In a recent paper by Casasanto and Pitt (2019), the authors addressed a debate regarding the role of order and magnitude in SNARC and SNARC‐like effects. Their position is that all these effects can be explained by order, while magnitude could only account for a subset of evidence. Although we agree that order can probably explain the majority of these effects, in this commentary we argue that magnitude is still relevant, since there is evidence that cannot be explained based on (...) ordinality alone. We argue that SNARC‐like effects can occur for magnitudes not clearly characterized by overlearned ordinality and that magnitude can prevail on order, when the two are pitted against each other. Finally, we propose that different interpretations of the role of order and magnitude depend on the interaction of stimulus properties and task demands. (shrink)

When participants are asked to make sensibility judgments on sentences that describe action toward the body (i.e., “Mark dealt the cards to you”) or away from the body (i.e., “You dealt the cards to Mark”), they are faster to respond when the response requires an arm movement in the same direction as the action described by the sentence. This congruence effect is known as the Action–Sentence Compatibility Effect (ACE). This study reports 4 experiments that extend our understanding of the ACE (...) by exploring how the time at which one prepares the motor response required for the sensibility judgment affects the magnitude of the ACE. Results show that the ACE arises only when participants have the opportunity to plan their motor response while they are processing the sentence. (shrink)

We show that the divergence between the predictions of quantum optics and the local realist theory known as stochastic optics, for the extended type of photon-coincidence experiment described recently by de Caro, is of the same order of magnitude as for Aspect-type experiments. This means that, in such new experiments, as in those so far performed, counting statistics will have to be greatly improved before a discrimination between the two theories becomes possible.We also show that the outstanding difference between the (...) two theories is that, while stochastic optics uses a genuine, that is, positive, detection probability, the corresponding quantum formalism leads to a pseudoprobability. Nevertheless, there is a striking parallel, in that both theories recognize the phenomenon known as enhancement, and both describe it as having its origin in a mixing of the signal field with the zero-point field by a polarizing device. (shrink)

According to the Spatial Quantity Association of Response Codes (SQUARC), people hold a mental association between horizontal position and quantity (lower quantities left, higher quantities right). While a large body of research has explored this effect for response speed and judgment accuracy, the affective downstream consequences of the SQUARC remain unexplored. Aiming to address this gap, the present two experiments (pre-registered, total N = 521) investigated whether stimulus arrangements that are compatible with the SQUARC for luminance are affectively preferred (...) to stimulus arrangements that are incompatible. SQUARC-compatible square arrangements (dark-left, bright-right) were preferred over SQUARC-incompatible square arrangements (dark-right, bright-left). The preference for SQUARC compatibility was not moderated by the horizontal orientation of the response scale. Our results confirm the direction of the spatial-luminance association and provide initial support that the cognitive processing of SQUARC compatibility is hedonically marked and appears sufficient to impact affective evaluations. (shrink)

This paper proposes Gilbert Simondon’s ontogenetic theory of individuation as an overarching framework for multilevel semiosis. What renders this theory suitable for this role is the fact that it shares a significant part of its heritage with biosemiotics, which provides compatibility between them. Unlike many philosophers who have worked on individuation, Simondon envisages a general process of individuation that starts with a metastable preindividual. This process ultimately constitutes an axiomatisation of ontogenesis and manifests itself in three basic modes: physical, vital (...) and psycho-collective. In any of these modes a transductive operation is at work resolving the disparities of the preindividual whereby new structures emerge. Depending on the mode of individuation, the emerging structures can create new disparities that ask for further individuation. Simondon refers to such conversion of structure to operation and vice versa as allagmatics. He also extends his theory to scientific methodology establishing a healthy balance between reductionism and holism. His theory can be used to amend Peircean metaphysics to improve its compatibility with contemporary scientific discourse. (shrink)

A theory of magnitudes involves criteria for their equivalence, comparison and addition. In this article we examine these aspects from an abstract viewpoint, by focusing on the so-called De Zolt’s postulate in the theory of equivalence of plane polygons (“If a polygon is divided into polygonal parts in any given way, then the union of all but one of these parts is not equivalent to the given polygon”). We formulate an abstract version of this postulate and derive it from (...) some selected principles for magnitudes. We also formulate and derive an abstract version of Euclid’s Common Notion 5 (“The whole is greater than the part”), and analyze its logical relation to the former proposition. These results prove to be relevant for the clarification of some key conceptual aspects of Hilbert’s proof of De Zolt’s postulate, in his classicalFoundations of Geometry(1899). Furthermore, our abstract treatment of this central proposition provides interesting insights for the development of a well-behaved theory ofcompatiblemagnitudes. (shrink)

