem. It is the fact that there are limits to formalization. Any consistent system sufficiently rich to contain elementary arithmetic cannot prove its own consistency. (...)

The third reason why formalization is not enough is that epistemology sets out to explain knowledge as it actually is within the areas of science, and this knowledge is, in fact not purely formal: there are other aspects to it. (Piaget 1970)

Despite his recognition of these difficulties, Piaget has never adopted a non-formal logic, and Grize project of a Natural Logic (Beth et al. 1962) is developed after his work for the Center of Genetic Epistemology. Piaget grounded his Logic of signification on the notion of implication, an alternative to the physical causality which allowed him to keep the same logical framework (Piaget and Garcia 1987). Grize (1982) takes distance with this option and develops a non-formal logic, better suited for representing thinking and, in particular, better suited for describing human rationality operating with and on meaning, in particular the rationality found in discourse and various languages, i.e., semiotics.
Grize (1982) came to the conclusion that formal logic is unadapted to represent the logic of thinking, notably because it is a formal system and, as such, a closed system. Formal logic is per definition only valid within a closed system, closed by a statement such as: “No element belong to the defined set, except by the presented definitions” (Grize 1982). In the General Theory of Systems (Bertalanffy 1973), only open systems are considered adequate for giving account of living organisms. Grize explains a few consequences of the closure of a system:
  • The system is identical for any person using it, i.e., it is defined independently from any users, and therefore the closed system does not include any emic perspective.

  • The system remains ever the same over time: it is atemporal.

  • Anything possible in the system is set from its very beginning: it is universal.

  • Nothing can be added to the system from outside, all knowledge must be deduced from a finished number of elements and definitions (whatever great), and therefore it cannot transform itself: it is monotonic.

  • The system has been isolated from the content considered to build the system, for instance laws of physics are abstracted from the particular experiment that were crucial for its making as soon as it is axiomatized into a closed system: it now applies to any content identically.

Grize provides a brief account of how closed systems and formal models, made of univocal definitions of concepts, proceed from a theory based on less defined notions which are grounded on natural everyday language. The term “natural” comes from an historical analysis, showing that contemporary formal logic needed first to be elaborated from a natural language.2 The development of knowledge for a single learner seems to follow the same path, as it has been stressed in Educational Psychology by studies showing the need for children to acquire a specific language from everyday language for succeeding in math or physics (Halbwachs and Torunczyk 1985, for instance).

The formal system, once closed, cannot produce new knowledge strictly speaking, as it only allows deductions, which are set once for all when the theory is axiomatized. At this point, the choice of axioms among the true statement of the theory is crucial for the closure. If the theory needs to be revised, it becomes a schematization again, for which the meaning can be ambiguous, differentiated, or changed. In Grize’s logical analysis of the making of a theory, this issue raises a crucial question: How does Logic deals with the content of the theory and its relation to the world?

When it comes to study meaning, it is easy to envisage how important the content is. Natural language takes in consideration the content even for setting its own rules (syntactic, semantic, and conversational rules, for instance), contrarily to formal language. Grize provides many examples to show how important the content is for the meaning making processes:

“The donkey eats the straw” does not make any problem, but “The straw eats the donkey” is more difficult to accept. (Grize 1984, p.233)

Using the logic of predicate, the problem raised by Grize is simply overlooked: Each sentence is expressed by a symbol, “p” or “q,” identically, whatever its content. It is another reason raised by Grize to explain why natural thinking cannot be represented with formal logic. More should be said about the limits of formal logic, yet a detailed examination of the debate is not the objective of this paper.

Neo-Piagetian Development: Natural Logic

The few examples presented above are sufficient to raise a few of the major issues the use of formal models is confronted with, when representing human rationality in psychological research. Such models correspond to a very specific rationality, coming last in human history, in education, and development, and which is always built on natural language and its own rationality. Moreover, such formal model of rationality tend to be too good to describe accurately the way we think, as a few researchers have started to point out: Gigerenzer (1997), for instance, presents the idea of heuristics, for representing various rationalities depending on the context. Yet, the description of these heuristics is nevertheless made by the authors with formal logic (Gigerenzer and Todd 1999). Instead, Grize (1982) goes back to the roots of the formal logic we know today, with example such as Arnauld et Nicole publishing “L’art de penser” in 1662 and Boole publishing “An investigation of the laws of thought” in 1854 (p. 26), in order to show that logic was not always formal, and that it is possible to set a Natural Logic to describe human rationality as an open system.

