Kant's Schematism of the categories: An interpretation and defence

The aim of the Schematism chapter of the Critique of Pure Reason is to solve the problem posed by the “inhomogeneity” of intuitions and categories: the sensible properties of objects represented in intuition are of a different kind than the properties represented by categories. Kant's solution is to introduce what he calls “transcendental schemata,” which mediate the subsumption of objects under categories. I reconstruct Kant's solution in terms of two substantive premises, which I call Subsumption Sufficiency (i.e., that subsuming an object under a transcendental schema is sufficient to subsume it under the corresponding category) and Real Possibility (i.e., that it is really possible to subsume objects under each of the transcendental schemata). These two principles, together with a trivial modal one (the Subsumption-Possibility Link), entail that it is possible to subsume objects under categories; in other words, the argument of the Schematism is valid. The main work of the paper consists in reconstructing Kant's arguments for, and explanations of, these premises. I argue that they hinge on Kant's claim that transcendental schemata are “time-determinations,” which I interpret to mean: rules for reflexively representing the temporal relations among our own representational states. On the basis of this reading, I reconstruct Kant's argument for Subsumption Sufficiency, category by category. I also explain why Real Possibility follows almost immediately. Granting Kant the argument up to this point in the Critique, the argument of the Schematism is sound.     

The uniqueness problem in Kant's transcendental doctrine of method

Conclusion The verificationist defense of Kant's refutation of idealism is a specimen of the reconstructive work that needs to be done in evaluating Kant's transcendental philosophy. It is necessary to proceed piecemeal in the critical examination of each of Kant's arguments, fitting it to the proposed indirect proof model, and rethinking its soundness or unsoundness. There may be few conclusions that can stand just as they are. The justification of Kant's transcendental proof that there are unknowable things in themselves establishes an important first step in this continuing inquiry.     

Concept learning,memory and transfer of dot pattern categories

In the first experiment, subjects rated the similarity of a sample of pairs of random dot patterns generated from 3 prototypes consisting of either 4, 6, or 9 dots. The results of the experiment tended to confirm the structure imposed on the patterns by the construction method. In the second experiment, subjects learned to classify random patterns generated from 2 prototypes with either short or long interprototype distance and consisting of either 4, 6, or 9 dots in a traditional concept identification task. After acquisition, memory for old and new distortions and the prototype, which was not presented during learning, was assessed. The tendency to call a pattern “new” increased with the distance between the pattern and its prototype. In a subsequent transfer test, all subjects saw patterns of either 4, 6, or 9 dots. Performance was above chance and the transfer from larger to smaller patterns tended to be greater than the transfer from smaller to larger patterns. This is consistent with a process of schema formation based on features common to most exemplars of the category. The results are discussed in relation to several theories of concept learning and schema abstraction.     

Developing race categories in infancy via Bayesian face recognition

The other-race effect emerges during infancy following the perceptual narrowing of face recognition. Other-race faces that were previously discriminable in early infancy cannot be distinguished by older infants. I discuss a Bayesian model of this process that posits that the other-race effect may be a consequence of learning to distinguish between intrapersonal variation (changes to face appearance that preserve identity) and extrapersonal variation (changes that do not preserve identity) in a visual environment in which a subset of race categories dominate. I demonstrate that race categories, which I have previously argued are a critical precursor to the emergence of the other-race effect in infancy, are a natural by-product of this model. Perceptual narrowing for race may thus be a natural consequence of visual experience and the estimation of face variability based on a growing number of exemplars. I describe the basic architecture of the model, its applicability to a range of visual learning scenarios, and identify critical choices one faces in applying the model to a specific perceptual task. Despite the success of the model in accounting for these behavioural results, I conclude by identifying important shortcomings of the model and describe important challenges for future efforts to characterize the development of the other-race effect computationally.     

Reviving the no‐bad‐action problem in Kant's ethics

In the final section of the Groundwork, Kant famously declares that “a free will and a will under moral laws are one and the same.” Though this claim is put to use in Kant's eventual deduction of the moral law, it appears to introduce a difficulty of its own: It complicates Kant's ability to describe immoral action as free action. Over the last 3 decades, no scholar has done more to exonerate Kant from this apparent problem than Henry Allison. Allison's chief strategy has been to show (a) that the volitional apparatus (i.e., the executive will) Kant develops in his late Religion is present from the beginning of the critical project and (b) that this apparatus dissolves the apparent worry. In this paper, I argue that even if Allison succeeds in establishing (a), it puts him no closer to establishing (b). Kant does not think that agents, good or bad, can act out of character.     