Recent findings indicate that the constituting digits of multi-digit numbers are processed, decomposed into units, tens, and so on, rather than integrated into one entity. This is suggested by interfering effects of unit digit processing on two-digit number comparison. In the present study, we extended the computational model for two-digit number magnitude comparison of Moeller, Huber, Nuerk, and Willmes (2011a) to the case of three-digit number comparison (e.g., 371_826). In a second step, we evaluated how hundred-decade and hundred-unit compatibility effects (...) were moderated by varying the percentage of within-hundred (e.g., 539_582) and within-hundred-and-decade filler items (e.g., 483_489). From the results we predict that numerical distance as well as compatibility effects should indeed be modulated by the relevance of tens and units in three-digit number magnitude comparison: While in particular the hundred distance effect should decrease, we predict hundred-decade and hundred-unit compatibility effects to increase with the relevance of tens and units. (shrink)

In the second chapter of his book Kant and the Exact Sciences Michael Friedman deals with two different interpretations of the relation or the difference between algebra and arithmetic in Kant's thought. According to the first interpretation algebra can be described as general arithmetic because it generalizes over all numbers by the use of variables, whereas arithmetic only deals with particular numbers. The alternative suggestion is that algebra is more general than arithmetic because it considers a more general class of (...) magnitudes. This means that arithmetic is concerned only with rational magnitudes, whereas algebra is also concerned with irrational magnitudes. In this article, I will discuss which of the two aforementioned approaches is to be considered the most plausible interpretation of Kant's theory of algebra and arithmetic. According to Friedman, the first interpretation cannot be reconciled with certain statements made by Kant on various occasions. The second interpretation is developed by Friedman himself. It is meant to be an attempt to avoid such inconsistencies. By a detailed analysis of the texts Friedman himself cites I shall examine the soundness of his arguments against the first interpretation and the compatibility of his own interpretation of the difference between algebra and arithmetic with the relevant passages in Kant's texts. It will turn out that the reasons that make Friedman reject the first interpretation are invalid as they are based on misunderstandings and that his own interpretation does not expound Kant's notions on that subject correctly, whereas the first interpretation is compatible with these passages. Thus, I conclude that the interpretation rejected by Friedman, unlike his own approach, is actually the more adequate interpretation of Kant. (shrink)

Previous studies have confirmed that the temporal attentional control created by the repetition of stimulus-response compatibility (SRC) tasks was transferred to shooting skills in lacrosse players. In the current study, we investigated whether combining motor imagery training with SRC tasks could enhance the scoring ability of lacrosse players. We grouped 33 male lacrosse players into three groups: an SRC task and motor imagery group (referred as to SRC+Image), an SRC task group, and a control group. Players in the first two (...) groups underwent five sessions of 200 SRC task trials. In addition, the SRC+Image group completed five sessions of motor imagery training. The control group underwent no training interventions. All three groups performed a lacrosse shooting test and a Simon task before and after training sessions to assess the magnitude of the interference effects of the various types of training they underwent. The results of the Simon task showed that repetition of 1,000 trials was enough to create a short-term representation with the incompatible special mapping being transferred to a dynamic activity like lacrosse shooting. Moreover, combination of a computer-based Type 2 task and motor-imagery training could effectively increase players’ scoring ability in a field of large spatial conflict. (shrink)

Transposable elements (TEs) are powerful facilitators of genome evolution, and hence of phenotypic diversity as they can cause genetic changes of great magnitude and variety. TEs are ubiquitous and extremely ancient, and although harmful to some individuals, they can be very beneficial to lineages. TEs can build, sculpt, and reformat genomes by both active and passive means. Lineages with active TEs or with abundant homogeneous inactive populations of TEs that can act passively by causing ectopic recombination are potentially fecund, adaptable, (...) and taxonate readily. Conversely, taxa deficient in TEs or possessing heterogeneous populations of inactive TEs may be well adapted in their niche, but tend to prolonged stasis and may risk extinction by lacking the capacity to adapt to change, or diversify. Because of recurring intermittent waves of TE infestation, available data indicate a compatibility with punctuated equilibrium, in keeping with widely accepted interpretations of evidence from the fossil record. We propose a general and holistic synthesis on how the presence of TEs within genomes makes them flexible and dynamic, so that genomes themselves are powerful facilitators of their own evolution. (shrink)

