Notes on Kant's derivation of the various formulae of the categorical imperative

Abstract

This article is concerned with examining Kant's derivation of the various formulae of his Categorical Imperative. It is in agreement with Paton in maintaining that Kant actually mentions five formulae. But it is not in agreement with him, and some others, in maintaining that they are ultimately reducible to three. Nor is it in agreement with those who maintain that they are ultimately reducible to just one. According to the present article, they are ultimately reducible to two: that about a moral law being a universal law; and that about a moral law involving treating human beings as ends in themselves.     

Extrafoveal Processing in Categorical Search for Geometric Shapes: General Tendencies and Individual Variations

The paper addresses the capabilities and limitations of extrafoveal processing during a categorical visual search. Previous research has established that a target could be identified from the very first or without any saccade, suggesting that extrafoveal perception is necessarily involved. However, the limits in complexity defining the processed information are still not clear. We performed four experiments with a gradual increase of stimuli complexity to determine the role of extrafoveal processing in searching for the categorically defined geometric shape. The series of experiments demonstrated a significant role of extrafoveal processing while searching for simple two-dimensional shapes and its gradual decrease in a condition with more complicated three-dimensional shapes. The factors of objects’ spatial orientation and distractor homogeneity significantly influenced both reaction time and the number of saccades required to identify a categorically defined target. An analysis of the individual p-value distributions revealed pronounced individual differences in using extrafoveal analysis and allowed examination of the performance of each particular participant. The condition with the forced prohibition of eye movements enabled us to investigate the efficacy of covert attention in the condition with complicated shapes. Our results indicate that both foveal and extrafoveal processing are simultaneously involved during a categorical search, and the specificity of their interaction is determined by the spatial orientation of objects, type of distractors, the prohibition to use overt attention, and individual characteristics of the participants.     

The nature of learned categorical perception effects: a psychophysical approach

Categorical perception is often cited as a striking example of cognitive influences on perception. However, some evidence suggests the term is a misnomer, with effects based on cognitive not perceptual processing. Here, using a psychophysical approach, we provide evidence consistent with a learned categorical perception effect that is dependent on analysis within the visual processing stream. An improvement in participants' discrimination between grating patterns that they had learned to place in different categories was 'tuned' around the orientation of the patterns experienced during category learning. Thus, here, categorical perception may result from attentionally modulated perceptual learning about diagnostic category features, based upon orientation-selective stages of analysis. This argues strongly that category learning can alter our perception of the world.     

The development of categorical and coordinate spatial relations

Two classes of spatial relations can be distinguished in between and within object representations. Kosslyn [Kosslyn, S. M. (1987). Seeing and imagining in the cerebral hemispheres: A computational approach. Psychological Review, 94, 148–175] suggested that the right hemisphere (RH) is specialized for processing coordinate (metric) spatial information and the left hemisphere (LH) processes categorical (abstract) information more effectively. The present study examined the developmental pattern of spatial relation processing in 6–8-year old, 10–12-year old and adults. Using signal detection analyses we calculated sensitivity and bias scores for all age groups. The results indicated that older children and adults showed a greater response bias than younger children. Also, discrimination sensitivity for spatial relation changes clearly improved with age. For the oldest children (10–12-year old) and adults this improvement was accompanied by a RH specialization. In contrast with Kosslyn's claim, this RH advantage also applied to the processing of categorical spatial information. The results are discussed in terms of a right hemispheric specialization for spatial relation processing which matures with age.     

