Number concepts for the concept empiricist

Dove (2009) and Machery (2007) both argue that recent findings about the nature of numerical representation present problems for Concept Empiricism (CE). I shall argue that, whilst this evidence does challenge certain versions of CE, such as Prinz (2002), it needn’t be seen as problematic to the general CE approach. Recent research can arguably be seen to support a CE account of number concepts. Neurological and behavioral evidence suggests that systems involved in the perception of numerical properties are also implicated in numerical cognition. Furthermore, the discovery of associations between spatial and numerical representations also lends independent support to a CE approach. Although these findings support CE in general, certain versions of the theory may need revising in order to accommodate them. In particular, it may be necessary to either jettison Prinz's (2002) Modal Specificity Hypothesis or to revise one’s method for individuating modal representational formats.     

Autism,episodic memory,and moral exemplars

This paper presents a challenge for exemplar theories of moral concepts. Some have proposed that we acquire moral concepts by way of exemplars of actions that are prohibited as well as of actions that are required, and we classify newly encountered actions based on their similarity to these exemplars. Judgments of (im)permissibility then follow from these exemplar-based classifications. However, if this were true, then we would expect that individuals who lacked, or were deficient in, the capacity to form or access exemplars of this kind would be similarly deficient in the ability to classify new actions according to them, and this relative inability would be manifested in the moral judgments made by such individuals. However, there is reason to suspect, I think, that a number of individuals who have been diagnosed with Autism Spectrum Disorder (ASD) actually have the deficiencies I have described here but are nevertheless fully able to make sound moral judgments. If this is so, then it must be the case that classifying actions as instances of a given moral concept and making judgments based on said classification does not rely solely on exemplars.     

Ethics and Imagination

Cognitive semantics has made important empirical findings about human conceptualization. In this paper some findings concerning moral concepts are analyzed and their implications for medical ethics discussed. The key idea is that morality has to do with metaphors and imagination rather than with well-defined concepts and deduction. It is argued that normative medical ethics to be psychologically realistic should take these findings seriously. This means that an imaginative casuistry is to be preferred compared to principlism and to other forms of casuistry. Furthermore, the metaphorical character of central principles in medical ethics such as autonomy, utility, justice, and integrity is indicated. Such principles are interpreted as rules of thumb summarizing the collective wisdom concerning prototype cases.     

The most efficient sequence of study depends on the type of test

Across three experiments featuring naturalistic concepts (psychology concepts) and naïve learners, we extend previous research showing an effect of the sequence of study on learning outcomes, by demonstrating that the sequence of examples during study changes the representation the learner creates of the study materials. We compared participants' performance in test tasks requiring different representations and evaluated which sequence yields better learning in which type of tests. We found that interleaved study, in which examples from different concepts are mixed, leads to the creation of relatively interrelated concepts that are represented by contrast to each other and based on discriminating properties. Conversely, blocked study, in which several examples of the same concept are presented together, leads to the creation of relatively isolated concepts that are represented in terms of their central and characteristic properties. These results argue for the integrated investigation of the benefits of different sequences of study as depending on the characteristics of the study and testing situation.     

Children's Understanding of the Natural Numbers’ Structure

When young children attempt to locate numbers along a number line, they show logarithmic (or other compressive) placement. For example, the distance between “5” and “10” is larger than the distance between “75” and “80.” This has often been explained by assuming that children have a logarithmically scaled mental representation of number (e.g., Berteletti, Lucangeli, Piazza, Dehaene, & Zorzi, 2010 ; Siegler & Opfer, 2003 ). However, several investigators have questioned this argument (e.g., Barth & Paladino, 2011 ; Cantlon, Cordes, Libertus, & Brannon, 2009 ; Cohen & Blanc‐Goldhammer, 2011 ). We show here that children prefer linear number lines over logarithmic lines when they do not have to deal with the meanings of individual numerals (i.e., number symbols, such as “5” or “80”). In Experiments 1 and 2, when 5‐ and 6‐year‐olds choose between number lines in a forced‐choice task, they prefer linear to logarithmic and exponential displays. However, this preference does not persist when Experiment 3 presents the same lines without reference to numbers, and children simply choose which line they like best. In Experiments 4 and 5, children position beads on a number line to indicate how the integers 1–100 are arranged. The bead placement of 4‐ and 5‐year‐olds is better fit by a linear than by a logarithmic model. We argue that previous results from the number‐line task may depend on strategies specific to the task.     

The Human Condition and the Gift: Towards a Theoretical Perspective on Close Relationships

Hannah Arendt’s exposition of the human condition provides the basic framework for a theoretical perspective on close relationships. According to Arendt, the human condition is comprised of three modes of activity: labor, work, and action. Labor is need-driven behavior, work concerns goal-directed activity and the fabrication of things, and action involves the mutual validation of unique individuals. Within this framework, the gift is the means by which relational ties are made concrete. I propose a model of gift-giving organized by two axes: whether or not the partner is singularized by the gift and whether or not the gift is given with an expectation of a return gift. I then apply this model to the three modes of the human condition.

Do children learn the integers by induction?

According to one theory about how children learn the meaning of the words for the positive integers, they first learn that "one," "two," and "three" stand for appropriately sized sets. They then conclude by inductive inference that the next numeral in the count sequence denotes the size of sets containing one more object than the size denoted by the preceding numeral. We have previously argued, however, that the conclusion of this Induction does not distinguish the standard meaning of the integers from nonstandard meanings in which, for example, "ten" could mean set sizes of 10, 20, 30,... elements. Margolis and Laurence [Margolis, E., & Laurence, S. (2008). How to learn the natural numbers: Inductive inference and the acquisition of number concepts. Cognition, 106, 924-939] believe that our argument depends on attributing to children "radically indeterminate" concepts. We show, first, that our conclusion is compatible with perfectly determinate meanings for "one" through "three." Second, although the inductive inference is indeed indeterminate - which is why it is consistent with nonstandard meanings - making it determinate presupposes the constraints that the inference is supposed to produce.     

Costs and benefits of representational change: effects of context on age and sex differences in symbolic magnitude estimation

Studies have reported high correlations in accuracy across estimation contexts, robust transfer of estimation training to novel numerical contexts, and adults drawing mistaken analogies between numerical and fractional values. We hypothesized that these disparate findings may reflect the benefits and costs of learning linear representations of numerical magnitude. Specifically, children learn that their default logarithmic representations are inappropriate for many numerical tasks, leading them to adopt more appropriate linear representations despite linear representations being inappropriate for estimating fractional magnitude. In Experiment 1, this hypothesis accurately predicted a developmental shift from logarithmic to linear estimates of numerical magnitude and a negative correlation between accuracy of numerical and fractional magnitude estimates (r = −.80). In Experiment 2, training that improved numerical estimates also led to poorer fractional magnitude estimates. Finally, both before and after training that eliminated age differences in estimation accuracy, complementary sex differences were observed across the two estimation contexts.     

Inscrutability and ontological commitment

There are two doctrines for which Quine is particularly well known: the doctrine of ontological commitment and the inscrutability thesis—the thesis that reference and quantification are inscrutable. At first glance, the two doctrines are squarely at odds. If there is no fact of the matter as to what our expressions refer to, then it would appear that no determinate commitments can be read off of our best theories. We argue here that the appearance of a clash between the two doctrines is illusory. The reason that there is no real conflict is not simply that in determining our theories’ ontological commitments we naturally rely on our home language but also (and more importantly) that ontological commitment is not intimately tied to objectual quantification and a reference-first approach to language. Or so we will argue. We conclude with a new inscrutability argument which rests on the observation that the notion of objectual quantification, when properly cashed out, deflates.