Cognitive diagnosis models allow classifying respondents into a set of discrete attribute profiles. The internal structure of the test is determined in a Q-matrix, whose correct specification is necessary to achieve an accurate attribute profile classification. Several empirical Q-matrix estimation and validation methods have been proposed with the aim of providing well-specified Q-matrices. However, these methods require the number of attributes to be set in advance. No systematic studies about CDMs dimensionality assessment have been conducted, which contrasts (...) with the vast existing literature for the factor analysis framework. To address this gap, the present study evaluates the performance of several dimensionality assessment methods from the factor analysis literature in determining the number of attributes in the context of CDMs. The explored methods were parallel analysis, minimum average partial, very simple structure, DETECT, empirical Kaiser criterion, exploratory graph analysis, and a machine learning factor forest model. Additionally, a model comparison approach was considered, which consists in comparing the model-fit of empirically estimated Q-matrices. The performance of these methods was assessed by means of a comprehensive simulation study that included different generating number of attributes, item qualities, sample sizes, ratios of the number of items to attribute, correlations among the attributes, attributes thresholds, and generating CDM. Results showed that parallel analysis, factor forest model, and model comparison are suitable alternatives to determine the number of attributes in CDM applications, with an overall percentage of correct estimates above 76% of the conditions. The accuracy increased to 97% when these three methods agreed on the number of attributes. In short, the present study supports the use of three methods in assessing the dimensionality of CDMs. This will allow to test the assumption of correct dimensionality present in the Q-matrix estimation and validation methods, as well as to gather evidence of validity to support the use of the scores obtained with these models. The findings of this study are illustrated using real data from an intelligence test to provide guidelines for assessing the dimensionality of CDM data in applied settings. (shrink)

Trapezoidal cubic fuzzy numbers (TzCFNs) are an extraordinary cubic fuzzy set on a real number set. TzCFNs are useful for dealing with well-known quantities in decision data and decision making problems themselves. This paper is about multi-attribute group decision making problems in which the attribute values are stated with TzCFNs, which are solved by developing a new decision method based on power average operators of TzCFNs. The new operation laws for TzCFNs are given. Hereby, the power average (...) operator of real numbers is extended to four kinds of power average operators of TzCFNs, involving the power average operator of TzCFNs, the weighted power average operator of TzCFNs, the power ordered weighted average operator of TzCFNs, and the power hybrid average operator of TzCFNs. In the proposed group decision method, the individual overall evaluation values of alternatives are generated by using the power average operator of TzCFNs. Applying the hybrid average operator of TzCFNs, the specific general evaluation standards of alternatives are then combined into the collective ones, which are used to rank the alternatives. The example analysis shows the practicality and effectiveness of the proposed method. (shrink)

It is often assumed that adaptation — a temporary change in sensitivity to a perceptual dimension following exposure to that dimension — is a litmus test for what is and is not a “primary visual attribute”. Thus, papers purporting to find evidence of number adaptation motivate a claim of great philosophical significance: That number is something that can be seen in much the way that canonical visual features, like color, contrast, size, and speed, can. Fifteen years after (...) its reported discovery, number adaptation’s existence seems to be nearly undisputed, with dozens of papers documenting support for the phenomenon. The aim of this paper is to offer a counterweight — to critically assess the evidence for and against number adaptation. After surveying the many reasons for thinking that number adaptation exists, we introduce several lesser-known reasons to be skeptical. We then advance an alternative account — the old news hypothesis — which can accommodate previously published findings while explaining various (otherwise unexplained) anomalies in the existing literature. Next, we describe the results of eight pre-registered experiments which pit our novel old news hypothesis against the received number adaptation hypothesis. Collectively, the results of these experiments undermine the number adaptation hypothesis on several fronts, whilst consistently supporting the old news hypothesis. More broadly our work raises questions about the status of adaptation itself as a means of discerning what is and is not a visual attribute. (shrink)

The number of speaking actors in Old Comedy has been much discussed, but no consensus has been reached. The old assumption that the number was three, as in tragedy, was shaken when it was realized that some scenes of Aristophanes have four characters on-stage at once, all taking part in the dialogue: for example, in Lys. 77–253 we have Lysistrate, Kalonike, Myrrhine, and Lampito, and in Frogs 1414–81 we have Dionysos, Aiskhylos, Euripides, and Plouton. Rees therefore argued that (...) there was no fixed number, but that view was not generally accepted. A more widely held view is that there were three principal actors with additional performers for small parts. However, there is no evidence contemporary with Aristophanes which distinguishes three actors from the others in this way, and it is probable that writers of later periods who mention three actors are referring to their own times and did not have authentic information about the fifth century. The passage which DFA, p. 149, seems to regard as the most trustworthy is in a brief account of comedy attributed to Tzetzes: πιγενμενος δ Κρατνος κατστησε μν πρτον τ ν τ κωμδ πρσωπα μεχρ τριν, στσας τν ταξαν4 DFA paraphrases this as ‘Cratinus reduced the disorderliness and, in some sense, fixed the number of regular actors at three’. But πρσωπα means ‘masks’ or ‘characters’; it does not mean ‘actors’ . What the writer meant by saying that Kratinos settled the masks or characters in comedy at ‘up to three’ is not clear, but his statement is useless as evidence for the number of actors. (shrink)

