The authors propose a nested dissection approach to finding a fundamental cycle basis in a planar graph. The cycle basis corresponds to a fundamental null-space basis of the adjacency matrix. This problem is meant to model sparse null-space basis computations occurring in a variety of settings. An O(n3/2) bound is achieved on the nullspace basis size (i.e., the number of nonzero entries in the basis), and an O(n log n) bound on the size in the special case of (...) grid graphs. (shrink)

The purpose of this article is to present several immediate consequences of the introduction of a new constant called Lambda in order to represent the object ``nothing" or ``void" into a standard set theory. The use of Lambda will appear natural thanks to its role of condition of possibility of sets. On a conceptual level, the use of Lambda leads to a legitimation of the empty set and to a redefinition of the notion of set. It lets also clearly appear (...) the distinction between the empty set, the nothing and the ur-elements. On a technical level, we introduce the notion of pre-element and we suggest a formal definition of the nothing distinct of that of the null-class. Among other results, we get a relative resolution of the anomaly of the intersection of a family free of sets and the possibility of building the empty set from ``nothing". The theory is presented with equi-consistency results . On both conceptual and technical levels, the introduction of Lambda leads to a resolution of the Russell's puzzle of the null-class. (shrink)

The significance and use of absence of a thing is highlighted as its presence. The role of absence in various disciplines of mathematics, physics, semi-conductor electronics, computing and cognitive sciences for ease in conceptualizing is discussed. The use of null set, null vector and null matrix are also presented.

Girolamo Saccheri (1667--1733) was an Italian Jesuit priest, scholastic philosopher, and mathematician. He earned a permanent place in the history of mathematics by discovering and rigorously deducing an elaborate chain of consequences of an axiom-set for what is now known as hyperbolic (or Lobachevskian) plane geometry. Reviewer's remarks: (1) On two pages of this book Saccheri refers to his previous and equally original book Logica demonstrativa (Turin, 1697) to which 14 of the 16 pages of the editor's "Introduction" are devoted. (...) At the time of the first edition, 1920, the editor was apparently not acquainted with the secondary literature on Logica demonstrativa which continued to grow in the period preceding the second edition \ref[see D. J. Struik, in Dictionary of scientific biography, Vol. 12, 55--57, Scribner's, New York, 1975]. Of special interest in this connection is a series of three articles by A. F. Emch [Scripta Math. 3 (1935), 51--60; Zbl 10, 386; ibid. 3 (1935), 143--152; Zbl 11, 193; ibid. 3 (1935), 221--333; Zbl 12, 98]. (2) It seems curious that modern writers believe that demonstration of the "nondeducibility" of the parallel postulate vindicates Euclid whereas at first Saccheri seems to have thought that demonstration of its "deducibility" is what would vindicate Euclid. Saccheri is perfectly clear in his commitment to the ancient (and now discredited) view that it is wrong to take as an "axiom" a proposition which is not a "primal verity", which is not "known through itself". So it would seem that Saccheri should think that he was convicting Euclid of error by deducing the parallel postulate. The resolution of this confusion is that Saccheri thought that he had proved, not merely that the parallel postulate was true, but that it was a "primal verity" and, thus, that Euclid was correct in taking it as an "axiom". As implausible as this claim about Saccheri may seem, the passage on p. 237, lines 3--15, seems to admit of no other interpretation. Indeed, Emch takes it this way. (3) As has been noted by many others, Saccheri was fascinated, if not obsessed, by what may be called "reflexive indirect deductions", indirect deductions which show that a conclusion follows from given premises by a chain of reasoning beginning with the given premises augmented by the denial of the desired conclusion and ending with the conclusion itself. It is obvious, of course, that this is simply a species of ordinary indirect deduction; a conclusion follows from given premises if a contradiction is deducible from those given premises augmented by the denial of the conclusion---and it is immaterial whether the contradiction involves one of the premises, the denial of the conclusion, or even, as often happens, intermediate propositions distinct from the given premises and the denial of the conclusion. Saccheri seemed to think that a proposition proved in this way was deduced from its own denial and, thus, that its denial was self-contradictory (p. 207). Inference from this mistake to the idea that propositions proved in this way are "primal verities" would involve yet another confusion. The reviewer gratefully acknowledges extensive communication with his former doctoral students J. Gasser and M. Scanlan. ADDED 14 March 14, 2015: (1) Wikipedia reports that many of Saccheri's ideas have a precedent in the 11th Century Persian polymath Omar Khayyám's Discussion of Difficulties in Euclid, a fact ignored in most Western sources until recently. It is unclear whether Saccheri had access to this work in translation, or developed his ideas independently. (2) This book is another exemplification of the huge difference between indirect deduction and indirect reduction. Indirect deduction requires making an assumption that is inconsistent with the premises previously adopted. This means that the reasoner must perform a certain mental act of assuming a certain proposition. It case the premises are all known truths, indirect deduction—which would then be indirect proof—requires the reasoner to assume a falsehood. This fact has been noted by several prominent mathematicians including Hardy, Hilbert, and Tarski. Indirect reduction requires no new assumption. Indirect reduction is simply a transformation of an argument in one form into another argument in a different form. In an indirect reduction one proposition in the old premise set is replaced by the contradictory opposite of the old conclusion and the new conclusion becomes the contradictory opposite of the replaced premise. Roughly and schematically, P,Q/R becomes P,~R/~Q or ~R, Q/~P. Saccheri’s work involved indirect deduction not indirect reduction. (3) The distinction between indirect deduction and indirect reduction has largely slipped through the cracks, the cracks between medieval-oriented logic and modern-oriented logic. The medievalists have a heavy investment in reduction and, though they have heard of deduction, they think that deduction is a form of reduction, or vice versa, or in some cases they think that the word ‘deduction’ is the modern way of referring to reduction. The modernists have no interest in reduction, i.e. in the process of transforming one argument into another having exactly the same number of premises. Modern logicians, like Aristotle, are concerned with deducing a single proposition from a set of propositions. Some focus on deducing a single proposition from the null set—something difficult to relate to reduction. (shrink)

