Recent work has defended “Euclidean” theories of set size, in which Cantor’s Principle (two sets have equally many elements if and only if there is a one-to-one correspondence between them) is abandoned in favor of the Part-Whole Principle (if A is a proper subset of B then A is smaller than B). It has also been suggested that Gödel’s argument for the unique correctness of Cantor’s Principle is inadequate. Here we see from simple examples, not that Euclidean theories of (...) set size are wrong, but that they must be either very weak and narrow or largely arbitrary and misleading. (shrink)

The word ‘equality’ often requires disambiguation, which is provided by context or by an explicit modifier. For each sort of magnitude, there is at least one sense of ‘equals’ with its correlated senses of ‘is greater than’ and ‘is less than’. Given any two magnitudes of the same sort—two line segments, two plane figures, two solids, two time intervals, two temperature intervals, two amounts of money in a single currency, and the like—the one equals the other or the one is (...) greater than the other or the one is greater than the other [sc. in appropriate correlated senses of ‘equals’, ‘is greater than’ and ‘is less than’]. In case there are two or more appropriate senses of ‘equals’, the one intended is often indicated by an adverb. For example, one plane figure may be said to be equal in area to another and, in certain cases, one plane figure may be said to be equal in length to another. Each sense of ‘equality’ is tied to a specific domain and is therefore non-logical. Notice that in every cases ‘equality’ is definable in terms of ‘is greater than’ and also in terms of ‘is less than’ both of which are routinely considered domain specific, non-logical. The word ‘identity’ in the logical sense does not require disambiguation. Moreover, it is not correlated ‘is greater than’ and ‘is less than’. If it is not the case that a certain designated triangle is [sc. is identical to] an otherwise designated triangle, it is not necessary for the one to be greater than or less than the other. Moreover, if two magnitudes are equal then a unit of measure can be chosen and, no matter what unit is chosen, each magnitude is the same multiple of the unit that the other is. But identity does not require units. In this regard, congruence is like identity and unlike equality. In arithmetic, the logical concept of identity is coextensive with the arithmetic concept of equality. The logical concept of identity admits of an analytically adequate definition in terms of logical concepts: given any number x and any number y, x is y iff x has every property that y has. The arithmetical concept of equality admits of an analytically adequate definition in terms of arithmetical concepts: given any number x and any number y, x equals y iff x is neither less than nor greater than y. As Aristotle told us and as Frege retold us, just because one relation is coextensive with another is no reason to conclude that they are one. (shrink)

Are there different sizes of infinity? That is, are there infinite sets of different sizes? This is one of the most natural questions that one can ask about the infinite. But it is of course generally taken to be settled by mathematical results, such as Cantor’s theorem, to the effect that there are infinite sets without bijections between them. These results settle the question, given an almost universally accepted principle relating size to the existence of functions. The principle is: (...) for any sets A and B, if A is the same size as B, then there is a bijection from A to B. The aim of the paper, however, is to argue that this question is in fact wide open: to argue that we are not in a position to know the answer, because we are not in one to know the principle. The aim, that is, is to argue that for all we know there is only one size of infinity. (shrink)

DOI: 10.1080/00031305.2018.1564697 When the editors of Basic and Applied Social Psychology effectively banned the use of null hypothesis significance testing (NHST) from articles published in their journal, it set off a fire-storm of discussions both supporting the decision and defending the utility of NHST in scientific research. At the heart of NHST is the p-value which is the probability of obtaining an effect equal to or more extreme than the one observed in the sample data, given the null hypothesis and (...) other model assumptions. Although this is conceptually different from the probability of the null hypothesis being true, given the sample, p-values nonetheless can provide evidential information, toward making an inference about a parameter. Applying a 10,000-case simulation described in this article, the authors found that p-values’ inferential signals to either reject or not reject a null hypothesis about the mean (α = 0.05) were consistent for almost 70% of the cases with the parameter’s true location for the sampled-from population. Success increases if a hybrid decision criterion, minimum effect size plus p-value (MESP), is used. Here, rejecting the null also requires the difference of the observed statistic from the exact null to be meaningfully large or practically significant, in the researcher’s judgment and experience. The simulation compares performances of several methods: from p-value and/or effect size-based, to confidence-interval based, under various conditions of true location of the mean, test power, and comparative sizes of the meaningful distance and population variability. For any inference procedure that outputs a binary indicator, like flagging whether a p-value is significant, the output of one single experiment is not sufficient evidence for a definitive conclusion. Yet, if a tool like MESP generates a relatively reliable signal and is used knowledgeably as part of a research process, it can provide useful information. (shrink)

Consider an infinite set of discrete, finite-sized solid balls (i.e., elements) extending in all directions forever. Here, infinite set is not meant so much in the abstract, mathematical sense but in more of a physical sense where the balls have physical size and physical location-type relationships with their neighbors. In this sense, the set is used as an analogy for our possibly infinite physical universe. Two observers are viewing this set. One observer is internal to the set and is (...) of the same finite size scale as the ball elements. Another observer is external to the set and is infinite in size relative to the balls and observer within the set. This observer is of the same size scale as the set as a whole. What do these sets look like to the two observers? The finite-sized (relative to the balls inside the set) observer within the set would view the set as a space composed of discrete, finite-sized objects. The external infinite-sized (relative to the inside the set) observer would view the very same set as a continuous space and would see no distinct elements within the set. How does this relate to us? First, the differing views of set N as being composed of a discrete versus continuous space may be related to the differing views of spacetime as discrete and continuous. Second, the perspective of the observer would have an impact on the assignment of a cardinality to an infinite set. (shrink)

Objective: Evidence suggests people experience an oral size illusion and commonly perceive oral size inaccurately; however, the nature of the illusion remains unclear. The objectives of the present study were to confirm the presence of an oral size illusion, determine the magnitude (amount) and direction (underestimation or overestimation) of the illusion, and determine whether immediately prior crossmodal perceptual experiences affected the magnitude and direction. Design: Participants (N = 27) orally assessed 9 sizes of stainless steel spheres (1/16 (...) in to 1/2 in) categorized as small, medium, or big, and matched them with digital and visual reference sets. Each participant completed 20 matching tasks in 3 assessments. For control assessments, 6 oral spheres were matched with reference sets of same-sized spheres. For primer-control assessments, similar to control, 6 matching tasks were preceded by cross-modal experiences of the same-sized sphere. For experimental assessments, 8 matching tasks were preceded by a cross-modal experience of a differently sized sphere. Results: For control assessments, small and medium spheres were consistently underestimated, and big spheres were consistently overestimated. For experimental assessments, magnitude and direction of the oral size illusion varied according to the size of the sphere used in the cross-modal experience. Conclusion: Results seemed to confirm an oral size illusion, but direction of the illusion depended on the size of the object. Immediately prior cross-modal experiences influenced magnitude and direction of the illusion, suggesting that aspects of oral perceptual experience are dependent upon factors outside of oral perceptual anatomy and the properties of the oral stimulus. (shrink)