For the logician of Genetic Epistemology, the logic of thinking must be “a logic of action instead of a systematic logic” (Grize 2010, p. 91). In addition, such a logic must keep the link with the particular content of the reasoning or thinking processes under analysis. Indeed, the logic of thought is a logic about particular thinking taking place at a given time and in given situations, not a logic about universal, atemporal thought without any subject. However, Grize (1982) provides a clear account of the consequences of using an open system in the project of developing a logic of thinking. He draws a few requirements a logic of everyday thinking should meet. It should be:
  • genetic, that is it must provide an account of how it appears to the agents in the system (emic perspectives);

  • such as it is unfolding over time (Grize 2005);

  • able to change itself;

  • keeping the content combined to the form;

  • leading to a limited and partial rationality, with incomplete and biased result of thinking, such as observed in the practice of thinking with a natural language.

These properties of open systems invite to reconsider the role of contradiction in such a logic (Grize and Bonniec 1983): Are we in contradiction with ourselves when we are changing our mind over time? Many questions could be addressed that are impossible to deal within closed systems. Still, one may question the idea to develop a logic without formalization: In which way can such a logic be more synthetic, or general, if it includes particular content and context?

Grize’s Natural Logic postulates a set of thought operations in order to build a logic of meaning making. Natural Logic is a Piagetian inheritance, which means it fits in the global theory of knowledge development of Piaget. Hence, the term operation must be understood according to the Piagetian definition, as an interiorized action which are transforming something. Operations are not procedures but transformations of objects or states. The Piagetian term “object,” also used as “an object of thought,” can be understood within a systemic approach as a certain state in the system at a given moment. A more scientifically informed understanding of “material objects” leads to the same idea: An ice cube, for instance, can be understood as a state of matter within a system of relations. This comment addresses the recurrent critique of Piaget’s epistemology being based on a duality subject-object, which is often interpreted in a very simplistic way. Transposed in the world of representations or meaning, operations are transformation of theses representations or meanings, or “objects of thought.”

If it is correct to consider the set of operations as a postulate in Natural Logic theory, these operations should not be considered the result of a merely speculative work, since each operation has been carefully defined and selected from empirical case studies, in a collective work throughout several decades (Grize 1996, 2010).

Hence, I argue that psychologists interested in thinking processes, as naturally occuring, do not need expert formal models but a logic allowing a descriptive representation of thinking processes as they are when using natural everyday language. Grize’s theory provides a set of operations that are closely related to what can be observed in discourse. Grize’s operations are not merely linguistic but represent thinking processes operating with and through language. This is the reason why Natural Logic is chiefly concerned by argumentation, which is a type of discourse that is particularly involved in reasoning with natural language. Other theoretical approaches have been recently proposed, to give a descriptive account of human reasonableness from studying argumentative practices (Eemeren et al. 2009). Moreover, Eemeren et al. (2014) present an overview on the work about rationality in argumentation, and more specifically the contribution of Natural Logic to this field of research. In this article, I am focusing solely on the psychological aspect of Natural Logic, and on its possible use as a method for analyzing meaning making in a way that combines cognitive and discursive processes. Any type of discursive material can be analyzed with Natural Logic, not only argumentation, in order to elicit the reasoning taking place within language. Here, I will present the result of an analysis of oral and written answers to school tasks, in order to propose a description of two different perspectives.

A Proposal: Describing Perspectives

A Socio-cognitive Approach

The development of an empirical research on perspective can rest on socio-cognitive development of Genetic Epistemology (Perret-Clermont 1979; Perret-Clermont, Carugati, and Oates 2004; Psaltis and Zapiti 2014; Zittoun and Iannaccone 2014) showing that investigating human thinking requires to investigate the frame in which such thinking is constructed (Perret-Clermont et al. 2004). More precisely, the investigation of thinking requires a micro-genetic analysis of its making in its specific and particular situation, frame, and historico-cultural context (Tartas, Perret-Clermont, and Baucal 2016). For instance, analysis including conversational pragmatics and logic in the theoretical framework (Trognon et al. 2006) can contribute to a description of thinking processes as it occurs in its natural environment. Interdisciplinary research articulating socio-cognitive approaches with communication, language, and logic are also emerging (Rebuschi et al. 2016).

This paper participates of this current of research, with the specific aim to contribute to the construction of a theoretical framework and methodology allowing for the description of perspectives from. Such description, base on micro-genetic analysis of empirical data collected from specific and situated points of view, may provide a way to address the perspectival aspect of knowledge, and later may allow for explicit discussion on the coordination of various perspectives. Such discussion about the coordination of perspectives reconstructed for the investigation on specific knowledge takes up the challenge that is to integrate the coordination of points of view of particular psychological subjects with the general features of knowledge studied in cognitive science.