Over the past hundred years, a number of scientific investigators claim to have adduced experimental evidence for phenomena information” seems to behave like a weak signal that has to compete for the information-processing resources of the organism, a reduction of ongoing sensorimotor activity may facilitate ESP detection. Such a meaningful convergence of results suggests that psi phenomena may represent a unitary, coherent process whose nature and compatibility with current physical theory have yet to be determined. The theoretical implications and potential (...) practical applications of psi could be significant, irrespective of the small magnitude of psi effects in laboratory settings. (shrink)

According to the traditional inferential theory of perception, percepts of object motion or stationarity stem from an evaluation of afferent retinal signals (which encode image motion) with the help of extraretinal signals (which encode eye movements). According to direct perception theory, on the other hand, the percepts derive from retinally conveyed information only. Neither view is compatible with a perceptual phenomenon that occurs during visually induced sensations of ego motion (vection). A modified version of inferential theory yields a model (...) in which the concept of extraretinal signals is replaced by that of reference signals, which do not encode how the eyes move in their orbits but how they move in space. Hence reference signals are produced not only during eye movements but also during ego motion (i.e., in response to vestibular stimulation and to retinal image flow, which may induce vection). The present theory describes the interface between self-motion and object-motion percepts. An experimental paradigm that allows quantitative measurement of the magnitude and gain of reference signals and the size of the just noticeable difference (JND) between retinal and reference signals reveals that the distinction between direct and inferential theories largely depends on: (1) a mistaken belief that perceptual veridicality is evidence that extraretinal information is not involved, and (2) a failure to distinguish between (the perception of) absolute object motion in space and relative motion of objects with respect to each other. The model corrects these errors, and provides a new, unified framework for interpreting many phenomena in the field of motion perception. (shrink)

Universal basic income proposes providing instalments of constant magnitude to all. One problem with a stable basic income across life is that it seems unfair to shorter-lived persons, who are worst-off due to premature death and receive less over their whole lives. Basic capital solves this problem by providing a one-off grant to the young, but I argue that it mistreats long-lived persons, as it does not guarantee their real freedom across life. There is a dilemma between these proposals regarding (...) their respective unfairness to the short- and long-lived. The solution I propose is a net basic income of decreasing magnitude until a specific age, after which the income is constant. This solution is compatible with constant income benefits across life, and it offers a fair answer to the problem of unequal longevity, a widely neglected but essential challenge in debates about basic income. (shrink)

In this introductory article to the special issue on Multi-level semiosis we attempt to stage the background for qualifying the notion of “multi-levelness” when considering communication processes and semiosis in all life forms, i.e. from the cellular to the organismic level. While structures are organized hierarchically, communication processes require a kind of processual organization that may be better described as being heterarchical. Theoretically, the challenge arises in the temporal domain, that is, in the developmental and evolutionary dimension of dynamic semiotic (...) processes. We discuss the importance of this fundamental difference in order to explain how levels, domains and orders of magnitude, on the one hand, and synchronic and diachronic processes, on the other, contribute to the overall organization of every living being. To account for such multi-level organization, semiotic freedom is assumed to be a scalar property that endows living systems at different levels and domains with the capacity to ponder selectively the overall structural coherence and functional compatibility of their heterarchical processing, which is increasingly less conditioned by the underlying molecular determinism. (shrink)

