Necessary Knowledge

Piagetian Perspectives on Constructivism

Leslie Smith

• Publisher: Routledge
• Year: 2017
• ISBN:
  9781351710855
• Edition: 1
• Topic: Psychology
• Subtopic: Developmental Psychology
• Index: Psychology

Originally published in 1993, this monograph addresses a central problem in Piaget's work, which is the temporal construction of necessary knowledge. The main argument is that both normative and empirical issues are relevant to a minimally adequate account of the development of modal understanding. This central argument embodies three main claims. One claim is philosophical. Although the concepts of knowledge and necessity are problematic, there is sufficient agreement about their core elements due to the fundamental difference between truth-value and modality. Any account of human rationality has to respect this distinction. The second claim is that this normative distinction is not always respected in psychological research on the origins of knowledge where emphasis is placed on the procedures and methods used to gain good empirical evidence. An account of the initial acquisition of knowledge is not thereby an account of its legitimation in the human mind. The third claim relates to epistemology. Intellectual development is a process in which available knowledge is used in the construction of better knowledge. The monograph identifies features of a modal model of intellectual construction, whereby some form of necessary knowledge is always used. Intellectual development occurs as the reduction of modal errors through the differentiation and coordination of available forms of modal understanding. Piaget's work continues to provide distinctive and intelligible answers to a substantive and outstanding problem.

CHAPTER ONE

Towards an Epistemology of Necessary Knowledge

“We are careful in particular to recognise our personal debt in this respect, that almost all the questions that we have studied in psychology had a philosophical inspiration” (Piaget, 1975a, p. 18).

[1] INTRODUCTION

Piaget has given an exact formulation of the problem which he takes to be central when questions about the development of knowledge arise.

The main problem of any epistemology, but principally of any genetic epistemology, is in fact to understand how the mind succeeds in constructing necessary relationships, which appear to be “independent of time”, if the instruments of thought are merely psychological operations that are subject to evolution and are constituted in time (Piaget, 1950, p.23; my emphasis).

This problem concerns the construction during time of necessary knowledge that is true throughout time. According to Piaget, necessary knowledge is a constitutive feature of rationality and also a human construction. Several initial comments can be made about this position. Firstly, Piaget’s problem has been one main problem in philosophy since it concerns the distinction between the origins of knowledge and the legitimation of knowledge in the light of the standards of rationality. In traditional epistemology, this distinction is forcefully stated by Hume (1739/1965, p. 165). It re-appears in the distinction between the empirical basis of knowledge and its rational validity (Kant, 1787/1933, B3-4), or in the distinction between the origins of mathematical ideas and their proof (Frege, 1888/1980, p.vi), or in the distinction between the origins of human beliefs and the reasons for those beliefs (Sainsbury, 1991, p.5). Secondly, some version of Piaget’s problem continues to be regarded as one of the principal, unresolved problems in contemporary epistemology (Kitchener, 1986, p.99). Philosophers issue the reminder that questions such as “What, exactly, distinguishes logical from psychological study of reasoning … What has logic to tell us about rationality?” (Haack, 1978, p.242) or the problem of “explaining how a physical organism can be subject to the norms of rationality” (McGinn, 1991, p.23) are intriguing, important but unresolved. Thirdly, Piaget’s main proposal is that questions about the development of necessary knowledge bear upon both its psycho-social origins and its rational legitimation in the human mind. On this view, an answer to Piaget’s main problem would have to include both empirical and rational elements which would be reducible neither to empirical psychology nor to a priori epistemology.

The interpretation of Piaget’s account that is outlined here assigns a key role to the notion of necessity which is used in three ways. Piaget’s account is taken to lay down empirically necessary conditions of the understanding of logical necessity through a process of constructive necessity (Smith, 1987a). Allied to this interpretation are three main claims: one philosophical, a second psychological, and a third epistemological.

The philosophical claim states that the concepts (categories, relations, structures) that are central to research in developmental psychology and empirical epistemology have both defining and non-defining properties. Defining properties are necessary properties that lay down all-and-only the properties which must be possessed for a case to fall under that concept. The non-defining properties of a concept are contingent and so are not necessary in this sense, even though cases that fall under the concept may commonly possess them. Necessary properties lay down both why something is, and has to be, what it is and why it is not, and cannot be, something else. A simple statistical example is provided by the notion of an average score. The (common sense) notion of an average is not well defined, unlike the statistical notions of median and mean. The third score in a series of five scores is not always the mean, even if it is the median. Further, even when the third score is the mean, that score is not on that account the mean, since the properties of being the middle score and being the mean score are distinct. Thus knowing that a score is the middle score may coincide with knowledge of the mean of the scores, even though the former is not the latter. This logical claim has been at centre stage in epistemological discussions from Plato to the present day. One implication of this logical claim is that intellectual development can be successful only if an understanding of necessity is attained.

