What can the Philosophy of Mathematics Learn from the History of Mathematics?

This article canvasses five senses in which one might introduce an historical element into the philosophy of mathematics: 1. The temporal dimension of logic; 2. Explanatory Appeal to Context rather than to General Principles; 3. Heraclitean Flux; 4. All history is the History of Thought; and 5. History is Non-Judgmental. It concludes by adapting Bernard Williams’ distinction between ‘history of philosophy’ and ‘history of ideas’ to argue that the philosophy of mathematics is unavoidably historical, but need not and must not merge with historiography.

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The Spiritual,the Cultural and the Religious: What can we learn from a study of boy choristers?

This article reports on a study of the boys in a major city centre church choir. It is treated as a case study of the potential confusion between the spiritual, the cultural and the religious. The study shows that the performance of religious rituals might, for many of the boys, be more accurately described as a cultural phenomenon. A deep appreciation of music, with evidence of 'peak experiences', describes a reality which has been called 'spiritual' in humanistic phenomenological writings. All the boys in the study were found to be 'spiritual' in that they loved and were moved by the music they sang in church, but few perceived their singing as a form of religious ministry. Religious commitment and faith development was found to range from piety to atheism, with an increasing tendency towards Enlightenment scepticism amongst the older boys. The boys could be identified as a social group by their shared love for music, but not by a shared religious faith. Discussion is developed about the reality of the spiritual with and without a religious commitment, in which credal literalism is seen as cultural rather than spiritual. A call for greater recognition of the significance of the cultural and social is made.     

The surface structure and the deep structure of sequential control: What can we learn from task span switch costs?

A large component of response time switch costs in the cued task-switching paradigm is linked to cue changes without task changes, suggesting costs might reflect passive priming rather than endogenous control. In contrast, the task span procedure requires subjects to guide task selection via sequences of memorized task cues and therefore may be better suited to reflect endogenous switch processes (Logan, 2004). The present experiments combined the task span procedure with a 2:1 mapping between cues and tasks, allowing separation of cue-switch costs from true task-switch costs. Replicating findings with the cued task-switching paradigm, results showed both substantial cue-switch costs and actual task-switch costs (Experiments 1 and 2) as well as sensitivity of cue-switch costs, but not of task-switch costs, to opportunity for preparation (Experiment 2). Apparently, simple action plans use “surface level” phonological or articulatory codes that contain no task information. These results suggest that the distinction between cue-related and task-related processes is critical no matter whether tasks are cued exogenously or endogenously.     

The Rorschach and traumatic loss: can the presence of traumatic loss be detected from the Rorschach?

Loss, an expected part of everyone's life, can be a catalyst promoting significant growth. But all losses are not the same or affect everyone in like manner. Some losses are of such magnitude and intensity that individuals cannot cope, and, therefore, they keep reliving them (posttraumatic stress syndrome) as if through repeated attempts (Freud, 1923-1922/1961) they might master what had been initially so overwhelming. This study, using an inpatient hospital sample, examines the Rorschach protocols of individuals who had experienced traumatic loss in childhood or early adolescence and compares them with a control group of individuals who appear to have no such history. Our hypotheses that victims of early trauma have a distinguishing Rorschach profile was validated in the exploratory study. Further study is needed to clarify whether factors other than traumatic loss may be contributing to this profile.     

The professionalism movement: can we pause?

The topic of developing professionalism dominated the content of many academic medicine publications and conference agendas during the past decade. Calls to address the development of professionalism among medical students and residents have come from professional societies, accrediting agencies, and a host of educators in the biomedical sciences. The language of the professionalism movement is now a given among those in academic medicine. We raise serious concerns about the professionalism discourse and how the specialized language of academic medicine disciplines has defined, organized, contained, and made seemingly immutable a group of attitudes, values, and behaviors subsumed under the label of "professionalism." In particular, we argue that the professionalism discourse needs to pay more attention to the academic environment in which students are educated, that it should articulate specific positive behaviors, that the theory of professionalism must be constructed from a dialogue with those we are educating, and that this theoretical and practical discourse must aim at a deeper understanding of social justice and the role of medicine within a just society.     

Information pick-up by infants: what is it, and how can we tell?

Young infants spend the better portion of their 1st year merely looking around, and what they notice can have critical cognitive consequences. Although looking measures are commonly used to predict what information infants pick up about objects and/or their relationship to other objects, these predictions are often ambiguous. Ultimately, that knowledge can be unambiguously revealed only by giving infants an opportunity to directly act on or use it.     

How virtuous is humor? What we can learn from current instruments

Despite the diverse philosophical accounts of the relation of humor to virtue or vice, this ethical dimension has not been included explicitly in psychological humor instruments. Yet, behavior described in humor questionnaires covering a broad variety of components can be used to study an implicit relation of humor to vices and virtues. The main aim of the present paper was (1) to find humorous behavior and attitudes representing virtues and vices within an item pool of 12 popular humor questionnaires; and (2) to investigate the nature of the virtues represented by their item contents. A comprehensive measure of humor covered the entire range from virtue to vice, with the majority of items evaluated as neutral. Humanity and wisdom were most strongly represented, but the items cover all six core virtues (Dahlsgaard, 2004 Dahlsgaard, K. 2004. “Universal virtues?—Lessons from history”. In Character strengths and virtues, Edited by: Peterson, C and Seligman, MEP. 33–52. New York: Oxford University Press.  [Google Scholar]) to varying degrees. Further research can now investigate the relationship of humor and individual virtues more closely.     