Expertise in tactile pattern recognition

This article explores expertise in tactile object recognition. In one study, participants were trained to differing degrees of accuracy on tactile identification of two-dimensional patterns. Recognition of these patterns, of inverted versions of these patterns, and of subparts of these patterns was then tested. The inversion effect (better recognition of upright than inverted patterns) and the part-whole effect (better recognition of the whole than a part pattern), traditionally considered signatures of visual expertise, were observed for tactile experts but not for novices. In a second study, participants were trained as visual or tactile experts and then tested in the trained and nontrained modalities. Whereas expertise effects were observed in the modality of training, cross-modal transfer was asymmetric; visual experts showed generalization to haptic recognition, but tactile experts did not show generalization to visual recognition. Tactile expertise is not obviously attributable to visual mediation and emerges from domain-general principles that operate independently of modality.     

Auditory pattern recognition by untrained listeners

Earlier work with unpracticed Ss has indicated that identification (naming) of the temporal order of components within repeated sequences consisting of three or four unrelated sounds cannot be accomplished when the item durations are 200 msec or less. In the present experiment, separate groups of 30 unpracticed Ss were required to teil whether alternated sequences, each consisting of reiterated presentations of the same three or four successive items, were in identical or permuted order. Naming of the order within the sequences was not required. Accuracy of same/different judgments was significantly better than chance when all items lasted 200 msec. Changing the duration of each item in one of the two sequences above or below 200 msec made the task more difficult. These results, together with other evidence, suggest that: (1) identification of order and recognition of auditory temporal patterns may represent fundamentally different processes, and (2) recognition may involve matching of “temporal templates.”     

Size scaling in visual pattern recognition

Human visual recognition on the basis of shape but regardless of size was investigated by reaction time methods. For successive matching of random figures, reaction time increased linearly with the linear size ratio of stimulus pairs. For single-character classification, reaction time increased with divergence between cued size format and stimulus format such that for character nonrepetitions, the increment in latency was approximately proportional to the logarithm of the linear size ratio of the two formats. However, when reactions to character repetitions were faster than those to nonrepetitions, the repetition reaction time function was similar to that for successive matching of random figures. The results suggested two processes of size scaling: mental-image transformation and perceptual-scale transformation. Image transformation accounted for matching performance based on visual short-term memory, whereas scale transformation accounted for size invariance in recognition based on comparison against visual representations in long-term memory.     

Correlation of movement patterns via pattern recognition

A structural pattern recognition method for the quantitative determination of equivalence or similarity between movement patterns was examined. A chain encoding technique was implemented for the analysis of lower limb trajectories during walking and running. Conjoint angular displacement or angular velocity patterns provided kinematic data which were cross-correlated to determine geometric congruity of within and between subject motor patterns. The correlations of the movement patterns during different speeds of locomotion revealed numerical coefficients which consistently and quantitatively discriminated the similarity or dissimilarity of limb movement patterns.     

A pattern recognition account of decision making

In the domain of pattern recognition, experiments have shown that perceivers integrate multiple sources of information in an optimal manner. In contrast, other research has been interpreted to mean that decision making is nonoptimal. As an example, Tversky and Kahneman (1983) have shown that subjects commit a conjunction fallacy because they judge it more likely that a fictitious person named Linda is a bank teller and a feminist than just a bank teller. This judgment supposedly violates probability theory, because the probability of two events can never be greater than the probability of either event alone. The present research tests the hypothesis that subjects interpret this judgment task as a pattern recognition task. If this hypothesis is correct, subjects’ judgments should be described accurately by the fuzzy logical model of perception (FLMP)—a successful model of pattern recognition. In the first experiment, the Linda task was extended to an expanded factorial design with five vocations and five avocations. The probability ratings were described well by the FLMP and described poorly by a simple probability model. The second experiment included (1) two fictitious people, Linda and Joan, as response alternatives and (2) both ratings and categorization judgments. Although the ratings were accurately described by both the FLMP and an averaging of the sources of information, the categorization judgments were described better by the FLMP. These results reveal important similarities in recognizing patterns and in decision making. Given that the FLMP is an optimal method for combining multiple sources of information, the probability judgments appear to be optimal in the same manner as pattern-recognition judgments.     

Stimulus correlates of visual pattern discrimination and the problem of grain

Attention, Perception, & Psychophysics - A recent paper by V. J. Polidora (1966) is criticized on the basis that the experimental design did not provide an adequate test of the usefulness of 15...