A truth-preservation fallacy is using the concept of truth-preservation where some other concept is needed. For example, in certain contexts saying that consequences can be deduced from premises using truth-preserving deduction rules is a fallacy if it suggests that all truth-preserving rules are consequence-preserving. The arithmetic additive-associativity rule that yields 6 = (3 + (2 + 1)) from 6 = ((3 + 2) + 1) is truth-preserving but not consequence-preserving. As noted in James Gasser’s dissertation, Leibniz has been criticized for (...) using that rule in attempting to show that arithmetic equations are consequences of definitions. -/- A system of deductions is truth-preserving if each of its deductions having true premises has a true conclusion—and consequence-preserving if, for any given set of sentences, each deduction having premises that are consequences of that set has a conclusion that is a consequence of that set. Consequence-preserving amounts to: in each of its deductions the conclusion is a consequence of the premises. The same definitions apply to deduction rules considered as systems of deductions. Every consequence-preserving system is truth-preserving. It is not as well-known that the converse fails: not every truth-preserving system is consequence-preserving. Likewise for rules: not every truth-preserving rule is consequence-preserving. There are many famous examples. In ordinary first-order Peano-Arithmetic, the induction rule yields the conclusion ‘every number x is such that: x is zero or x is a successor’—which is not a consequence of the null set—from two tautological premises, which are consequences of the null set, of course. The arithmetic induction rule is truth-preserving but not consequence-preserving. Truth-preserving rules that are not consequence-preserving are non-logical or extra-logical rules. Such rules are unacceptable to persons espousing traditional truth-and-consequence conceptions of demonstration: a demonstration shows its conclusion is true by showing that its conclusion is a consequence of premises already known to be true. The 1965 Preface in Benson Mates (1972, vii) contains the first occurrence of truth-preservation fallacies in the book. (shrink)

Transformed RAVAL NOTATION solves Syllogism problems very quickly and accurately. This method solves any categorical syllogism problem with same ease and is as simple as ABC… In Transformed RAVAL NOTATION, each premise and conclusion is written in abbreviated form, and then conclusion is reached simply by connecting abbreviated premises.NOTATION: Statements (both premises and conclusions) are represented as follows: Statement Notation a) All S are P, SS-P b) Some S are P, S-P c) Some S are not P, S / PP (...) d) No S is P, SS / PP (- implies are and / implies are not) All is represented by double letters; Some is represented by single letter. No S is P implies No P is S so its notation contains double letters on both sides. -/- RULES: (1) Conclusions are reached by connecting Notations. Two notations can be linked only through common linking terms. When the common linking term multiplies (becomes double from single), divides (becomes single from double) or remains double then conclusion is arrived between terminal terms. (Aristotle’s rule: the middle term must be distributed at least once) -/- (2)If both statements linked are having – signs, resulting conclusion carries – sign (Aristotle’s rule: two affirmatives imply an affirmative) -/- (3) Whenever statements having – and / signs are linked, resulting conclusion carries / sign. (Aristotle’s rule: if one premise is negative, then the conclusion must be negative) -/- (4)Statement having / sign cannot be linked with another statement having / sign to derive any conclusion. (Aristotle’s rule: Two negative premises imply no valid conclusion) Syllogism conclusion by Tranformed Raval’s Notation is in accordance with Aristotle’s rules for the same. It is visually very transparent and conclusions can be deduced at a glance, moreover it solves syllogism problems with any number of statements and it is quickest of all available methods. By new Raval method for solving categorical syllogism, solving categorical syllogism is as simple as pronouncing ABC and it is just continuance of Aristotle work on categorical syllogism. It’s believed that Boole's system could handle multi-term propositions and arguments, whereas Aristotle could handle only two-termed subject-predicate propositions and arguments. For example, it’s claimed that Aristotle's system could not deduce: "No quadrangle that is a square is a rectangle that is a rhombus" from "No square that is a quadrangle is a rhombus that is a rectangle" or from "No rhombus that is a rectangle is a square that is a quadrangle". Above conclusion is reached at a glance with Raval's Notations (Symbolic Aristotle’s syllogism rules). Premise: "No (square that is a quadrangle) is a (rhombus that is a rectangle)" Raval's Representations: S – Q, S – Q / Rh – Re, Rh – Re Premise: "No (rhombus that is a rectangle) is a (square that is a quadrangle)". Raval's Representations: Rh – Re, Rh – Re / S – Q, S - Q Conclusion: "No (quadrangle that is a square) is a (rectangle that is a rhombus)" Raval’s Representations: Q – S, Q – S / Re – Rh, Re – Rh As “ Q – S” follows from “S – Q” and “Re – Rh” from “Rh – Re”. Given conclusion follows from the given premises. Author disregards existential fallacy, as subset of a null set has to be a null set. -/- . (shrink)

This article consists in two parts that are complementary and autonomous at the same time. -/- In the first one, we develop some surprising consequences of the introduction of a new constant called Lambda in order to represent the object ``nothing" or ``void" into a standard set theory. On a conceptual level, it allows to see sets in a new light and to give a legitimacy to the empty set. On a technical level, it leads to a relative resolution of (...) the anomaly of the intersection of a family free of sets. -/- In the second part, we show the interest of introducing an operator of potentiality into a standard set theory. Among other results, this operator allows to prove the existence of a hierarchy of empty sets and to propose a solution to the puzzle of "ubiquity" of the empty set. -/- Both theories are presented with equi-consistency results (model and interpretation). -/- Here is a declaration of intent : in each case, the starting point is a conceptual questionning; the technical tools come in a second time\\[0.4cm] \textbf{Keywords:} nothing, void, empty set, null-class, zero-order logic with quantifiers, potential, effective, empty set, ubiquity, hierarchy, equality, equality by the bottom, identity, identification. (shrink)