Reclamation from Absence? Luce Irigaray and Women in the History of Philosophy

Luce Irigaray's work does not present an obvious resource for projects seeking to reclaim women in the history of philosophy. Indeed, many authors introduce their reclamation project with an argument against conceptions, attributed to Irigaray or “French feminists” more generally, that the feminine is the excluded other of discourse. These authors claim that if the feminine is the excluded other of discourse, then we must conclude that even if women have written philosophy they have not given voice to feminine subjectivity; therefore, reclamation is a futile project. In this essay, I argue against such conclusions. Rather, I argue, Irigaray's work requires that philosophy be transformed through the reclamation of women's writing. She gives us a method of reclamation for the most difficult cases: those in which we have no record of women's writing. Irigaray offers this method through an engagement with the character of Diotima in Plato's Symposium. The method Irigaray demonstrates is reclamation as love.     

The role of attention in the affordance effect: can we afford to ignore it?

It has been established that the task-irrelevant orientation of an object's graspable handle produces a stimulus-response compatibility effect, resulting in faster reaction times when the location of the response corresponds to that of the object's handle. There is ongoing debate whether to attribute this affordance effect to motoric or to attentional components. In an attempt to reconcile these two viewpoints, we employed a novel experimental approach for investigating the relationship between attention and affordance. Using 3-D positional sound, auditory spatial attention was manipulated in order to explore its effects on affordance. Subjects were presented images of everyday graspable objects and had to respond bimanually (left or right) whether the object (featuring a leftward or rightward handle) was presented upright or upside-down. Prior to each affording object, sound localization cues were manipulated so as to orient auditory attention to the left, or to the right of the interaural axis (control). We obtained a peculiar pattern of results, which not only appears to provide support for an attention-shift account of affordance but does so in a cross-modal context.     

Creativity from Constraints: What can we learn from Motherwell? from Modrian? from Klee?

This article presents a problem‐solving model of variability and creativity built on the classic Reitman and Simon analyses of musical composition and architectural design. The model focuses on paired constraints: one precluding (or limiting search among) reliable, existing solutions, the other promoting (or directing search to) novel, often opposite, ones. The primary constraint pair precludes an existing goal criterion and promotes a novel one. Other constraints — source (elements for recombination), task (how materials are used) and subject (motif, theme) — are then strategically selected to realize the goal. A brief discussion of Abstract Expressionism introduces the model, which is then applied to the painting careers of Piet Modrian and Paul Klee.     

The ball vanishes in the air: can we blame representational momentum?

In the vanishing ball illusion (VBI), the magician throws a ball up into the air twice and then pretends to do a third throw. On the third (fake) throw, the audience sees the ball go up and then disappear. In this article, we study the psychological mechanisms at play in this magic trick. We test the hypothesis that the illusion is based on representational momentum (RM), a psychological phenomenon in which the observer perceives the stopping point of a moving scene as being located farther ahead in the direction of motion than it really is. To determine whether the mechanisms involved in VBI are similar to those underlying RM, we compared the results of a standard VBI task to those obtained on an RM task designed to be very close to the VBI task. The results showed that VBI sensitivity was not associated with a higher anticipation score on the RM task. Unexpectedly, we found that participants who were sensitive to the illusion even obtained a weaker RM effect. We discuss several hypotheses that might account for these results.     

When can we trust theF-approximation of the box-test?

Consider a multivariate context withp variates andk independent samples, each of sizen. To test equality of thek population covariance matrices, the likelihood ratio test is commonly employed. Box'sF-approximation to the null distribution of the test statistic can be used to computep-values, if sample sizes are not too small. It is suggested to regard theF-approximation as accurate if the sample sizesn are greater than or equal to 1+0.0613p ²+2.7265p-1.4182p ^0.5+0.235p ^1.4* In (k), for 5p30,k20.This research was supported by the Deutsche Forschungsgemeinschaft through Ste 405/2-1.     

What can we learn about physical laws from the fact that we have memories only of the past?

Not much. I demonstrate this by constructing a model of a memory system governed by deterministic, time reversible laws only, thereby showing that the mere fact of our having memories solely of the past does not necessitate an indeterministic, time asymmetric or stochastic physics, essentially thermodynamic processes or a primitive notion of time asymmetric causation.     

How can we detect when language emerged?

Views differ radically as to how deep the roots of language lie in human phylogeny, largely because prior to the development of writing systems, this striking human attribute has to be inferred from indirect proxies preserved in the material record. Here I argue that the most appropriate such archaeological proxies encode the modern human symbolic cognitive system from which language emerges. Throughout the 2.5 million years or more for which an archaeological record has existed, change has been both sporadic and rare—until symbolic objects and behaviors begin to appear, well within the tenure of our highly apomorphic species Homo sapiens. I propose that the biology underwriting our unusual cognitive and linguistic systems was acquired in the major developmental reorganization that gave rise to our anatomically distinctive species around 200,000 years ago in Africa. However, the material record indicates that this new potential lay fallow for around 100,000 years, following which it was released by what was necessarily a behavioral stimulus. By far the best candidate for that stimulus is the spontaneous invention of language, which is plausibly underwritten by a relatively simple mental algorithm, and could readily have spurred symbolic cognitive processes in a feedback process. None of this means that earlier hominid vocal communication systems were not complex, or that extinct hominid species were not highly intelligent. But it does emphasize the qualitative distinctiveness of both modern symbolic cognition and language.     

Neuropsychological identification of motor problems: Can we learn something from the feet and legs that hands and arms will not tell us?

The degree of structural and functional specialization that differentiates between upper and lower limb use in humans is quite unparalleled among primates. It is argued that less neural resources are devoted to leg and foot control than to arm and hand control, and that this aspect of lower limb innervation, together with the uniquely restricted use of the lower limb, renders lower limb function more sensitive to general neural insult. In addition, the status of leg and foot control differs from that of arm and hand control both early in life and during the later years of decline.