Organic Unities, Non-Trade-Off, and the Additivity of Intrinsic Value

Whether or not intrinsic valueis additively measurable is often thought todepend on the truth or falsity of G. E. Moore'sprinciple of organic unities. I argue that thetruth of this principle is, contrary to received opinion, compatible with additivemeasurement. However, there are other veryplausible evaluative claims that are moredifficult to combine with the additivity ofintrinsic value. A plausible theory of the goodshould allow that there are certain kinds ofstates of affairs whose intrinsic value cannotbe outweighed by any number of states ofcertain other, less valuable, kinds. Such``non-trade-off' cannot reasonably be explainedin terms of organic unities, and it can bereconciled with the additivity thesis only ifwe are prepared to give up some traditionalclaims about the nature of intrinsic value.     

Associative isolation: Unifying associative and list memory

Rather than treating paired associate and serial learning as involving the acquisition of distinct types of information [e.g. Murdock (1974). Human memory: Theory and data. New York: Wiley] I propose an Isolation Principle which treats the two as ends of a continuum. According to this principle, consecutive pairs of items are relatively isolated from other studied items in paired associates learning, but not isolated in serial list learning. The consequence is that variability that dominates forward and backward probed recall is highly correlated in pairs but less so, due to differential interference, in lists. This can explain an important dissociation: whereas forward and backward probes of pairs are nearly perfectly correlated, the correlation is only moderate for serial lists. I demonstrate this in a chaining model by varying item-to-item associative strengths and in a positional coding model by varying the similarity structure of item positions. This enables a range of models to account for data on pairs and lists, as well as potential intermediate or hybrid paradigms, within a single theoretical framework.     

Everybody Will Win,and All Must Be Hired: Comparing Additivity Neglect with the Nonselective Superiority Bias

Two streams of research looking at referent‐dependent judgments from slightly different angles are subadditivity research and research on the nonselective superiority bias. Both biases violate basic formal constraints: the probabilities of a set of exclusive events cannot add up to more than 100%, and a set of attractive candidates cannot all be rated as superior to the group mean. We examine in three experiments how these two biases are related, by asking the same participants to perform both kinds of tasks on the same material. Both biases appear to be widespread, even for sets where all alternatives are presented together, but they differ in the way they are affected by response format and experimental setup. Thus, presenting participants with an unbiased set of ratings will reduce but not normalize their probability estimates of the same alternatives; while presenting them with an unbiased (additive) set of probabilities will make most alternatives appear inferior to the group mean, inverting the superiority bias. Self‐reports reveal that additivity neglect and the nonselective superiority bias can be based on two main response‐strategies: (i) considering each alternative independently or (ii) comparing alternatives, while neglecting their complementarity. In both cases, assessments will be the outcome of a compromise between the perceived “absolute” merits of each alternative, its standing relative to referents, and properties of the response scale. Copyright © 2015 John Wiley & Sons, Ltd.     

The effects of ordinal load on incidental temporal learning

How can we grasp the temporal structure of events? A few studies have indicated that representations of temporal structure are acquired when there is an intention to learn, but not when learning is incidental. Response-to-stimulus intervals, uncorrelated temporal structures, unpredictable ordinal information, and lack of metrical organization have been pointed out as key obstacles to incidental temporal learning, but the literature includes piecemeal demonstrations of learning under all these circumstances. We suggest that the unacknowledged effects of ordinal load may help reconcile these conflicting findings, ordinal load referring to the cost of identifying the sequence of events (e.g., tones, locations) where a temporal pattern is embedded. In a first experiment, we manipulated ordinal load into simple and complex levels. Participants learned ordinal-simple sequences, despite their uncorrelated temporal structure and lack of metrical organization. They did not learn ordinal-complex sequences, even though there were no response-to-stimulus intervals nor unpredictable ordinal information. In a second experiment, we probed learning of ordinal-complex sequences with strong metrical organization, and again there was no learning. We conclude that ordinal load is a key obstacle to incidental temporal learning. Further analyses showed that the effect of ordinal load is to mask the expression of temporal knowledge, rather than to prevent learning.     

Anticipation measures of sequence learning: manual versus oculomotor versions of the serial reaction time task

The serial reaction time (SRT) task has generated a very large amount of research. Nevertheless the debate continues as to the exact cognitive processes underlying implicit sequence learning. Thus, the first goal of this study is to elucidate the underlying cognitive processes enabling sequence acquisition. We therefore compared reaction time (RT) in sequence learning in a standard manual activated (MA) to that in an ocular activated (OA) version of the task, within a single experimental setting. The second goal is to use eye movement measures to compare anticipation, as an additional indication of sequence learning, between the two versions of the SRT. Performance of the group given the MA version of the task (n = 29) was compared with that of the group given the OA version (n = 30). The results showed that although overall, RT was faster for the OA group, the rate of sequence learning was similar to that of the MA group performing the standard version of the SRT. Because the stimulus-response association is automatic and exists prior to training in the OA task, the decreased reaction time in this version of the task reflects a purer measure of the sequence learning that occurs in the SRT task. The results of this study show that eye tracking anticipation can be measured directly and can serve as a direct measure of sequence learning. Finally, using the OA version of the SRT to study sequence learning presents a significant methodological contribution by making sequence learning studies possible among populations that struggle to perform manual responses.     

