Students do not necessarily use the definitions presented to them when determining examples or non-examples of given mathematical ideas. Instead, they utilize the concept image they carry with them as a result of experiences with such examples and nonexamples. Hence, teachers should try exploring students‟ images of various mathematical concepts in order to improve communication between students and teachers. This suggestion can be addressed through error analysis. This study therefore is a descriptive-qualitative type that looked into the errors (...) committed by senior high school students in dealing with mathematical functions, explored the underlying reasons for such errors, and provided recommendations on how students could learn to manage their errors and how teachers could realize how to manage students‟ errors. Initial findings showed that the students generally demonstrated mathematical, logical and strategic errors. Mathematical error was generally exhibited in their inability to use properties and operations properly. Logical error was exhibited in their false arguments, rearranging concepts, improper classifications, arguing cyclically, and using equivalent transforms. Strategic error was manifested in their not being able to distinguish patterns, lack of integral concept, and not being able to transform a word problem into symbols. Errors prevailed despite the students‟ positive view and confidence in mathematics not only because of poor image concepts but because of lack of exposure to certain important mathematical tasks. Further investigation on the other sources of these errors is therefore necessary. (shrink)

Libertarians are mistaken to seek foundations, to take sides over moral approaches, and to have no proper theory of liberty.

In this paper, I propose to discuss the theory of error or Khyativāda with special reference to Nyāya philosophy. The error is an epistemological concept. As such it is contrasted with the truth. Philosophers, while dealing with the concept of error, have analyzed it from logical, metaphysical and psychological perspective. The problem of error in Indian philosophy is discussed in the different theories known as the Khyativāda. According to Nyāya School error is known as anyathākhyativāda. (...) Here 'anyathā' literally means 'otherwise' or 'else-wise'. When shell is perceived as silver, the erroneous cognition consists in the fact that the shell is perceived otherwise i.e. as other than what it really is. Error is an instance of erroneous judgement resulting from mischaracterization. Naiyāyikas bring in jñānalaksana pratyaksa to account for perceptual error. And the later Naiyāyikas are trying to explain the perceptual character of illusory experience, undoubtedly, an illusion, there is the attribution of false character to a perceived fact. (shrink)

Recent debate about the error theory has taken a ‘formal turn’. On the one hand, there are those who argue that the error theory should be rejected because of its difficulties in providing a convincing formal account of the logic and semantics of moral claims. On the other hand, there are those who claim that such formal objections fail, maintaining that arguments against the error theory must be of a substantive rather than a formal kind. In this (...) paper, we argue that formal objections to the error theory cannot be eschewed but must be met head-on. (shrink)

In Unbelievable Errors, Bart Streumer argues via elimination for a global error theory, according to which all normative judgments ascribe properties that do not exist. Streumer also argues that it is not possible to believe his view, which is a claim he uses in defending his view against several objections. I argue that reductivists and nonreductivists have compelling responses to Streumer's elimination argument – responses constituting strong reason to reject Streumer’s diagnosis of any alleged incredulity about his error (...) theory. (shrink)

heart attack analysis & prediction dataset is a major cause of death worldwide. Early detection and intervention are essential for improving the chances of a positive outcome. This study presents a novel approach to predicting the likelihood of a person having heart failure using a neural network model. The dataset comprises 304 samples with 11 features, such as age, sex, chest pain type, Trtbps, cholesterol, fasting blood sugar, resting electrocardiogram results, maximum heart rate achieved, exercise-induced angina, oldpeak, ST_Slope, and (...) HeartDisease. A neural network model with four layers (1 input, 2 hidden, 1 output) was trained on the dataset and achieved an accuracy of 88% and an average error of 0078296. The most influential factors in heart failure prediction were found to be oldpeak, ST_Slope, sex, fastingBS, chestPainType, exerciseAngina, cholesterol, restingBP, maxHR, restingBP, and age. This study provides a valuable tool for early detection and intervention of heart failure, thereby contributing to the field of health and medicine. (shrink)

