Numeral Classifiers and the White Horse Paradox

This paper presents an interpretation of Gongsun Long＇s white horse paradox. The Chinese sentence he uses to state his main thesis （Bai ma fei ma） has two potential readings： （a） The white horses are not horses. （b） The white horses are not the horses Although （a） gives the usual and correct reading of the sentence, according to the interpretation, Gongsun Long takes it to state （b）. He gives good arguments for （b） while taking them to establish （a） as well, for he fails to distinguish between the two different theses. In presenting this interpretation, the paper gives an account of the function of numeral classifiers and discusses the semantics of count nouns in languages with no grammatical number system, including classical Chinese and classifier languages （e.g., contemporary Chinese）.     

Horse (Equus caballus) whinnies: a source of social information

Many animal species that rely mainly on calls to communicate produce individual acoustic structures, but we wondered whether individuals of species better known as visual communicants, with small vocal repertoires, would also exhibit individual distinctiveness in calls. Moreover, theoretical advances concerning the evolution of social intelligence are usually based on primate species data, but relatively little is known about the social cognitive capacities of non-primate mammals. However, some non-primate species demonstrate auditory recognition of social categories and possess mental representation of their social network. Horses (Equus caballus) form stable social networks and although they display a large range of visual signals, they also use long-distance whinny calls to maintain contact. Here, we investigated the potential existence of individual acoustic signatures in whinny calls and the ability of horses to discriminate by ear individuals varying in their degree of familiarity. Our analysis of the acoustic structure of whinnies of 30 adult domestic horses (ten stallions, ten geldings, ten mares) revealed that some of the frequency and temporal parameters carried reliable information about the caller’s sex, body size and identity. However, no correlations with age were found. Playback experiments evaluated the behavioural significance of this variability. Twelve horses heard either control white noise or whinnies emitted by group members, familiar neighbours or unfamiliar horses. While control sounds did not induce any particular response, horses discriminated the social category of the callers and reacted with a sound-specific behaviour (vigilance and attraction varied with familiarity). Our results support the existence of social knowledge in horses and suggest a process of vocal coding/decoding of information.     

Generalization of a tactile stimulus in horses.

Using horses, we investigated the control of operant behavior by a tactile stimulus (the training stimulus) and the generalization of behavior to six other similar test stimuli. In a stall, the experimenters mounted a response panel in the doorway. Located on this panel were a response lever and a grain dispenser. The experimenters secured a tactile-stimulus belt to the horse's back. The stimulus belt was constructed by mounting seven solenoids along a piece of burlap in a manner that allowed each to provide the delivery of a tactile stimulus, a repetitive light tapping, at different locations (spaced 10.0 cm apart) along the horse's back. Two preliminary steps were necessary before generalization testing: training a measurable response (lip pressing) and training on several reinforcement schedules in the presence of a training stimulus (tapping by one of the solenoids). We then gave each horse two generalization test sessions. Results indicated that the horses' behavior was effectively controlled by the training stimulus. Horses made the greatest number of responses to the training stimulus, and the tendency to respond to the other test stimuli diminished as the stimuli became farther away from the training stimulus. These findings are discussed in the context of behavioral principles and their relevance to the training of horses.     

Specificity and variability of trunk kinematics on a mechanical horse

As perturbation training is gaining popularity, it is important to better understand postural control during complex three-dimensional stimuli. One clinically relevant and commonly used three-dimensional stimulus is found in hippotherapy and simulated hippotherapy on a mechanical horse. We tested nine healthy participants on a horse simulator, measured head and trunk kinematics, and characterized data in time (root-mean-square and variability) and frequency (amplitude spectra, gains, and phases) domains. We addressed three fundamental questions: 1) What is the specificity of postural responses to the simulator? 2) Which plane of motion is associated with the most and least variability (repeatable movements across repeated stimuli and across participants)? 3) To what extent are postural responses influenced by different degrees of stability (addition of pelvis straps and trunk support)? We found head and trunk responses were highly specific to the three-dimensional simulator perturbation direction and frequency. Frontal plane responses had the least variability across repetitions and participants whereas transverse motion was most variable. Head motion was more variable than the trunk at low frequencies and exhibited a marked decrease in tilt in the sagittal plane. Finally, the inclusion of pelvis straps had minimal effect on kinematics at low frequencies but altered higher frequencies; whereas added trunk support reduced head and trunk responses to perturbations and altered timing characteristics in all three planes. In conclusion, the present study suggests that frontal plane motion was under a high level of control, and results support the idea that specific head and trunk postural responses can be elicited from a complex three-dimensional stimuli, such as those found in hippotherapy. Researchers and clinicians can use results from this study to help interpret variability, implement mechanical adjustments to stability, and assess responses in pathological populations.     