Attribution theory has played a major role in social-psychological research. Unfortunately, the term attribution is ambiguous. According to one meaning, forming an attribution is making a dispositional (trait) inference from behavior; according to another meaning, forming an attribution is giving an explanation (especially of behavior). The focus of this paper is on the latter phenomenon of behavior explanations. In particular, I discuss a new theory of explanation that provides an alternative to classic attribution theory as it dominates the textbooks and (...) handbooks—which is typically as a version of Kelley’s (1967) model of attribution as covariation detection. I begin with a brief critique of this theory and, out of this critique, develop a list of requirements that an improved theory has to meet. I then introduce the new theory, report empirical data in its support, and apply it to a number of psychological phenomena. I finally conclude with an assessment of how much progress we have made in understanding behavior explanations and what has yet to be learned. (shrink)

Many philosophers and brain scientists hold that explaining consciousness is one of the major outstanding problems facing modern science today. One type of consciousness in particular—phenomenal consciousness—is thought to be especially problematic. The reasons given for believing that this phenomenon exists in the first place, however, often hinge on the claim that its existence is simply obvious in ordinary perceptual experience. Such claims motivate the study of people's intuitions about consciousness. In recent years a number of researchers in experimental (...) philosophy of mind have begun to shed light on this area, investigating how people understand and attribute those mental states that have been thought to be phenomenally conscious. In this article, we discuss the philosophical concept of phenomenal consciousness and detail the work that has been done on the question of whether lay people have this concept. (shrink)

It is common to distinguish between attributive and predicative goodness. There are good reasons to think that artistic value is a kind of attributive goodness. Surprisingly, however, much debate in philosophical aesthetics has proceeded as though artistic value is a kind of predicative goodness. As I shall argue, recognising that artistic value is attributive goodness has important consequences for a number of debates in aesthetics.

In this article the history of the attribution approach to emotion and motivation is reviewed. Early motivation theorists incorporated emotion within the pleasure/pain principle but they did not recognize specific emotions. This changed when Atkinson introduced his theory of achievement motivation, which argued that achievement strivings are determined by the anticipated emotions of pride and shame. Attribution theorists then suggested many other emotional reactions to success and failure that are determined by the perceived causes of achievement outcomes and the shared (...) characteristics or dimensions of causality. The article outlines the hypothesized dimensional antecedents of a number of self- and other-directed achievement-related emotions following success and failure. Motivational consequences of emotions also are highlighted. (shrink)

We assessed the automaticity of spatial-numerical and spatial-musical associations by testing their intentionality and load sensitivity in a dual-task paradigm. In separate sessions, 16 healthy adults performed magnitude and pitch comparisons on sung numbers with variable pitch. Stimuli and response alternatives were identical, but the relevant stimulus attribute (pitch or number) differed between tasks. Concomitant tasks required retention of either color or location information. Results show that spatial associations of both magnitude and pitch are load sensitive and that (...) the spatial association for pitch is more powerful than that for magnitude. These findings argue against the automaticity of spatial mappings in either stimulus dimension. (shrink)

We propose a descriptive version of the classical multi-attribute utility model; to that end, we add a new parameter, momentary salience, to the customary formulation. The addition of this parameter allows the theory to accommodate changes in the decision maker’s mood and circumstances, as the saliencies of anticipated consequences are driven by concerns of the moment. By allowing for the number of consequences given attention at the moment of decision to vary, the new model mutes the criticism that (...) SEU models call for an omniscient decision maker. Use of the model is illustrated with a large-scale longitudinal study showing that adolescent smokers have higher utility for smoking than nonsmokers. We also propose to use the model hierarchically to describe everyday decisions that people deal with repeatedly. Big decisions, which set policy, guide a host of nested little decisions, which in turn lead to action. For a little decision, one of the options will be consistent with the policy, and will inherit its high utility. Accordingly, most little decisions will be made quickly and will follow the policy. However, people do sometimes decide to violate their own policies, and we describe how these lapses can lead to collapse of the policy. (shrink)

Research on the cognitive abilities involved in decision making has shown that, under objective risk conditions (i.e., when explicit information about possible outcomes and risks is available), superior decisions are especially predicted by executive functions and exact number processing skills, also referred to as objective numeracy. So far, decision-making research has mainly focused on exact number processing skills, such as performing calculations or transformations of symbolic numbers. There is evidence that such exact numeric skills are based on approximate (...) number processing (ANP) skills, which enable quick and accurate processing of non-symbolic numbers (e.g. Chen and Li, 2014). Very few studies, however, have investigated ANP skills in the context of risky decision making and have analyzed direct associations among the aforementioned sub functions. Possible interactions between the closely related skills have not been considered. The current study (N = 128) examines interactions of ANP skills with executive functions and objective numeracy, in predicting risky choice behavior. ANP skills are represented by the accuracy in a dot-comparison task. Decision making is measured by two versions of the Game of Dice Task (GDT), which place different emphases on the reflection of potential risks. The results show two-way as well as three-way interactions between the measures of ANP skills, executive functions, and objective numeracy in predicting risky decisions in both GDT versions. The riskiest decisions were most frequently made in case of low scores in all of the three competencies, while good performance in any one of them resulted in significant reductions of disadvantageous decisions. The findings indicate that high ANP skills can positively affect choice behavior in individuals who have weaknesses in reflectively attributed skills, namely executive functions and objective numeracy. Potential compensatory effects and mechanisms of ANP in decision making are discussed. (shrink)