Finitistic and Frequentistic Approximation of Probability Measures with or without <Emphasis Type="Italic">σ</Emphasis>-Additivity

In this paper a theory of finitistic and frequentistic approximations — in short: f-approximations — of probability measures P over a countably infinite outcome space N is developed. The family of subsets of N for which f-approximations converge to a frequency limit forms a pre-Dynkin system . The limiting probability measure over D can always be extended to a probability measure over , but this measure is not always σ-additive. We conclude that probability measures can be regarded as idealizations of limiting frequencies if and only if σ-additivity is not assumed as a necessary axiom for probabilities. We prove that σ-additive probability measures can be characterized in terms of so-called canonical and in terms of so-called full f-approximations. We also show that every non-σ-additive probability measure is f-approximable, though neither canonically nor fully f-approximable. Finally, we transfer our results to probability measures on open or closed formulas of first-order languages.     

Key-peck durations under behavioral contrast and differential reinforcement

Pigeons were maintained on a multiple schedule in which both components were variable-interval one-minute schedules. When they were switched to a condition in which one component was extinction, behavioral contrast was observed. The median durations of the key pecks in the unchanged component did not decrease in size. The results are incompatible with a theory of behavioral contrast which considers the added pecks to be short-duration responses. In a second experiment, pigeons were required to emit short-duration key pecks in one component of a multiple schedule, and long-duration pecks in the other. Two of three pigeons learned to emit responses appropriate to the requirements of the component in effect, suggesting that the duration of the key-peck response is sensitive to differential reinforcement.     

Macaque monkeys discriminate pitch relationships

This study demonstrates that non-human primates can categorize the direction of the pitch change of tones in a sequence. Two Macaca fascicularis were trained in a positive-reinforcement behavioral paradigm in which they listened to sequences of a variable number of different acoustic items. The training of discriminating pitch direction was divided into three phases with increasing task complexity. In the first two phases, subjects learned to employ a same/different rule. In phase 1, they discriminated acoustic items of different sound quality. Subjects had to respond when there was a change from repeating noise bursts to repeating click trains or vice versa. In phase II, acoustic items differed along one physical dimension only. Subjects had to respond to a change of the frequency of a repeating series of pure tones. In phase III, sequences consisted of three series of repeating tones of different frequency. Subjects were required to respond when the frequency of the tones changed in a downward direction and to refrain from responding when the frequency remained constant or increased. After several ten thousand trials, subjects categorized pitch direction well above chance level. The discrimination was performed over a 4.5-octave range of frequencies and was largely independent of the temporal and ordinal position of the downward pitch direction within the sequence. These results demonstrate that monkeys can recognize pitch relationships and thus that monkeys have the concept of ordinal relations between acoustic items.     

Numerical order and quantity processing in number comparison

We investigated processing of numerical order information and its relation to mechanisms of numerical quantity processing. In two experiments, performance on a quantity-comparison task (e.g. 2 5; which is larger?) was compared with performance on a relative-order judgment task (e.g. 2 5; ascending or descending order?). The comparison task consistently produced the standard distance effect (faster judgments for far relative to close number pairs), but the distance effect was smaller for ascending (e.g. 2 5) compared to descending pairs (e.g. 5 2). The order task produced a pair-order effect (faster judgments for ascending pairs) and a reverse distance effect for consecutive pairs in ascending order. The reverse effect implies an order-specific process, such as serial search or direct recognition of order for successive numbers. Thus, numerical quantity and order judgments recruited different cognitive mechanisms. Nonetheless, the reduced distance effect for ascending pairs in the quantity task implies involvement of order-related processes in magnitude comparison. Accordingly, distance effects in the quantity-comparison task are not necessarily a process-pure measure of magnitude representation.     

Relations between vocabulary development and verbal short-term memory: The relative importance of short-term memory for serial order and item information

Although many studies have shown an association between verbal short-term memory (STM) and vocabulary development, the precise nature of this association is not yet clear. The current study reexamined this relation in 4- to 6-year-olds by designing verbal STM tasks that maximized memory for either item or serial order information. Although empirical data suggest that distinct STM processes determine item and serial order recall, these were generally confounded in previous developmental studies. We observed that item and order memory tasks were independently related to vocabulary development. Furthermore, vocabulary development was more strongly associated with STM for order information in 4- and 6-year-olds and with STM for item information in 5-year-olds. These data highlight the specificity of verbal STM for serial order and item information and suggest a causal association between order STM processes and vocabulary development, at least in 4- and 6-year-olds.