Working memory and number line representations in single-digit addition: Approximate versus exact,nonsymbolic versus symbolic

How do kindergarteners solve different single-digit addition problem formats? We administered problems that differed solely on the basis of two dimensions: response type (approximate or exact), and stimulus type (nonsymbolic, i.e., dots, or symbolic, i.e., Arabic numbers). We examined how performance differs across these dimensions, and which cognitive mechanism (mental model, transcoding, or phonological storage) underlies performance in each problem format with respect to working memory (WM) resources and mental number line representations. As expected, nonsymbolic problem formats were easier than symbolic ones. The visuospatial sketchpad was the primary predictor of nonsymbolic addition. Symbolic problem formats were harder because they either required the storage and manipulation of quantitative symbols phonologically or taxed more WM resources than their nonsymbolic counterparts. In symbolic addition, WM and mental number line results showed that when an approximate response was needed, children transcoded the information to the nonsymbolic code. When an exact response was needed, however, they phonologically stored numerical information in the symbolic code. Lastly, we found that more accurate symbolic mental number line representations were related to better performance in exact addition problem formats, not the approximate ones. This study extends our understanding of the cognitive processes underlying children's simple addition skills.     

Running in Circles about Begging the Question

In a published exchange, Richard Robinson and Roy A. Sorenson debate the matter of whether begging the question is a fallacy; Robinson thinks it is not, but Sorenson argues that it is. Norman Ten attempts to resolve this debate by making a distinction between begging the question and fallaciously begging the question. While Teng is right to note that Robinson and Sorenson are talking past each other, he incorrectly diagnoses the source of this miscommunication. In this paper, then, I offer what I take to be a more illuminating distinction 3; viz. that between logical and rhetorical fallacies 3; and employ that distinction to resolve the debate.     

Comprehending Noun Phrase Arguments and Adjuncts

Two experiments investigated how readers comprehend noun phrase (NP) arguments and adjuncts. Previous research suggested that argument phrases are processed more quickly than adjunct phrases (Clifton, Speer, & Abney, 1991; Kennison, 1999; Schütze & Gibson, 1999; Speer & Clifton, 1998). The present experiments investigated whether the type of verb in the sentence context could influence how NP arguments and adjuncts were processed. Reading time was measured on sentences containing NP arguments and adjuncts preceded either by verbs occurring most frequently with NP arguments (biased transitive verbs) or by verbs occurring most frequently without NP arguments (biased intransitive verbs) (e.g., Meredith read/performed every play/week.). In Experiment 1, reading time was measured using a self-paced phrase-by-phrase moving window. In Experiment 2, reading time was measured using eye tracking. The results of both experiments indicated that, following biased transitive verbs, NP arguments were processed more quickly than NP adjuncts. When NPs followed biased intransitive verbs, there was no significant difference between the processing time of NP arguments and adjuncts.     

Evaluating the Meta-Slope: Is there a Slippery Slope Argument against Slippery Slope Arguments?

Slippery slope arguments (SSAs) have often been viewed as inherently weak arguments, to be classified together with traditional fallacies of reasoning and argumentation such as circular arguments and arguments from ignorance. Over the last two decades several philosophers have taken a kinder view, often providing historical examples of the kind of gradual change on which slippery slope arguments rely. Against this background, Enoch (2001, Oxford Journal of Legal Studies 21(4), 629–647) presented a novel argument against SSA use that itself invokes a slippery slope. Specifically, he argued that the very reasons that can make SSAs strong arguments mean that we should be poor at abiding by the distinction between good and bad SSAs, making SSAs inherently undesirable. We argue that Enoch’s meta-level SSA fails on both conceptual and empirical grounds.     

Productivity of Noun Slots in Verb Frames

Productivity is a central concept in the study of language and language acquisition. As a test case for exploring the notion of productivity, we focus on the noun slots of verb frames, such as __want__, __see__, and __get__. We develop a novel combination of measures designed to assess both the flexibility and creativity of use in these slots. We do so using a rigorously controlled sample of child speech and child directed speech from three English‐speaking children between the ages of 2–3 years and their caregivers. We find different levels of creativity and flexibility between the adult and child samples for some measures, for some slots, and for some developmental periods. We discuss these differences in the context of verb frame semantics, conventionality versus creativity and child errors, and draw some tentative conclusions regarding developmental changes in children's early grammatical representations.     

Against Perceptual Conceptualism

This paper is concerned with the question of whether mature human experience is thoroughly conceptual, or whether it involves non-conceptual elements or layers. It has two central goals. The first goal is methodological. It aims to establish that that question is, to a large extent, an empirical question. The question cannot be answered by appealing to purely a priori and transcendental considerations. The second goal is to argue, inter alia by relying on empirical findings, that the view known as ‘state-conceptualism’ is false. We will argue that our experiences do involve non-conceptual elements. That is, a subject may enjoy an experience with a particular phenomenal aspect, without possessing the concept needed for the specification of the content of that aspect, and moreover, without being able to acquire that concept upon having that experience.     

Ontological Soufflé

Possibilities are so much easier to swallow. So transform those left‐over cosmological arguments into scrumptious new ontological arguments.     

Two types of debunking arguments

Debunking arguments are arguments that seek to undermine a belief or doctrine by exposing its causal origins. Two prominent proponents of such arguments are the utilitarians Joshua Greene and Peter Singer. They draw on evidence from moral psychology, neuroscience, and evolutionary theory in an effort to show that there is something wrong with how deontological judgments are typically formed and with where our deontological intuitions come from. They offer debunking explanations of our emotion-driven deontological intuitions and dismiss complex deontological theories as products of confabulatory post hoc rationalization. Through my discussion of Greene and Singer’s empirically informed debunking of deontology, I introduce the distinction between two different types of debunking arguments. The first type of debunking argument operates through regular undercutting defeat, whereas the second type relies on higher-order evidence. I argue that the latter type of debunking argument, of which the argument from confabulation is an example, is objectionably sloppy and therefore inadmissible in academic discussion.     

A Stronger Doctrine of Double Effect

Many believe that intended harms are more difficult to justify than are harms that result as a foreseen side effect of one's conduct. We describe cases of harming in which the harm is not intended, yet the harmful act nevertheless runs afoul of the intuitive moral constraint that governs intended harms. We note that these cases provide new and improved counterexamples to the so-called Simple View, according to which intentionally phi-ing requires intending to phi. We then give a new theory of the moral relevance of intention. This theory yields the traditional constraint on intending harm as a special case, along with several stronger demands.