In this paper, I develop an essentialist model of the semantics of slurs. I defend the view that slurs are a species of kind terms: Slur concepts encode mini-theories which represent an essence-like element that is causally connected to a set of negatively-valenced stereotypical features of a social group. The truth-conditional contribution of slur nouns can then be captured by the following schema: For a given slur S of a social group G and a person P, S is true of (...) P iff P bears the “essence” of G—whatever this essence is—which is causally responsible for stereotypical negative features associated with G and predicted of P. Since there is no essence that is causally responsible for stereotypical negative features of a social group, slurs have null-extension, and consequently, many sentences containing them are either meaningless or false. After giving a detailed outline of my theory, I show that it receives strong linguistic support. In particular, it can account for a wide range of linguistic cases that are regarded as challenging, central data for any theory of slurs. Finally, I show that my theory also receives convergent support from cognitive psychology and psycholinguistics. (shrink)

From The Cone of Perception, volume one of my collected works, you will remember that one of the main topics in that work was V-Curvature, also called, "phenomenological velocity." In that work, although a solution to the v - curvature variable was provided as well as many graphs that yielded numerous jewels of spiral formulations in exquisite 3D color formations, that method by which the solution was found was not iterated. This chapter begins by showing how it is possible to (...) solve for something that ideally ought cancel out with itself and how, although commutation between square roots is valid, there may be room here for an alternate route of accessing a hidden dimension - that dimension we call V-Curvature, or, "Phenomenological Velocity." Herein is provided the pathway for solving for V-Curvature in terms of Csc, which can be translated into Sin and Cos functionality. Furthermore, the processing these equations through WolframAlpha yielded other insights into limits, roots, and series that logically follow. How did the solutions to the, "velocity," v - variable curvature in the Lorentz coefficient, "manifest," when the Lorentz coefficient ought cancel out with itself? The step - by - step solution below illustrates the algebraic process by which a specific solution for something that ought cancel out with itself can be found. The Sphere of Realization is a groundbreaking work of philosophical and mathematical theory. The first volume of this epic collection examines the concept of V-Curvature, or Phenomenological Velocity, using algebraic equations to explain how this phenomenon can be solved. This book goes on to explore the implications of these equations, such as limits, roots, series, and introspection into infinity, providing an alternate route for accessing a 'hidden dimension' that connects physical laws with abstract philosophical ideas. By utilizing this understanding, the author creates a platform for introspection into life and nature, and considers the philosophical implications of this perception, from the exploration of the infinity of angles to theions of time, velocity, the emergence of real numbers, and the meanings of eternity, forever, infinity, and never ending. This landmark work of mathematical exploration and philosophical discovery will challenge and expand our understanding of the universe, and invite us into a journey of introspection and understanding. An exploration of the esoteric terms therein, and the pathways they provide to access new modes of thought, will give the reader the ability to gain a greater insight into the intricacies of reality. The Sphere of Realization provides a unique and comprehensive approach to a difficult concept. Through a blend of philosophical and mathematical exploration, the author delves into the concept of V-Curvature, or Phenomenological Velocity to unlock the mysteries of "hidden dimensions" within our reality. These equations and theories allow the reader to explore angles, time, velocity, roots, series, and other related concepts. In so doing, the book offers an exciting journey into the esoteric. The author also provides insights into the emergence of real numbers from infinity, introducing concepts such as eternity, forever, and never ending in the process. A comprehensive discussion of the applicable equations and transformations, immune to the construct of time, serves as a powerful tool for unlocking a meaningful understanding of the universe. The Sphere of Realization is an opportunity to gain a deeper appreciation of the reality of our world. (shrink)

The full Bayesian signi/cance test (FBST) for precise hypotheses is presented, with some illustrative applications. In the FBST we compute the evidence against the precise hypothesis. We discuss some of the theoretical properties of the FBST, and provide an invariant formulation for coordinate transformations, provided a reference density has been established. This evidence is the probability of the highest relative surprise set, “tangential” to the sub-manifold (of the parameter space) that defines the null hypothesis.

This study assessed quality assurance practices and students’ performance evaluation in universities of South-South Nigeria using an SEM approach. Three null hypotheses guided the study. Based on factorial research design, and using a stratified random sampling technique, a sample of 878 academic staff were drawn from a sampling frame of 15 universities in South-South Nigeria. Quality Assurance Practices Students’ Performance Evaluation Scale (QAPSPES) with split-half reliability estimates ranging from .86–.92, was used as the instruments for data collection. Multiple regression (...) and Confirmatory Factor Analyses (CFA) were used for the analysis of data, model building, and testing of the hypotheses at .05 alpha level. Findings showed a significant composite and relative influence (F=48.19, P<.05) of school management, staff, and students’ quality assurance practices on students’ performance evaluation. The results also indicated that there were positive and significant covariances between the four variables of this study, with the CFI, RMSEA, TLI, and SRMR values indicating a good model fit. It was recommended, based on the findings of this study that, each school should organize quality assurance orientation campaigns for new students and set up quality assurance committees at the school, faculty and departmental levels for optimal performance in schools. (shrink)