Horse-parts,White-parts,and Naming: Semantics,Ontology, and Compound Terms in the White Horse Dialogue

In this article I argue against Chad Hansen’s version of the “White Horse Dialogue” (Baimalun) of Gongsun Longzi as intelligible through writings of the later Moists. Hansen regards the Baimalun as an attempt to demonstrate how the compound baima, “white horse,” is correctly analyzed in one of the Moist ways of analyzing compound term semantics but not the other. I present an alternative reading in which the Baimalun arguments point out, via reductio, the failure of either Moist analysis; in particular they point out how neither analysis accounts for ordinary, acceptable inferences like “There is a white horse; therefore there is a horse.” At issue for Gongsun Longzi is a fundamental problem with atomic terms: none of them seems capable of referring to a particular, “stand-alone” individual.     

How horses (Equus caballus) see the world: humans as significant “objects”

This study aimed to determine whether horses have a kind of memory of humans (based on previous interactions), leading to a general significance of humans revealed by their reactions to humans in subsequent interactions. Subjects were 59 adult horses used to interact daily with humans. Three types of behavioural tests involving an unknown experimenter evaluated three possibly different memorized types of human–animal interactions (not work-related, using work-related objects, unfamiliar working task). We also performed standardized observations of routine interactions between each horse and its familiar handler (caretaker). To get a broad overview of the horses’ reactions to humans, we recorded both investigative and aggressive behaviours during the tests, representing respectively a “positive” and a “negative” memory of the relationship. Whereas correlations between tests revealed a general perception of humans as either positive or negative, unusual tests, i.e. that are not usually performed, elicited more positive reactions. Moreover, some horses reacted positively to a motionless person in their box, but negatively when this same person approached them, for example for halter fitting. Overall, aggressive reactions were more reliable indicators of the relationship than positive reactions, both between tests and between familiar and unfamiliar humans. Our results also show generalization of the perception of humans. These results support our hypothesis that perception of humans by horses may be based on experience, i.e. repeated interactions. Altogether, our results support the hypothesis that horses can form a memory of humans that impacts their reactions in subsequent interactions.     

Denoting and Disquoting

Fregeans hold that predicates denote things, albeit things different in kind from what singular terms denote. This leads to a familiar problem: it seems impossible to say what any given predicate denotes. One strategy for avoiding this problem reduces the Fregean position to form of nominalism. I develop an alternative strategy that lets the Fregean hold on to the view that predicate denote things by reconceiving the nature of singular denotation and of Fregean objects.     

Human Energy Expenditure and Postural Coordination on the Mechanical Horse

The authors investigated and compared the energy expenditure and postural coordination of two groups of healthy subjects on a mechanical horse at 4 increasing oscillation frequencies. Energy expenditure was assessed from the oxygen consumption, respiratory quotient, and heart rate values, and postural coordination was characterized by relative phase computations between subjects (elbow, head, trunk) and horse. The results showed that the postural coordination of the riders was better adapted (i.e., maintenance of in-phase and antiphase) than that of the nonriders, but the energy expenditure remains the same. Likewise, we observed an energy system shifting only for nonriders (from aerobic to lactic anaerobic mode). Finally, cross-correlations showed a link between energy expenditure and postural coordination in the riders (i.e., effectiveness).