Understanding the hadiths requires not only knowing the language well but also knowing the intention of the narrator, the environment and context in which the word is uttered. Furthermore, within a language, the presence of the words which have entirely disconnected from their real meaning due to the metaphoric and idiomatic use of them developed in time requires making more efforts to understand them. In this respect, the expression ‘Aqrā-Ḥalqā’ used by Prophet Muhammad (PBUH) for Ṣafiyya in the Farewell Sermon (...) when he was leaving Mecca, is mostly attributed to inauspiciousness and thus, requires special investigation. Determination of the correct meaning and use of the expression will prevent any misunderstanding. However, only the literal equivalences of the expression have been used in its annotations and translations until now. By including the annotations and translations of the expression in dictionaries and Ġarību'l- Ḥadīth books, which were written with a more specific purpose, this study aims to find the most suitable meaning by considering all these data and the data which compatible with the sunnah.Summary: Before the leaving of Prophet Muhammad after the Farewell Sermon, he learned that one of his wife Ṣafiyya is in her period (ḥayḍ). After hearing this, he used the expression ‘Aqrā-Ḥalqā’. These statements are not frequently used in the Arabic language. The expressions, which we encounter in some ancient Arab poems, were mentioned several times in some hadiths while narrating the stories of the past societies (ummah), and as far as we can see they were used only for Ṣafiyya by the Prophet. The reason for Prophet's expression was because after he was informed that Ṣafiyya was in period, he thought that she did not make the obligatory circumambulation. Depending on this, the Prophet thought that they could not returning to Medina immediately; thus, he said this word with the confusion and anxiety caused by the difficulty of staying in Mecca for a while with a crowded pilgrim group. With regard to the meaning of these words, both the diversity in the translations and some negative comments and inferences in the annotations, this study was written.There is a sufficient amount of information about the meanings of this expression in classical dictionaries and works such as Ġarību'l- Ḥadīth. These works state that they have meanings such as death, injury, infertility, illness, bad luck and mourning at the root of the words. Although the fundamental roots of the words have these meanings, the expressions have undergone a change and transformation. As with some other examples in the Arabic language, these words have lost their relevance for their meaning root gradually and have been used more often for astonishment. This information is included in both classical sources and contemporary studies on the subject.Despite the fact that the expression has become independent from their root meaning and has an astonishing sense used in case of confusion, negative emphasis comes to the fore both in Turkish translations and in some commentaries. In Turkish translations, the usages which are related directly to the word itself and emphasizing its meaning for bad luck are dominant, but sometimes translations that give the meaning of astonishment, sometimes translations that are not related to the word have been made, and sometimes they have been contented with latinizing the word instead of translation. Additionally, the malediction used in searching the correct meaning to the word leads to an emphasize toward negativity.While most of the annotations do not give much information about the expressions, it is seen that some authors give a negative meaning to the words and accordingly, they make a comparison between Ṣafiyya and ‘Ā’isha. Because of the special situation of ‘Ā’isha, she was upset that she could not make umrah and she conveyed this situation to our Prophet. Hence the Prophet produced a solution for her to complete her umrah. In the one hand, producing a solution to ‘Ā’isha by the Prophet and comforting her, on the other hand, his expression ‘Aqrā-Ḥalqā’ for Ṣafiyya in a similar situation led some scholars to conclude that Ṣafiyya was not as valuable as ‘Ā’isha in the eyes of the Prophet. However, this result is not acceptable. Although there is no evidence for this, in another annotation, it is conveyed that the Prophet had said these words to her by its meaning for “her tongue is long” because Ṣafiyya spoke to the Prophet with disrespect. Another commentary based on this promise makes the provision that a man can talk heavily to his wife when she delays something.The implications that depend on the assumption these words have negative meanings and produce results related to this assumption are incompatible with other data of circumcision. It could not be possible that the Prophet, who defended Ṣafiyya against the criticism against Ṣafiyya and who even guided him to defend himself, had a bad word for his wife. If the meaning of bad luck is given, then the Prophet will be the first person who disregards his own word “there is no bad luck”. Besides, the Prophet's good communication with the women in all areas of his life makes it impossible for him to say "damn" to one of his wives. It seems it is not logical for the Prophet to say this word to his wife, who is waiting in sorrow in front of his tent even after special worship Hajj.The translations, which are opposed to both the basic principles of religion and the guide life of Prophet, bring many problems. This translations, on the one hand, are drawing a portrait of a prophet who is intolerant to women and their specific situations, degrading women, and able to say rude and bad words whenever he wishes, on the other hand, are reflecting an image for the Prophet who does not comply with his own warnings. However, based on the information provided by the classical dictionaries, translations such as "Alas!" to indicate the magnitude and gravity of the situation that the word is currently facing, or "Wow!" to express the astonishment, will prevent all these negative consequences.As in many other fields, the translation of religious texts, especially hadiths, appears as an area that needs to be carefully considered in this regard. Thus, the expression ‘Aqrā-Ḥalqā’ was chosen as the main theme of this study. The translation of hadiths has an essential function and the only way for those who do not speak Arabic is to learn about the life of the Prophet. For this reason, one of the main results of the study is that only knowledge on grammar is not sufficient for the translation of the hadiths. On the contrary, the persons who will translate hadiths must have many competencies in the field such as the reasons for hadiths, their relationship with other hadiths, and understanding the hadith in line with the basic principles. Beyond this knowledge, it should be expected to master areas that require particular studies such as strange words in the language, meaningful constrictions, enlargements and shifts over time, proverbs and idiomatic expressions. Otherwise, it will be impossible to prevent a biased and wrong prophet representation. (shrink)