In order to avoid confusion about the level of abstraction about which I make statements, I will use the concept of points of view for the outlook taken by a particular person on a particular topic at a particular occasion, which is situated (culturally, socially, historically, etc.), and perspective for what can be abstracted from such points of view in a way that several people can adopt a common perspective. Alternatively, perspective can be abstracted from the same person switch between various perspectives. This paper focuses on an instrument for the description perspectives, since it is another type of work to develop micro-level instruments allowing the reconstruction of particular points of view (see for instance: Tartas, Perret-Clermont, and Baucal 2016).

The Coordination of Point of Views in Genetic Epistemology

Of particular interest for perspectivism, Genetic Epistemology attempted to provide a logic for coordination of points of view, specifically in the objective of providing an account of meaning and interpretation in the theory of knowledge. Mounoud (2000) stresses the importance of the concept of point of views in Genetic Epistemology, and the fact that the relevance of the coordination of points of views has been recognized by exact sciences long ago, while Psychology is still reluctant. Mounoud recalls the experiment of the Three Mountains (see Fig. 1), elaborated by Edith Meyer for Genetic Epistemology, in which a child has to imagine the mountains from various points of view, or recognize the adopted points of view on the mountains from a visual representation.
Fig. 1

Experiment of the Three Mountains (adapted from Mounoud 2000)

This experiment stressed that the coordination of points of view is among the latest cognitive achievement, and Mounoud stresses its importance for adult cognitive activities and for the most complex forms of knowledge. He points out the slow, progressive acquisition of competence in coordinating points of view, and the fact it is not achieved once and for all, but constitutes a recursive problem which reappears at various phases of stages of development of knowledge and in various domains of knowledge. It means that there is not just one coordination of points of view, and even if Genetic Epistemology mostly focused on the development of decentration moving progressively from the indifferenciation of points of view to a more accurate representation of various points of view, the question of the nature of such coordination still requires much work.

Since coordination in Piaget’s theory is referring to some sort of undefined logical relation, the question that remains open could be expressed as: “What is the logic of the coordination of points of view?” Obviously, in the task of the three mountains, the logical relations between points of view are partly topographical relations, and the perspectives on the mountains are related to optics: The way the light is reflected on the objects together with human visual functioning can make sense of it. Yet, for another task, the logic of coordination of points of view is different, and this is of particular interest, since I will try to show in the next sections that it is possible to study the specific logic of a particular task within a given situation with Grize’s Natural Logic. In a debate, for instance, a specific way to coordinate points of view may be to oppose them, while it makes no sense to oppose perspectives as in a debate on the Three Mountains Experiment: opposing the perspective from one side of the table to the perspective from another side hasn’t got the same meaning as in a debate. In other case, it is by developing a third point of view—a new perspective—that two previously conflicting points of view can be reconciliated. Mounoud stresses the crucial role of the coordination of points of view in the development of new knowledge: “The development is before all the transformation of the determinants of our actions, thanks to the construction of new points of view, new representations, new conceptions or theories (new systems of knowledge)” (2000, p.209).

If the work on the coordination of points of view was unachieved at the time, development in Socio-cognitive Psychology and in Natural Logic provides nowadays elements for a further development of Genetic Epistemology as an empirical Socio-Genetic Perspectivist Epistemology.

Illustrations in Educational Research

The Case

Traces of students’ activities used for the following empirical example are taken from recordings in a Swiss college (high-school), made for a doctoral research on situations of misunderstanding in science education (Kohler unpublished). The pedagogical approach aims at fostering argumentation between students in science education, and participates was defined by an international research consortium (Perret-Clermont et al. 2008). For the purpose of this paper, a selection of written paper-and-pencil exercises and audio-video recordings of the students’ conversation are presented, stressing two different perspectives from the students on the same task. The task addressed to students consists first in a paper-and-pencil question reproduced in Fig. 2.
Fig. 2

Paper-and-pencil exercise addressed to students individually

After an individual written answer, students gather in small groups and discuss in order to choose a common answer. Later, students have some material to perform experiments, which consists in a timer, a car spring launcher, and two small metal cars of different mass (see Fig. 3).
Fig. 3

Picture of the material at disposal for students to perform experiments

In a group of three female students, a rather hot conversation progressively emerges. Aurélie, Barbara, and Sylvie are focused on their work. Aurélie did not participate to the individual exercise, she was absent from school that day. Barbara provided the following answer to the paper-and-pencil exercise:

“the heaviest wagon since it does not attract the ground with its heaviness3

Sylvie answered something similar :

“the heaviest wagon since the weight increases the velocity in presence of a supporting force like a floor, a ground (e.g. in a bobsley, if the person who is driving is heavier than another, she has more chances to arrive first at the bottom)4

Barbara and Sylvie agree on the answer: The lighter wagon reaches the arrival line first. Yet, they initially disagree on the reason for it. After taking several measures of the time for each car to move from the launcher to a marked line, they conclude that their initial answer is right. Yet, a debate emerges after a question from Aurélie to the group, addressed a second time more specifically to Sylvie:

“Here can you explain to me

. why ↑ (...)