In his late fragment, ‘Sources of Knowledge of Mathematics and Natural Sciences’ Frege laments the tendency to confuse functions with objects and says, ‘It is here that the tendency of language by its use of the definite article to stamp as an object what is a function and hence a non-object, proves itself to be the source of inaccurate and misleading expressions and also of errors of thought. Probably most of the impurities that contaminate the logical source of knowledge have (...) their origins in this.’ This paper applies Frege’s logical insights to a series of influential modal arguments for the existence of souls or minds, in order to demonstrate that they hinge on the error of treating functions as objects. Related arguments have also resulted in the claim that identity statements are necessary, and that apparent identities ‘really’ involve relations of constitution. Here it is argued that once we recognise that all these arguments involve the assimilation of objects and concepts (which Frege identifies with functions) they can be seen to be defective. (shrink)

The attempt to narrow the general discourse of the problem of error and to focus it on the specific problem of experimental error may be approached from different directions. One possibility is to establish a focusing process from the standpoint of history; such an approach requires a careful scrutiny of the history of science with a view to identifying the juncture when the problem of experimental error was properly understood and accounted for. In a study of this (...) kind one would have to examine the evolution of the method of experimentation and related topics so that clear criteria would underlie the analysis. (shrink)

Early in his career and in critical engagement with ordinary language philosophy, John Mackie developed the roots of a methodology that would be fundamental to his thinking: Mackie argues that we need to clearly separate the conceptual analysis which determines the meaning of an ordinary term and the factual analysis which is concerned with the question what, if anything, our language corresponds to in the world. I discuss how Mackie came to develop this distinction and how central ideas (...) of his philosophy are based on it. Using the examples of Mackie’s moral skepticism and his work on Locke’s theory of perception I show how his methodology opens the door to error theories but can also support more positive claims. Finally, I put Mackie’s methodology in a historical perspective and argue that in cases like the Gettier debate, we can use it to cast light on the vagueness of the underlying methodology in some philosophical debates. (shrink)

Abū Hāmid al-Ghazālī (1058–1111 c.e .) is well known, among other things, for his account, in al-Munqidh min al-ḍalāl (Deliverance from error), of a struggle with philosophical skepticism that bears a striking resemblance to that described by Descartes in the Meditations . This essay aims to give a close comparative analysis of these respective accounts, and will concentrate solely on the processes of invoking or entertaining doubt that al-Ghazālī and Descartes describe, respectively. In the process some subtle differences (...) between them in this regard will be brought to light that are relevant to the comparative issue of the respective solutions at which they arrive. The latter issue will not be touched upon here, although the present discussion is intended as a prelude to a future treatment of that topic. (shrink)

This study aimed to investigate the longitudinal trends in mathematical competencies of Grade 8 students in a public high school located in Zamboanga del Sur, Philippines. The study collected data over a period of six academic years, allowing for a comprehensive analysis of students' performance in 16 distinct mathematical competences of basic education curriculum. These topics include, but are not limited to, special products and factors, factoring, and basic concepts of probability. Using a quantitative research design, the study analyzed (...) both numerical and secondary data to identify patterns or trends in students' mathematical competencies. Trends were analyzed through regression analysis using slopes. The significance of these trends was then evaluated using t-tests for the standard error of slopes. The statistical analysis revealed significant upward trends in certain mathematical topics, indicating an improvement in the students' competencies over the six academic years. However, certain topics displayed downward or stable trends, indicating areas for improvement in the teaching methods used for these topics. The study highlights the importance of flexible and adaptable approaches to mathematics education. It emphasizes the need for constant evaluation and improvement of teaching methods to enhance student learning outcomes. The findings of this study provide valuable insights for educators and policymakers to guide evidence-based decision-making and improve the quality of mathematics education in the new normal setup. Implications and future research directions are incorporated in the study. (shrink)

We present a formal mechanical analysis using sweeping net methods to approximate surfacing singularities of saddle maps. By constructing densified sweeping subnets for individual vertices and integrating them, we create a comprehensive approximation of singularities. This approach utilizes geometric concepts, analytical methods, and theorems that demonstrate the robustness and stability of the nets under perturbations. Through detailed proofs and visualizations, we provide a new perspective on singularities and their approximations in analytic geometry.