A growing number of commentators have, in recent years, noted the important affinities in the views of Immanuel Kant and Niels Bohr. While these commentators are correct, the picture they present of the connections between Bohr and Kant is painted in broad strokes; it is open to the criticism that these affinities are merely superficial. In this essay, I provide a closer, structural, analysis of both Bohr's and Kant's views that makes these connections more explicit. In particular, I demonstrate the (...) similarities between Bohr's argument, on the one hand, that neither the wave nor the particle description of atomic phenomena pick out an object in the ordinary sense of the word, and Kant's requirement, on the other hand, that both ‘mathematical’ (having to do with magnitude) and ‘dynamical’ (having to do with an object's interaction with other objects) principles must be applicable to appearances in order for us to determine them as objects of experience. I argue that Bohr's ‘complementarity interpretation’ of quantum mechanics, which views atomic objects as idealizations, and which licenses the repeal of the principle of causality for the domain of atomic physics, is perfectly compatible with, and indeed follows naturally from a broadly Kantian epistemological framework. (shrink)

Number concepts must support arithmetic inference. Using this principle, it can be argued that the integer concept of exactly ONE is a necessary part of the psychological foundations of number, as is the notion of the exact equality - that is, perfect substitutability. The inability to support reasoning involving exact equality is a shortcoming in current theories about the development of numerical reasoning. A simple innate basis for the natural number concepts can be proposed that embodies the arithmetic principle, supports (...) exact equality and also enables computational compatibility with real- or rational-valued mental magnitudes. (shrink)

In this paper, I analyze William Crathorn’s view on extension and compare it to William Ockham’s reductionist view, according to which extension is not really distinct from substance or quality. In my view, Crathorn elaborates a metaphysical machinery based on mereological and topological relationships in order to solve what he considers to be problems in Ockham’s account of quantity. In order to make my point, I reconstruct Crathorn’s main arguments in favor of his finitist atomism. Crathorn claims that certain fundamental (...) spatial structures are of a mereological nature and that the mereological properties of located entities perfectly match those of their locations. This idea lies at the core of his solution to the paradox of touching and the metrical paradox. It allows him to redefine contiguity in such a way that extensionless magnitudes can touch and succeed each other. Crathorn goes one step further and claims that indivisibles are extended in the sense that they occupy an extended incorporeal space, which is their dimension. In this sense, they can come together to form a continuous magnitude. Thus, Crathorn succeeds in defining a concept of continuity that is compatible with his finitist atomism and that addresses what he takes to be a major weakness in Ockham’s view on extension, namely a murky concept of impenetrability. (shrink)

Recent discussions on Fregean and neo-Fregean foundations for arithmetic and real analysis pay much attention to what is called either ‘Application Constraint’ ($AC$) or ‘Frege Constraint’ ($FC$), the requirement that a mathematical theory be so outlined that it immediately allows explaining for its applicability. We distinguish between two constraints, which we, respectively, denote by the latter of these two names, by showing how$AC$generalizes Frege’s views while$FC$comes closer to his original conceptions. Different authors diverge on the interpretation of$FC$and on whether it (...) applies to definitions of both natural and real numbers. Our aim is to trace the origins of$FC$and to explore how different understandings of it can be faithful to Frege’s views about such definitions and to his foundational program. After rehearsing the essential elements of the relevant debate (§1), we appropriately distinguish$AC$from$FC$(§2). We discuss six rationales which may motivate the adoption of different instances of$AC$and$FC$(§3). We turn to the possible interpretations of$FC$(§4), and advance a Semantic$FC$(§4.1), arguing that while it suits Frege’s definition of natural numbers (4.1.1), it cannot reasonably be imposed on definitions of real numbers (§4.1.2), for reasons only partly similar to those offered by Crispin Wright (§4.1.3). We then rehearse a recent exchange between Bob Hale and Vadim Batitzky to shed light on Frege’s conception of real numbers and magnitudes (§4.2). We argue that an Architectonic version of$FC$is indeed faithful to Frege’s definition of real numbers, and compatible with his views on natural ones. Finally, we consider how attributing different instances of$FC$to Frege and appreciating the role of the Architectonic$FC$can provide a more perspicuous understanding of his foundational program, by questioning common pictures of his logicism (§5). (shrink)