The psychological claim states that, in fact, children typically gain their initial knowledge by use of the non-defining properties of the concepts at their disposal. There are an indefinite number of ways in which this may occur and psychological accounts are advanced as to how the process of acquisition takes place. In turn, psychological research has the role of systematically investigating the local contingencies that operate in a social context and which help to shape human understanding. Knowledge based on non-defining properties is, of course, knowledge. Further, it may sometimes coincide with knowledge based on the defining properties of the concept, and thus psychological research which is directed to its characterisation and explanation is valid in its own right. Yet necessary knowledge is always distinguishable from empirical knowledge and the understanding of proportionality is, according to Spinoza (1660/1963), an illustrious case in point. It is psychologically interesting that street-trading children have developed their own way of understanding proportionality (Saxe, 1991; Carraher, 1991). It is also epistemologically important to ascertain the extent to which their way amounts to rational understanding which has the Kantian properties of universality and necessity. The modal concepts of necessity and possibility are important just because their use is required in the acquisition of all forms of conceptual knowledge. Such concepts are invariably used throughout intellectual development, even though they have variable exemplifications at different developmental points.

The epistemological claim states that progress occurs as a process of differentiation whereby properties which are initially conflated are severally demarcated and ultimately coordinated into a coherent system of thought. Intellectual development is a search for coherence, marked by the progressive construction and conservation of the categories of thought. This search is required because of the conflation of the necessary and empirical properties of concepts. Reverting to a statistical analogy relating to significance testing, modal errors occur either as type I (false-positive) or as type II (false-negative) errors. The growth of knowledge in children is a special case of epistemic search, which is activated by the occurrence of modal errors in understanding and whose successful completion can never be attained, since necessary properties are always co-instantiated with empirical properties in the human understanding. The growth of necessary knowledge is a process that is both co-extensive with all intelligent life and which is never complete. There are however degrees of success which occur as the progressive attainment of rationality. Intellectual search directed towards coherence is an epistemological process, since it bears on the formal characteristics of knowledge which are universally and atemporally valid. That is, these characteristics apply to all knowledge everywhere and always apply without exception. But this epistemic search has its origin in psychological functioning which is constrained by context and contingency. That is, the characteristics of these psychological forms of knowledge are situationally specific and dependent on the particular factors at work. An adequate account of intellectual development will have to do justice to both epistemological and psychological dimensions. If more attention has been given to the former in Piaget’s account, and to the latter in Piagetian research, a minimally adequate account is still awaited. It is for this fundamental reason that Piagetian hill-climbing is difficult.

[2] PIAGET’S PROBLEM:
THE CONSTRUCTION OF NECESSARY KNOWLEDGE

Four introductory comments can be made about Piaget’s problem, which is a central and epistemological one but neither the sole nor a resolved problem in his work. First, the problem has been central throughout Piaget’s work. Second, it is one essential problem that developmentalists must address. Third, it is not the sole problem in human development. Finally, Piaget’s problem has its basis in epistemology.

First, the construction of necessary knowledge was one of Piaget’s central concerns in his early, empirical studies (Piaget, 1922, p.222, my emphasis): “I call formal reasoning the reasoning which, from one or several propositions, draws a conclusion to which the mind assents with certainty, without thereby having recourse to observation. What is beyond dispute is that such reasoning exists”. In this paper, the empirical question is to ascertain whether formal reasoning, which is logically necessary, is present in children’s thinking. Piaget’s question has normative presuppositions since a norm—in this case, necessity—is required to identify the species of knowledge. But the question is posed as one to which an empirical answer can be given. Traditionally, normative questions have been the concern of philosophers. Piaget set out to show that his question can be investigated empirically, even though it also embodies a normative component. Because Piaget’s findings indicated that not all children do display formal reasoning, the problem of how such necessary knowledge is constructed is posed, as Piaget assumes that such reasoning is present in the thinking of adults.

The same interest is evident throughout Piaget’s work, including his final papers. One statement (Piaget, 1967a, p.391; cf. 1977/1986) of this problem is that “the manifestation of logical necessity constitutes the central problem of the psycho-genesis of operational structures”. His epistemological interests are stated to lie in accounting for the actual construction of new knowledge, in which process the construction of new necessities would play an essential role. Thus the construction of necessary knowledge has been one of Piaget’s concerns for almost the whole of his work.

Second, Piaget claimed that the construction of necessary knowledge is the principal problem in epistemology. This is a strong claim in two respects. There are other epistemological problems which demand equal priority. There are other problems which gain equal attention in Piaget’s work, such as the construction of knowledge tout court (Kitchener, 1986, p.175) or the origin of universal ideas in individual thinking (Chapman, 1988, p.5). A more modest proposal is that the construction of necessary knowledge is one of the essential problems which will have to be tackled in any minimally adequate epistemology. Necessary knowledge is one species of knowledge. This species of knowledge is important, and so essential, on four counts. First, necessary knowledge is a paradigm example of knowledge because such knowledge is true and atemporally so. Second, such knowledge is a constitutive feature of knowledge in certain domains, such as mathematics. Third, necessary knowledge is a pervasive feature of every domain where necessary conclusions permit the knower to go beyond the information given. Fourth, necessary knowledge has a biological origin. However in the present discussion it is sufficient to state that necessary knowledge has its origins in non-necessary knowledge. The importance of necessary knowledge to developmental theory has been noticed (Campbell & Bickhard, 1986; Chapman, 1988; Kitchener, 1986; Moshman, 1990; Murray, 1990; Smith, 1992a).

