“Microhistory” is a method used by historians: we investigate something small to derive new insights that reveal something big (see Burman Reference Burman2017, pp. 119–120). Here, I focus on the target article's mention of Piaget's object permanence as part of its engagement with representation. It is an aside, there, and not used to advance the authors’ argument. But it could have. As a result, we can use the microhistorical method to fill in some of the theoretical details that would otherwise be missing from subsequent discussions.
First, though, some basics: object permanence is the result of constructing the logical operation of identity, such that sensations at time “n” following a particular motor interaction become associated with the same sensations that are observed at time “n + 1” following the same interaction. The consequence is then the abstraction – note my slightly different usage – of a representation (an “object”) that persists over time. Piaget (Reference Piaget and Campbell1977/2001) ultimately called this process “empirical abstraction” (passim).
Once objects have been abstracted (constructed) from movements-and-sensations (phenomena), they become the new basis for the child's conception of reality. The sensorimotor is thus replaced with the concrete. Abstraction then changes too. From the persistence of represented-objects are abstracted sets, and laws, and these can in turn be applied to imaginary objects (themselves also a kind of representation). The resulting reflected abstractions and meta-reflections are also treated as if they were real. Therefore, the world changes again.
Several scholarly commentaries explain the details (see, especially, Campbell Reference Campbell and Piaget2001; Reference Campbell, Müller, Carpendale and Smith2009; Moessinger & Poulin-Dubois Reference Moessinger and Poulin-Dubois1981). Here, though, I want to focus on the big picture; to use the micro to exemplify the macro. And even though the insights I cite are from the end of Piaget's life, quite a lot happened in those final years. They need to be considered together.
An important related observation is that what Piaget was doing in Geneva is not identical to how his work was understood and popularized by American Psychologists. As a result, it has become common to refer to the divergence as “Piaget's new theory” (following, especially, Beilin Reference Beilin, Beilin and Pufall1992). This involved several changes, made in parallel, but it is typically characterized in the secondary literature as involving a shift from logics of extension to those of intension (Davidson Reference Davidson1988; Reference Davidson1993; Ducret Reference Ducret1988; after Piaget & Garcia Reference Piaget, Garcia, Davidson, Easley, De Caprona and Davidson1987/1991).
For us, this change enables the treatment of abstraction as involving functional identities (implication, signification, and meaning) rather than strict identities (between sensations or objects in themselves). And that was in turn made possible by the replacement of stages, at the start of the new theory period, with levels of relative incompleteness.
This is the so-called neo-Gödelian turn in Piaget's theorizing: It replaced the popular staircase metaphor of cognitive development with “an upwardly broadening spiral” (translated by Burman Reference Burman2016, p. 762). It also clarified the notion of abstraction by enabling the recognition of identities across levels in that spiral.
The easiest way to understand the part of this that matters for our purposes is to read it through Bruner's (Reference Bruner1960) reinterpretation of Piaget for American teachers. In particular, I am thinking of the “spiral curriculum” (pp. 13, 52–54) that became so influential during the post-Sputnik period of education reform.
In a spiral curriculum, the same topic is revisited at different levels of complexity across different grade levels. New insights are then derived by reflecting on the similarities: Although the externally-provided educational structures are different in different grades, the functional consequences for their understanding of the issue-at-hand are similar. Hence, the levels in this spiral are comparable by virtue of their reference to the identity of the pedagogical object being considered.
Something like this occurs during cognitive development too, in Piaget's new theory, except that the scaffolding is provided endogenously: functionally-identical consequences are derived from quite different interactions, treated across levels, such that the lineage of related representations is unified by different kinds of abstractions. (In Piaget's later language, this is possible because the comparisons involve “morphisms” [see, especially, Piaget et al. Reference Piaget, Henriques, Ascher and Brown1990/1992].) This in turn enables the construction of correspondences between different functional-structures and then generalizations within, between, and across levels (Piaget Reference Piaget1980b; Piaget & Henriques Reference Piaget and Henriques1978). Therefore, non-overlapping areas can be filled-in. And that is why Piaget's (Reference Piaget1980a) conception of dialectics includes periods of calm between its dialectical punctuations; how you get the appearance of discontinuous stages despite continuous change.
