It seems an implicit axiom of Cimpian & Salomon (C&S) that the form of reasoning its authors are studying is childish and unwise. The authors have very little good to say about the inherence heuristic or the essentialism to which it leads. It is characteristic of children as young as 4 years of age, of persons needing reassurance, and of people with a low cognitive capacity or under conditions of high cognitive load. It leads to “errors in moral reasoning” (cf. the target article abstract), “the correspondence bias” (sect. 5.4), and so forth. It is responsible for prejudice and perhaps for religious warfare. Even Kahneman's great essay of Reference Kahneman2011 was not so negative. There this form of reasoning was explicated not as childish but as “System 1,” the making of a decision speedily or without concentrating overmuch on the weighing of evidence. In other words, Kahneman used the category to characterize not people but episodes of reasoning.
And yet the inherence heuristic and essentialism that have been derogated in this wise characterize the core of contemporary statistical data analysis across the sciences, including the developmental cognitive sciences that are the domain of C&S's argument. I mean this literally: the authors' assertion that “this heuristic is a pervasive feature of human cognition” (sect. 1, para. 4) is actually an example of that selfsame essentialism.
Consider, for instance, the statistical notion of an average, which runs inexorably through all these reports of what is found in studies of children aged 3, 21, or in between. In any report of an empirical psychological investigation, averages are always to be found. Within any sampling frame, the optimality (maximum likelihood) of an average is indistinguishable from the (very simple) theory entailed in that computation: that there exists an inherent true value (mean) characterizing measurements made on the members of that group, such that deviations from that value are distributed in a bell curve (a Gaussian distribution). This argument was first made by Carl Friedrich Gauss himself in this context – hence the distribution's name. In other words, anyone who computes an average is already working inside the inherence heuristic. Similarly, a regression coefficient is the weighted average of a collection of separate estimates of the same (sub)sample-specific slope, which thereby becomes an “inherent” characteristic of a sample right alongside its average. This point was made by the British statistician Francis Y. Edgeworth in the 1890s (Stigler Reference Stigler1986). A correlation, if required, is just a small arithmetical modification of this same averaged slope. Further out on this thread of statistical reductionism are the path coefficients generalizing multiple regressions into interlinked linear causal laws (Wright Reference Wright1968; Reference Wright1969; Reference Wright1977; Reference Wright1978), the advances in econometric method that are two-stage and three-stage least squares (Malinvaud Reference Malinvaud1966) and the combination of either of these with factor analysis in the formalism of “structural equation models” (Wold & Joreskog Reference Wold and Joreskog1982). All such coefficients are instances of essentialism.
Indeed, everywhere we look in the statistical sciences, whether physical sciences, natural sciences, psychological sciences, or social sciences, we encounter this same urge toward the inherency of summary numerical parameters. Some contemporary statisticians place this drive at the very center of the statistical mind-set, as, for instance, when Cox (Reference Cox2006, p. 7) states that statistical inference “takes the family of models as given and aims to give intervals or in general sets of values within which [the parameter] is likely to lie, [and] to assess the consistency of the data with a particular parameter value.” The consilience of statistical parameters that lies at the core of all of quantitative science (Bookstein Reference Bookstein2014) is at root little more than the extension of C&S's ideas of inherence to the objective subworlds of controlled observations that are the object of scientific study discipline by discipline. What could be more “essentialist” than the periodic table of the elements, which is posted on the wall of every high-school chemistry classroom? The authors inadvertently make the point that essentialism and the inherence heuristic likewise characterize academic psychology.
Even more generally, the inherence heuristic may interact closely with the “Ionian enchantment” (Wilson Reference Wilson1998, pp. 4–5), the trust that our understanding of the patterns of this world rests at least as much upon some fundamental structures in that world as upon cognitive customs of our minds. Philosophers (e.g., Peirce Reference Peirce, Hartshorne and Weiss1934; Russell Reference Russell1967, p. 3) have often agreed with physicists (e.g., Wigner Reference Wigner1960) that the role of numbers in describing our world is ultimately transcendental. For this to be inherent in human reasoning by the age of 4, even if limited to the aspects of numeracy that deal with size, count, and direction, must be an aspect of that “unreasonable effectiveness of mathematics” that Wigner refers to.
Perhaps the authors' objection is not really to essentialism and the inherency heuristic per se but instead to a mildly age-graded category error governing its typical applications. The child likely lacks understanding of the difference between aspects of the objects in our world that are appropriately taken as inherent or essentialist, such as the properties of water or our usually pentadactyl limbs, and aspects such as personality that are properly studied only after careful, controlled observation. But even in the academy, these are not distinctions of mind but only of subject matter.
To this extent, the child's essentialism is not to be deprecated or deplored, but celebrated. Recourse to inherence and essentialism, far from being a pejorative characteristic of mainly the youngest children, the intellectually challenged, those of a System 1 cognitive style, and the like, appears to be an inherent theme of human ratiocination at all levels from earliest childhood through the halls of academe. Our authors should be reveling in their discovery that ordinary human childhood prepares us in part to be scientists, not just large, unusually fecund, eusocial mammals. Meanwhile, from its very first sentence to its last, the article by C&S serves as much as an example of its subject as it does an analysis.