Kidney stones pose a significant health concern, and early detection can lead to timely intervention and improved patient outcomes. This research endeavours to predict the presence of kidney stones based on urine analysis, utilizing a neural network model. A dataset of 552 urine specimens, comprising six essential physical characteristics (specific gravity, pH, osmolarity, conductivity, urea concentration, and calcium concentration), was collected and prepared. Our proposed neural network architecture, featuring three layers (input, hidden, output), was trained and validated, achieving an (...) impressive accuracy of 98.67% and an average error of 0.012. In addition to model performance, feature importance analysis was conducted to determine the most influential factors in predicting kidney stone presence. The findings underscore the significance of urea concentration, specific gravity, calcium concentration, conductivity, osmolarity, and pH as key indicators. This research contributes to the early diagnosis of kidney stones and demonstrates the potential of neural networks in medical diagnostics. The clinical implications of these findings are discussed, emphasizing the importance of timely intervention in managing kidney stone-related health issues. (shrink)

The ambiguity theory of ‘knows’ is the view that ‘knows’ and its cognates have more than one propositional sense – i.e. more than one sense that can properly be used in ‘knows that’ etc. constructions. Given that most of us are ‘intuitive invariantists’ – i.e. most of us initially have the intuition that ‘knows’ is univocal – defenders of the ambiguity theory need to offer an explanation for the semantic blindness present if ‘knows’ is in fact ambiguous. This paper is (...) an attempt to offer such an explanation. Section 1 contains a general argument for the ubiquity of semantic blindness for ambiguous words; the upshot being that semantic blindness for the ambiguity of ‘knows’ is thus unsurprising. Section 2 offers more specific arguments for why ‘knows’ is the type of ambiguous word that we’re very unlikely to quickly recognize is ambiguous. (shrink)

I argue that dimensional analysis provides an answer to a skeptical challenge to the theory of model mediated measurement. The problem arises when considering the task of calibrating a novel measurement procedure, with greater range, to the results of a prior measurement procedure. The skeptical worry is that the agreement of the novel and prior measurement procedures in their shared range may only be apparent due to the emergence of systematic error in the exclusive range of the novel (...) measurement procedure. Alternatively: what if the two measurement procedures are not in fact measuring the same quantity? The theory of model mediated measurement can only say that we _assume_ that there is a common quantity. In contrast, I show that the satisfaction of dimensional homogeneity across the metrological extension is independent evidence for the so-called assumption. This is illustrated by the use of dimensional analysis in high pressure experiments. This results in an extension of the theory of model mediated measurement, in which a common quantity in metrological extension is no longer assumed, but hypothesized. (shrink)

Abstract: This research paper presents a novel approach to predict audit risks using a neural network model. The dataset used for this study was obtained from Kaggle and comprises 774 samples with 18 features, including Sector_score, PARA_A, SCORE_A, PARA_B, SCORE_B, TOTAL, numbers, marks, Money_Value, District, Loss, Loss_SCORE, History, History_score, score, and Risk. The proposed neural network architecture consists of three layers, including one input layer, one hidden layer, and one output layer. The neural network model was trained and validated, achieving (...) an impressive accuracy of 100% and an average error of 0.000015, indicating its robust predictive capability. Moreover, we conducted feature importance analysis to identify the most influential features for predicting audit risk. The key features found to be critical for classifying fraudulent activities in audit risk prediction are Sector_score, PARA_A, SCORE_A, PARA_B, SCORE_B, TOTAL, numbers, marks, Money_Value, District, Loss, Loss_SCORE, History, and History_score. This research contributes to the field of audit risk prediction by demonstrating the effectiveness of a neural network-based approach and highlighting the importance of specific features in detecting fraudulent activities. The findings have significant implications for auditors and organizations seeking to enhance their audit risk assessment processes, ultimately leading to improved financial transparency and fraud detection. (shrink)

These involved theorems on sweeping nets, saddle maps and complex analysis are a thorough examination of the method an its fundamental mechanics. The basic foundation of this analytical method is useful to any artificer of mechanical programs or development of software applications that involve computer vision or graphics. These methods will have application to further theories and methods in string theory and cosmology or even approximation of environmental factors for machine learning. -/- .