This is part what's missing in the authors’ view of representation, but which we can see as a result of adopting a microhistorical approach. That also affords the main historical criticism of such work: contemporary authors are too embedded in the post-Sputnik popularization of Piaget as a theorist of cognition, and insufficiently grounded in what the Genevans were actually doing. As a result, they miss the same things that were omitted during Piaget's original importation into American Psychology: the neglected “foreign invisibles” (Burman Reference Burman2015).
In other words, the article is missing those aspects of abstraction that Piaget used throughout his interdisciplinary program. Yet, this is equally as important as his psychology (Ratcliff & Burman Reference Burman2017). The recognition of what's necessary – given the intensional interpretation of identity as functional equivalence – drives the exploration of what's possible so that what's constructed is new rather than a copy (Piaget Reference Piaget and Feider1981/1987; Reference Piaget and Feider1983/1987). This thinking also informed the basis for his misunderstood evolutionary-developmental theory, updating the Baldwin effect (Piaget Reference Piaget and Nicholson-Smith1976/1979; discussed by Burman Reference Burman2013; Reference Burman, Sternberg and Pickren2019). And the same formal principles afforded new comparisons between child development and scientific change (Piaget & Garcia Reference Piaget, Garcia and Feider1983/1989).
Thus, for Piaget, abstraction and representation were not only properties of cognitive development. Nor were they solely a function of the development of knowledge in general. Rather, they were a function of life (Burman, Reference Burman, Callard and Millardin press). And so research like the authors’ contributes to more than just psychological knowledge. It also advances the role of psychological theorists at the frontier of the extended evolutionary synthesis; the move toward “evo-devo/psych-know” (Burman Reference Burman, Sternberg and Pickren2019, pp. 292, 307). Or rather, they can do so long as we are able to recognize the unexamined implications of their sources.
“Microhistory” is a method used by historians: we investigate something small to derive new insights that reveal something big (see Burman Reference Burman2017, pp. 119–120). Here, I focus on the target article's mention of Piaget's object permanence as part of its engagement with representation. It is an aside, there, and not used to advance the authors’ argument. But it could have. As a result, we can use the microhistorical method to fill in some of the theoretical details that would otherwise be missing from subsequent discussions.
First, though, some basics: object permanence is the result of constructing the logical operation of identity, such that sensations at time “n” following a particular motor interaction become associated with the same sensations that are observed at time “n + 1” following the same interaction. The consequence is then the abstraction – note my slightly different usage – of a representation (an “object”) that persists over time. Piaget (Reference Piaget and Campbell1977/2001) ultimately called this process “empirical abstraction” (passim).
Once objects have been abstracted (constructed) from movements-and-sensations (phenomena), they become the new basis for the child's conception of reality. The sensorimotor is thus replaced with the concrete. Abstraction then changes too. From the persistence of represented-objects are abstracted sets, and laws, and these can in turn be applied to imaginary objects (themselves also a kind of representation). The resulting reflected abstractions and meta-reflections are also treated as if they were real. Therefore, the world changes again.
Several scholarly commentaries explain the details (see, especially, Campbell Reference Campbell and Piaget2001; Reference Campbell, Müller, Carpendale and Smith2009; Moessinger & Poulin-Dubois Reference Moessinger and Poulin-Dubois1981). Here, though, I want to focus on the big picture; to use the micro to exemplify the macro. And even though the insights I cite are from the end of Piaget's life, quite a lot happened in those final years. They need to be considered together.
An important related observation is that what Piaget was doing in Geneva is not identical to how his work was understood and popularized by American Psychologists. As a result, it has become common to refer to the divergence as “Piaget's new theory” (following, especially, Beilin Reference Beilin, Beilin and Pufall1992). This involved several changes, made in parallel, but it is typically characterized in the secondary literature as involving a shift from logics of extension to those of intension (Davidson Reference Davidson1988; Reference Davidson1993; Ducret Reference Ducret1988; after Piaget & Garcia Reference Piaget, Garcia, Davidson, Easley, De Caprona and Davidson1987/1991).