. why hu

. why the fact it is lighter at the end it is not the same ↑

((to Sylvie))

could you explain to me ↑”

A rather long conversation follows in which Barbara and Sylvie try to answer to Aurélie, who repeatedly expresses her lack of understanding. It ends with marks of an open conflict, notably Sylvie raising her voice up and the other two students giving up, telling her to write what she wants to write. At the end of the lesson, the teacher offers students the opportunity to evaluate the teaching sequence in an open discussion with the whole class. Sylvie comes back on her experience, telling the teacher:

“I would have liked maybe

. more hu

. understand more the fact

. why the . the marble one gives its velocity and mass to the second marble

. understand why

. because we have only done two

. well its velocity

. because for now we have only done the experiment well

. we have only described and all”5

When inquiring what the issue is about, the analysis showed that two different ways to address the school task entered in conflict in the conversation of this group. Yet, both are “correct” in respect to the Physics to-be-taught. I propose a description of these different ways as two perspectives on the task. The methodology of analysis used for reconstructing the perspectives, which consist in a case-study approach with a specific use of Natural Logic, is explained in details elsewhere (Kohler 2015; submitted).

Illustration: Two Perspectives on the Same Task

When referring to perspective, academic literature often remains implicit about what is the description of a perspective. Often in papers, authors are suddenly stating “this perspective” without defining it precisely, or even simply calls for new perspectives, without any more description. How to describe a perspective? For the purpose of this paper, I draw from photography various elements that can be informed for a description of perspectives (see Fig. 4). It is however only a first metaphorical model, which requires further discussion and development.
Fig. 4

A metaphorical model of a perspective, inspired from photography

The standpoint represents the place, position, or even posture from which the perspective is cast. It can be as concrete as a topographical location from which to look at something, as in the Three Mountains Experiment. It can also be used in a more abstract sense, referring to a social role, a positioning (Hermans and Hermans-Konopka 2010) or, at a more micro-level, a posture in discursive practices (Salgado et al. 2013).

In addition to the standpoint, the direction and sense of the perspective describe the type of involvement with the object. At a micro-level, the direction of attention may inform us about a perspective. The direction has something to do with the intentionality, and the finality in the involvement with the object. For instance, an economical perspective can be described as directed on profitability, cost-effectiveness, and return on investment. In school practices, the direction is related to questions such as “what is there to learn?” and “what do we learn it for?” The sense is not necessarily one-sided, yet when it is, it could be related to the “direction of fit” in speech-act theory, as to either world-to-word or word-to-world. Widened from a discursive feature to an epistemic involvement, the sense could be either self-to-world or world-to-self in reference to the dual process of adaptation in the Piagetian theory of knowledge, i.e., accommodation and assimilation. In school practices, the flip between teaching and learning has to do with the sense of a perspective, when teacher and learner share its direction. What is teaching to one is learning to the other, opposite senses of a shared perspective. The teacher draws from the theory to speak of the world, while the learner draws from the world to understand the theory being taught.

A third characteristics of a perspective is its scope (or focus), that is the wideness of the outlook on the object, the size, and corresponding precision embraced by the perspective. This is probably the most common feature of a perspective, and is often explicited, for instance as a level of analysis.

Inspired from Grize’s concept of éclairage, a fourth element in the model refers to the quality of the light that is cast with the perspective, something that provides a particular coloration to it. In a daily conversation, the perspective may be related to emotional coloration, in the meaning that the same story can be told as a funny story or maybe as a scary one, depending only on the way it is told. In academic perspectives, the coloration is often as neutral as possible, yet this idea of “neutrality” has been criticized as fundamentally problematic. Metaphorically, the same issue can be discussed with light bulbs: The invention of new technologies for producing light bulb led consumers and manufacturers to take interest in the color of the produced light, often qualified as rather warm or cold, depending on the lengthwave. In school practices, the coloration of a perspective can describe various affective involvement with learning: taking the task for a challenge or for work makes the knowledge learned quite a different one.