Learner-centered approaches have emerged as the fundamental pillar of effective pedagogy in the rapidly evolving landscape of 21st century education. This paradigm shift places the learner at the heart of the educational process, recognizing their diverse needs and aspirations. Consequently, the achievements of learners have become crucial indicators of institutional success. While extensive research has focused on student affairs and services, limited attention has been given to understanding the impact of administration on realizing the objectives of these support systems. This (...) study aims to investigate the relationship between the administration of learner-centered academic support systems and the attainment of desired outcomes in student affairs and services within higher education institutions in the Philippines. Utilizing a non-experimental correlational quantitative research design, a sample of three hundred fifty university students from various academic disciplines was randomly selected as participants. The findings demonstrate a strong positive correlation between the administration of learner-centered academic support systems and the achievement of desired outcomes in student affairs and services. As a result, the null hypothesis was rejected based on statistical analysis employing Pearson Correlation (r). These findings highlight the significant impact that learner-centered academic support system administration has on the realization of objectives in student affairs and services within the contemporary higher educational setting. To ensure sustained best practices in student development, it is imperative for the administration to foster collaboration with internal stakeholders and external partners. Recognizing that students are the focal point of instruction, their performance serves as a reflection of the institution’s commitment to providing quality education. By aligning administrative efforts with the evolving needs of students, institutions can enhance student affairs and services and create an optimal learning environment in the 21st century. (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)

Successful teamwork doesn't work overnight, what makes teamwork potent is team building. (Plagiarism) According to Abdullah, et. al., (2022) team building training can improve group cohesiveness or the quality of sticking together or unity teamwork more likely to be higher with a significant score difference. This study used mixed methods both qualitative and quantitative data collection, and an analysis method to answer the research method, random sampling is named as such because the data set is chosen via random selection, where (...) every member of the population has an equal probability of being selected (Tao, 2023). The respondents were 100 restaurant employees and 10 managers from the chosen restaurant in Malolos City in Bulacan. The subcategories of team building, including activities, communication, skills, personality, problem-solving, and values, have all received a consensus of strong agreement, with weighted averages falling within the range of 3.26 to 3.44. This level of agreement aligns with the scores for motivation at 3.43 and productivity at 3.38. These values have been calculated by determining the mean, which spans from 3.25 to 4.00. The advantages of team building that is being observed by the managers is to create familiarity and teamwork among the employees, to improve the quality of service and the quality of the food especially the respondents are in the food service sector, development, and training for the employees to achieve the establishments’ goal and lastly rebuilding and build a relationship with one employee to another. However, for the disadvantages, it costs a lot of money to conduct team building in the management. Therefore, the null hypothesis is rejected. Despite the fact that there is a low correlation between teambuilding activities and motivation and employee productivity, there is still a significant relationship between the variables. (shrink)

This study assessed administrative networking strategies and principals’ supervisory effectiveness in assessing teachers’ notes of lessons, teachers’ instructional delivery, students’ records, and non-academic activities in Cross River State, Nigeria. Three null hypotheses were formulated accordingly to direct the study. The study adopted a descriptive survey design. Census technique was adopted in selecting the entire population of 667 secondary school administrators in Cross River State. The instruments used for data collection were two set of questionnaires designed by the researchers including: (...) Administrative Networking Strategies Questionnaire (ANSQ)”, and “Principals’ Supervisory Effectiveness Questionnaire (PSEQ)” respectively. The reliability of the instruments was established through Cronbach Alpha, and reliability estimates of .89 and .92 were obtained for the two instruments respectively. The null hypotheses were all tested at .05 level of significance using Pearson Product Moment Correlation Analysis with the aid of SPSS v21. Findings from the study revealed that; there is a significant relationship between principals’ effective communication, school-community relationship, and teachers’ involvement in decision-making, with their supervisory effectiveness respectively. Based on the findings of the study, it was recommended amongst others that; secondary school principals should endeavour to communicate relevant ideas, messages, and information to both teaching and non-academic staff of the school; and ensure that appropriate feedback mechanisms are provided based on such information. (shrink)

Abstract: The Pull Bayesian Significance Test (FBST) for precise hy- potheses is applied to a Multivariate Normal Structure (MNS) model. In the FBST we compute the evidence against the precise hypothesis. This evi- dence is the probability of the Highest Relative Surprise Set (HRSS) tangent to the sub-manifold (of the parameter space) that defines the null hypothesis. The MNS model we present appears when testing equivalence conditions for genetic expression measurements, using micro-array technology.

A Bayesian measure of evidence for precise hypotheses is presented. The intention is to give a Bayesian alternative to significance tests or, equivalently, to p-values. In fact, a set is defined in the parameter space and the posterior probability, its credibility, is evaluated. This set is the “Highest Posterior Density Region” that is “tangent” to the set that defines the null hypothesis. Our measure of evidence is the complement of the credibility of the “tangent” region.

The Full Bayesian Significance Test (FBST) for precise hypotheses is presented, with some applications relevant to reliability theory. The FBST is an alternative to significance tests or, equivalently, to p-ualue.s. In the FBST we compute the evidence of the precise hypothesis. This evidence is the probability of the complement of a credible set "tangent" to the sub-manifold (of the para,rreter space) that defines the null hypothesis. We use the FBST in an application requiring a quality control of used components, (...) based on remaining life statistics. (shrink)

The unit root problem plays a central role in empirical applications in the time series econometric literature. However, significance tests developed under the frequentist tradition present various conceptual problems that jeopardize the power of these tests, especially for small samples. Bayesian alternatives, although having interesting interpretations and being precisely defined, experience problems due to the fact that that the hypothesis of interest in this case is sharp or precise. The Bayesian significance test used in this article, for the unit root (...) hypothesis, is based solely on the posterior density function, without the need of imposing positive probabilities to sets of zero Lebesgue measure. Furthermore, it is conducted under strict observance of the likelihood principle. It was designed mainly for testing sharp null hypotheses and it is called FBST for Full Bayesian Significance Test. (shrink)