Is the way we use propositions to individuate beliefs and other intentional states analogous to the way we use numbers to measure weights and other physical magnitudes? In an earlier paper [2], I argued that there is an important disanalogy. One and the same weight can be 'related to' different numbers under different units of measurement. Moreover, the choice of a unit of measurement is arbitrary,in the sense that which way we choose doesn't affect the weight attributed to the object. (...) But it makes little sense to say that one and the same belief can be related to different propositions: different proposition means different belief. So there is no analogous arbitrary choice. (shrink)

This work has four aims: (i) to provide an overview of the current debate about the semantics of knowledge attributions, i.e. sentences of the form ⌜S knows that Φ⌝; (ii) to ground the debate in a single semantic-pragmatic framework; (iii) to identify a methodology for describing the semantics of knowledge attributions; (iv) to go some way towards describing the semantics of knowledge attributions in light of this methodology, and in particular to defend moderate invariantist semantics against its main current rivals. (...) Aims (i) and (ii) are largely clarificatory; in §1 I set out a single semantic-pragmatic framework and over the course of this work show that it can be modified to explain and distinguish the various theories of the semantics of knowledge attributions currently on offer. Aim (iii) is also met in §1. I argue that a theory of the semantics of knowledge attributions T must be able to account for at least some ordinary speakers’ intuitions about the felicity or infelicity of utterances of the sentence ⌜S knows that Φ⌝ (felicity intuitions) purely in terms of its semantics. I also identify a number of theoretical considerations about knowledge and argue that if T conflicts with any one of these considerations, we should presume that T is false. Aim (iv) is met over the course of this work. According to moderate invariantism ⌜S knows that Φ⌝ is true if and only if S confidently believes the proposition expressed by Φ, this proposition is true and S’s epistemic position with respect to this proposition meets a moderately high epistemic standard. In §§2 – 5 I argue that the main current rivals to moderate invariantism – attributor contextualism, contrastivism, subject-sensitive invariantism and assessor relativism – conflict with at least one of the theoretical considerations identified in §1. In §6 I argue that moderate invariantism accounts for some ordinary speakers’ felicity intuitions purely in terms of the semantics of ⌜S knows that Φ⌝; I also argue that it is consistent with all of the theoretical considerations identified in §1. Moreover, in §§2 – 6 I argue that no theory is capable of accounting for all felicity intuitions purely in terms of the semantics of ⌜S knows that Φ⌝, and that only moderate invariantism can successfully explain why speakers have all of these intuitions. In §7 I conclude that moderate invariantism correctly describes of the semantics of knowledge attributions, or at least does so better than its main current rivals. (shrink)

A growing body of empirical evidence suggests that folk knowledge attribution practices regarding some epistemological thought experiments differ significantly from the consensus found in the philosophical literature. More specifically, laypersons are likely to ascribe knowledge in the so-called Authentic Evidence Gettier-style cases, while most philosophers deny knowledge in these cases. The intuitions shared by philosophers are often used as evidence in favor (or against) certain philosophical analyses of the notion of knowledge. However, the fact that these intuitions are not universal, (...) as non-philosophers do not sympathize with verdicts made by philosophers, is problematic and requires some explanation. Recently, a promising theoretical approach emerged that could be used to explain away unexpected folk knowledge attributions. According to the protagonist projection hypothesis, when subjects answer questions about some hypothetical scenario, their judgments might result from adopting the cognitive perspective of the protagonist in the given scenario. Previous experimental findings suggest protagonist projection might be responsible for problematic knowledge attributions in Gettier-style cases. This paper reports data collected in an experiment which focused on five different Authentic Evidence Gettier-style scenarios and investigated the impact of protagonist projection on folk knowledge ascriptions in such cases. The results bring some support to the protagonist projection hypothesis, but do not allow to explain away a substantial number of problematic folk knowledge attributions. (shrink)

While there is convincing evidence that preverbal human infants and non-human primates can spontaneously represent number, considerable debate surrounds the possibility that such capacity is also present in other animals. Fish show a remarkable ability to discriminate between different numbers of social companions. Previous work has demonstrated that in fish the same set of signature limits that characterize non-verbal numerical systems in primates is present but yet to provide any demonstration that fish can really represent number rather than (...) basing their discrimination on continuous attributes that co-vary with number. In the present work, using the method of 'item by item' presentation, we provide the first evidence that fish are capable of selecting the larger group of social companions relying exclusively on numerical information. In our tests subjects could choose between one large and one small group of companions when permitted to see only one fish at a time. Fish were successful when both small (3 vs. 2) and large numbers (8 vs. 4) were involved and their performance was not affected by the density of the fish or by the overall space occupied by the group. (shrink)

Small numbers are spontaneously associated with left space and larger numbers with right space (the SNARC effect), for example when classifying numbers by parity. This effect is often attributed to reading habits but a causal link has so far never been documented. We report that bilingual Russian-Hebrew readers show a SNARC effect after reading Cyrillic script (from left-to-right) that is significantly reduced after reading Hebrew script (from right-to-left). In contrast, they have similar SNARC effects after listening to texts in either (...) language. These results support the view that spatially directional scanning habits contribute to the spatial association of numbers but also emphasize its flexibility. (shrink)

This paper identifies ‘savage numbers’ – number-like or number-replacing concepts and practices attributed to peoples viewed as civilizationally inferior – as a crucial and hitherto unrecognized body of evidence in the first two decades of the Victorian science of prehistory. It traces the changing and often ambivalent status of savage numbers in the period after the 1858–1859 ‘time revolution’ in the human sciences by following successive reappropriations of an iconic 1853 story from Francis Galton's African travels. In response (...) to a fundamental lack of physical evidence concerning prehistoric men, savage numbers offered a readily available body of data that helped scholars envisage great extremes of civilizational lowliness in a way that was at once analysable and comparable, and anecdotes like Galton's made those data vivid and compelling. Moreover, they provided a simple and direct means of conceiving of the progressive scale of civilizational development, uniting societies and races past and present, at the heart of Victorian scientific racism. (shrink)