Abstract: The efficiency and performance of sorting algorithms play a crucial role in various applications and industries. In this research paper, we present a comprehensive comparative analysis of popular sorting algorithms on datasets of different sizes and characteristics. The aim is to evaluate the algorithms' performance and identify their strengths and weaknesses under varying scenarios. We consider six commonly used sorting algorithms: QuickSort, TimSort, MergeSort, HeapSort, RadixSort, and ShellSort. These algorithms represent a range of approaches and techniques, including divide-and-conquer, hybrid (...) sorting, and simple comparison-based methods. To assess their performance, we employ a diverse set of datasets, including the Iris dataset (1K), student dataset (5.8K), Wine dataset (6.5K), Uniform (10K), Normal (10K), Exponential (10K), Bimodal (10K), Yelp dataset (10K), MNIST dataset (42K), Uniform (100K), Normal (100K), Exponential (100K), Bimodal (100K), Uniform (500K), Normal (500K), Exponential (500K), Bimodal (500K), Uniform (1M), Normal (1M), Exponential (1M), and Bimodal (1M). These datasets cover a wide range of sizes and characteristics, allowing us to analyze the algorithms' performance across different dimensions. We measure and compare several key metrics, including execution time, memory usage, algorithmic complexity and stability. By analyzing these metrics, we gain insights into the efficiency and suitability of each algorithm for different dataset sizes and characteristics. We also discuss the implications of the findings in practical applications. Our results reveal important trade-offs among the sorting algorithms. While some algorithms excel in certain scenarios, others demonstrate better scalability or memory efficiency. We identify the best-performing algorithms for specific dataset characteristics and highlight their strengths and limitations. This research can assist developers and practitioners in selecting appropriate sorting algorithms based on their specific requirements and dataset characteristics. In conclusion, this comparative analysis provides a valuable contribution to the understanding of sorting algorithm performance. The findings contribute insights into the efficiency and suitability of popular sorting algorithms across datasets of different sizes and characteristics. By evaluating key metrics and discussing the implications, we offer guidance for selecting the most appropriate sorting algorithm in various practical scenarios. (shrink)

Sustainability is a crucial issue for many sectors in Malaysia, including the manufacturing sector. Many businesses, especially the chemical manufacturing industry, aim to achieve a sustainable business through the implementation of green practices. Green practices provide guidelines for the employees to simultaneously sustain the organisation in a sustainable manner and carry out the required manufacturing activities. Focusing on that, this study aimed to examine the effects of green practices on corporate sustainability performance through Islamic work ethics, organisation size, and (...) organisation age as moderators. Using the stratified random sampling technique, 344 chemical manufacturing organisations in Malaysia were invited to participate in a survey. Data from 130 completed questionnaire sets were subjected to partial least square (PLS) analysis. The results demonstrated significant effects of green practices on corporate sustainability performance via Islamic work ethics and organisation size. However, organisation age was found to exhibit no moderation effect on the relationship between green practices and corporate sustainability performance. Conclusively, as part of the organisational strategies, the sustainability of chemical manufacturing organisations must involve successful implementation of green practices, Islamic work ethics, and organisation size. This study offered several theoretical and practical contributions on green practices, Islamic work ethics, organisation size, and organisation age, and corporate sustainability performance. Theoretically, this study extended literature on the resource-based view theory, natural-resource-based view theory, and stakeholder theory. Al-Quran and hadith were used to support this study to link the relationships of the variables under study, particularly in the context of chemical manufacturing organisations in Malaysia. Practically, this study was expected to assist chemical manufacturers in selecting the appropriate green practices to achieve corporate sustainability performance and good implementation of Islamic work ethics. Additionally, it is recommended for future research to explore other types of industries in the manufacturing sector given the focus of this study on the chemical manufacturing industry only. (shrink)

According to Cantor (Mathematische Annalen 21:545–586, 1883 ; Cantor’s letter to Dedekind, 1899 ) a set is any multitude which can be thought of as one (“jedes Viele, welches sich als Eines denken läßt”) without contradiction—a consistent multitude. Other multitudes are inconsistent or paradoxical. Set theoretical paradoxes have common root—lack of understanding why some multitudes are not sets. Why some multitudes of objects of thought cannot themselves be objects of thought? Moreover, it is a logical truth that such multitudes do (...) exist. However we do not understand this logical truth so well as we understand, for example, the logical truth $${\forall x \, x = x}$$ . In this paper we formulate a logical truth which we call the productivity principle. Rusell (Proc Lond Math Soc 4(2):29–53, 1906 ) was the first one to formulate this principle, but in a restricted form and with a different purpose. The principle explicates a logical mechanism that lies behind paradoxical multitudes, and is understandable as well as any simple logical truth. However, it does not explain the concept of set. It only sets logical bounds of the concept within the framework of the classical two valued $${\in}$$ -language. The principle behaves as a logical regulator of any theory we formulate to explain and describe sets. It provides tools to identify paradoxical classes inside the theory. We show how the known paradoxical classes follow from the productivity principle and how the principle gives us a uniform way to generate new paradoxical classes. In the case of ZFC set theory the productivity principle shows that the limitation of size principles are of a restrictive nature and that they do not explain which classes are sets. The productivity principle, as a logical regulator, can have a definite heuristic role in the development of a consistent set theory. We sketch such a theory—the cumulative cardinal theory of sets. The theory is based on the idea of cardinality of collecting objects into sets. Its development is guided by means of the productivity principle in such a way that its consistency seems plausible. Moreover, the theory inherits good properties from cardinal conception and from cumulative conception of sets. Because of the cardinality principle it can easily justify the replacement axiom, and because of the cumulative property it can easily justify the power set axiom and the union axiom. It would be possible to prove that the cumulative cardinal theory of sets is equivalent to the Morse–Kelley set theory. In this way we provide a natural and plausibly consistent axiomatization for the Morse–Kelley set theory. (shrink)

In this article we derived an important example of the inconsistent countable set in second order ZFC (ZFC_2) with the full second-order semantics. Main results: (i) :~Con(ZFC2_); (ii) let k be an inaccessible cardinal, V is an standard model of ZFC (ZFC_2) and H_k is a set of all sets having hereditary size less then k; then : ~Con(ZFC + E(V)(V = Hk)):.