This research was carried out in order to verify by simulation Mendel’s laws and seek for the clarification, from the author’s point of view, the Mendel-Fisher controversy. It was demonstrated from: the experimental procedure and the first two steps of the Hardy-Weinberg law, that the null hypothesis in such experiments is absolutely and undeniably true. Consequently, repeating hybridizing experiments as those showed by Mendel, it makes sense to expect a highly coincidence between the observed and the expected cell frequencies. (...) By simulation, 30 random samples were generated with size equal to the number of observations reported by Mendel for his single trait trial, in this case, seed shape; assuming complete dominance, with genes A and a; likewise, it was simulated the results for the experiment with two traits, segregating in separate chromosomes, in this case seed shape, as before, and albumen color, with genes B and b, both loci with complete dominance. In the case of a single trait, the data only showed evidence for rejecting the null hypothesis (Ho ) in 1/30 samples, with (P<0.05). In the case of the 30 samples of the two traits experiment, (Ho ) was rejected only on 3/30 times, when it was set a = 0.05. In both simulations there was a high correspondence between the observed and expected cell frequencies, which is simply due to the fact that (Ho ) is true, and under these conditions, that is what would to expect. It was concluded, that Mendel had no reason to manipulate his data in order to make them to coincide with his beliefs. Therefore, in experiment with a single trait, and in experiments with two traits assuming complete dominance, segregation ratios are 3:1; and 9:3:3:1, respectively. Consequently, Mendel’s laws, under the conditions as were described are absolutely valid and universal. (shrink)

A short formal actually-onepage proof that proves all things must be interpretable in at least more than one way , as any determination to an exact unary finitude is an overdetermination in necessitation that obtains an analytic contradiction which would thus be a doubly determinable conclusivity, which if as assumed would not be analytically so; thus, one must have, for any axiomatic set theoretic construction to number count to properly function toward any decision making aprioretically founded actual aposteriori -- and (...) NOT a stochastic at most-base ontologic -- at least more than one concomitant incorporated-definition to any null object that its nullity being erroneously considered null is not actually so as null , since upon a minimal sufficience obtained positive differentiation is self-proved via plurality indefining its own underdeterminability, null is also naught is also ø is also orthogonal to some "you" physically reading this abstract . (shrink)

This paper contributes to the debate regarding the semantic type of singular referential names. According to one view, known as referentialism, names rigidly designate individuals (Kripke 1972, Abbott 2002, Leckie 2013, Jeshion 2015, Schoubye 2017). According to another view, known as predicativism, names designate properties of individuals (Burge 1973, Geurts 1997, Bach 2002, Elbourne 2005, Matushansky 2008, Fara 2015). Most predicativist accounts claim that bare names in English occur with a phonologically null determiner, a proposal that is based on (...) languages like Greek where names require a determiner in argument position. Novel data from both English and Greek show that names can be nonrigid designators under modal operators ("Aristotle may teach Socrates") and bound variables under quantifiers ("in every set of twins, Helen is a musician"), challenging referentialism. As for rigidity, one possible source of this phenomenon is the proprial article, a name-specific determiner found in Catalan and other languages that may be null in English and homophonous with the definite article in Greek (Ghomeshi and Massam 2009, Muñoz 2019, Izumi and Erickson 2021). While much further research is needed, the data suggest that the proper analysis of names is grounded in predicativism rather than referentialism. (shrink)

The main aim of this study was to evaluate the effects of school heads’ new normal leadership on collaborative school culture. To achieve this aim, the researcher conducted a survey to a number of school principals and teachers inFukuoka and Hiroshima Prefectures during the school year 2020-2021. The data were collected and processed using the Statistical Packages for Social Sciences. Results indicated that the three (3) variables of new normal leadership of school heads affect the collaborative school culture in varying (...) extent as shown by the obtained B Coefficients 1.170 (adaptability), 1.132 (decision-making), 0.430 (planning and implementation). This means that for every unit improvement in the new normal leadership mentioned could generate a 1.170, 1.132, 0.430 increase on collaborative school culture. A closer look at the obtained Beta Coefficients, one could infer that of the 3 variables of school new normal leadership, it was the ‘adaptability’ that exert a greatest influence (Beta=1.170) on the collaborative school culture. The R able to denote multiple correlation coefficient between the different variables as a predictor of the dependent variable. It could be noted that the R is .895 which indicated a level of prediction while R2 figure is a statistical measure on closeness of the data in regression line as the coefficient of determination or simply the coefficient of multiple determination for multiple regression. It can be indicated that the explanatory powers of the dependent variable of 0.698 implies that 69.8% or 70% of the variation in new normal leadership is accounted by changes in the collaborative school culture. Furthermore, results of analysis of variance revealed an F ratio equal to 1.642 with an associated probability equal to .000.Since the p-value is lower than the significance level set at 0.05, the null hypothesis is rejected. It may be safely concluded that the new normal leadership of school heads produce significant combined effects on collaborative school culture. (shrink)

Translating risk estimates derived from epidemiologic study into evidence of causality for a particular patient is problematic. The difficulty of this process is not unique to the medical context; rather, courts are also challenged with the task of using risk estimates to infer evidence of cause in particular cases. Thus, an examination of how this is done in a legal context might provide insight into when and how it is appropriate to use risk information as evidence of cause in a (...) medical context. A careful study of the case of Goodman v. Viljoen, a medical malpractice suit litigated in the Ontario Superior Court of Justice in 2011, reveals different approaches to how risk information is used as or might be considered a substitute for evidence of causation, and the pitfalls associated with these approaches. Achieving statistical thresholds, specifically minimizing the probability of falsely rejecting the null hypothesis, and exceeding a relative risk of 2, plays a significant role in establishing causality of the particular in the legal setting. However, providing a reasonable explanation or establishing “biological plausibility” of the causal association also seems important, and (to some) may even take precedent over statistical thresholds for a given context. (shrink)