An influential argument is that mental processes can be explained at three different levels of analysis: the functional, algorithmic, and implementation level. Identity attribution (the process whereby an identity is attributed to another individual or to the self) has been rarely explored at the functional level. To address this, here I propose a theory of identity attribution grounded on Bayesian inference, being the latter a well-established functional perspective in cognitive science. The theory posits that an identity is inferred based on (...) observations about a target’s features, about the context, and about motivational factors. This inference can be made based upon multiple sources of observations, with prior beliefs becoming more prominent when observations are fewer in number. The theory offers an interpretation of key processes driving identity attribution, potentially providing a platform for integrating different perspectives on identity in psychology and sociology. (shrink)

Textual and historical subtleties aside, let's call the idea that numbers are properties of equinumerous sets ‘the Fregean thesis.’ In a recent paper, Palle Yourgrau claims to have found a decisive refutation of this thesis. More surprising still, he claims in addition that the essence of this refutation is found in the Grundlagen itself – the very masterpiece in which Frege first proffered his thesis. My intention in this note is to evaluate these claims, and along the way to shed (...) some light on relevant passages of the Grundlagen. I will argue that Yourgrau does not make his case.The arguments with which we are concerned are found in the last three sections of Yourgrau's paper. A pervasive difficulty in these sections is that it is not clear exactly what Yourgrau is arguing against. The stated object of his attack is the Fregean thesis, a thesis about what numbers are; however, instead of a frontal assault, his strategy is to embark on a foray into the ill-defined issue of what it is that numbers number, where, roughly speaking, a number n numbers an object x just in case n can be legitimately assigned to x. The reason for this shift in emphasis appears to be rooted in a misconception. As we’ll see in more detail shortly, Yourgrau's argument against the Fregean thesis is based on an extension of a well known argument of Frege's found in §§22-3 of the Grundlagen, which Glenn Kessler has tagged the ‘relativity argument,’. According to Yourgrau, this is an argument ‘to the effect that what is literally numbered cannot simply be concrete objects’. This is incorrect. Frege himself clarifies the point of the argument in §21 with the following preface:In language, numbers (i.e., numerals] most commonly appear in adjectival form and attributive construction in the same sort of way as the words "hard" or "heavy" or "red," which have for their meanings properties of external things. It is natural to ask whether we must think of the individual numbers too as such properties, and whether, accordingly, the concept of number can be classed along with that, say, of color. (shrink)

The clustering of mixed-attribute data is a vital and challenging issue. The density peaks clustering algorithm brings us a simple and efficient solution, but it mainly focuses on numerical attribute data clustering and cannot be adaptive. In this paper, we studied the adaptive improvement method of such an algorithm and proposed an adaptive mixed-attribute data clustering method based on density peaks called AMDPC. In this algorithm, we used the unified distance metric of mixed-attribute data to construct (...) the distance matrix, calculated the local density based on K-nearest neighbors, and proposed the automatic determination method of cluster centers based on three inflection points. Experimental results on real University of California-Irvine datasets showed that the proposed AMDPC algorithm could realize adaptive clustering of mixed-attribute data, can automatically obtain the correct number of clusters, and improved the clustering accuracy of all datasets by more than 22.58%, by 24.25%, by 28.03%, by 22.5%, and by 10.12% for the Heart, Cleveland, Credit, Acute, and Adult datasets compared to that of the traditional K-prototype algorithm, respectively. It also outperformed a modified density peaks clustering algorithm for mixed-attribute data algorithms. (shrink)

Employee attributions and emotional reactions to unethical behavior of top leaders in an organization recently involved in a highly publicized ethics scandal were examined. Participants (n = 76) from a large southern California government agency completed an ethical climate assessment. Secondary data analysis was performed on the written commentary to an open-ended question seeking employees' perceptions of the ethical climate. Employees attributed the organization's poor ethical leadership to a number of causes, including: lack of moral reasoning, breaches of trust, (...) hypocrisy, and poor ethical behavior role modeling. Emotional reactions to corruption included cynicism, optimism, pessimism, paranoia and fear, and were targeted at top leaders, organizational practices (i.e., the old boy network, nepotism, and cronyism) and ethics interventions. Implications for leadership training and other organizational ethics interventions are discussed. (shrink)

It is the traditional view of psychology that the attributes of sensation show a one-to-one correspondence to the dimensions of the stimulus. Some such view is also implicit in the naïve epistemology of the physicist. He often thinks of pitch as if it were the perception of the frequency of a tone, but that view soon runs into difficulties. Within psychology it was Wundt who originally equipped sensation with two attributes, quality and intensity, thus making sensations mirror the more obvious (...) aspects of stimuli which differ as to kind and in degree. Later it became clear to Külpe that extension must be an attribute of visual and tactual sensations because the retina and the skin are areal organs and because extent enters into perception quite as ‘immediately’ as does intensity. A loud sound is not a congeries of faint sounds, nor is a perceived line a row of sensations. In a similar reaction against Wundtian atomism Külpe also added duration to the list, for a tone that lasts 0.8 sec. yields a different perception from one that lasts 0.6 sec. and yet there is no sense to saying that the first represents a greater number of seried sensations than the second. Thus the four classical attributes of sensation are quality, intensity, extensity and protensity. The conventional view has been that they are respectively correlated with four aspects of the stimulus, and this paper is written with the intention of refuting this view. (shrink)