I defend the idea that a liberal commitment to value neutrality is best honoured by maintaining a pure cardinality component in our rankings of opportunity or liberty sets. I consider two challenges to this idea. The first holds that cardinality rankings are unnecessary for neutrality, because what is valuable about a set of liberties from a liberal point of view is not its size but rather its variety. The second holds that pure cardinality metrics are insufficient for neutrality, because (...) liberties cannot be individuated into countable entities without presupposing some relevantly partisan evaluative perspective. I argue that a clear understanding of the liberal basis for valuing liberty shows the way to satisfying responses to both challenges. (shrink)

Suppose one has a system, the infinite set of positive integers, P, and one wants to study the characteristics of a subset (or subsystem) of that system, the infinite subset of odd positives, O, relative to the overall system. In mathematics, this is done by pairing off each odd with a positive, using a function such as O=2P+1. This puts the odds in a one-to-one correspondence with the positives, thereby, showing that the subset of odds and the original set of (...) positives are the same size, or have the same cardinality. This counter-intuitive result ignores the “natural” relationship of one odd for every two positives in the sequence of positive integers, which would suggest that O is one-half the size of P. However, in the set of axioms that constitute mathematics, it is considered valid. Fair enough. In the physical universe (i.e., the starting system), though, relationships between entities matter. In biochemistry, if you start with an organism, say a rat, and you want to study its heart, you can do this by removing some heart cells and studying them in isolation in a cell culture system. But, the results often differ compared to what occurs in the intact animal because studying the isolated cultured cells ignores the relationships in the intact body between the cells, the rest of the heart tissue and the rest of the rat. In chemistry, if a copper atom were studied in isolation, it would never be known that copper atoms in bulk can conduct electricity because the atoms share their electrons. In physics, the relationships between inertial reference frames in relativity, and observer and observed in quantum physics can't be ignored. Relationships matter in the physical world, but the mathematics of infinite sets is still used to describe it. Does this matter? It seems to, at least in physics. Infinities cause numerous problems in theoretical physics such as non-renormalizability and problems in unifying quantum mehanics and general relativity . This suggests that the pairing off method and the mathematics of infinite sets based on it are analogous to a cell culture system or studying a copper atom in isolation if they are used in studying the physical universe because they ignore the inherent relationships between entities. In the real, physical world, the natural, inherent, relationships between entities can't be ignored. Said another way, the set of axioms that constitute abstract mathematics may be similar but not identical to the set of physical axioms by which the real, physical universe runs. This suggests that the results from abstract mathematics about infinities may not apply to or should be modified for use in physics. (shrink)

I propose a revision of Cantor’s account of set size that understands comparisons of set size fundamentally in terms of surjections rather than injections. This revised account is equivalent to Cantor's account if the Axiom of Choice is true, but its consequences differ from those of Cantor’s if the Axiom of Choice is false. I argue that the revised account is an intuitive generalization of Cantor’s account, blocks paradoxes—most notably, that a set can be partitioned into a set (...) that is bigger than it—that can arise from Cantor’s account if the Axiom of Choice is false, illuminates the debate over whether the Axiom of Choice is true, is a mathematically fruitful alternative to Cantor’s account, and sheds philosophical light on one of the oldest unsolved problems in set theory. (shrink)

In standard probability theory, probability zero is not the same as impossibility. But many have suggested that only impossible events should have probability zero. This can be arranged if we allow infinitesimal probabilities, but infinitesimals do not solve all of the problems. We will see that regular probabilities are not invariant over rigid transformations, even for simple, bounded, countable, constructive, and disjoint sets. Hence, regular chances cannot be determined by space-time invariant physical laws, and regular credences cannot satisfy seemingly reasonable (...) symmetry principles. Moreover, the examples here are immune to the objections against Williamson’s infinite coin flips. (shrink)

Advances in neuroscience implicate reentrant signaling as the predominant form of communication between brain areas. This principle was used in a series of masking experiments that defy explanation by feed-forward theories. The masking occurs when a brief display of target plus mask is continued with the mask alone. Two masking processes were found: an early process affected by physical factors such as adapting luminance and a later process affected by attentional factors such as set size. This later process is (...) called masking by object substitution, because it occurs whenever there is a mismatch between the reentrant visual representation and the ongoing lower level activity. Iterative reentrant processing was formalized in a computational model that provides an excellent fit to the data. The model provides a more comprehensive account of all forms of visual masking than do the long-held feed-forward views based on inhibitory contour interactions. (shrink)

Big Data is a large-sized and complex dataset, which cannot be managed using traditional data processing tools. Mining process of big data is the ability to extract valuable information from these large datasets. Association rule mining is a type of data mining process, which is indented to determine interesting associations between items and to establish a set of association rules whose support is greater than a specific threshold. The classical association rules can only be extracted from binary data where an (...) item exists in a transaction, but it fails to deal effectively with quantitative attributes, through decreasing the quality of generated association rules due to sharp boundary problems. In order to overcome the drawbacks of classical association rule mining, we propose in this research a new neutrosophic association rule algorithm. The algorithm uses a new approach for generating association rules by dealing with membership, indeterminacy, and non-membership functions of items, conducting to an efficient decision-making system by considering all vague association rules. To prove the validity of the method, we compare the fuzzy mining and the neutrosophic mining. The results show that the proposed approach increases the number of generated association rules. (shrink)

Probability can be used to measure degree of belief in two ways: objectively and subjectively. The objective measure is a measure of the rational degree of belief in a proposition given a set of evidential propositions. The subjective measure is the measure of a particular subject’s dispositions to decide between options. In both measures, certainty is a degree of belief 1. I will show, however, that there can be cases where one belief is stronger than another yet both beliefs are (...) plausibly measurable as objectively and subjectively certain. In ordinary language, we can say that while both beliefs are certain, one belief is more certain than the other. I will then propose second, non probabilistic dimension of measurement, which tracks this variation in certainty in such cases where the probability is 1. A general principle of rationality is that one’s subjective degree of belief should match the rational degree of belief given the evidence available. In this paper I hope to show that it is also a rational principle that the maximum stake size at which one should remain certain should match the rational weight of certainty given the evidence available. Neither objective nor subjective measures of certainty conform to the axioms of probability, but instead are measured in utility. This has the consequence that, although it is often rational to be certain to some degree, there is no such thing as absolute certainty. (shrink)