This study assessed two motivational strategies and their respective ties to the service delivery in public universities in Cross River State. In achieving the central and specific targets of this research, four research questions and two null hypotheses were answered and tested in the study. The entire population of 440 security personnel in two public universities was studied, based on the census approach and following the ex-post facto research design. Three sets of expert-validated questionnaires, with Cronbach reliability estimates of (...) 0.80, 0.79 and 0.83 respectively, were used for data collection. Collected data were analysed using descriptive statistics and inferential statistics such as Pearson Product Moment Correlation and the One-way ANOVA. The level of incentives provision and security service delivery in universities was moderate. There were notable disparities between promotion, provision of incentives and security service delivery in universities. Security personnel discharged, on average, services beyond the extent of promotion and incentives provided to them. Provision of incentives did not relate significantly to security service delivery; however, staff promotion significantly influences security service delivery in universities. It was concluded that there are loopholes in the motivational practices of universities for security personnel. The service delivery of security personnel at universities in Cross River State is yet to be at an acceptable point that can promote institutional safety and goal attainment in the short- and long run. It was recommended, among other things, that security personnel who are due for promotion should not be denied such an opportunity, as it represents one of the strongest motivational factors in universities. (shrink)

In Tractatus, Wittgenstein held that there are null sentences – prominently including logical truths and the truths of mathematics. He says that such sentences are without sense (sinnlos), that they say nothing; he also denies that they are nonsensical (unsinning). Surely it is what a sentence says which is true or false. So if a sentence says nothing, how can it be true or false? The paper discusses the issue.

The meaning of an experimental result depends on the experiment's conceptual backdrop, particularly its null hypothesis. This observation provides the basis for a functional interpretation of belief in the base rate fallacy. On this interpretation, if the base rate fallacy is to be labelled a “myth,” then it should be recognized that this label is not necessarily a disparaging one.

Set-theoretic pluralism is an increasingly influential position in the philosophy of set theory (Balaguer [1998], Linksy and Zalta [1995], Hamkins [2012]). There is considerable room for debate about how best to formulate set-theoretic pluralism, and even about whether the view is coherent. But there is widespread agreement as to what there is to recommend the view (given that it can be formulated coherently). Unlike set-theoretic universalism, set-theoretic pluralism affords an answer to Benacerraf’s epistemological challenge. The purpose of this paper is (...) to determine what Benacerraf’s challenge could be such that this view is warranted. I argue that it could not be any of the challenges with which it has been traditionally identified by its advocates, like of Benacerraf and Field. Not only are none of the challenges easier for the pluralist to meet. None satisfies a key constraint that has been placed on Benacerraf’s challenge. However, I argue that Benacerraf’s challenge could be the challenge to show that our set-theoretic beliefs are safe – i.e., to show that we could not have easily had false ones. Whether the pluralist is, in fact, better positioned to show that our set-theoretic beliefs are safe turns on a broadly empirical conjecture which is outstanding. If this conjecture proves to be false, then it is unclear what the epistemological argument for set-theoretic pluralism is supposed to be. (shrink)

Critical-set views avoid the Repugnant Conclusion by subtracting some constant from the welfare score of each life in a population. These views are thus sensitive to facts about biographical identity: identity between lives. In this paper, I argue that questions of biographical identity give us reason to reject critical-set views and embrace the total view. I end with a practical implication. If we shift our credences towards the total view, we should also shift our efforts towards ensuring that humanity survives (...) for the long term. (shrink)

In the real word, in most cases, everything (an attribute, event, proposition, theory, idea, person, object, action, etc.) is evaluated in general by many sources (called experts), not only one. The more sources evaluate a subject, the better accurate result (after fusioning all evaluations). That’s why, in this paper, we straightforwardly extend the Refined Neutrosophic Set to the MultiNeutrosophic Set, and we show that the last two are isomorphic. A MultiNeutrosophic Set is a Neutrosophic Set whose all elements’ degrees of (...) truth/indeterminacy/falsehood are evaluated by many (Multi) sources. Afterwards, we introduce a total order on the set of n-plets of the form (p, r, s), we build the operators on the (p, r, s)-plets, and show several applications of the MultiNeutrosophic Sets. Several particular cases of the MultiNeutrosophic Sets are presented: such as MultiFuzzy Set, MultiIntuitionistic Fuzzy Set, MultiPicture Fuzzy Set, and other Multi(Fuzzy Extension) Set. (shrink)

The iterative conception of set is typically considered to provide the intuitive underpinnings for ZFCU (ZFC+Urelements). It is an easy theorem of ZFCU that all sets have a definite cardinality. But the iterative conception seems to be entirely consistent with the existence of “wide” sets, sets (of, in particular, urelements) that are larger than any cardinal. This paper diagnoses the source of the apparent disconnect here and proposes modifications of the Replacement and Powerset axioms so as to allow for the (...) existence of wide sets. Drawing upon Cantor’s notion of the absolute infinite, the paper argues that the modifications are warranted and preserve a robust iterative conception of set. The resulting theory is proved consistent relative to ZFC + “there exists an inaccessible cardinal number.”. (shrink)

In this article I give a critical evaluation of the use and limitations of null-model-based hypothesis testing as a research strategy in the biological sciences. According to this strategy, the null model based on a randomization procedure provides an appropriate null hypothesis stating that the existence of a pattern is the result of random processes or can be expected by chance alone, and proponents of other hypotheses should first try to reject this null hypothesis in order (...) to demonstrate their own hypotheses. Using as an example the controversy over the use of null hypotheses and null models in species co-occurrence studies, I argue that null-model-based hypothesis testing fails to work as a proper analog to traditional statistical null-hypothesis testing as used in well-controlled experimental research, and that the random process hypothesis should not be privileged as a null hypothesis. Instead, the possible use of the null model resides in its role of providing a way to challenge scientists’ commonsense judgments about how a seemingly unusual pattern could have come to be. Despite this possible use, null-model-based hypothesis testing still carries certain limitations, and it should not be regarded as an obligation for biologists who are interested in explaining patterns in nature to first conduct such a test before pursuing their own hypotheses. (shrink)