For us, this change enables the treatment of abstraction as involving functional identities (implication, signification, and meaning) rather than strict identities (between sensations or objects in themselves). And that was in turn made possible by the replacement of stages, at the start of the new theory period, with levels of relative incompleteness.
This is the so-called neo-Gödelian turn in Piaget's theorizing: It replaced the popular staircase metaphor of cognitive development with “an upwardly broadening spiral” (translated by Burman Reference Burman2016, p. 762). It also clarified the notion of abstraction by enabling the recognition of identities across levels in that spiral.
The easiest way to understand the part of this that matters for our purposes is to read it through Bruner's (Reference Bruner1960) reinterpretation of Piaget for American teachers. In particular, I am thinking of the “spiral curriculum” (pp. 13, 52–54) that became so influential during the post-Sputnik period of education reform.
In a spiral curriculum, the same topic is revisited at different levels of complexity across different grade levels. New insights are then derived by reflecting on the similarities: Although the externally-provided educational structures are different in different grades, the functional consequences for their understanding of the issue-at-hand are similar. Hence, the levels in this spiral are comparable by virtue of their reference to the identity of the pedagogical object being considered.
Something like this occurs during cognitive development too, in Piaget's new theory, except that the scaffolding is provided endogenously: functionally-identical consequences are derived from quite different interactions, treated across levels, such that the lineage of related representations is unified by different kinds of abstractions. (In Piaget's later language, this is possible because the comparisons involve “morphisms” [see, especially, Piaget et al. Reference Piaget, Henriques, Ascher and Brown1990/1992].) This in turn enables the construction of correspondences between different functional-structures and then generalizations within, between, and across levels (Piaget Reference Piaget1980b; Piaget & Henriques Reference Piaget and Henriques1978). Therefore, non-overlapping areas can be filled-in. And that is why Piaget's (Reference Piaget1980a) conception of dialectics includes periods of calm between its dialectical punctuations; how you get the appearance of discontinuous stages despite continuous change.
This is part what's missing in the authors’ view of representation, but which we can see as a result of adopting a microhistorical approach. That also affords the main historical criticism of such work: contemporary authors are too embedded in the post-Sputnik popularization of Piaget as a theorist of cognition, and insufficiently grounded in what the Genevans were actually doing. As a result, they miss the same things that were omitted during Piaget's original importation into American Psychology: the neglected “foreign invisibles” (Burman Reference Burman2015).
In other words, the article is missing those aspects of abstraction that Piaget used throughout his interdisciplinary program. Yet, this is equally as important as his psychology (Ratcliff & Burman Reference Burman2017). The recognition of what's necessary – given the intensional interpretation of identity as functional equivalence – drives the exploration of what's possible so that what's constructed is new rather than a copy (Piaget Reference Piaget and Feider1981/1987; Reference Piaget and Feider1983/1987). This thinking also informed the basis for his misunderstood evolutionary-developmental theory, updating the Baldwin effect (Piaget Reference Piaget and Nicholson-Smith1976/1979; discussed by Burman Reference Burman2013; Reference Burman, Sternberg and Pickren2019). And the same formal principles afforded new comparisons between child development and scientific change (Piaget & Garcia Reference Piaget, Garcia and Feider1983/1989).
Thus, for Piaget, abstraction and representation were not only properties of cognitive development. Nor were they solely a function of the development of knowledge in general. Rather, they were a function of life (Burman, Reference Burman, Callard and Millardin press). And so research like the authors’ contributes to more than just psychological knowledge. It also advances the role of psychological theorists at the frontier of the extended evolutionary synthesis; the move toward “evo-devo/psych-know” (Burman Reference Burman, Sternberg and Pickren2019, pp. 292, 307). Or rather, they can do so long as we are able to recognize the unexamined implications of their sources.