Third, the problem of how necessary knowledge is constructed could not be the sole problem that an account of human development would have to address. To be sure, Piaget’s problem is far-reaching because necessity is domain independent. But necessary knowledge is a sub-species of knowledge which is itself a sub-species of mental states. An account of the human construction of necessary knowledge could not be a comprehensive account of the person. Of course, Piaget never claimed that his position could be comprehensive in this sense. The positions attributed to him in Piagetian commentary are another matter.

Fourth, even if Piaget has clearly stated what he takes his principal problem to be, this is not to say that the full nature of this problem is clear, still less clearly answerable. On the contrary: the problem is a formidable problem in epistemology. Although Piaget (1970, p.25) stated that “all the problems I have attacked are epistemological”, there is continuing controversy about the extent to which, and the respects in which these problems have a psychological component. In his chef d’oeuvre, Piaget (1950) took his work primarily to be a contribution to genetic epistemology. There are two points to notice here. In one respect, Piaget’s work is a contribution to methodology as he outlines and defends proposals about the main elements in any theory of the development of knowledge. In this sense, Piaget’s work is a contribution to the philosophy of science, which is further noted in [10]. But there is a different respect to consider as well, since specific accounts of how the construction of knowledge occurs are also elaborated by Piaget. In this sense, Piaget’s work is a contribution to empirical epistemology, which accords joint recognition to both rational and empirical issues.

In the present volume, the discussion of Piaget’s work has three strands. One strand is philosophical and concerns the importance of normative issues when epistemological questions arise [3]—[7]. A second strand is psychological and concerns the extent to which Piaget’s position is vulnerable to psychological challenges [9]—[22]. The third strand is epistemological and concerns the respects in which Piaget’s position is an intelligible position relevant to his main question [8], [23]—[26]. An overview of the whole discussion, which could also serve as an introduction, is provided in [27]. A guide to, and commentary on, current research on the development of necessary knowledge is offered in [28].

The primary aim of sections [3]—[10] of Chapters 1-2 is twofold. One aim is to illustrate some of the theoretical issues that have arisen in philosophical discussions of knowledge and necessity. This first aim has two dependent objectives. First, the illustrations in [3.1] are designed to show that problems of knowledge and necessity have been a central preoccupation in philosophical epistemology for two millennia. The second objective is to show that these problems are not merely of antique interest but continue to occupy a central place in current philosophical discussion. Illustrative use is made of the work of Karl Popper and Saul Kripke in [3.2] followed by a selection of case studies in [4] and [5]. The implied conclusion in these sections is that the complexity of these problems resists a facile resolution through over-hasty operationalisation in empirical research. The second aim is to show that Piaget’s genetic epistemology addresses epistemological problems of knowledge and necessity by the express introduction of an empirical control. His argument is that there are empirical, and not merely rational, issues to confront when problems of the development of necessary knowledge arise. The central presumption of Piagetian epistemology is that both the derogation of the empirical issues on philosophical grounds, and the derogation of rational issues on methodological grounds, are equally unacceptable. It is for this reason that Piaget takes his position to offer a mediating, middle course, a tertium quid. Piaget’s argument for this mediating position is reviewed in [7]. A sketch of the general features of Piaget’s position is given in [8]. It is this sketch that is later elaborated in [23]—[26] of Chapter 7. The main implication of the discussion in sections [3]—[8] is that a minimally adequate theory of the development of necessary knowledge must be both empirically and rationally acceptable. The argument in [9] is that psychological research on intellectual development should be evaluated with this implication in mind.

In fact, this main implication has been so far out of sight in some psychological research that it appears never to be in view at all. The case for this last claim is elaborated in section [10]—[22] of Chapters 3-6. Although some readers might prefer to address this case directly, either because they prefer to leave the consideration of rational issues to others or because their interest lies exclusively in empirical considerations, they are welcome to by-pass sections [3]—[8] only if prior credence is given to the main implication, that rational and empirical issues require joint consideration. Readers who neither accept this main implication nor the case against certain types of psychological research outlined in [10]—[22] are not in a good position to by-pass sections [3]—[8] completely.

[3] NECESSITY IN PHILOSOPHICAL EPISTEMOLOGY

As a guide to the discussion, Piaget’s objection to philosophical epistemology can be stated at the outset (Piaget, 1970/1977, pp.12/*5; my translation and emphasis):

Platonic, rationalist or apriorist epistemologies suppose themselves to have found some fundamental instrument of knowledge that is extraneous, superior or prior to experience … Such doctrines, though careful to characterise the properties which they attribute to this instrument… have omitted to verify that it was actually at the subject’s disposal. Here, whether we like it or not, is a question of fact.

The objection is that some philosophical questions about human understanding have an empirical component. An exclusively a priori approach is stated to be unacceptable because of its neglect of the facts. The objection is a denial neither of the importance nor of the relevance of the philosophical questions. The objection is instead that an a priori approach will not lead to their resolution. T...