A left cerebral hemisphere’s superiority in processing spatial-categorical information in a non-verbal semantic format

It has been shown that the left and right cerebral hemispheres (LH and RH) respectively process qualitative or “categorical” spatial relations and metric or “coordinate” spatial relations. However, categorical spatial information could be thought as divided into two types: semantically-coded and visuospatially-coded categorical information. We examined whether a LH’s advantage in processing semantic-categorical information is observed in a non-verbal format, and also whether semantic- and visuospatial-categorical processing are differentially lateralized. We manipulated the colors and positions of the standard traffic light sign as semantic- and visuospatial-categorical information respectively, and tested performance with the divided visual field method. In the semantic-categorical matching task, in which the participants judged if the semantic-categorical information of a successive cue and target was the same, a right visual field advantage was observed, suggesting a LH’s preference for processing semantic-categorical information in a non-verbal format. In the visuospatial-categorical matching task, in which the participants judged if the visuospatial-categorical information of a successive cue and target was identical, a left visual field advantage was obtained. These results suggest that the processing of semantic-categorical information is lateralized in LH, and we discuss the dissociation between the two types of categorical information.     

A model of type theory in simplicial sets: A brief introduction to Voevodsky's homotopy type theory

We describe how to interpret constructive type theory in the topos of simplicial sets where types appear as Kan complexes and families of types as Kan fibrations. Since Kan complexes may be understood as weak higher-dimensional groupoids this model generalizes and extends the (ordinary) groupoid model which was introduced by M. Hofmann and the author about 20 years ago. Finally, we discuss Voevodsky's Univalence Axiom which has been shown to hold in this model. This axiom roughly states that isomorphic types are equal. The type theoretic notion of isomorphism provided by this model coincides with homotopy equivalence of Kan complexes. For this reason it has become common to refer to it as Homotopy Type Theory.     

Perceiving expressions of emotion: What evidence could bear on questions about perceptual experience of mental states?

What evidence could bear on questions about whether humans ever perceptually experience any of another’s mental states, and how might those questions be made precise enough to test experimentally? This paper focusses on emotions and their expression. It is proposed that research on perceptual experiences of physical properties provides one model for thinking about what evidence concerning expressions of emotion might reveal about perceptual experiences of others’ mental states. This proposal motivates consideration of the hypothesis that categorical perception of expressions of emotion occurs, can be facilitated by information about agents’ emotions, and gives rise to phenomenal expectations. It is argued that the truth of this hypothesis would support a modest version of the claim that humans sometimes perceptually experience some of another’s mental states. Much available evidence is consistent with, but insufficient to establish, the truth of the hypothesis. We are probably not yet in a position to know whether humans ever perceptually experience others’ mental states.     

Complexity of categorical syllogisms: An integration of two metrics

The complexity of categorical syllogisms was assessed using the relational complexity metric, which is based on the number of entities that are related in a single cognitive representation. This was compared with number of mental models in an experiment in which adult participants solved all 64 syllogisms. Both metrics accounted for similarly large proportions of the variance, showing that complexity depends on the number of categories that are related in a representation of the combined premises, whether represented in multiple mental models, or by a single model. This obviates the difficulty with mental models theory due to equivocal evidence for construction of more than one mental model. The “no valid conclusion” response was used for complex syllogisms that had valid conclusions. The results are interpreted as showing that the relational complexity metric can be applied to syllogistic reasoning, and can be integrated with mental models theory, which together account for a wide range of cognitive performances.     

Categorical perception of colour in the left and right visual field is verbally mediated: evidence from Korean

In this study we demonstrate that Korean (but not English) speakers show Categorical perception (CP) on a visual search task for a boundary between two Korean colour categories that is not marked in English. These effects were observed regardless of whether target items were presented to the left or right visual field. Because this boundary is unique to Korean, these results are not consistent with a suggestion made by Drivonikou [Drivonikou, G. V., Kay, P., Regier, T., Ivry, R. B., Gilbert, A. L., Franklin, A. et al. (2007) Further evidence that Whorfian effects are stronger in the right visual field than in the left. Proceedings of the National Academy of Sciences 104, 1097-1102] that CP effects in the left visual field provide evidence for the existence of a set of universal colour categories. Dividing Korean participants into fast and slow responders demonstrated that fast responders show CP only in the right visual field while slow responders show CP in both visual fields. We argue that this finding is consistent with the view that CP in both visual fields is verbally mediated by the left hemisphere language system.