The Forrest-Armstrong argument, as reconfigured by David Lewis, is a reductio against an unrestricted principle of recombination. There is a gap in the argument which Lewis thought could be bridged by an appeal to recombination. After presenting the argument, I show that no plausible principle of recombination can bridge the gap. But other plausible principles of plenitude can bridge the gap, both principles of plenitude for world contents and principles of plenitude for world structures. I conclude that the Forrest-Armstrong argument, (...) when fortified in one of these ways, demands that unrestricted recombination be rejected. The appropriate restriction comes from a consideration of what world structures are possible. I argue that, although there are too many worlds to form a set, for any world, the individuals at that world do form a set. To defend it I invoke a principle of Limitation of Size together with an iterative conception of structure. (shrink)

Abstract The Preface Paradox, first introduced by David Makinson (1961), presents a plausible scenario where an agent is evidentially certain of each of a set of propositions without being evidentially certain of the conjunction of the set of propositions. Given reasonable assumptions about the nature of evidential certainty, this appears to be a straightforward contradiction. We solve the paradox by appeal to stake size sensitivity, which is the claim that evidential probability is sensitive to stake size. The argument (...) is that because the informational content in the conjunction is greater than the sum of the informational content of the conjuncts, the stake size in the conjunction is higher than the sum of the stake sizes in the conjuncts. We present a theory of evidential probability that identifies knowledge with value and allows for coherent stake sensitive beliefs. An agent’s beliefs are represented two dimensionally as a bid – ask spread, which gives a bid price and an ask price for bets at each stake size. The bid ask spread gets wider when there is less valuable evidence relative to the stake size, and narrower when there is more valuable evidence according to a simple formula. The bid-ask spread can represent the uncertainty in the first order probabilistic judgement. According to the theory it can be coherent to be evidentially certain at low stakes, but less than certain at high stakes, and therefore there is no contradiction in the Preface. The theory not only solves the paradox, but also gives a good model of decisions under risk that overcomes many of the problems associated with classic expected utility theory. (shrink)

In Mathematics is megethology. Philosophia Mathematica, 1, 3–23) David K. Lewis proposes a structuralist reconstruction of classical set theory based on mereology. In order to formulate suitable hypotheses about the size of the universe of individuals without the help of set-theoretical notions, he uses the device of Boolos’ plural quantification for treating second order logic without commitment to set-theoretical entities. In this paper we show how, assuming the existence of a pairing function on atoms, as the unique assumption non (...) expressed in a mereological language, a mereological foundation of set theory is achievable within first order logic. Furthermore, we show how a mereological codification of ordered pairs is achievable with a very restricted use of the notion of plurality without plural quantification. (shrink)

This study sets out to examine the ways Nigerian cyber-fraudsters (Yahoo-Boys) are represented in hip-hop music. The empirical basis of this article is lyrics from 18 hip-hop artists, which were subjected to a directed approach to qualitative content analysis and coded based on the moral disengagement mechanisms proposed by Bandura (1999). While results revealed that the ethics of Yahoo-Boys, as expressed by musicians, embody a range of moral disengagement mechanisms, they also shed light on the motives for the Nigerian cybercriminals' (...) actions. Further analysis revealed additional findings: “glamorization/de-glamorization of cyber-fraud” and “sex-roles-and-cultures”. Having operated within the constraint of what is currently available (a small sample size), this article has drawn attention to the notion that Yahoo-Boys and some musicians may be “birds of a feather.” Secondly, it has exposed a “hunter-and-antelope-relationship” between Yahoo-Boys and their victims. Thirdly, it has also highlighted that some ethos of law-abiding citizens is central to Yahoo-Boys’ moral enterprise. Yahoo-Boys, therefore, represent reflections of society. Arguably, given that Yahoo-Boys and singers are connected, and the oratory messages of singers may attract more followers than questioners, this study illuminates the cultural dimensions of cyber-fraud that emanate from Nigeria. In particular, insights from this study suggest that cyber-fraud researchers might look beyond traditional data sources (e.g., cyber-fraud statistics) for the empirical traces of “culture in action” that render fraudulently practices acceptable career paths for some Nigerian youths. (shrink)

In Lewis reconstructs set theory using mereology and plural quantification (MPQ). In his recontruction he assumes from the beginning that there is an infinite plurality of atoms, whose size is equivalent to that of the set theoretical universe. Since this assumption is far beyond the basic axioms of mereology, it might seem that MPQ do not play any role in order to guarantee the existence of a large infinity of objects. However, we intend to demonstrate that mereology and plural (...) quantification are, in some ways, particularly relevant to a certain conception of the infinite. More precisely, though the principles of mereology and plural quantification do not guarantee the existence of an infinite number of objects, nevertheless, once the existence of any infinite object is admitted, they are able to assure the existence of an uncountable infinity of objects. So, ifMPQ were parts of logic, the implausible consequence would follow that, given a countable infinity of individuals, logic would be able to guarantee an uncountable infinity of objects. (shrink)

Introduction to mathematical logic. Part 2.Textbook for students in mathematical logic and foundations of mathematics. Platonism, Intuition, Formalism. Axiomatic set theory. Around the Continuum Problem. Axiom of Determinacy. Large Cardinal Axioms. Ackermann's Set Theory. First order arithmetic. Hilbert's 10th problem. Incompleteness theorems. Consequences. Connected results: double incompleteness theorem, unsolvability of reasoning, theorem on the size of proofs, diophantine incompleteness, Loeb's theorem, consistent universal statements are provable, Berry's paradox, incompleteness and Chaitin's theorem. Around Ramsey's theorem.

Is it possible to know anything about life we have not yet encountered? We know of only one example of life: our own. Given this, many scientists are inclined to doubt that any principles of Earth’s biology will generalize to other worlds in which life might exist. Let’s call this the “N = 1 problem.” By comparison, we expect the principles of geometry, mechanics, and chemistry would generalize. Interestingly, each of these has predictable consequences when applied to biology. The surface-to-volume (...) property of geometry, for example, limits the size of unassisted cells in a given medium. This effect is real, precise, universal, and predictive. Furthermore, there are basic problems all life must solve if it is to persist, such as resistance to radiation, faithful inheritance, and energy regulation. If these universal problems have a limited set of possible solutions, some common outcomes must consistently emerge. In this chapter, I discuss the N = 1 problem, its implications, and my response (Mariscal 2014). I hold that our current knowledge of biology can justify believing certain generalizations as holding for life anywhere. Life on Earth may be our only example of life, but this is only a reason to be cautious in our approach to life in the universe, not a reason to give up altogether. In my account, a candidate biological generalization is assessed by the assumptions it makes. A claim is accepted only if its justification includes principles of evolution, but no contingent facts of life on Earth. (shrink)

