What's in a function?

In this paper we argue that Revision Rules, introduced by Anil Gupta and Nuel Belnap as a tool for the analysis of the concept of truth, also provide a useful tool for defining computable functions. This also makes good on Gupta's and Belnap's claim that Revision Rules provide a general theory of definition, a claim for which they supply only the example of truth. In particular we show how Revision Rules arise naturally from relaxing and generalizing a classical construction due to Kleene, and indicate how they can be employed to reconstruct the class of the general recursive functions. We also point at how Revision Rules can be employed to access non-minimal fixed points of partially defined computing procedures.I thank Nuel Belnap, Rich Thomason, Ken Manders, and Jamie Tappenden for much helpful advice given while I was trying to get clear on the ideas presented here. I also thank two anonymous referees for helpful comments and criticisms on an earlier version of this paper.     

Why worry? The cognitive function of anxiety

The phenomenon of worry is considered to arise from cognitive processes involved in anxiety, that serve to maintain high levels of vigilance for personal danger. Rather than rely on self-report alone, the research described here draws on information processing methodology, to investigate this hypothesized cognitive function. Evidence is summarized to show that anxious subjects selectively attend to threatening information, and interpret ambiguous events in a relatively threatening way. However, the evidence on memory suggests that although such information may be easily activated, it is not necessarily more accessible. The allocation of attentional priority to threatening information is seen as a characteristic of anxious (rather than depressed) mood, while the ease with which this processing mode is adopted may underlie trait anxiety and vulnerability to anxiety disorders.     

Does happiness function like a motivational state?

According to Brehm's intensity of emotion theory, if an emotion has motivational properties, its intensity should be non-monotonically affected by factors similar to those determining the intensity of motivational states. These factors are called deterrents. In the case of emotion, one category of deterrents consists of factors that can potentially interfere with feeling the emotion, such as reasons for not feeling the emotion. Two experiments were carried out to examine whether happiness is a motivational state and, thus, if its intensity is non-monotonically determined by the importance of reasons for not feeling happy. We expected happiness to be reduced by a low importance reason for not feeling happy, to remain high in the presence of a moderately important reason, and to be reduced or eliminated by a very important reason. Both experiments supported the cubic function that results from these expectations, and when the results of the two studies were combined, each of the individual legs of the cubic function was found to be reliable along with the cubic function itself. The theoretical implications of these results are discussed.     

The Piéron function in the threshold region

The Piéron function (Piéron, 1914, 1920, 1952) describes the decay of reaction time (RT) when the intensity of the stimulus is increased. It is generally demonstrated within a suprathreshold range of intensities. However, in some studies, for the lowest range of intensities, the exponent of the function is clearly greater than that for the upper ranges of intensities. Such an increase in the exponent for the lowest intensities is assumed to result from a combined effect of stimulus intensity and of stimulis uncertainty in detection. Our first experiment used luminance levels that covered all the scotopic range and a spatial two-alternative forced-choice task in which both accuracy and RT were measured. It demonstrated a drastic increase in the exponent in the Piéron function when the intensities reached the threshold region. Since the estimates of the threshold region may have been biased by the use of a much larger range of luminances, a second experiment was conducted using luminances that covered only the threshold region. This experiment confirmed the previous estimates for the threshold region.     

PRAXIS: Brent’s algorithm for function minimization

Implementations of Brent’s (1973) PRincipal AXIS (PRAXIS) algorithm in the widely used C and PASCAL programming languages are presented. The algorithm minimizes a multivariate function without using derivatives. An example computer program that calculates a maximum likelihood estimate of the parameters of a psychometric function illustrates the use of the routine. Another algorithm, Localmin, also due to Brent (1973), efficiently finds the minimum of a univariate function. An example program uses this algorithm to estimate the polychoric correlation coefficient from a pxq table of observed frequencies.     

The transcendent function in Spitteler’s Prometheus and Epimetheus

In August 2020, John Beebe and Steve Myers met via Zoom to discuss their differing interpretations of psychological typology and the different sources within Jung’s writings that influenced their books: Integrity in Depth: Energies and Patterns in Psychological Type (Beebe), and Myers-Briggs Typology vs Jungian Individuation (Myers). The discussion centred on Spitteler’s epic poem Prometheus und Epimetheus, which forms the basis of chapter V of Psychological Types. This is both the largest chapter and one of two chapters that Jung highlighted in the Argentine foreword as containing the essence of the book. Jung’s book is primarily about the transformation of personality rather than the categorization of people. Although it contains a critical psychology that deconstructs the nature of consciousness, that is only one half of the book and a stepping-stone to the other half, which is the reconciliation of opposites with particular emphasis on the relation of consciousness and the unconscious. Jung assumed that readers were already familiar with Prometheus und Epimetheus, an understanding of which sheds light on the nature of the transformation that Jung described – the development of a new attitude towards attitude itself.     