In this contribution, I explore the possibility of characterizing the emergence of time in causal set theory (CST) in terms of the growing block universe (GBU) metaphysics. I show that although GBU seems to be the most intuitive time metaphysics for CST, it leaves us with a number of interpretation problems, independently of which dynamics we choose to favor for the theory —here I shall consider the Classical Sequential Growth and the Covariant model. Discrete general covariance of the CSG dynamics (...) does not allow us to individuate a single history of the universe (defined by a causal history of different causal sets), thereby making the claim that ‘the past exists’ at best problematic. In addition, because the evolution of the universe in CSG dynamics leads to an outward branching causal tree, it becomes impossible to determine a proper ‘line of becoming’, thereby blurring the presentists’ claim that only the present exists. Similarly, the covariant approach runs into the same, if not even more severe problems, since each configuration of the universe would amount to a set of possible causal sets, thereby making the individuation of a single configuration of the universe —and thus the physical interpretation of the theory— implausible. (shrink)

Philosophers of science since Nagel have been interested in the links between intertheoretic reduction and explanation, understanding and other forms of epistemic progress. Although intertheoretic reduction is widely agreed to occur in pure mathematics as well as empirical science, the relationship between reduction and explanation in the mathematical setting has rarely been investigated in a similarly serious way. This paper examines an important particular case: the reduction of arithmetic to set theory. I claim that the reduction is unexplanatory. In defense (...) of this claim, I offer evidence from mathematical practice, and I respond to contrary suggestions due to Steinhart, Maddy, Kitcher and Quine. I then show how, even if set-theoretic reductions are generally not explanatory, set theory can nevertheless serve as a legitimate foundation for mathematics. Finally, some implications of my thesis for philosophy of mathematics and philosophy of science are discussed. In particular, I suggest that some reductions in mathematics are probably explanatory, and I propose that differing standards of theory acceptance might account for the apparent lack of unexplanatory reductions in the empirical sciences. (shrink)

In this paper we introduce the notion of filter on the neutrosophic crisp set, then we consider a generalization of the filter’s studies. Afterwards, we present the important neutrosophic crisp filters. We also study several relations between different neutrosophic crisp filters and neutrosophic topologies. Possible applications to database systems are touched upon.

Set-theoretic and category-theoretic foundations represent different perspectives on mathematical subject matter. In particular, category-theoretic language focusses on properties that can be determined up to isomorphism within a category, whereas set theory admits of properties determined by the internal structure of the membership relation. Various objections have been raised against this aspect of set theory in the category-theoretic literature. In this article, we advocate a methodological pluralism concerning the two foundational languages, and provide a theory that fruitfully interrelates a ‘structural’ perspective (...) to a set-theoretic one. We present a set-theoretic system that is able to talk about structures more naturally, and argue that it provides an important perspective on plausibly structural properties such as cardinality. We conclude the language of set theory can provide useful information about the notion of mathematical structure. (shrink)

In this paper, I explore Bach’s idea (Bach, 2000) that null appositives, intended as expanded qua-clauses, can resolve the puzzles of belief reports. These puzzles are crucial in understanding the semantics and pragmatics of belief reports and are presented in a section. I propose that Bach’s strategy is not only a way of dealing with puzzles, but also an ideal way of dealing with belief reports. I argue that even simple unproblematic cases of belief reports are cases of pragmatic (...) intrusion, involving null appositives, or to use the words of Bach, ‘qua-clauses’. The main difference between my pragmatic approach and the one by Salmon (1986) is that this author uses the notion of conversational implicature, whereas I use the notion of pragmatic intrusion and explicature. From my point of view, statements such as ‘‘John believes that Cicero is clever’’ and ‘‘John believes that Tully is clever’’ have got distinct truth-values. In other words, I claim that belief reports in the default case illuminate the hearer on the mental life of the believer, that includes specific modes of presentation of the referents talked about. Furthermore, while in the other pragmatic approaches, it is mysterious how a mode of presentation is assumed to be the main filter of the believer’s mental life, here I provide an explanatory account in terms of relevance, cognitive effects, and processing efforts. The most important part of the paper is devoted to showing that null appositives are required, in the case of belief reports, to explain certain anaphoric effects, which would otherwise be mysterious. My examples show that null appositives are not necessitated at logical form, but only at the level of the explicature, in line with the standard assumptions by Carston and Recanati on pragmatic intrusion. I develop a potentially useful analysis of belief reports by exploiting syntactic and semantic considerations on presuppositional clitics in Romance. (shrink)

Algorithmic governmentality is a new form of political governance interconnected with technology and computation. By coining the term “algorithmic governmentality,” Antoinette Rouvroy argues that this mode of governance reduces everything to data, and people are no longer individuals but dividuals (able to be divided) or readable data profiles. Implementing the concept of algorithmic governmentality, the current study analyses Project Itoh’s award-winning novel Harmony in terms of such relevant concepts as “subjectivity,” “infra-individuality” and “control,” as suggested by Rouvroy and colleagues. The (...) analysis further draws on Foucault’s ideas of “governmentality” and “neoliberalism” and Deleuze’s concepts of “dividuality” and “society of control.” In Itoh’s fictional world, the entire society is subject to the new medical government, which replaced the chaotic world with a perfect but harrowing benevolent society, eradicating disease, suicide and crime. As elucidated in this paper, despite the dominant controlling government, there is a hope for humans to regain and reestablish their subjectivity and give meaning to their own personality by defying the nihilistic computational system. (shrink)