Abstract: Smoke detectors are critical devices for early fire detection and life-saving interventions. This research paper explores the application of Artificial Neural Networks (ANNs) in smoke detection systems. The study aims to develop a robust and accurate smoke detection model using ANNs. Surprisingly, the results indicate a 100% accuracy rate, suggesting promising potential for ANNs in enhancing smoke detection technology. However, this paper acknowledges the need for a comprehensive evaluation beyond accuracy. It discusses potential challenges, such as overfitting, dataset (...) class='Hi'>size, and class imbalance, and presents strategies employed to address these issues. Additionally, the paper emphasizes the importance of alternative evaluation metrics, including precision, recall, and F1-score, to assess the model's performance comprehensively. Detailed information regarding the model architecture, data preprocessing, and hyperparameter tuning is provided to enhance the reproducibility of the research. The study also discusses ethical considerations and the implications of false positives and false negatives in smoke detection applications. While achieving 100% accuracy is a notable accomplishment, this paper calls for cautious interpretation and further validation in real-world settings. It concludes by highlighting areas for future research and improvement in smoke detection technology, emphasizing the need for practical deployment and the reduction of false alarms. (shrink)

Economic policy evaluations require social welfare functions for variable-size populations. Two important candidates are critical-level generalized utilitarianism (CLGU) and rank-discounted critical-level generalized utilitarianism, which was recently characterized by Asheim and Zuber (2014) (AZ). AZ introduce a novel axiom, existence of egalitarian equivalence (EEE). First, we show that, under some uncontroversial criteria for a plausible social welfare relation, EEE suffices to rule out the Repugnant Conclusion of population ethics (without AZ’s other novel axioms). Second, we provide a new characterization of (...) CLGU: AZ’s set of axioms is equivalent to CLGU when EEE is replaced by the axiom same-number independence. (shrink)

Population axiology concerns how to evaluate populations in terms of their moral goodness, that is, how to order populations by the relations “is better than” and “is as good as”. The task has been to find an adequate theory about the moral value of states of affairs where the number of people, the quality of their lives, and their identities may vary. So far, this field has largely ignored issues about uncertainty and the conditions that have been discussed mostly pertain (...) to the ranking of risk-free outcomes. Most public policy choices, however, are decisions under uncertainty, including policy choices that affect the size of a population. Here, we shall address the question of how to rank population prospects—that is, alternatives that contain uncertainty as to which population they will bring about—by the relations “is better than” and “is as good as”. We start by illustrating how well-known population axiologies can be extended to population prospect axiologies. And we show that new problems arise when extending population axiologies to prospects. In particular, traditional population axiologies lead to prospect-versions of the problems that they praised for avoiding in the risk-free settings. Finally, we identify an intuitive adequacy condition that, we contend, should be satisfied by any population prospect axiology, and show how given this condition, the impossibility theorems in population axiology can be extended to (non-trivial) impossibility theorems for population prospect axiology. (shrink)

This study aims to identify the strengthening of the global entrepreneurial orientation practice for employees at the University of Palestine, where the researchers used the descriptive and analytical approach, through a questionnaire distributed to a sample of employees at the University of Palestine, where the size of the study population is (234) employees and the sample size is (117) Employees, of whom (90) employees responded. The study found a set of results, the most important of which are: that (...) there is a good degree of global entrepreneurial orientation for employees, as the percentage reached (70.25%), and the results also showed that there are no statistically significant differences in the smart university transformation and their impact on the global entrepreneurial trend according to personal and organizational data. The study presented a set of recommendations, the most important of which are: The need to work to enhance the global entrepreneurial orientation of the university's employees. (shrink)

The study aimed to identify the strategic sensitivity and its impact on enhancing the creative behavior of Palestinian NGOs in Gaza Strip, and the study used the descriptive analytical approach and the questionnaire as a main tool for collecting data from employees of associations working in Gaza Strip governorates, and the cluster sample method was used and the sample size reached (343) individuals (298) questionnaires were retrieved, and the following results were reached: The relative weight of strategic sensitivity was (...) 79.22 (%), and the relative weight of creative behavior was 78.99 (%), a statistically significant relationship between all strategic sensitivity and creative behavior, and the presence of a sensitivity effect The strategy’s strategy on creative behavior, there are statistically significant differences in the scale dimensions attributable to the gender variable and the differences were in favor of females, there are no statistically significant differences between the averages of strategic sensitivity due to the age variable, and the educational qualification, and there were no statistically significant differences in creative behavior according to The gender variable, age, educational qualification, specialization, and the study presented a set of recommendations, the most important of which are: the need for civil organizations in Gaza Strip to seek funding from external countries in order to provide self-income for associations to face crises and give them independence Mechanism in order to keep them to carry out their role in society, the need to follow up the strategic plan of civil organizations using e-mails as they pave the way to reach excellence and creativity in the field of work. (shrink)

Purpose ‐ The purpose of this paper is to explore the "resource curse" problem as a counter-example of creative performance and innovation by examining reliance on capital and physical resources, showing the gap between expectations and ex-post actual performance that became clearer under conditions of economic turmoil. Design/methodology/approach ‐ The analysis uses logistic regressions with dichotomous response and predictor variables on structured tables of count data, representing firm performance as an outcome of capital resources, physical resources and innovation where appropriate. (...) Findings ‐ Key findings relevant to economic and business practice follow. First, a typical characteristic of successful Vietnamese firms in the transition period is their reliance on either capital resources or physical asset endowments. Second, poor performers exhibit evidence of over-reliance on both capital and physical assets. Third, firms that relied on both types of resources tended to downplay creative performance. Some evidence suggests that firms face more acute problem caused by the law of diminishing returns in troubled times. Fourth, the "innovation factor" has not been tapped as a source of economic growth. Research limitations/implications ‐ This study has some limitations. The size of the survey sample is approximately 150 firms, while the potential sample of > 300 should be possible in the future. When the size increases, the research could be expanded to include further variables that will help investigate more deeply into the related issues and business implications. With regard to the implications of the study, the absence of innovations has made the notion of "resource curse" identical to "destructive creation" implemented by ex-ante resource-rich firms, and worsened the problem of resource misallocation in transition turmoil. The Vietnamese corporate sector's addiction to resources may contribute to economic deterioration, through a downward spiral of lower efficiency leading to consumption of more resources. Practical implications ‐ Insights obtained from this study could save transition economies' resources which have almost always been considered sine qua non before any critical major policymaking, while this is not necessarily true, and in many cases, even counterproductive. Originality/value ‐ Original data set on Vietnam stock market are collected, processed, prepared and used by the authors. Original design by the authors for regression equations with dichotomous predictor variables: dependence on endowed physical assets, reliance on capital resources and significant signs of creative performance/innovations. Original idea of viewing "resource curse" as absence of innovation and due to uncreative "destructive creation" of poor-performing commercial operations by resource-rich firms is used in the paper. We have searched the literature in business research and found that the empirical results have not been previously reported. (shrink)