How could phenomenal consciousness be involved in mental function?

In a phylogenetic perspective, the phenomenal and the functional aspects of consciousness cannot be separated because consciousness, as a phenomenal experience, must be causally effective. The hypothesis I propose is that the fundamental property of consciousness consists of a self-organizing process: the differentiation of a content. The differentiation of a content occurs on the basis of the relations internal to a representational whole, which behaves like a field and tends towards a condition of equilibrium. This hypothesis can be somehow considered an extension of Gestalt visual perceptual theory. Unlike neurocomputational processes, which are non-conscious and extrinsic to the representation, conscious processes are intrinsic to the representational whole. Consciousness, as an intrinsically self-organizing process interwoven with its phenomenal aspects, can be more than epiphenomenal and it can be involved in mental function. The paper then discusses the implications of this hypothesis for subjectivity and the explanatory gap.     

On the function of redfronted lemur’s close calls

In order to maintain group cohesion, many social mammals and birds regularly produce close calls. In some primate species, close calls appear to have a dual function: calls addressed at a broad class of targets serve to maintain group cohesion, whereas the same calls directed at a specific target serve to regulate subsequent social interactions. Redfronted lemurs (Eulemur rufifrons) produce different types of close calls: grunts, long grunts, hoos and meows. In order to study the function of these calls, we conducted focal observations and vocal recordings from eight adult males and females out of four social groups in Kirindy Forest, Western Madagascar. Redfronted lemurs produce long grunts, hoos and meows at relatively low rates during foraging, resting or group movements, respectively. Grunts were given most often and more or less constantly during foraging and traveling. Calling rate increased when the risk of separation increased and may thus promote group cohesion. Grunts given during approaches of other group members resulted more often in friendly interactions than approaches that were not accompanied by a grunt. Thus, redfronted lemurs produce specific but also generic contact calls, whereas the latter calls have a dual function that varies depending on the addressed audience: they act as an auditory beacon to maintain group cohesion and serve as signals of benign intent to avoid costly conflicts and facilitating social interactions.     

Real or imagined incomplete lateralization of function in females?

Visual field effects for 30 normal familial right-handed females were investigated with 4-point random forms known to be recognized more accurately in the right visual field by normal familial right-handed males, and the relationship between spatial ability and various performance patterns was examined. The forms were presented 2 deg in the left or right visual field. After a 10-sec delay, the subject decided whether or not a form exposed in central vision was the same as the stimulus. Incomplete lateralization of function appeared to be supported by the finding of no field differences. An alternative explanation was discussed since visual field superiority was significantly correlated with WAIS Block Design scores scaled for age, females with relatively low scores showing a right visual field superiority and females with relatively high scores showing a left visual field superiority. The experiment was repeated with 30 familial right-handed males. A significant right visual field superiority was obtained, but visual field superiorities were not correlated with measures of visuo-spatial or verbal ability.     

Is preschool executive function causally related to academic achievement?

The primary objective of this study was to reevaluate the well-established result that preschoolers' performance on executive function tasks are positively associated with their performance on academic achievement tests. The current study replicated the previously established concurrent associations between children's performance on EF tasks and academic achievement tests. Specifically, children's performance on measures of inhibitory and motor control were positively associated with their performance on tests of reading, writing, and mathematics achievement (rs?=?.2?.5); moreover, although diminished in magnitude, most of these associations held up even after including an earlier measure of academic achievement as a covariate (rs?=?.1?.3). However, the application of an alternative analytic method, fixed effects analysis, a method that capitalizes on repeated measures data to control for all time stable measured and unmeasured covariates, rendered the apparent positive associations between executive function and academic achievement nonsignificant (rs?=?.0?.1). Taken together, these results suggest that the well-replicated association between executive function abilities and academic achievement may be spurious. Results are discussed with respect to the importance of utilizing analytic methods and research designs that facilitate strong causal inferences between executive function and academic achievement in early childhood, as well as the limitations of making curriculum development recommendations and/or public policy decisions based on studies that have failed to do so.     