A growing body of empirical evidence suggests that folk knowledge attribution practices regarding some epistemological thought experiments differ significantly from the consensus found in the philosophical literature. More specifically, laypersons are likely to ascribe knowledge in the so-called Authentic Evidence Gettier-style cases, while most philosophers deny knowledge in these cases. The intuitions shared by philosophers are often used as evidence in favor (or against) certain philosophical analyses of the notion of knowledge. However, the fact that these intuitions are not universal, (...) as non-philosophers do not sympathize with verdicts made by philosophers, is problematic and requires some explanation. Recently, a promising theoretical approach emerged that could be used to explain away unexpected folk knowledge attributions. According to the protagonist projection hypothesis, when subjects answer questions about some hypothetical scenario, their judgments might result from adopting the cognitive perspective of the protagonist in the given scenario. Previous experimental findings suggest protagonist projection might be responsible for problematic knowledge attributions in Gettier-style cases. This paper reports data collected in an experiment which focused on five different Authentic Evidence Gettier-style scenarios and investigated the impact of protagonist projection on folk knowledge ascriptions in such cases. The results bring some support to the protagonist projection hypothesis, but do not allow to explain away a substantial number of problematic folk knowledge attributions. (shrink)

The aim of this paper is to show that John Wyclif’s theory of space is at once an interpretation of the Platonic theory of place and a Neopythagorean conception of magnitudes and numbers. The result is an original form of mathematical atomism in which atoms are point-like entities with a particular situation in space. If the core of this view comes from Boethius’ De arithmetica, John Wyclif is also influenced by Robert Grosseteste’s metaphysics, which includes the Boethian number theory (...) within the Christian tale of the creation of the world ex nihilo. John Wyclif, however, adds some novelty to this theory concerning the epistemological status of this hypothetical description of the creation of the world out of atoms. First, according to Wyclif, whereas geometry is concerned with sensible and imaginable beings, arithmetic, which is purely intellectual, has access to the deep mathematical structure of the universe. He then suggests a subordination of geometry under arithmetic, which he considers the most solid basis for his metaphysics. As a result, with the attribution of numbers and units to every level of reality, it becomes possible to reform our natural imagination, so that it can imagine the atomic structure of matter and space. (shrink)

Em seu livro recente, Engelmann (2021) avançou uma leitura do Tractatus que, a seu ver, removeria as dificuldades presentes em outras leituras (em particular, nas leituras “metafísica” e “resoluta”). Neste artigo, ocupar-me-ei da crítica de Engelmann às leituras metafísicas do Tractatus. Tal crítica baseia-se na ideia de que essas leituras estão comprometidas com algumas necessidades de re, o que violaria a autonomia da lógica e a ideia Tractariana segundo a qual só há necessidade lógica. Analisarei o caso particular de uma (...) suposta necessidade de re, a saber, a do número de objetos no mundo. Depois de descrever alguns aspectos positivos e alguns obstáculos à interpretação de Engelmann desse caso, sugerirei que Engelmann está inconscientemente atribuindo ao Tractatus uma concepção de lógica que Wittgenstein, por sua vez, criticamente atribuiu a Russell e a Ramsey e que, portanto, não pode ser a sua. Por fim, retornarei à motivação original para a interpretação de Engelmann, que é a de salvar a autonomia da lógica, mostrando de maneira breve como conciliar a autonomia da lógica com um número fixo de objetos.AbstractIn a recent book, Engelmann (2021) has put forward a reading of the Tractatus which he maintains would remove the difficulties presented in other readings, particularly the “metaphysical” and the “resolute” readings. In this paper, my concern will be with Engelmann’s criticism of the metaphysical readings of the Tractatus. This criticism is centered on the idea that such readings are committed to some de re necessities,which violates the autonomy of logic and the Tractarian idea that there is only logical necessity. I analyze the particular case of a supposed de re necessity, namely, the number of objects in the world. After describing some positive aspects and drawbacks of Engelmann’s interpretation of this case, I suggest that Engelmann is unconsciously attributing to the Tractatus a conception of logic that Wittgenstein in turncritically attributed to Russell and Ramsey; thus, this conception cannot be his own. Finally, I return to the original motivation for Engelmann’s interpretation, which is to save the autonomy of logic, and briefly show how to conciliate the autonomy of logic with a fixed number of objects. (shrink)

This paper advances a new agentially undemanding account of the conditions of attributability, the Minimal Approval account, and argues that it has a number of advantages over traditional Deep Self theories, including the way in which it handles agents with conditions like addiction, Tourette syndrome, and misophonia. It is argued that in order for an agent to be attributionally responsible, the mental process that leads to her action must dispose her to be such that she would, upon reflec-tion, approve (...) to some minimal degree of being moved to action by the motive on which she in fact acts. (shrink)

Many have argued that Plato’s intermediates are not independent entities. Rather, they exemplify the incapacity of discursive thought to cognizing Forms. But just what does this incapacity consist in? Any successful answer will require going beyond the intermediates themselves to another aspect of Plato’s mathematical thought - his attribution of a quasi-numerical structure to Forms. For our purposes, the most penetrating account of eidetic numbers is Jacob Klein’s, who saw clearly that eidetic numbers are part of Plato’s inquiry into the (...) ontological basis for all counting: the existence of a plurality of formal elements, distinct yet combinable into internally articulate unities. However, Klein’s study of the Sophist reveals such articulate unities as imperfectly countable and therefore opaque to διάνοια. And only this opacity, I argue, successfully explains the relationship of intermediates to Forms. (shrink)