Abstract: This study aims to identify the level of creativity in the University of Palestine from the point of view of the employees, as the researchers used the descriptive and analytical method, through a questionnaire distributed to a sample of employees at the University of Palestine, where the size of the study population is (234) employees, and the size of the sample (117) employees, of which (90) employees responded. The study reached a set of results, the most important (...) of which are: A high degree of creativity from the employees 'point of view, and the study confirmed that there were no differences in the level of creativity at the University of Palestine from the Employees point of view, according to demographic variables. The study presented a set of recommendations, the most important of which are: The need for universities to enhance creativity. (shrink)

In one of the earlier influential papers in the field of experimental philosophy titled Normativity and Epistemic Intuitions published in 2001, Jonathan M. Weinberg, Shaun Nichols and Stephen Stich reported that respondents answered Gettier type questions differently depending on their ethnic background as well as socioeconomic status. There is currently a debate going on, on the significance of the results of Weinberg et al. (2001) and its implications for philosophical methodology in general and epistemology in specific. Despite the debates, however, (...) to our knowledge, there has not been a replication attempt of the experiments of the original paper. We collected data from four different sources (two on-line and two in-person) to replicate the experiments. Despite several different data sets and in various cases larger sample sizes and hence greater power to detect differences, we failed to detect significant differences between the above-mentioned ethnic and socioeconomic groups. Our results suggest that epistemic intuitions are more robust across ethnic and socioeconomic groups than Weinberg et al. (2001) indicates. Given our data, we believe that the notion of differences in epistemic intuitions among different ethnic and socioeconomic groups that follows from Weinberg et al. (2001) needs to be corrected. (shrink)

In this paper, I will argue that it is a moral obligation for companies, firstly, to accept their moral responsibility with respect to non-discrimination, and secondly, to address the issue with a full-fledged programme, including but not limited to the countering of microsocial discrimination processes through specific policies. On the basis of a broad sketch of how some discrimination mechanisms are actually influencing decisions, that is, causing intended as well as unintended bias in Human Resources Management, I will argue that (...) the well known tools of legislation and ethical codes are necessary although insufficient to cope with the problem. However, based on empirical evidence, we know which set of measures is likely to diminish discrimination. Taking non-discrimination seriously implies complex and longitudinal policies which include assigning responsibility for a non-discrimination policy within the firm, making managers conscious of implicit stereotypes and helping them to cope with prejudices that no one can totally overcome. Insofar as corporate responsibility with respect to non-discrimination is accepted and strategies that are not prohibitively expensive are known, companies are bound to implement them. Not implementing the best set of measures may be considered at least as a moral shortcoming or, depending on the size of the company, mere lip service to the non-discrimination principle. Although the paper refers to empirical material of diverse backgrounds, its intent is clearly normative. It wishes to spell out what companies ought to do if they are committed to responsible behaviour. The discussion of effective remedies against discrimination is based on a case study of a French company. The retailer Auchan was recently surprised to learn that it was discriminating against ethnic minorities despite strong ethical standards, an ethics committee and ethical leadership. The company dropped its naïve beliefs and set up an ambitious policy cope with the issue. The case illustrates what recent empirical research has revealed about the effectiveness of diversity policies: establishing responsibility for diversity results, firm ethical commitment and support from top management make diversity programs effective. (shrink)

This study aims to identify the digital reputation at the University of Palestine: an analytical perspective of the employees ’point of view, where the researchers used the descriptive and analytical approach, through a questionnaire distributed to a sample of employees at the University of Palestine, where the size of the study population is (234) employees, and the size of The sample is (117) employees, of whom (90) employees responded. The study provided a theoretical framework for what the writers (...) and researchers presented about the study variables, as well as a practical analytical framework for the opinions of employees at the University of Palestine. The digital reputation was expressed as an independent variable through its four indicators (feeling about the organization (satisfaction), admiration and respect, and trust, and social responsibility). The study found a set of results, the most important of which are: the existence of a high degree of digital reputation at the University of Palestine from the viewpoint of employees, and the absence of differences in the opinions of the study sample about digital reputation according to demographic variables. The study presented a set of recommendations, the most important of which are: The need for universities to enhance their digital reputation and raise its level. (shrink)

This article is an attempt to defend Scanlon's contractualism against the so-called aggregation problems. Scanlon's contractualism attempts to make sense of right and wrong in terms of principles which no one could reasonably reject. These principles are a function of what kind personal objections persons can make to alternative sets of moral principles. Because of this, it has been argued that contractualism is unable to account for how groups of different sizes are to be treated. In this article, I argue (...) that contactualism, even if with its focus on personal burdens, can come to plausible conclusions in the group cases. (shrink)

With the current international competition among global companies, Business English as a Lingua Franca (BEFL) has become a necessity. As for one, Boardwalk Direct Selling Company recognizes the adoption of the BEFL concept within the organization to equip its workforce with adequate English language skills at par with global standards. This study aims to assess the organization’s current English proficiency and the readiness of its employees to embrace BEFL. This also presents the major English language skills areas that need improvement (...) through training intervention. A stratified sampling method is utilized to extract data via an online survey. Respondents are strategically chosen to represent different strata such as organizational departments or groups, job levels, tenure, and age. A convenient size of 34 respondents participated in this study. Generally, respondents acknowledge the importance of the English language skill set in their job functions and as criteria for their career growth. Half of the sampling population affirms their English language proficiency. However, the study reveals that Boardwalk employees are willing to subject themselves to improving their English skills, most particularly in speaking and writing aspects. Given their willingness, the employees recommend that the company strengthen its BEFL trainings across the organization. Moreover, with the current setup of mostly working from home due to COVID restrictions, majority of the employees prefer online learning. (shrink)

