The representation of negative numbers: exploring the effects of mode of processing and notation

The representation of negative numbers was explored during intentional processing (i.e., when participants performed a numerical comparison task) and during automatic processing (i.e., when participants performed a physical comparison task). Performance in both cases suggested that negative numbers were not represented as a whole but rather their polarity and numerical magnitudes were represented separately. To explore whether this was due to the fact that polarity and magnitude are marked by two spatially separated symbols, participants were trained to mark polarity by colour. In this case there was still evidence for a separate representation of polarity and magnitude. However, when a different set of stimuli was used to refer to positive and negative numbers, and polarity was not marked separately, participants were able to represent polarity and magnitude together when numerical processing was performed intentionally but not when it was conducted automatically. These results suggest that notation is only partly responsible for the components representation of negative numbers and that the concept of negative numbers can be grasped only through that of positive numbers.     

Erratum: Decision anomalies,experimenter assumptions,and participants' comprehension: Revaluating the uncertainty effect

The above article (DOI: 10.1002/bdm.628 ) was published online on 14 November 2008 inWiley InterScience ( www.interscience.wiley.com ). An error was subsequently identified: Page 3, line 22: “certainty effect,” should read “uncertainty effect,”.     

Predicting the directionality of probability words from their membership functions

Teigen and Brun have suggested that distinct from their numerical implications, most probability phrases are either positive or negative, in that they encourage one to think of reasons why the target event will or will not occur. We report two experiments testing our hypotheses that (a) the direction of a phrase can be predicted from properties of its membership function, and (b) this relation is invariant across contexts, and (c) —originally formulated by Teigen and Brun (1999)—that strong modifiers intensify phrase directionality. For each phrase, participants encoded membership functions by judging the degree to which it described the numerical probabilities 0.0, 0.1, …, 1.0, and also completed sentences including the target phrase. The types of reasons given in the sentence completion task were used to determine the phrase's directionality. The results support our hypotheses (a) and (b) regarding the relation between directionality and the membership functions, but we found only limited support for hypothesis (c) regarding the effects of modifiers on directionality. A secondary goal, to validate an efficient method of encoding membership functions, was also achieved. Copyright © 2003 John Wiley & Sons, Ltd.     

The meaning of indifference in choice behavior: Asymmetries in adjustments embodied in matching

Measuring and assessing people’s preferences is an intricate task that can be realized by different methods. Evidently, the different methods do not necessarily yield consistent results. In the present paper we examine the matching procedure and demonstrate inconsistencies within the method itself. It is shown that the inconsistencies stem from: (1) asymmetry in upward and downward matching (i.e., matching options by increasing or lowering values do not yield the same tradeoffs) and (2) participants’ tendency to match (adjust) the options such that they become more similar, eventually facilitating the choice process. Matching is the most straightforward method of eliciting indifference. Hence, the observed inconsistencies, encapsulated in the matching procedure, have direct implications for the construction of indifference curves (equal-utility contours) that are examined in the final section.     

Negative-based prominence: the role of negative features in matching and choice

Previous research related to the prominence effect (e.g., Tversky, Sattath, & Slovic, 1988) has mainly focused on the causes and boundary conditions of the effect. This article investigates the determinants of prominence and explores a negative-based prominence effect in which the negative attribute becomes the prominent one. Using a matching-choice procedure, Experiments 1 and 2 show that the negative dimension became the prominent one under two different cover stories, suggesting that the negative feature looms larger in choice than in matching. The robustness of negative-based prominence was further demonstrated in a direct choice task without matching (Experiment 3) and was shown to be resistant to the impact of added positive features (Experiment 4). Finally, Experiments 5 and 6 distinguish between two determinants of prominence: intrinsic prominence caused by attribute importance and negative-based prominence caused by negative attribute values. By lowering the values on the positive dimension and enhancing the values on the negative dimension, one can reverse the prominence effect. The results suggest that, compared to a matching task, choice leads to enhanced sensitivity to negative features. The relations between negative characteristics of an attribute and other factors that determine prominence are discussed in the final section.     

Hemispheric visual atentional imbalance in patients with traumatic brain injury

We find a spatially asymmetric allocation of attention in patients with traumatic brain injury (TBI) despite the lack of obvious asymmetry in neurological indicators. Identification performance was measured for simple spatial patterns presented briefly to a locus 5 degrees into the left or right hemifield, after precuing attention to the same (ipsilateral) or opposite (cross-hemifield) side. Though the cue was non-predictive of target location overall, performance was significantly slower for cross than for ipsilateral trials in both patients and controls. We tested 21 TBI patients without overt focal brain damage and nine control subjects. Only patients demonstrated significantly worse performance for left side presentation in the ipsilateral condition. Furthermore, in the cross-hemifield condition, the left-right difference seen in TBI patients was significantly larger-reflecting a failure in producing a leftward attention shift. Again no significant difference was found in controls. These hemifield effects suggest an asymmetry in the ability of TBI patients in shifting attention to the left hemifield, whether from central fixation or from a cue in the contra-lateral hemifield. The results support basic hypotheses regarding visual attention: Attentional control may be asymmetric and attention may be a distributed, rather than localized cortical function.     

Segment duration as a cue to word boundaries in spoken-word recognition

In two eye-tracking experiments, we examined the degree to which listeners use acoustic cues to word boundaries. Dutch participants listened to ambiguous sentences in which stop-initial words (e.g., pot, jar) were preceded by eens (once); the sentences could thus also refer to cluster-initial words (e.g., een spot, a spotlight). The participants made fewer fixations to target pictures (e.g., ajar) when the target and the preceding [s] were replaced by a recording of the cluster-initial word than when they were spliced from another token of the target-bearing sentence (Experiment 1). Although acoustic analyses revealed several differences between the two recordings, only [s] duration correlated with the participants' fixations (more target fixations for shorter [s]s). Thus, we found that listeners apparently do not use all available acoustic differences equally. In Experiment 2, the participants made more fixations to target pictures when the [s] was shortened than when it was lengthened. Utterance interpretation can therefore be influenced by individual segment duration alone.     

(Re)encountering Individuality: Schlegel's Romantic Imperative as a Response to Nihilism

According to Friedrich Schlegel: “The Romantic imperative demands [that] all nature and science should become art [and] art should become nature and science”; “[P]oetry and philosophy should be made unified”, and “life and society [should be made] poetic”. The aim of this paper is to explain why Schlegel believes that this is an imperative that constrains philosophy and ordinary life. I argue that the answer to this question requires that we regard the Romantic imperative as a response to the skeptical worry that was introduced by Friedrich Heinrich Jacobi as nihilism. The aspect of nihilism that I discuss concerns the worry that we are incapable of experiencing individuals qua individuals. According to Schlegel, this skeptical threat requires a reorientation in thought and philosophical method, one that must be modeled on the aesthetic orientation towards the world. More precisely, the experience of individuals qua individuals, which is called into question by the nihilist, depends on the special normative structure of the creative and critical attitude towards art and beauty that Schlegel called Romantic Poesie. Kant failed to address nihilism because he failed to recognize that the normative structure that he himself ascribed to the judgment of taste is required also for experiencing individuals as individuals, and for being properly responsive to persons.