From the standpoint of logic, Piaget's genetic epistemology is a half-way house between formal logic and dialectical logic; from the standpoint of epistemology, Piaget's genetic epistemology is a half-way house between objective idealism and materialism.
Piaget's schema is this:
Thought passes through a series of stages of development; at each stage there applies formal logic at a specific stage of differentiation which may be characterised by an algebra in which exactly such-and-such a mathematical structure applies, corresponding to the axioms of logic at that stage; this logic is manifested first in actions, then at a relatively early stage in sensori-motor operations (in the specific mathematical sense of the word, as opposed to "actions" which are equivalent to relations but not yet mathematical operations), and finally in operations which express thoughts, conscious purposive activity.
The material basis for transition from sensori-motor intelligence to representation and from representation to conceptual thought is the interiorisation of practical activity.
The successive stages of concepts manifested in child development imply relations of deduction in mathematical logic and in the development of thinking in other planes of development, such as in the history of science and the history of knowledge in the anthropological domain.
Piaget draws on the full range of contemporary mathematical knowledge, a vast empirical base of observation of the learning of very young children built up at his institute and reports of observations of older children and a general knowledge of the development of knowledge in history.
(1) From the standpoint of dialectical logic, we must agree that at each stage of development, at each "definition of the Absolute" in Hegel's terminology, formal logic is applicable. Piaget's proof of this is striking, and his demonstration of how the stages of development in child thought pass through a specific series which is deductive in a specific sense from the standpoint of mathematics is original and profound.
However, from the standpoint of understanding development (and this is Piaget's standpoint), what is important is not the definition of each stage but the transition from one to the next; and for this it is necessary to demonstrate the internal contradiction within the logic of that plane.
Since Piaget draws on mathematical logic more developed than what was known to Hegel, it will be necessary to investigate these structures to see if this speculative proposition proves to be valid.
(2) The concept of interiorisation is indeed the basis of the materialist view of the development of thought. However, Piaget, as a professional child-psychologist falls prey to the objective idealism of any professional, of elevating the subject matter of his particular profession from being an aspect of the material world to being its master. [The charge of objective idealism is qualified, for Piaget is quite unambiguous that relations conceived of in thought exist objectively in the material world].
Thus, since his body of authoritative empirical work is in relation to early childhood development, he imposes the schema appropriate to this semi-human subject on to adolescent development, speculates on its possible reflection in anthropological development and confounds it with the history of development of science and philosophy. I say "confounds" because Piaget is aware that his schemas do not seem to apply in this domain. In this sense, the charge of objective idealism would seem unfair, but from confounding he does not go further and seek the implication of this lack of correspondence, but seeks to minimise it.
By focussing on early childhood (as indeed he must; that is his profession, and his institute has contributed a vast body of empirical material), Piaget sees what is biologically (zoologically?) human but not what is socially (historically) human, and humanity is essentially social, after all.
(3) On the plus side, it has to be said that Piaget deals once and for all with any idea of innate intelligence, and makes fully convincing the prospect of a fully genetic (i.e. developmental) elaboration of intelligence, assuming only animal instincts such as grasping and sucking and sensori-motor "equipment" capable of reflecting highly developed relations.
Piaget's comments on Vygotsky are on record, but Piaget was apparently made aware only of Vygotsky's work on egocentric speech and Vygotsky's criticisms of Piaget. Among the many other areas of overlap between Vygotsky's observations and Piaget's area of work is the development of concepts. Vygotsky observed several different stages in the development of concepts, which include a very early stage before the development of "abstract universal operations", viz., the grouping of objects into "family groups", ie. sets made up of "one of each type", as opposed to sets made up of "all having such-and-such common property", and also insists that the "abstract universal" attained by the child in early adolescence is not yet a true concept. The first is not reported (to my knowledge) by Piaget, but relates to what Piaget would view as ordinal relations appearing prior to fully-fledged number relations (it is first necessary to be able to put the members of a class in order to test one-to-one correspondence which is the foundation of number); The second could not be observed by Piaget, because Piaget himself is not aware of the fact that the abstract universal is not a fully developed concept.
Piaget's theory of early childhood development is not easily overthrown without substantial empirical observation. What is more, it must be accepted that to the extent of the scope of his observation, Piaget's theory is valid. We can only look to where Piaget could not see because he lacked certain concepts himself, or outside the domain of early childhood development.