Abstract cantaloupe and honeydew melons are part of the muskmelon family, which originated in the Middle East. When picking either cantaloupe or honeydew melons to eat, you should choose a firm fruit that is heavy for its size, with no obvious signs of bruising. They can be stored at room temperature until you cut them, after which they should be kept in the refrigerator in an airtight container for up to five days. You should always wash and scrub the (...) rind of your melon before you cut it to remove any dirt or bacteria on the outside. In this paper, cantaloupe classification approach is presented with a dataset that contains approximately 1,312 of Cantaloupes and honeydews. Convolutional Neural Network (CNN) algorithms, a deep learning technique extensively applied to image recognition was used, for this task. The results found that CNN-driven classification applications when used in farming automation have the latent to enhance crop harvest and improve output and productivity when designed properly. The trained model achieved an accuracy of 99.74% on a held-out test set, demonstrating the feasibility of this approach. (shrink)

A number of philosophers of science and statisticians have attempted to justify conclusions drawn from a finite sequence of evidence by appealing to results about what happens if the length of that sequence tends to infinity. If their justifications are to be successful, they need to rely on the finite sequence being either indefinitely increasing or of a large size. These assumptions are often not met in practice. This paper analyzes a simple model of collecting evidence and finds that (...) the practice of collecting only very small sets of evidence before taking a question to be settled is rationally justified. This shows that the appeal to long run results can be used neither to explain the success of actual scientific practice nor to give a rational reconstruction of that practice. (shrink)

As we look beyond our terrestrial boundary to a multi-planetary future for humankind, it becomes paramount to anticipate the challenges of various human factors on the most likely scenario for this future: permanent human settlement of Mars. Even if technical hurdles are circumvented to provide adequate resources for basic physiological and psychological needs, Homo sapiens will not survive on an alien planet if a dysfunctional psyche prohibits the utilization of these resources. No matter how far we soar into the stars, (...) our psychologies for future generations will be forever tethered to the totality of our surroundings. By shaping our environment toward survival and welfare during the voyage to Mars and in a Martian colony, we indirectly shape our psyches and prepare them for a mission of unprecedented alienation and duration. Once on Mars, human factors such as leadership structure, social organization and code of conduct, group size, gender balance, developmental cycle, mobility, length of stay and the ecological settings and type and manner of subsistence, will create a novel Martian culture. The degree that settlers are severed from the Earth will affect how radically foreign this culture will be when compared with cultures on Earth. (shrink)

The quantization error in a fixed-size Self-Organizing Map (SOM) with unsupervised winner-take-all learning has previously been used successfully to detect, in minimal computation time, highly meaningful changes across images in medical time series and in time series of satellite images. Here, the functional properties of the quantization error in SOM are explored further to show that the metric is capable of reliably discriminating between the finest differences in local contrast intensities and contrast signs. While this capability of the QE (...) is akin to functional characteristics of a specific class of retinal ganglion cells (the so-called Y-cells) in the visual systems of the primate and the cat, the sensitivity of the QE surpasses the capacity limits of human visual detection. Here, the quantization error in the SOM is found to reliably signal changes in contrast or colour when contrast information is removed from or added to the image, but not when the amount and relative weight of contrast information is constant and only the local spatial position of contrast elements in the pattern changes. While the RGB Mean reflects coarser changes in colour or contrast well enough, the SOM-QE is shown to outperform the RGB Mean in the detection of single-pixel changes in images with up to five million pixels. This could have important implications in the context of unsupervised image learning and computational building block approaches to large sets of image data (big data). (shrink)

Over 1.5 million living animal species have been described—of which around 1 million are insects—but it has been estimated there are over 7 million animal species in total. Animals range in length from 8.5 micrometres to 33.6 metres. In this paper an Artificial Neural Network (ANN) model, was developed and tested to predict animal species. There are a number of features that influence the classification of animal species. Such as the existence of hair/ feather, if the animal gives birth or (...) spawns, it is airborne, aquatic, predator, toothed, backboned, venomous, has –fins, has-tail, cat-sized, and domestic. A model based on the Multilayer Perceptron Topology was proposed and trained, using data set what was collected from UCI Machine Learning Repository. Evaluation of the proposed model shows that the ANN model is able to correctly predict the animal category with 100% accuracy. (shrink)

It is common to assume that the problem of induction arises only because of small sample sizes or unreliable data. In this paper, I argue that the piecemeal collection of data can also lead to underdetermination of theories by evidence, even if arbitrarily large amounts of completely reliable experimental and observational data are collected. Specifically, I focus on the construction of causal theories from the results of many studies (perhaps hundreds), including randomized controlled trials and observational studies, where the studies (...) focus on overlapping, but not identical, sets of variables. Two theorems reveal that, for any collection of variables V, there exist fundamentally different causal theories over V that cannot be distinguished unless all variables are simultaneously measured. Underdetermination can result from piecemeal measurement, regardless of the quantity and quality of the data. Moreover, I generalize these results to show that, a priori, it is impossible to choose a series of small (in terms of number of variables) observational studies that will be most informative with respect to the causal theory describing the variables under investigation. This final result suggests that scientific institutions may need to play a larger role in coordinating differing research programs during inquiry. (shrink)

The research aims to identify the impact of the strategic orientations (Vision, Mission, goals) on crisis management agency, international relief in Gaza, the researchers used the descriptive and analytical approach and a survey for collection data, amounted to community size (881), and the study sample (268), and the sample was a stratified random. SPSS program used for entry, processing and analysis of data. The most important findings of the study: The results showed that the organization develop a clearly written (...) vision, mission and strategic goals and the organization's strategic objectives are consistent with the vision and mission of the organization. The results also showed that the organization develop a clear stage objectives framed with time bass which can be achieved on the ground. The employees in the organization's behavior comes within a disciplined set of principles and values that underpin the organization. Also the concept of the organization vision and mission are familiar for the employees. In general the views of the research sample agreed that there is a presence of strategic orientations (vision, message, goals). A direct positive correlation between the presence of strategic orientations (vision, mission and goals) and crisis management (before, during and after the crisis) in the international relief agency in Gaza. The research also concluded a series of recommendations, Researchers consistently recommend the continuous existence of strategic orientation and continue to develop the vision, mission and objectives in a clearly written method. In addition to that, the organization must develop in advance plans to deal with crises, taking into account past experience in this field through a specialized team, hold continuous meetings and discussions and workshops with the emergency team who has previous experience in dealing with crises. (shrink)