The side-effect effect, in which an agent who does not speci␣cally intend an outcome is seen as having brought it about intentionally, is thought to show that moral factors inappropriately bias judgments of intentionality, and to challenge standard mental state models of intentionality judgments. This study used matched vignettes to dissociate a number of moral factors and mental states. Results support the view that mental states, and not moral factors, explain the side-effect effect. However, the critical mental states appear (...) not to be desires as proposed in standard models, but rather ‘deeper’ evaluative states including values and core evaluative attitudes. (shrink)

The Frege-Russell view is that existence is a second-order property rather than a property of individuals. One of the most compelling arguments for this view is based on the premise that there is an especially close connection between existence and number. The most promising version of this argument is by C.J.F Williams (1981, 1992). In what follows, I argue that this argument fails. I then defend an account according to which both predications of number and existence attribute (...) properties to individuals. (shrink)

What is it for an attribute to be psychological? One clever and inventive, albeit somewhat Byzantine answer to this vexing philosophical question has lately been proposed by Roderick M. Chisholm. Chisholm’s approach is to take a small number of technical philosophical notions as given and then employ these in a series of definitions which together yield an account of the psychological. I examine Chisholm’s account and show that it doesn’t work.

It has been claimed that empirical work in psychology requires the attribution of representational content to perceptual states: that is, the attribution of veridicality conditions to those states. This is a claim that can only be evaluated by the examination of actual empirical research. In this paper I argue that talk of ‘representation’ in at least one area of research in the psychology of perception can be reinterpreted so as to avoid the attribution of veridicality conditions. This area is the (...) study of human capacities to perceive the relative numerosities of collections of objects. (shrink)

Despite the importance of Kant's claims about mathematical cognition for his philosophy as a whole and for subsequent philosophy of mathematics, there is still no consensus on his philosophy of arithmetic, and in particular the role he assigns intuition in it. This inquiry sets aside the role of intuition for the nonce to investigate Kant's conception of natural number. Although Kant himself doesn't distinguish between a cardinal and an ordinal conception of number, some of the properties Kant attributes (...) to number can be characterized as cardinal or ordinal. This essay argues that Kant's conception of number includes both cardinal and ordinal elements; it suggests that the cardinal elements provide the basis of a conception of number in general, while the ordinal elements contribute to specifying the exact size of particular collections. In considering these elements, roles for intuition begin to emerge, setting the stage for a reevaluation of the role of intuition in Kant's arithmetic. (shrink)

Consciousness is defined as operating with the meanings of representations, which are what arises in mind under the influence of a stimulus (primary representations) as well as what arises as a result of their transformation (secondary, combined representations). In a first approximation, a representation is expressed by words. The concept of “representation” is a special case of the concept of “information-certainty”, which is the result of distinction. Any distinction is a distinction by a specific attribute and representation is the (...) value of the attribute. In relative ontology, distinction is an essential condition of being that is formalized quantitatively through the operation of ontological subtraction, which is a quantitative expression of representation in relation to consciousness. The finite set of representations for one attribute can always be sorted in ascending order of this attribute values. In the order constructed, each representation corresponds to an attribute number, the only difference of which from a number in mathematics is that the one is always associated with a specific attribute, and the other is not associated with any attribute. The meaning of a representation expressed by an attribute number has a place in an ordered quantitative series of other representations of the same attribute, which is the basis of distinction. Operating with meanings is operating with attributive numbers-meanings. This method of the meaning describing is called the relative method. All operations with the meanings of representations are performed in a multidimensional cognitive space. Each axis of the cognitive space corresponds to an attribute by which representations differ. On each axis there are attribute numbers corresponding to the meanings of representations for the attribute. This approach is a quantitative method of describing of all experimental processes of consciousness, which allows to build a scientific, i.e. quantitative, theory of consciousness with laws written down in a quantitative way. Based on this, it is possible to construct a quantitative calculation of this theory predictions. Such a prediction allows to make an accurate (unambiguous) experimental verification. Due to the quantitative way of describing the operation of meanings, such a theory of consciousness is easily modeled in information technologies, since the latter are also based on the numerical nature of all their processes. The main difference between the relative method and the vast majority of methods using information technologies for text processing is that the relative method, firstly, is not statistical, and secondly, conveys the meaning of the text fully and most adequately. The relative method is effective in operating not only with text data, but also with any data of a different nature, for example, with video data, audio data. (shrink)

The purpose of our study is to investigate the effects of the number of products, product attributes, and prices on consumer confusion, conduct a numerical analysis to check the robustness of the results, and present an example of the cell phone market in Japan. Following an ideal point model and embedding the number of products and product attributes, we clarify how these factors affect consumer confusion and purchase probability. We show that as the number of product attributes (...) increases, the choice probability of each product becomes equal, implying that consumer confusion occurs. This result is robust to the introduction of prices as strategic variables. (shrink)

