Material representations in mathematical research practice

Synthese - Mathematicians’ use of external representations, such as symbols and diagrams, constitutes an important focal point in current philosophical attempts to understand mathematical...     

Are there representational shifts during category learning?

Early theories of categorization assumed that either rules, or prototypes, or exemplars were exclusively used to mentally represent categories of objects. More recently, hybrid theories of categorization have been proposed that variously combine these different forms of category representation. Our research addressed the question of whether there are representational shifts during category learning. We report a series of experiments that tracked how individual subjects generalized their acquired category knowledge to classifying new critical transfer items as a function of learning. Individual differences were observed in the generalization patterns exhibited by subjects, and those generalizations changed systematically with experience. Early in learning, subjects generalized on the basis of single diagnostic dimensions, consistent with the use of simple categorization rules. Later in learning, subjects generalized in a manner consistent with the use of similarity-based exemplar retrieval, attending to multiple stimulus dimensions. Theoretical modeling was used to formally corroborate these empirical observations by comparing fits of rule, prototype, and exemplar models to the observed categorization data. Although we provide strong evidence for shifts in the kind of information used to classify objects as a function of categorization experience, interpreting these results in terms of shifts in representational systems underlying perceptual categorization is a far thornier issue. We provide a discussion of the challenges of making claims about category representation, making reference to a wide body of literature suggesting different kinds of representational systems in perceptual categorization and related domains of human cognition.     

Salience Not Status: How Category Labels Influence Feature Inference

Two main uses of categories are classification and feature inference, and category labels have been widely shown to play a dominant role in feature inference. However, the nature of this influence remains unclear, and we evaluate two contrasting hypotheses formalized as mathematical models: the label special‐mechanism hypothesis and the label super‐salience hypothesis. The special‐mechanism hypothesis is that category labels, unlike other features, trigger inference decision making in reference to the category prototypes. This results in a tendency for prototype‐compatible inferences because the labels trigger a special mechanism rather than because of any influences they have on similarity evaluation. The super‐salience hypothesis assumes that the large label influence is due to their high salience and corresponding impact on similarity without any need for a special mechanism. Application of the two models to a feature inference task based on a family resemblance category structure yields strong support for the label super‐salience hypothesis and in particular does not support the need for a special mechanism based on prototypes.     

Computers as a Source of A Posteriori Knowledge in Mathematics

Electronic computers form an integral part of modern mathematical practice. Several high-profile results have been proven with techniques where computer calculations form an essential part of the proof. In the traditional philosophical literature, such proofs have been taken to constitute a posteriori knowledge. However, this traditional stance has recently been challenged by Mark McEvoy, who claims that computer calculations can constitute a priori mathematical proofs, even in cases where the calculations made by the computer are too numerous to be surveyed by human agents. In this article we point out the deficits of the traditional literature that has called for McEvoy’s correction. We also explain why McEvoy’s defence of mathematical apriorism fails and we discuss how the debate over the epistemological status of computer-assisted mathematics contains several unfortunate conceptual reductions.     

Capacity and Potentiality: Aristotle’s Metaphysics Θ.6–7 from the Perspective of the De Anima

The notion of a capacity (dunamis) in the sense of a power to bring about or undergo change plays a key role in Aristotle??s theories about the natural world. However, in Metaphysics ?? Aristotle also extends ??capacity??, and the corresponding concept of ??activity?? (energeia), to cases where we want to say that something is in capacity, or in activity, such and such but not, or not directly, in virtue of being capable of initiating or undergoing change. This paper seeks to clarify and confirm a certain view of how Aristotle wishes us to see the relationship between the two uses of ??capacity?? and ??activity??. To that end, I consider also Aristotle??s employment of the terms in the De Anima, which sheds light on the key examples which direct the discussion in Metaph. ??.     

Pointing and the interference effect in obsessive‐compulsive disorder (OCD)

The interference effect in obsessive‐compulsive disorder (OCD) was investigated in order to analyze cognitive aspects of motor stereotypy in OCD‐related compulsions. So far, the domain of cognitive control in compulsive behavior has been under‐investigated. Twelve participants (OCD patients and healthy controls) completed a newly created computer‐based pointing task as well as standard clinical and psychological background measures. Findings showed that the patients displayed a larger visual interference effect compared to the controls and pointing paths were longer in time as well as distance when a distractor stimulus was present. It is concluded that, for compensation, patients would need to generate excessive amounts of attentional resources not available to overcome motor rigidity on the one side and visual distraction on the other side.     

Emotional dysfunction in avoidant compared to borderline personality disorder: A study of affect consciousness

Knowledge of emotional dysfunction in patients with avoidant personality disorder (APD) is much needed. The present study examined affect consciousness (AC) in patients with APD compared to borderline personality disorder (BPD). AC, defined as capacity to perceive, reflect on, tolerate, and express emotional experiences, is assumed to be central to structure‐building in personality. The study tested the hypotheses that patients with APD have lower general AC and lower AC for pleasant affects compared to BPD. Fifty‐nine patients, 26 with APD and 33 with BPD were rated on several aspects of AC using the specialized AC interview. The structured interview SCID‐II was applied for diagnostic evaluations. The APD group had significantly lower levels of global AC and conceptual expressivity compared to the BPD group. Among 11 specific affects the APD group had significantly lower AC for interest and contempt. Emotional dysfunction is an important feature of APD and the findings indicate that psychotherapies for APD patients should focus on emotional experiences, aiming to improve emotional awareness, tolerance, and expressivity. The notion of a general avoidance of positive emotions in APD needs further exploration, including a possible dysfunction in the evolutionary based neuro‐affective Seeking system.     

Mapping the Structure of Human Values through Conceptual Representations

The present research provides the first direct examination of human values through concept categorization tasks that entail judging the meaning of values. Seven studies containing data from nine samples (N = 1086) in two countries (the UK and Brazil) asked participants to compare the meaning of different values found within influential quasi‐circumplex model of values. Different methods were used across experiments, including direct similarity judgment tasks, pile sorting, and spatial arrangement. The results of these diverse conceptual assessments corresponded to spatial configurations that are broadly convergent with Schwartz's model, both between and within participants. © 2018 The Authors. European Journal of Personality published by John Wiley & Sons Ltd on behalf of European Association of Personality Psychology