Masked stimuli can affect the preparation of a motor response to subsequently presented target stimuli. Under some conditions, reactions to the main stimulus can be facilitated or inhibited when preceded by a compatible prime . In the majority of studies in which inverse priming was demonstrated arrows pointing left or right were used as prime and targets. There is, however, evidence that arrows are special overlearned stimuli which are processed in a favorable way. Here we report three experiments designated (...) to test whether the “arrowness” of primes/targets is a sufficient condition for inverse priming. The results clearly show that although inverse priming appeared when non-arrow shapes were used, the magnitude of the priming effect was larger with arrows. The possible reasons for this effect are discussed. (shrink)

We investigated the influence of stimulus base rates on the Implicit Association Test . Using an East/West-German attitude-IAT, we demonstrated that both overall response speed and differential response speed underlying IAT effects depend on the relative frequencies of the stimulus categories. First, when those stimuli that are more common in reality also occurred more frequently in the stimulus list, response speed generally increased. Second, IAT effects increased when congruent blocks profited from the compatibility of frequency-based response biases , whereas IAT (...) effects decreased when incongruent trial blocks profited from response compatibility. These findings demonstrate that the stimulus context moderates the magnitude of the IAT effect. Simultaneously, they highlight the need to explore the extent to which implicit measures reflect properties of the task or the environment rather than attributes of test-takers. (shrink)

It is thought that just as hunger itself, the expectancy to eat impacts attention and cognitive control toward food stimuli, but this theory has not been extensively explored at a behavioral level. In order to study the effect of expectancy to eat on attentional and cognitive control mechanisms, 63 healthy fasting participants were presented with an affective priming spatial compatibility Simon task that included both food and object distracters. The participants were randomly assigned to two groups: an “immediate expectancy” group (...) made up of participants who expected to eat immediately after the task and a “delayed expectancy” cohort made up of individuals who expected to eat a few hours later. Slower reaction times toward the food and non-food distracters and a more pronounced effect on the RTs in the incompatible condition [i.e., the Simon effect ] were noted in both groups. The effect of the food and non-food distracters on the RTs was more pronounced in the immediate with respect to the delayed expectancy group. The magnitude of the SE for the food and the non-food distracters was also greater in the immediate with respect to the delayed expectancy group. These results seem to indicate that when the expectancy to eat is short, the RTs are delayed, and the SE is more pronounced when food and non-food distracters are presented. Instead, when the expectancy to eat is more distant, the distracters have less of an effect on the RTs and the correspondence effect is smaller. Our results suggest that the expectancy to eat can modulate both attention orienting and cognitive control mechanisms in healthy fasting individuals when distracting details are competing with information processing during goal directed behavior. (shrink)

In this work, we develop and propose an ontological formal definition of time, based on a topological analysis of the formal mathematical description of time, coming from approaches to both quantum theories and Relativity; thus, being compatible with all physical epistemological theories. We find out a mathematical topological invariability, thus establishing a rigorous definition of time, as fundamental generic magnitude. Very preliminary analysis of physical epistemology is provided; likely highlighting a path towards a final common vision between Quantum and (...) Cosmology ontology and human feeling of time. (shrink)

Four experiments investigated the extent to which abstract quantitative information can be conveyed by basic visual features. This was done by asking observers to estimate and discriminate Pearson correlation in graphical representations where the first data dimension of each element was encoded by its horizontal position, and the second by the value of one of its visual features; perceiving correlation then requires combining the information in the two encodings via a common abstract representation. Four visual features were examined: luminance, color, (...) orientation, and size. All were able to support the perception of correlation. Indeed, despite the strikingly different appearances of the associated stimuli, all gave rise to performance that was much the same: just noticeable difference was a linear function of distance from complete correlation, and estimated correlation a logarithmic function of this distance. Performance differed only in regards to the level of noise in the feature, with these values compatible with estimates of channel capacity encountered in classic experiments on absolute perceptual magnitudes. These results suggest that quantitative information can be conveyed by visual features that are abstracted at relatively low levels of visual processing, with little representation of the original sensory property. It is proposed that this is achieved via an abstract parameter space in which the values in each perceptual dimension are normalized to have the same means and variances, with perceived correlation based on the shape of the joint probability density function of the resultant elements. (shrink)