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It seems an implicit axiom of Cimpian & Salomon (C&S) that the form of reasoning its authors are studying is childish and unwise. The authors have very little good to say about the inherence heuristic or the essentialism to which it leads. It is characteristic of children as young as 4 years of age, of persons needing reassurance, and of people with a low cognitive capacity or under conditions of high cognitive load. It leads to “errors in moral reasoning” (cf. the target article abstract), “the correspondence bias” (sect. 5.4), and so forth. It is responsible for prejudice and perhaps for religious warfare. Even Kahneman's great essay of Reference Kahneman2011 was not so negative. There this form of reasoning was explicated not as childish but as “System 1,” the making of a decision speedily or without concentrating overmuch on the weighing of evidence. In other words, Kahneman used the category to characterize not people but episodes of reasoning.
And yet the inherence heuristic and essentialism that have been derogated in this wise characterize the core of contemporary statistical data analysis across the sciences, including the developmental cognitive sciences that are the domain of C&S's argument. I mean this literally: the authors' assertion that “this heuristic is a pervasive feature of human cognition” (sect. 1, para. 4) is actually an example of that selfsame essentialism.
Consider, for instance, the statistical notion of an average, which runs inexorably through all these reports of what is found in studies of children aged 3, 21, or in between. In any report of an empirical psychological investigation, averages are always to be found. Within any sampling frame, the optimality (maximum likelihood) of an average is indistinguishable from the (very simple) theory entailed in that computation: that there exists an inherent true value (mean) characterizing measurements made on the members of that group, such that deviations from that value are distributed in a bell curve (a Gaussian distribution). This argument was first made by Carl Friedrich Gauss himself in this context – hence the distribution's name. In other words, anyone who computes an average is already working inside the inherence heuristic. Similarly, a regression coefficient is the weighted average of a collection of separate estimates of the same (sub)sample-specific slope, which thereby becomes an “inherent” characteristic of a sample right alongside its average. This point was made by the British statistician Francis Y. Edgeworth in the 1890s (Stigler Reference Stigler1986). A correlation, if required, is just a small arithmetical modification of this same averaged slope. Further out on this thread of statistical reductionism are the path coefficients generalizing multiple regressions into interlinked linear causal laws (Wright Reference Wright1968; Reference Wright1969; Reference Wright1977; Reference Wright1978), the advances in econometric method that are two-stage and three-stage least squares (Malinvaud Reference Malinvaud1966) and the combination of either of these with factor analysis in the formalism of “structural equation models” (Wold & Joreskog Reference Wold and Joreskog1982). All such coefficients are instances of essentialism.
Indeed, everywhere we look in the statistical sciences, whether physical sciences, natural sciences, psychological sciences, or social sciences, we encounter this same urge toward the inherency of summary numerical parameters. Some contemporary statisticians place this drive at the very center of the statistical mind-set, as, for instance, when Cox (Reference Cox2006, p. 7) states that statistical inference “takes the family of models as given and aims to give intervals or in general sets of values within which [the parameter] is likely to lie, [and] to assess the consistency of the data with a particular parameter value.” The consilience of statistical parameters that lies at the core of all of quantitative science (Bookstein Reference Bookstein2014) is at root little more than the extension of C&S's ideas of inherence to the objective subworlds of controlled observations that are the object of scientific study discipline by discipline. What could be more “essentialist” than the periodic table of the elements, which is posted on the wall of every high-school chemistry classroom? The authors inadvertently make the point that essentialism and the inherence heuristic likewise characterize academic psychology.
Even more generally, the inherence heuristic may interact closely with the “Ionian enchantment” (Wilson Reference Wilson1998, pp. 4–5), the trust that our understanding of the patterns of this world rests at least as much upon some fundamental structures in that world as upon cognitive customs of our minds. Philosophers (e.g., Peirce Reference Peirce, Hartshorne and Weiss1934; Russell Reference Russell1967, p. 3) have often agreed with physicists (e.g., Wigner Reference Wigner1960) that the role of numbers in describing our world is ultimately transcendental. For this to be inherent in human reasoning by the age of 4, even if limited to the aspects of numeracy that deal with size, count, and direction, must be an aspect of that “unreasonable effectiveness of mathematics” that Wigner refers to.
Perhaps the authors' objection is not really to essentialism and the inherency heuristic per se but instead to a mildly age-graded category error governing its typical applications. The child likely lacks understanding of the difference between aspects of the objects in our world that are appropriately taken as inherent or essentialist, such as the properties of water or our usually pentadactyl limbs, and aspects such as personality that are properly studied only after careful, controlled observation. But even in the academy, these are not distinctions of mind but only of subject matter.
To this extent, the child's essentialism is not to be deprecated or deplored, but celebrated. Recourse to inherence and essentialism, far from being a pejorative characteristic of mainly the youngest children, the intellectually challenged, those of a System 1 cognitive style, and the like, appears to be an inherent theme of human ratiocination at all levels from earliest childhood through the halls of academe. Our authors should be reveling in their discovery that ordinary human childhood prepares us in part to be scientists, not just large, unusually fecund, eusocial mammals. Meanwhile, from its very first sentence to its last, the article by C&S serves as much as an example of its subject as it does an analysis.