From a speculative point of view, it would be worthwhile to critique the formal logical concepts of "group" and "operation" in particular, since these concepts loom so large in Piaget's analysis, and were not known to Hegel; there may be a logical clue to the issue of transition which is absent from the logical point of view in Piaget.
Piaget's developmental psychology most certainly has a lot to say in relation to epistemology, most particularly in uncovering the material basis of representational and operational thinking and in providing new observations about the relationships between different logical systems. However, it is limited and when the data of early childhood development is exaggerated in relation to, for example, historical development; individual development exaggerated in relation to social development, this is an error and leads to distortions. True, Piaget defines Genetic Epistemology as "attempting to explain knowledge, and in particular scientific knowledge, on the basis of its history, its sociogenesis, and especially the psychological origins of the notions and operations upon which it is based"[Genetic Epistemology, *1] This is a fair definition, but as it turns out, the word "especially" is somewhat understated in this definition and the word "sociogenesis" somewhat overstated.
In Genetic Epistemology, *3, Piaget says:
"Language appears somewhere about the middle of the second year, but before this, about the end of the first year or the beginning of the second year, there is a sensory-motor intelligence having its own logic - a logic of action. The actions that form sensori-motor intelligence are capable of being repeated and of being generalised. ... Whatever is repeatable and generalisable in an action is what I have called a scheme, and I maintain that there is a logic of schemes. Any given scheme in itself does not have a logical component, but schemes can be coordinated with one another, thus implying the general coordination of actions. These coordinations form a logic of actions that are the point of departure for the logical mathematical structures. ... At the later stage this relationship of class inclusion gives rise to concepts. At the sensori-motor stage a scheme is a sort of practical concept".
"Between the age of about 18 months and the age of 7 or 8 years when the operations appear [operations = actions which have group-logic - AB], the practical logic of sensori-motor intelligence goes through a period of being internalised, of taking shape in thought at the level of representation, rather than taking place only in the actual carrying out of actions. .. language is certainly not the exclusive means of representation .. [it] is the ability to represent something by a sign or a symbol or another object".
I notice a couple of things about these passages which are worthy of further thought:
(1) Piaget is with Hegel, Marx and Vygotsky in talking of a Logic which first exists in the world, then in human activity and then in human consciousness. But unlike these others, his field of observation is very narrow, and if we use the word "logic" we are looking for something which can be abstracted from the widest possible domain of observation. Therefore, there is reason to think that Hegel's logic, developed even before The Origin of Species, let alone developmental psychology, but on a very broad domain of observation, may have some superiority.
(2) I suspect that Vygotsky has the edge on Piaget in relation to the true state of things discussed in the second paragraph which refers to a domain outside of Piaget's specialist field of work but of the most profound social implications (after all, we all grow up, but the human of human being of an isolated valley in New Guinea has a very different mental world from the human of the New York skyscraper). There are many kinds of representation just as there are many kinds of language (Piaget would agree), but Piaget only knows representation by formal logical groups and classes and not a concrete universal.
Further, Piaget knows only one direction of development, from the abstract to the concrete in Hegelian terms, but all development is essentially taking place in two directions at once. This comes out when Piaget notes that the development of the mathematics of spatial relations develops in the pre-lingual child from topology to projective to Euclidean, but in history from Euclidean to Cartesian to Topology.
Piaget says that the first is the deductive direction (Cartesian and Euclidean can be derived from Topology mathematically speaking), in Hegelian terms this is the logic of the Notion. What of the second (the development of Reflection)? a curiosity or an accident of history? And what is the implication for pedagogy? Pedagogy has in the past recapitulated the historical development, not the deductive development and did not know of the psychogenesis. As I understand it, Constructivist pedagogy deliberatively bases itself on the deductive and by implication psychogenetic development and not the sociogenetic path (though I am ignorant of thinking in this discipline).
On face value, it is at least an open question in relation to education of school-age or older people. On face value, Vygotsky's notion of Zone of Proximal Development would seem to lead to a more fruitful approach to pedagogy.
However, Piaget's work is probably the greatest single investigation of the development of concepts in any one domain and should provide a substantial basis for the further concretisation of dialectical logic.