Empirical discussions of mental representation appeal to a wide variety of representational kinds. Some of these kinds, such as the sentential representations underlying language use and the pictorial representations of visual imagery, are thoroughly familiar to philosophers. Others have received almost no philosophical attention at all. Included in this latter category are analogue magnitude representations, which enable a wide range of organisms to primitively represent spatial, temporal, numerical, and related magnitudes. This article aims to introduce analogue magnitude representations to (...) a philosophical audience by rehearsing empirical evidence for their existence and analysing their format, their content, and the computations they support. 1 Background1.1 Evidence of analogue magnitude representations1.2 Weber’s law1.3 Scepticism about analogue magnitude representations2 Format2.1 Carey’s analogy2.2 Neural realization2.3 Analogue representation2.4 Analogue magnitude representation components3 Content3.1 Do analogue magnitude representations have representational content?3.2 What do analogue magnitude representations represent?3.3 What content types do analogue magnitude representations have?4 Computations4.1 Arithmetic computation4.2 Practical deliberation5 Conclusion. (shrink)

Do people represent space, time, number, and other conceptual domains using a generalized magnitude system (GMS)? To answer this question, numerous studies have used the spatial‐numerical association of response codes (SNARC) task and its variants. Yet, for a combination of reasons, SNARC‐like effects cannot provide evidence for a GMS, even in principle. Rather, these effects support a broader theory of how people use space metaphorically to scaffold their understanding of myriad non‐spatial domains, whether or not these domains exhibit variation in (...) magnitude. (shrink)

In [4] the lattice of all subvarieties of the variety G n Ex defined by so called externally compatible identities of Abelian groups together with the identity x n ≈ y n , for any n ∈ N and n ≥ 1 was described. In that paper classes of models of the type (2,1) where considered. It appears that diagrams of lattices of subvariaties defined by externally compatible identities satisfied in a given equational theory depend on the language (...) of the considered class of algebras. A question was asked to what extent the diagram of the lattice of subvarieties of the variety defined by externally compatible identities of a given variety will depend on changing the type of algebras. In general case, the answer to this question seems to be very complicated. In this paper we describe the variety of Abelian groups of exponent p·q, where p,q are different primes of type (2,1,0). (shrink)

In this work, we question the ability of existing ranking-based semantics to capture persuasion settings, emphasising in particular the phenomena of procatalepsis and of fading. Some widely accepted principles of ranking-based semantics are incompatible with a faithful treatment of these phenomena, which means that no existing ranking-based semantics can capture these two principles together. This motivates us to introduce a new parametrized ranking-based semantics based on the notion of propagation which extends the existing propagation semantics 139–150) by adding an additional (...) parameter allowing us to gradually decrease the impact of arguments when the length of the path between two arguments increases. We show that this parameter gives the possibility of choosing if one wants to satisfy the property Void Precedence or not and to control the scope of the impact of the arguments. We also propose an experiment to show that the new semantics remains stable when this parameter varies and an axiomatic evaluation to compare it with existing ranking-based semantics in the literature. (shrink)

Given a rich environment, how do we decide on what information to use? A view of a single entity (e.g., a group of birds) affords many distinct interpretations, including their number, average size, and spatial extent. An enduring challenge for cognition, therefore, is to focus resources on the most relevant evidence for any particular decision. In the present study, subjects completed three tasks—number discrimination, surface area discrimination, and convex hull discrimination—with the same stimulus set, where these three features were orthogonalized. (...) Therefore, only the relevant feature provided consistent evidence for decisions in each task. This allowed us to determine how well humans discriminate each feature dimension and what evidence they relied on to do so. We introduce a novel computational approach that fits both feature precision and feature use. We found that the most relevant feature for each decision is extracted and relied on, with minor contributions from competing features. These results suggest that multiple feature dimensions are separately represented for each attended ensemble of many items and that cognition is efficient at selecting the appropriate evidence for a decision. (shrink)

