A Theological Challenge: Coordinating Biological, Social, and Religious Visions of Humanity

This paper attempts two tasks. First, it sketches how the natural sciences (including especially the biological sciences), the social sciences, and the scientific study of religion can be understood to furnish complementary, consonant perspectives on human beings and human groups. This suggests that it is possible to speak of a modern secular interpretation of humanity (MSIH) to which these perspectives contribute (though not without tensions). MSIH is not a comprehensive interpretation of human beings, if only because it adopts a posture of neutrality with regard to the reality of religious objects and the truth of theological claims about them. MSIH is certainly an impressively forceful interpretation, however, and it needs to be reckoned with by any perspective on human life that seeks to insert its truth claims into the arena of public debate. Second, the paper considers two challenges that MSIH poses to specifically theological interpretations of human beings. On the one hand, in spite of its posture of religious neutrality, MSIH is a key element in a class of wider, seemingly antireligious interpretations of humanity, including especially projectionist and illusionist critiques of religion. It is consonance with MSIH that makes these critiques such formidable competitors for traditional theological interpretations of human beings. On the other hand, and taking the religiously neutral posture of MSIH at face value, theological accounts of humanity that seek to coordinate the insights of MSIH with positive religious visions of human life must find ways to overcome or manage such dissonance as arises. The goal of synthesis is defended as important, and strategies for managing these challenges, especially in light of the pluralism of extant philosophical and theological interpretations of human beings, are advocated.

Typability is Undecidable for F+Eta

System F is the well-known polymorphically-typed λ-calculus with universal quantifiers ("∀"). F+η is System F extended with the eta rule, which says that if term M can be given type τ and M η-reduces to N, then N can also be given the type τ. Adding the eta rule to System F is equivalent to adding the subsumption rule using the subtyping ("containment") relation that Mitchell defined and axiomatized [Mit88]. The subsumption rule says that if M can be given type τ and τ is a subtype of type σ, then M can be given type σ. Mitchell's subtyping relation involves no extensions to the syntax of types, i.e., no bounded polymorphism and no supertype of all types, and is thus unrelated to the system F≤("F-sub"). Typability for F+η is the problem of determining for any term M whether there is any type τ that can be given to it using the type inference rules of F+η. Typability has been proven undecidable for System F [Wel94] (without the eta rule), but the decidability of typability has been an open problem for F+η. Mitchell's subtyping relation has recently been proven undecidable [TU95, Wel95b], implying the undecidability of "type checking" for F+η. This paper reduces the problem of subtyping to the problem of typability for F+η, thus proving the undecidability of typability. The proof methods are similar in outline to those used to prove the undecidability of typability for System F, but the fine details differ greatly.

Task-Irrelevant Perceptual Learning Specific to the Contrast Polarity of Motion Stimuli

Studies of perceptual learning have focused on aspects of learning that are related to early stages of sensory processing. However, conclusions that perceptual learning results in low-level sensory plasticity are of great controversy, largely because such learning can often be attributed to plasticity in later stages of sensory processing or in the decision processes. To address this controversy, we developed a novel random dot motion (RDM) stimulus to target motion cells selective to contrast polarity, by ensuring the motion direction information arises only from signal dot onsets and not their offsets, and used these stimuli in conjunction with the paradigm of task-irrelevant perceptual learning (TIPL). In TIPL, learning is achieved in response to a stimulus by subliminally pairing that stimulus with the targets of an unrelated training task. In this manner, we are able to probe learning for an aspect of motion processing thought to be a function of directional V1 simple cells with a learning procedure that dissociates the learned stimulus from the decision processes relevant to the training task. Our results show learning for the exposed contrast polarity and that this learning does not transfer to the unexposed contrast polarity. These results suggest that TIPL for motion stimuli may occur at the stage of directional V1 simple cells.

Towards a Unified Theory of Neocortex: Laminar Cortical Circuits for Vision and Cognition

A key goal of computational neuroscience is to link brain mechanisms to behavioral functions. The present article describes recent progress towards explaining how laminar neocortical circuits give rise to biological intelligence. These circuits embody two new and revolutionary computational paradigms: Complementary Computing and Laminar Computing. Circuit properties include a novel synthesis of feedforward and feedback processing, of digital and analog processing, and of pre-attentive and attentive processing. This synthesis clarifies the appeal of Bayesian approaches but has a far greater predictive range that naturally extends to self-organizing processes. Examples from vision and cognition are summarized. A LAMINART architecture unifies properties of visual development, learning, perceptual grouping, attention, and 3D vision. A key modeling theme is that the mechanisms which enable development and learning to occur in a stable way imply properties of adult behavior. It is noted how higher-order attentional constraints can influence multiple cortical regions, and how spatial and object attention work together to learn view-invariant object categories. In particular, a form-fitting spatial attentional shroud can allow an emerging view-invariant object category to remain active while multiple view categories are associated with it during sequences of saccadic eye movements. Finally, the chapter summarizes recent work on the LIST PARSE model of cognitive information processing by the laminar circuits of prefrontal cortex. LIST PARSE models the short-term storage of event sequences in working memory, their unitization through learning into sequence, or list, chunks, and their read-out in planned sequential performance that is under volitional control. LIST PARSE provides a laminar embodiment of Item and Order working memories, also called Competitive Queuing models, that have been supported by both psychophysical and neurobiological data. These examples show how variations of a common laminar cortical design can embody properties of visual and cognitive intelligence that seem, at least on the surface, to be mechanistically unrelated.

A Unified Model of Spatiotemporal Processing in the Retina

A computational model of visual processing in the vertebrate retina provides a unified explanation of a range of data previously treated by disparate models. Three results are reported here: the model proposes a functional explanation for the primary feed-forward retinal circuit found in vertebrate retinae, it shows how this retinal circuit combines nonlinear adaptation with the desirable properties of linear processing, and it accounts for the origin of parallel transient (nonlinear) and sustained (linear) visual processing streams as simple variants of the same retinal circuit. The retina, owing to its accessibility and to its fundamental role in the initial transduction of light into neural signals, is among the most extensively studied neural structures in the nervous system. Since the pioneering anatomical work by Ramón y Cajal at the turn of the last century[1], technological advances have abetted detailed descriptions of the physiological, pharmacological, and functional properties of many types of retinal cells. However, the relationship between structure and function in the retina is still poorly understood. This article outlines a computational model developed to address fundamental constraints of biological visual systems. Neurons that process nonnegative input signals-such as retinal illuminance-are subject to an inescapable tradeoff between accurate processing in the spatial and temporal domains. Accurate processing in both domains can be achieved with a model that combines nonlinear mechanisms for temporal and spatial adaptation within three layers of feed-forward processing. The resulting architecture is structurally similar to the feed-forward retinal circuit connecting photoreceptors to retinal ganglion cells through bipolar cells. This similarity suggests that the three-layer structure observed in all vertebrate retinae[2] is a required minimal anatomy for accurate spatiotemporal visual processing. This hypothesis is supported through computer simulations showing that the model's output layer accounts for many properties of retinal ganglion cells[3],[4],[5],[6]. Moreover, the model shows how the retina can extend its dynamic range through nonlinear adaptation while exhibiting seemingly linear behavior in response to a variety of spatiotemporal input stimuli. This property is the basis for the prediction that the same retinal circuit can account for both sustained (X) and transient (Y) cat ganglion cells[7] by simple morphological changes. The ability to generate distinct functional behaviors by simple changes in cell morphology suggests that different functional pathways originating in the retina may have evolved from a unified anatomy designed to cope with the constraints of low-level biological vision.