Barbara’s and Sylvie’s perspectives can be now described through these four characteristics (see Table 1). Of course, each element is interdependent of the others—a change in direction changes the scope and so on—and the description of the perspective proposed here is to be considered as a whole.
Table 1

A brief description of two perspectives on the same task

Perspective (model)

Descriptors from Natural Logic

Barbara’s perspective

Sylvie’s perspective


-image of the interlocutors

-enunciative commitment

-previous knowledge (cultural preconstruct)

-speaks as a student in Physics

-refers to previous exercises

-speaks as a Physicist

-refers to Newton’s concepts


-finality of the schematization

-direction of attention with operation lambda λ

-the finality is to provide a correct answer to the teacher

-performing a school task the simplest and quickest way

-the finality is to explain the observation with the theory taught (Newton’s physics)

-solving a problem in Physics


-use of signs as referring to object of discourse or referent in the world

-adjusting schematization to the type of school task

-adjusting schematization to the theoretical knowledge and observation


-content and borders of the schematization

-word-class, etc.

-the trajectory of the trolley after leaving the spring, namely horizontal versus vertical trajectories

-indifferenciated {mass, weight}

-relations between concepts (mass, weight, force, acceleration, and velocity)

-focus on the difference between {mass} and {weight}


-configuration, structure (operation tau τ) of the schematization

-application of a rule: ignoring the {mass, weight} or not

-calculating the velocity from the acceleration depending on the weight according to the mass and the situation

The descriptors from Natural Logic are only provided as examples here, since there is no systematic correspondence between a type of operation and the elements used for the description of a perspective. It simply provides the reader references to where clues have been found in the analysis for describing the perspectives adopted by the two students in their discursive activity.

It supports the hypothesis that Aurélie struggles to understand the explanation provided alternatively by her two peers in the group, because there are incompatible perspectives on the task. Either the task is succeeded through a student’s strategy consisting in identifying the type of problem and using previously learned procedures to solve it (Barbara’s perspective), either through conceptual reasoning involving a modelization of the problem with the symbolic tools of Physics (Sylvie’s perspective).

Now that we have described these two perspectives, it is quite easy to comment on which one is intended by the teacher and, more generally, the school system: Sylvie’s perspective. Yet, it is also more demanding in terms of conceptual learning and cognitive activity for solving the problem. Moreover, the actual pedagogical setting does not necessarily encourage such perspective, despite its pedagogical orientation towards argumentative activities, notably since there are no feed-back on perspectives as such. Only the result matters, the process leading to it remains mostly invisible to the teacher, in this case.


Perspectivism needs empirical descriptions of specific perspectives, for opening up the possibility of explicit discussion on perspectives. These must be described both 1) for recognizing that there is knowledge in adopting a specific perspective and not only in stating something about something, and 2) for addressing the question of the coordination of various perspectives on a common object of study. The empirical illustration taken from science education shows that a main challenge in learning Newtonian physics is precisely to understand, and adopt, Newton’s mathematical perspective, such as it has been described in History of science by Koyré (1968). It is also an example of a failing coordination of perspectives, which is far from being uncommon among scientists developing new knowledge.

Hence, the interest for an empirical epistemology on the coordination of perspectives is both for education and theory of knowledge that includes perspectives as knowledge, and for science, as an epistemology making perspectivism a viable framework for confronting, discussing and coordinating perspectives in science or other domains of human activity. I have tried to show that the continuation and development of Genetic Epistemology based on a socio-cognitive approach and Grize’s Natural Logic is a viable modus operandi. Yet, there is much more research to be done before perspectivism can lead to a psychology of points of view, making possible the study of particular, singular and situated subjective points of view. This is nevertheless the focal point of the development of perspectivism: Making possible new theoretical development for describing, analyzing and discussing the coordination of points of view in the complexity of their singularity and situated use.


  1. 1.

    Original in French: “Enfin, il n’est. pas exclu que la classe ne soit pas plus la réalité psychologique dernière que la théorie des ensembles n’est. le dernier mot du fondement des mathématiques”.

  2. 2.

    In Grize’s terms “une langue d’usage.”

  3. 3.

    Translated from French “le chariot le plus lourd car il n’attire pas le sol avec sa lourdeur.”

  4. 4.

    Translated from French “le chariot le plus lourd car le poid augmente la vitesse en présence d’une force de soutien comme un planché, un sol (ex.: dans un bobsley, si la pers. qui la conduit est. plus lourd qu’une autre, elle a plus de chance d’arriver en bas en premier)”

  5. 5.

    The syntagmatic stacking has been represented with word wrap in order to emphasize the structure of the oral discourse, and according to the short pause in the course of the conversation, indicated with a dot.


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.HEP-BEJUNEBienneSwitzerland
  2. 2.University of NeuchâtelNeuchâtelSwitzerland

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