This paper examines the history of two related problems concerning earthquakes, and the way in which a theoretical advance was involved in their resolution. The first problem is the development of a physical, as opposed to empirical, scale for measuring the size of earthquakes. The second problem is that of understanding what happens at the source of an earthquake. There was a controversy about what the proper model for the seismic source mechanism is, which was finally resolved through advances in (...) the theory of elastic dislocations. These two problems are linked, because the development of a physically based magnitude scale requires an understanding of what goes on at the seismic source. I will show how the theoretical advances allowed seismologists to re-frame the questions they were trying to answer, so that the data they gathered could be brought to bear on the problem of seismic sources in new ways. (shrink)

Continuous magnitude estimation and continuous cross-modality matching with line length can efficiently track the momentary loudness of time-varying sounds in behavioural experiments. These methods are known to be prone to systematic biases but may be checked for consistency using their counterpart, magnitude production. Thus, in Experiment 1, we performed such an evaluation for time-varying sounds. Twenty participants produced continuous cross-modality matches to assess the momentary loudness of fourteen songs by continuously adjusting the length of a line. In Experiment 2, the (...) resulting temporal line length profile for each excerpt was played back like a video together with the given song and participants were asked to continuously adjust the volume to match the momentary line length. The recorded temporal line length profile, however, was manipulated for segments with durations between 7 to 12 s by eight factors between 0.5 and 2, corresponding to expected differences in adjusted level of −10, −6, −3, −1, 1, 3, 6, and 10 dB according to Stevens’s power law for loudness. The average adjustments 5 s after the onset of the change were −3.3, −2.4, −1.0, −0.2, 0.2, 1.4, 2.4, and 4.4 dB. Smaller adjustments than predicted by the power law are in line with magnitude-production results by Stevens and co-workers due to “regression effects.” Continuous cross-modality matches of line length turned out to be consistent with current loudness models, and by passing the consistency check with cross-modal productions, demonstrate that the method is suited to track the momentary loudness of time-varying sounds. (shrink)

In recent work, Christopher Peacocke has argued for a kind of realism (or anti-reductionism) about magnitudes such as temperature and spatial distance. Peacocke’s argument is that magnitudes are an ineliminable commitment of scientific and everyday explanations (including high-level explanations), and that they are the natural candidates for semantic values of our ordinary magnitude talk, and for contents of our mental states. I critique these arguments, in particular focusing on whether the realist has a satisfactory account of how high-level (...) magnitude facts are grounded in lower-level facts. I argue that a less realist (i.e., more reductionist approach) is preferable, or at least viable. I also aim to substantially clarify what is at stake in the debate. (shrink)

Vertical/compatible theoretical integration provides an alternative way of unifying sociocultural anthropology and related disciplines. It involves analyzing theoretical statements for their implicit and explicit assumptions at multiple levels of analysis and then determining whether these assumptions are compatible with consensus in the relevant disciplines (e.g., does the sociological theory include an assumption at odds with consensus psychology?). Incompatibilities indicate a need for further research. This approach is much more likely to salvage the bulk of humanities-oriented anthropology than is (...) that of the authors. (Published Online November 9 2006). (shrink)

It is not easy to be a materialist and yet believe that there is a way for human beings to survive death. Peter van Inwagen identifies the central obstacle the materialist faces: Namely, the need to posit appropriate “immanent-causal” connections between my body as it is at death and some living body elsewhere or elsewhen. I offer a proposal, consistent with van Inwagen’s own materialist metaphysics, for making materialism compatible with the possibility of survival.

Although most deaf individuals could use sign language or sign/spoken language mix, hearing loss would still affect their language acquisition. Compensatory plasticity holds that the lack of auditory stimulation experienced by deaf individuals, such as congenital deafness, can be met by enhancements in visual cognition. And the studies of hearing individuals have showed that visual form perception is the cognitive mechanism that could explain the association between numerical magnitude processing and arithmetic computation. Therefore, we examined numerical magnitude processing and its (...) contribution to arithmetical ability in deaf adolescents, and explored the differences between the congenital and acquired deafness. 112 deaf adolescents and 58 hearing adolescents performed a series of cognitive and mathematical tests, and it was found there was no significant differences between the congenital group and the hearing group, but congenital group outperformed acquired group in numerical magnitude processing and arithmetic computation. It was also found there was a close association between numerical magnitude processing and arithmetic computation in all deaf adolescents, and after controlling for the demographic variables and general cognitive abilities, numerical magnitude processing could predict arithmetic computation in all deaf adolescents but not in congenital group. The role of numerical magnitude processing in deaf adolescents' mathematical performance should be paid attention in the training of arithmetical ability. (shrink)