Why is the number seven lucky--even holy--in almost every culture? Why do we speak of the four corners of the earth? Why do cats have nine lives? From literature to folklore to private superstitions, numbers play a conspicuous role in our daily lives. But in this fascinating book, Annemarie Schimmel shows that numbers have been filled with mystery and meaning since the earliest times, and across every society. In The Mystery of Numbers Annemarie Schimmel conducts an illuminating tour of (...) the mysteries attributed to numbers over the centuries. She begins with an informative and often surprising introduction to the origins of number systems: pre-Roman Europeans, for example, may have had one based on twenty, not ten, while the Mayans had a system more sophisticated than our own. Schimmel also reveals how our fascination with numbers has led to a rich cross-fertilization of mathematical knowledge: "Arabic" numerals, for instance, were picked up by Europe from the Arabs, who had earlier adopted them from Indian sources. But the heart of the book is an engrossing guide to the symbolism of numbers. Number symbolism, she shows, has deep roots in Western culture, from the philosophy of the Pythagoreans and Platonists, to the religious mysticism of the Cabala and the Islamic Brethren of Purity, to Kepler's belief that the laws of planetary motion should be mathematically elegant, to the unlucky thirteen. After exploring the sources of number symbolism, Schimmel examines individual numbers ranging from one to ten thousand, discussing the meanings they have had for Judaic, Christian, and Islamic traditions, with examples from Indian, Chinese, and Native American cultures as well. Two, for instance, has widely been seen as a number of contradiction and polarity, a number of discord and antithesis. And six, according to ancient and neo-platonic thinking, is the most perfect number because it is both the sum and the product of its parts. Using examples ranging from the Bible to the Mayans to Shakespeare, she shows how numbers have been considered feminine and masculine, holy and evil, lucky and unlucky. A highly respected scholar of Islamic culture, Annemarie Schimmel draws on her vast knowledge to paint a rich, cross-cultural portrait of the many meanings of numbers. Engaging and accessible, her account uncovers the roots of a phenomenon we all feel every Friday the thirteenth. (shrink)

Color harmony is the focus of many researchers in the field of art and design, and its research results have been widely used in artistic creation and design activities. With the development of signal processing and artificial intelligence technology, new ideas and methods are provided for color harmony theory and color harmony calculation. In this article, psychological experimental methods and information technology are combined to design and quantify the 16-dimensional physical features of multiple colors, including multi-color statistical features and multi-color (...) contrast features. Eighty-four subjects are invited to give a 5-level score on the degree of color harmony for 164 multi-color materials selected from the screenshots of film and television scenes. Based on the multi-color physical features and the subjective evaluation experiment, the correlation analysis is firstly carried out, which shows that the overall lightness, difference of the color tones, number of multiple colors, lightness contrast, color tone contrast, and cool/warm contrast are significantly correlated with color harmony. On the other hand, the regression prediction model and classification prediction model of color harmony are constructed based on machine learning algorithms. In terms of regression prediction model, the prediction accuracy of linear models is higher than that of nonlinear models, with 63.9% as the highest, indicating that the multi-color physical features can explain color harmony well. In terms of classification prediction model, the Random Forest has the best prediction performance, with an accuracy of 80.2%. (shrink)

Ancient critics reproached Xenocrates for beginning his work on the dialectic with a discussion of voice, and until now the question why he did so has never been systematically explored. Neither do we know why Xenocrates counted syllables, as Plutarch reports, and how he arrived at such an implausibly high number. In the first part of this paper, I show that Xenocrates’ interest in voice was suggested by Plato’s discussion of letters in his later dialogues, such as the Theatetus, (...) the Sophist, the Statesman, and the Philebus. Second, a fragment from Sextus attributed to Xenocrates confirms that Xenocrates allowed for various ‘levels’ of elements, and that explains why Theuth’s method, recommended in the Philebus, is applied to syllables. Finally, I address the very possibility of knowing the actual number of syllables and words, and address some of the problems connected to the reconstruction of the mathematical argument. (shrink)

It is usual to identify initial conditions of classical dynamical systems with mathematical real numbers. However, almost all real numbers contain an infinite amount of information. I argue that a finite volume of space can’t contain more than a finite amount of information, hence that the mathematical real numbers are not physically relevant. Moreover, a better terminology for the so-called real numbers is “random numbers”, as their series of bits are truly random. I propose an alternative classical mechanics, which is (...) empirically equivalent to classical mechanics, but uses only finite-information numbers. This alternative classical mechanics is non-deterministic, despite the use of deterministic equations, in a way similar to quantum theory. Interestingly, both alternative classical mechanics and quantum theories can be supplemented by additional variables in such a way that the supplemented theory is deterministic. Most physicists straightforwardly supplement classical theory with real numbers to which they attribute physical existence, while most physicists reject Bohmian mechanics as supplemented quantum theory, arguing that Bohmian positions have no physical reality. (shrink)

This article is part of a series on the Shorter Chinese Sa?yukta-?gama. Continuing the investigation from previous research on the provenance of the BZA, it is concluded that the attribution of the BZA to the K??yap?ya school is mistaken. A comparison of the BZA’s?akra-sa?yukta with the P?li Sakka-sa?yutta shows that, with minor exceptions, the narrative content of both sa?yuttas is identical though the number of suttas varies. Finally, the article completes the translation of the?akra-sa?yukta, the first part of which (...) appeared in BSR 25. (shrink)