Priority setting in health care is ubiquitous and health authorities are increasingly recognising the need for priority setting guidelines to ensure efficient, fair, and equitable resource allocation. While cost-effectiveness concerns seem to dominate many policies, the tension between utilitarian and deontological concerns is salient to many, and various severity criteria appear to fill this gap. Severity, then, must be subjected to rigorous ethical and philosophical analysis. Here we first give a brief history of the path to today’s severity criteria in (...) Norway and Sweden. The Scandinavian perspective on severity might be conducive to the international discussion, given its long-standing use as a priority setting criterion, despite having reached rather different conclusions so far. We then argue that severity can be viewed as a multidimensional concept, drawing on accounts of need, urgency, fairness, duty to save lives, and human dignity. Such concerns will often be relative to local mores, and the weighting placed on the various dimensions cannot be expected to be fixed. Thirdly, we present what we think are the most pertinent questions to answer about severity in order to facilitate decision making in the coming years of increased scarcity, and to further the understanding of underlying assumptions and values that go into these decisions. We conclude that severity is poorly understood, and that the topic needs substantial further inquiry; thus we hope this article may set a challenging and important research agenda. (shrink)

Suppose that the members of a group each hold a rational set of judgments on some interconnected questions, and imagine that the group itself has to form a collective, rational set of judgments on those questions. How should it go about dealing with this task? We argue that the question raised is subject to a difficulty that has recently been noticed in discussion of the doctrinal paradox in jurisprudence. And we show that there is a general impossibility theorem that that (...) difficulty illustrates. Our paper describes this impossibility result and provides an exploration of its significance. The result naturally invites comparison with Kenneth Arrow's famous theorem (Arrow, 1963 and 1984; Sen, 1970) and we elaborate that comparison in a companion paper (List and Pettit, 2002). The paper is in four sections. The first section documents the need for various groups to aggregate its members' judgments; the second presents the discursive paradox; the third gives an informal statement of the more general impossibility result; the formal proof is presented in an appendix. The fourth section, finally, discusses some escape routes from that impossibility. (shrink)

In this article, we apply the notion of interval neutrosophic sets to ideal theory in BCK/BCI-algebras.

Consider a variant of the usual story about the iterative conception of sets. As usual, at every stage, you find all the (bland) sets of objects which you found earlier. But you also find the result of tapping any earlier-found object with any magic wand (from a given stock of magic wands). -/- By varying the number and behaviour of the wands, we can flesh out this idea in many different ways. This paper's main Theorem is that any loosely constructive (...) way of fleshing out this idea is synonymous with a ZF-like theory. -/- This Theorem has rich applications; it realizes John Conway's (1976) Mathematicians' Liberation Movement; and it connects with a lovely idea due to Alonzo Church (1974). (shrink)

In this paper, we first propose the concept of divergence measure on neutrosophic sets. We also provide some formulas for the divergence measure for neutrosophic sets. After that, we investigate the properties of proposed neutrosophic divergence measure. Finally, we also apply these formulas in medical problem and the classification problem.

The IndetermSoft Set is as an extension of the Soft Set, because the data, or the function, or the sets involved in the definition of the soft set have indeterminacy - as in our everyday life, and we still need to deal with such situations. And similarly, IndetermHyperSoft Set as extension of the HyperSoft Set, when there is indeterminate data, or indeterminate functions, or indeterminate sets. Herein, ‘Indeterm’ stands for ‘Indeterminate’ (uncertain, conflicting, incomplete, not unique outcome). We now introduce for (...) the first time the TreeSoft Set as extension of the MultiSoft Set. Several applications are presented for each type of soft set. (shrink)

This is a review paper, where we recall the definitions together with practical applications of the Soft Set and its extensions to HyperSoft Set, IndetermSoft Set, IndetermHyperSoft Set, and TreeSoft Set.

This article presents an overview of the basic philosophical motivations for, and some recent work in, modal set theory.

A decision maker (DM) selects a project from a set of alternatives with uncertain productivity. After the choice, she observes a signal about productivity and decides how much effort to put in. This paper analyzes the optimal decision problem of the DM who rationally filters information to deal with her post-decision cognitive dissonance. It is shown that the optimal effort level for a project can be affected by unchosen projects in her choice set, and the nature of the choice set-dependence (...) is determined by the signal structure. Some comparative statics of choice set-dependence is also provided. Finally, based on the results, the optimal choice set design is also explored. This paper offers a simple framework to explain the experimental finding in psychology that people’s effort level for a project can be enhanced when the project is chosen by themselves rather than by others. (shrink)

In this short note we show that the so-called Ambiguous Set (2019) is a subclass of the Double Refined Indeterminacy Neutrosophic Set (2017) and is a particular case of the Refined Neutrosophic Set (2013). Also, the Ambiguous Set is similar to the Quadripartitioned Neutrosophic Set (2016), and Belnap’s Four-Valued Logic (1975).

The incompleteness of set theory ZF C leads one to look for natural nonconservative extensions of ZF C in which one can prove statements independent of ZF C which appear to be “true”. One approach has been to add large cardinal axioms.Or, one can investigate second-order expansions like Kelley-Morse class theory, KM or Tarski-Grothendieck set theory T G or It is a nonconservative extension of ZF C and is obtained from other axiomatic set theories by the inclusion of Tarski’s axiom (...) which implies the existence of inaccessible cardinals. See also related set theory with a filter quantifier ZF (aa). In this paper we look at a set theory NC# ∞# , based on bivalent gyper infinitary logic with restricted Modus Ponens Rule In this paper we deal with set theory NC# ∞# based on bivalent gyper infinitary logic with Restricted Modus Ponens Rule. Nonconservative extensions of the canonical internal set theories IST and HST are proposed. (shrink)

As central as the method of forcing is within set theory, it has yet to be incorporated into the philosopher's toolbox. That strikes me as a shame, since it may well have important applications within philosophy. One barrier is that typical presentations of forcing are overly dry and technical and make it seem inherently bound up with its applications within set theory. The purpose of this note is to try to rectify this. In particular, I will explain how the method (...) of forcing can be seen as a way of constructing a certain kind of intensional model that philosophers are already interested in: namely, possibility models. (shrink)