What's mom got to do with it? Contributions of maternal executive function and caregiving to the development of executive function across early childhood

Executive functions (EFs; e.g. working memory, inhibitory control) are mediated by the prefrontal cortex and associated with optimal cognitive and socio‐emotional development. This study provides the first concurrent analysis of the relative contributions of maternal EF and caregiving to child EF. A group of children and their mothers (n = 62) completed age‐appropriate interaction (10, 24, 36 months) and EF tasks (child: 24, 36, and 48 months). Regression analyses revealed that by 36 months of age, maternal EF and negative caregiving behaviors accounted for unique variance in child EF, above and beyond maternal education and child verbal ability. These findings were confirmed when using an early child EF composite‐our most reliable measure of EF – and a similar pattern was found when controlling for stability in child EF. Furthermore, there was evidence that maternal EF had significant indirect effects on changes in child EF through maternal caregiving. At 24 months, EF was associated with maternal EF, but not negative caregiving behaviors. Taken together, these findings suggest that links between negative caregiving and child EF are increasingly manifested during early childhood. Although maternal EF and negative caregiving are related, they provide unique information about the development of child EF. A video abstract of this article can be viewed at http://www.youtube.com/watch?v=NPKXFbbrkps     

Journal review: Including the critical‐social function into psychology

PsychCritique: The International Journal of Critical Psychology and Psychoanalysis, Vol. 1, No. 1, 1985. Norwood, NJ: Ablex Publishing Corp.     

Do private gestures have a self-regulatory function? A case study

One of the most fascinating phenomena in early development is that babies not only understand signs others direct to them and later use them to communicate with others, but they also come to direct the same signs towards themselves in a private way. Private gestures become "tools of thought". There is a considerable literature about private language, but almost nothing about private gestures. Private gestures pose an intriguing communicative puzzle: they are communicative, but with the self. In this paper we study two types of private gestures (signs) before language: (1) private ostensive gestures and (2) private pointing gestures. We show in a case study of one child between 12 and 18 months of age that both are used with a self-reflexive function, as a way of "thinking" what to do, in order to solve a problem in the conventional use of an object. The private gestures become self-reflexive signs.     

On the adaptive function of children's and adults’ false memories

Recent research has shown that memory illusions can successfully prime both children's and adults' performance on complex, insight-based problems (compound remote associates tasks or CRATs). The current research aimed to clarify the locus of these priming effects. Like before, Deese–Roediger–McDermott (DRM) lists were selected to prime subsequent CRATs such that the critical lures were also the solution words to a subset of the CRATs participants attempted to solve. Unique to the present research, recognition memory tests were used and participants were either primed during the list study phase, during the memory test phase, or both. Across two experiments, primed problems were solved more frequently and significantly faster than unprimed problems. Moreover, when participants were primed during the list study phase, subsequent solution times and rates were considerably superior to those produced by those participants who were simply primed at test. Together, these are the first results to show that false-memory priming during encoding facilitates problem-solving in both children and adults.     

The containing object—a prerequisite for developing the symbolic function

The paper aims at investigating the prerequisites for the process of symbolisation to develop and to be used by the personality. The starting point for this exploration is the psychoanalysis with a little boy of four and a half who started analysis because of an encopresis that was an expression of an overwhelming and concrete annihilation anxiety. It is argued that the sym- bolisation process has its basis in the relation to a real, reliable object and that this relation is a prerequisite for the child to start trying to transmit his experiences. The clinical material shows the boy's efforts to find an object capable of containing his anxiety and giving words to his unbearable affects, and the way this is worked through in the transference. This process contributed to his growing capacity to use symbols as an expression of his emotional experiences and it offered him a way of thinking about them instead of acting them out concretely.     

Does the ADF fit function decrease when the kurtosis increases?

In this study we demonstrate how the asymptotically distribution‐free (ADF) fit function is affected by (excessive) kurtosis in the observed data. More specifically, we address how different levels of univariate kurtosis affect fit values (and therefore fit indices) for misspecified factor models. By using numerical calculation, we show (for 13 factor models) that the probability limit F₀ of F for the ADF fit function decreases considerably as the kurtosis increases. We also give a formal proof that the value of F₀ decreases monotonically with the kurtosis for a whole class of structural equation models.