The influence of Platonism on mathematics research and theological beliefs

An age-old debate in the philosophy of mathematics is whether mathematics is discovered or invented. There are four popular viewpoints in this debate, namely Platonism, formalism, intuitionism, and logicism. A natural question that arises is whether belief in one of these viewpoints affects the mathematician’s research? In particular, does subscribing to a Platonist or a formalist viewpoint influence how a mathematician conducts research? Does the area of research influence a mathematician’s beliefs on the nature of mathematics? How are the beliefs regarding the nature of mathematics connected to theological beliefs? In order to investigate these questions, five professional research mathematicians were interviewed. The mathematicians worked in diverse areas within analysis, algebra, and within applied mathematics, and had a combined 160 years of research experience. Although none of the mathematicians wanted to be pigeonholed into any one category of beliefs, the study revealed that four of the mathematicians leaned towards Platonism, which runs contrary to the popular notion that Platonism is an exception today. This study revealed that beliefs regarding the nature of mathematics influenced how mathematicians’ conducted research and were deeply connected to their theological beliefs. The findings are presented in the form of vignettes that give an insight into the mathematical and theological belief structures of the mathematicians.     

Audiovisual sentence recognition not predicted by susceptibility to the McGurk effect

In noisy situations, visual information plays a critical role in the success of speech communication: listeners are better able to understand speech when they can see the speaker. Visual influence on auditory speech perception is also observed in the McGurk effect, in which discrepant visual information alters listeners’ auditory perception of a spoken syllable. When hearing /ba/ while seeing a person saying /ga/, for example, listeners may report hearing /da/. Because these two phenomena have been assumed to arise from a common integration mechanism, the McGurk effect has often been used as a measure of audiovisual integration in speech perception. In this study, we test whether this assumed relationship exists within individual listeners. We measured participants’ susceptibility to the McGurk illusion as well as their ability to identify sentences in noise across a range of signal-to-noise ratios in audio-only and audiovisual modalities. Our results do not show a relationship between listeners’ McGurk susceptibility and their ability to use visual cues to understand spoken sentences in noise, suggesting that McGurk susceptibility may not be a valid measure of audiovisual integration in everyday speech processing.     

Consciousness and Science: an Advaita-Vedantic Perspective on the Theology – Science Dialogue

In modern science, the synthesis of “nature/mind” in observation, experiment, and explanation, especially in physics and biology increasingly reveal a “non-linear” totality in which subject, object, and situation have become inseparable. This raises the interesting ontological question of the true nature of reality. Western science as seen in its evolution from Socratic Greece has tried to understand the world by “objectifying” it, resulting in dualistic dilemmas. Indian “Science,” as seen in its evolution from the Vedic times (1500—500 BCE) has tried to understand the world by “subjectifying” our consciousness of reality. Within the Hindu tradition, the Advaita-Vedanta school of philosophy offers possibilities for resolving not only the Cartesian dilemma but also a solution to the nature of difference in a non-dualistic totality. We also present the Advaita-Vedanta principle of superimposition as a useful approach to modern physical and social science, which have been increasingly forced to reject the absolute reductionism and dualism of classical differences between subject and object.     

After justification: Toward a Dalit public Lutheran theology

The aim of this article is to construct a “Dalit public Lutheran theology” as an “after‐justification” conversation, which drafts an agenda for the future of Lutheran theology in the twenty‐first century. In moving toward that construction, I first briefly explain Dalit theology, public theology, and Lutheran theology and shall discuss the rationale for a Dalit public Lutheran theology. From there I propose that Lutheran theology needs to take a contextual, post‐colonial and subaltern turn. Then I discuss the contours of Dalit public Lutheran theology by discussing one of the pivotal doctrine of Luther, “justification by grace through faith,” by engaging in a Dalit public discourse and propose “hospitality by love” as what comes after justification. Finally, I bring out the relevance of such a theology for our present‐day context. The method I employ in this article is subaltern methodology, which is to “read from below” or “read against the grain.” “After justification” is understood as “beyond” the understanding of doctrine of justification, as a forward‐looking public theological understanding of justification, where it finds fecundity and validity.     

Relative influence of musical and linguistic experience on early cortical processing of pitch contours

To assess domain specificity of experience-dependent pitch representation we evaluated the mismatch negativity (MMN) and discrimination judgments of English musicians, English nonmusicians, and native Chinese for pitch contours presented in a nonspeech context using a passive oddball paradigm. Stimuli consisted of homologues of Mandarin high rising (T2) and high level (T1) tones, and a linear rising ramp (T2L). One condition involved a between-category contrast (T1/T2), the other, a within-category contrast (T2L/T2). Irrespective of condition, musicians and Chinese showed larger MMN responses than nonmusicians; Chinese larger than musicians. Chinese, however, were less accurate than nonnatives in overt discrimination of T2L and T2. Taken together, these findings suggest that experience-dependent effects to pitch contours are domain-general and not driven by linguistic categories. Yet specific differences in long-term experience in pitch processing between domains (music vs. language) may lead to gradations in cortical plasticity to pitch contours.     

Dual-learning systems during speech category learning

Dual-system models of visual category learning posit the existence of an explicit, hypothesis-testing reflective system, as well as an implicit, procedural-based reflexive system. The reflective and reflexive learning systems are competitive and neurally dissociable. Relatively little is known about the role of these domain-general learning systems in speech category learning. Given the multidimensional, redundant, and variable nature of acoustic cues in speech categories, our working hypothesis is that speech categories are learned reflexively. To this end, we examined the relative contribution of these learning systems to speech learning in adults. Native English speakers learned to categorize Mandarin tone categories over 480 trials. The training protocol involved trial-by-trial feedback and multiple talkers. Experiments 1 and 2 examined the effect of manipulating the timing (immediate vs. delayed) and information content (full vs. minimal) of feedback. Dual-system models of visual category learning predict that delayed feedback and providing rich, informational feedback enhance reflective learning, while immediate and minimally informative feedback enhance reflexive learning. Across the two experiments, our results show that feedback manipulations that targeted reflexive learning enhanced category learning success. In Experiment 3, we examined the role of trial-to-trial talker information (mixed vs. blocked presentation) on speech category learning success. We hypothesized that the mixed condition would enhance reflexive learning by not allowing an association between talker-related acoustic cues and speech categories. Our results show that the mixed talker condition led to relatively greater accuracies. Our experiments demonstrate that speech categories are optimally learned by training methods that target the reflexive learning system.