We propose a Bayesian framework for the attribution of knowledge, and apply this framework to generate novel predictions about knowledge attribution for different types of “Gettier cases”, in which an agent is led to a justified true belief yet has made erroneous assumptions. We tested these predictions using a paradigm based on semantic integration. We coded the frequencies with which participants falsely recalled the word “thought” as “knew” (or a near synonym), yielding an implicit measure of conceptual activation. Our experiments (...) confirmed the predictions of our Bayesian account of knowledge attribution across three experiments. We found that Gettier cases due to counterfeit objects were not treated as knowledge (Experiment 1), but those due to intentionally-replaced evidence were (Experiment 2). Our findings are not well explained by an alternative account focused only on luck, because accidentally-replaced evidence activated the knowledge concept more strongly than did similar false belief cases (Experiment 3). We observed a consistent pattern of results across a number of different vignettes that varied the quality and type of evidence available to agents, the relative stakes involved, and surface details of content. Accordingly, the present findings establish basic phenomena surrounding people’s knowledge attributions in Gettier cases, and provide explanations of these phenomena within a Bayesian framework. (shrink)

Over recent decades there has been a growing interest in the question of whether computer programs are capable of genuinely creative activity. Although this notion can be explored as a purely philosophical debate, an alternative perspective is to consider what aspects of the behaviour of a program might be noted or measured in order to arrive at an empirically supported judgement that creativity has occurred. We sketch out, in general abstract terms, what goes on when a potentially creative program is (...) constructed and run, and list some of the relationships (for example, between input and output) which might contribute to a decision about creativity. Specifically, we list a number of criteria which might indicate interesting properties of a program’s behaviour, from the perspective of possible creativity. We go on to review some ways in which these criteria have been applied to actual implementations, and some possible improvements to this way of assessing creativity. (shrink)

Children often personify non-living objects, such as puppets and stars. This attribution is considered a healthy phenomenon, which can simulate social exchange and enhance children's understanding of social relationships. In this study, we considered that the tendency of children to engage in personification could potentially be observed in abstract entities, such as numbers. We hypothesized that children tend to attribute personalities to numbers, which diminishes during the course of development. By consulting the methodology to measure ordinal linguistic personification (OLP), (...) which is a type of synesthesia, we quantified the frequency with which child and adult populations engage in number personification. Questionnaires were completed by 151 non-synesthetic children (9--12 years old) and 55 non-synesthetic adults. Children showed a higher tendency than adults to engage in number personification, with respect to temporal consistency and the frequency of choosing meaningful answers. Additionally, children tended to assign unique and exclusive descriptions to each number from zero to nine. By synthesizing the series of analyses, we revealed the process in which number personification diminishes throughout development. In the discussion, we examined the possibility that number personification serves as a discrimination clue to aid children's comprehension of the relationships between numbers. (shrink)

It has been argued that the approximate number system (ANS) constitutes a problem for the grounded approach to cognition because it implies that some conceptual tasks are performed by non-perceptual systems. The ANS is considered non-perceptual mainly because it processes stimuli from different modalities. Jones (2015) has recently argued that this system has many features (such as being modular) which are characteristic of sensory systems. Additionally, he affirms that traditional sensory systems also process inputs from different modalities. This suggests (...) that the ANS is a perceptual system and therefore it is not problematic for the grounded view. In this paper, I defend the amodal approach to the ANS against these two arguments. In the first place, perceptual systems do not possess the properties attributed to the ANS and therefore these properties do not imply that the ANS is perceptual. In the second place, I will propose that a sensory system only needs to be dedicated to process modality-specific information, which is consistent with responding to inputs from different modalities. I argue that the cross-modal responses exhibited by traditional sensory systems are consistent with modality-specific information whereas some responses exhibited by the ANS are not. (shrink)

This article explores the impact of an Increase in the average Number of Authors per Publication on known ethical issues of authorship. For this purpose, the ten most common ethical issues associated with scholarly authorship are used to set up a taxonomy of existing issues and raise awareness among the community to take precautionary measures and adopt best practices to minimize the negative impact of INAP. We confirm that intense international, interdisciplinary and complex collaborations are necessary, and INAP is (...) an expression of this trend. However, perverse incentives aimed to increase institutional and personal publication counts and egregious instances of guest or honorary authorship are problematic. We argue that whether INAP is due to increased complexity and scale of science, perverse incentives or undeserved authorship, it could negatively affect known ethical issues of authorship at some level. In the long run, INAP depreciates the value of authorship status and may disproportionately impact junior researchers and those who contribute to technical and routine tasks. We provide two suggestions that could reduce the long-term impact of INAP on the reward system of science. First, we suggest further refinement of the CRediT taxonomy including better integration into current systems of attribution and acknowledgement, and better harmony with major authorship guidelines such as those suggested by the ICMJE. Second, we propose adjustments to the academic recognition and promotion systems at an institutional level as well as the introduction of best practices. (shrink)

The purpose of the present study was to profile high school students’ achievement as a function of their demographic characteristics, parent attributes, and school behaviors. Students were nested within schools in the Saudi Arabia Kingdom. Out of a large sample of 500k, participants involved 3 random samples of 2,000 students measured during the years 2016, 2017, and 2018. Randomization was conducted at the student level to ensure that all school units will be represented and at their respective frequency. Students were (...) nested within 50 high schools. We adopted the multilevel latent profile analysis protocol put forth by Schmiege et al. and Mäkikangas et al. that account for nested data and tested latent class structure invariance over time. Results pointed to the presence of a 4-profile solution based on BIC, the Bayes factor, and several information criteria put forth by Masyn. Latent profile separation was mostly guided by parents’ education and the number of student absences. Two models tested whether the proportions of level 1 profiles to level 2 units are variable and whether level 2 profiles vary as a function of level 1 profiles. Results pointed to the presence of significant variability due to schools. (shrink)