Recent advances in neuroimaging technologies have rendered multimodal analysis of operators’ cognitive processes in complex task settings and environments increasingly more practical. In this exploratory study, we utilized optical brain imaging and mobile eye tracking technologies to investigate the behavioral and neurophysiological differences among expert and novice operators while they operated a human-machine interface in normal and adverse conditions. In congruence with related work, we observed that experts tended to have lower prefrontal oxygenation and exhibit gaze patterns that are better (...) aligned with the optimal task sequence with shorter fixation durations as compared to novices. These trends reached statistical significance only in the adverse condition where the operators were prompted with an unexpected error message. Comparisons between hemodynamic and gaze measures before and after the error message indicated that experts’ neurophysiological response to the error involved a systematic increase in bilateral dorsolateral prefrontal cortex (dlPFC) activity accompanied with an increase in fixation durations, which suggests a shift in their attentional state, possibly from routine process execution to problem detection and resolution. The novices’ response was not as strong as that of experts, including a slight increase only in the left dlPFC with a decreasing trend in fixation durations, which is indicative of visual search behavior for possible cues to make sense of the unanticipated situation. A linear discriminant analysis model capitalizing on the covariance structure among hemodynamic and eye movement measures could distinguish experts from novices with 91% accuracy. Despite the small sample size, the performance of the linear discriminant analysis combining eye fixation and dorsolateral oxygenation measures before and after an unexpected event suggests that multimodal approaches may be fruitful for distinguishing novice and expert performance in similar neuroergonomic applications in the field. (shrink)

In this paper, a framework incorporating flexibility as a characteristic is proposed for designing complex, resilient socio-ecological systems. In an interconnected complex system, flexibility allows prompt deployment of resources where they are needed and is crucial for both innovation and robustness. A comparative analysis of flexible manufacturing systems, economics, evolutionary biology, and supply chain management is conducted to identify the most important characteristics of flexibility. Evolutionary biology emphasises overlapping functions and multi-functionality, which allow a system with structurally different elements to (...) perform the same function, enhancing resilience. In economics, marginal cost and marginal expected profit are factors that are considered to be important in incorporating flexibility while making changes to the system. In flexible manufacturing systems, the size of choice sets is important in creating flexibility, as initial actions preserve more options for future actions that will enhance resilience. Given the dynamic nature of flexibility, identifying the characteristics that can lead to flexibility will introduce a crucial dimension to designing resilient and sustainable socio-ecological systems with a long-term perspective in mind. (shrink)

We show how faceted search using a combination of traditional classification systems and mixed-membership topic models can go beyond keyword search to inform resource discovery, hypothesis formulation, and argument extraction for interdisciplinary research. Our test domain is the history and philosophy of scientific work on animal mind and cognition. The methods can be generalized to other research areas and ultimately support a system for semi-automatic identification of argument structures. We provide a case study for the application of the methods to (...) the problem of identifying and extracting arguments about anthropomorphism during a critical period in the development of comparative psychology. We show how a combination of classification systems and mixed-membership models trained over large digital libraries can inform resource discovery in this domain. Through a novel approach of “drill-down” topic modeling—simultaneously reducing both the size of the corpus and the unit of analysis—we are able to reduce a large collection of fulltext volumes to a much smaller set of pages within six focal volumes containing arguments of interest to historians and philosophers of comparative psychology. The volumes identified in this way did not appear among the first ten results of the keyword search in the HathiTrust digital library and the pages bear the kind of “close reading” needed to generate original interpretations that is the heart of scholarly work in the humanities. Zooming back out, we provide a way to place the books onto a map of science originally constructed from very different data and for different purposes. The multilevel approach advances understanding of the intellectual and societal contexts in which writings are interpreted. (shrink)

I present a reconstruction of the logical system of the Tractatus, which differs from classical logic in two ways. It includes an account of Wittgenstein’s “form-series” device, which suffices to express some effectively generated countably infinite disjunctions. And its attendant notion of structure is relativized to the fixed underlying universe of what is named. -/- There follow three results. First, the class of concepts definable in the system is closed under finitary induction. Second, if the universe of objects is countably (...) infinite, then the property of being a tautology is \Pi^1_1-complete. But third, it is only granted the assumption of countability that the class of tautologies is \Sigma_1-definable in set theory. -/- Wittgenstein famously urges that logical relationships must show themselves in the structure of signs. He also urges that the size of the universe cannot be prejudged. The results of this paper indicate that there is no single way in which logical relationships could be held to make themselves manifest in signs, which does not prejudge the number of objects. (shrink)

Overpopulation is often identified as one of the key drivers of climate change. Further, it is often thought that the mechanism behind this is obvious: 'more people means more greenhouse gas emissions'. However, in light of the fact that climate change depends most closely on cumulative emissions rather than on emissions rates, the relationship between population size and climate change is more subtle than this. Reducing the size of instantaneous populations can fruitfully be thought of as spreading out (...) a fixed number of people more thinly over time, and (in light of the significance of cumulative emissions) it is not immediately clear whether or how such a 'spreading' would help with climate change. To bring the point into sharp relief, I first set out a simple model according to which population reduction would not lead to any climate-change-related improvement. I then critically examine the assumptions of the model. If population reduction would lead to a significant climate-change-related improvement, this must be because (i) population reduction would significantly reduce even cumulative emissions, and/or (ii) climate damages are, to a significant extent, driven by the pace of climate change, and not only the eventual extent of the change. (shrink)

Much forensic inference based upon DNA evidence is made assuming Hardy-Weinberg Equilibrium (HWE) for the genetic loci being used. Several statistical tests to detect and measure deviation from HWE have been devised, and their limitations become more obvious when testing for deviation within multiallelic DNA loci. The most popular methods-Chi-square and Likelihood-ratio tests-are based on asymptotic results and cannot guarantee a good performance in the presence of low frequency genotypes. Since the parameter space dimension increases at a quadratic rate on (...) the number of alleles, some authors suggest applying sequential methods, where the multiallelic case is reformulated as a sequence of “biallelic” tests. However, in this approach it is not obvious how to assess the general evidence of the original hypothesis; nor is it clear how to establish the significance level for its acceptance/rejection. In this work, we introduce a straightforward method for the multiallelic HWE test, which overcomes the aforementioned issues of sequential methods. The core theory for the proposed method is given by the Full Bayesian Significance Test (FBST), an intuitive Bayesian approach which does not assign positive probabilities to zero measure sets when testing sharp hypotheses. We compare FBST performance to Chi-square, Likelihood-ratio and Markov chain tests, in three numerical experiments. The results suggest that FBST is a robust and high performance method for the HWE test, even in the presence of several alleles and small sample sizes. (shrink)

Card argues that we should not give injustice priority over evil. I agree. But I think Card sets us up for some difficult balancings, for example of small evils against middle sized injustices. I suggest some ways of staying off the tightrope.