Abstract—Breast cancer is considered the second most common cancer in women compared to all other cancers. It is fatal in less than half of all cases and is the main cause of mortality in women. It accounts for 16% of all cancer mortalities worldwide. Early diagnosis of breast cancer increases the chance of recovery. Data mining techniques can be utilized in the early diagnosis of breast cancer. In this paper, an academic experimental breast cancer dataset is used to perform a (...) data mining practical experiment using the Waikato Environment for Knowledge Analysis (WEKA) tool. The WEKA Java application represents a rich resource for conducting performance metrics during the execution of experiments. Pre-processing and feature extraction are used to optimize the data. The classification process used in this study was summarized through thirteen experiments. Additionally, 10 experiments using various different classification algorithms were conducted. The introduced algorithms were: Naïve Bayes, Logistic Regression, Lazy IBK (Instance-Bases learning with parameter K), Lazy Kstar, Lazy Locally Weighted Learner, Rules ZeroR, Decision Stump, Decision Trees J48, Random Forest and Random Trees. The process of producing a predictive model was automated with the use of classification accuracy. Further, several experiments on classification of Wisconsin Diagnostic Breast Cancer and Wisconsin Breast Cancer, were conducted to compare the success rates of the different methods. Results conclude that Lazy IBK classifier k-NN can achieve 98% accuracy among other classifiers. The main advantages of the study were the compactness of using 13 different data mining models and 10 different performance measurements, and plotting figures of classifications errors. (shrink)

This study employs machine learning to predict diabetes using a Kaggle dataset with 13 features. Our three-layer model achieves an accuracy of 98.73% and an average error of 0.01%. Feature analysis identifies Age, Gender, Polyuria, Polydipsia, Visual blurring, sudden weight loss, partial paresis, delayed healing, irritability, Muscle stiffness, Alopecia, Genital thrush, Weakness, and Obesity as influential predictors. These findings have clinical significance for early diabetes risk assessment. While our research addresses gaps in the field, further work is needed (...) to enhance model generalizability. (shrink)

Critical notice of Puddifoot, Katherine. 2021. How Stereotypes Deceive Us. NY: OUP.--------- -/- Kathy Puddifoot makes a compelling and enlightening case for a striking pair of claims: 1) false stereotypes sometimes steer us to the truth, while 2) true stereotypes often lead us into error. This is a wonderful book, a seamless integration of epistemology with ethics, of philosophy with social science, and of “mainstream” or “Western analytic” approaches with marginalized and underappreciated contributions from critical social traditions, especially black (...) feminism. The integrations are so seamless, in fact, as to give the reader the impression that Puddifoot is simply picking up conversations already underway. Instead, she has done a tremendous service in bringing representatives from wide-ranging, often-siloed disciplines into dialogue. Another virtue of Puddifoot’s book is how thoroughly it maps out the actual and possible views and logical spaces revolving around each topic she addresses. How Stereotypes Deceive Us could therefore be used to introduce budding epistemologists to the field, as it offers clear and careful explanations of leading approaches to a range of topics, including virtue epistemology, theory of mind, and more. (shrink)

Breast cancer remains a significant health concern worldwide, necessitating the development of effective diagnostic tools. In this study, we employ a neural network-based approach to analyze the Wisconsin Breast Cancer dataset, sourced from Kaggle, comprising 570 samples and 30 features. Our proposed model features six layers (1 input, 1 hidden, 1 output), and through rigorous training and validation, we achieve a remarkable accuracy rate of 99.57% and an average error of 0.000170 as shown in the image below. Furthermore, our (...) investigation identifies the most influential features in breast cancer diagnosis, shedding light on the key determinants of malignancy. Notably, we find that factors such as fractal dimension_se, symmetry worst, compactness_worst, symmetry_se, and smoothness_se play pivotal roles in distinguishing between benign and malignant cases. This research contributes to the ongoing efforts to enhance breast cancer diagnosis, providing valuable insights into feature importance and showcasing the potential of neural networks in medical applications. Our findings have implications for improving early detection and treatment strategies, ultimately contributing to improved patient outcomes. (shrink)

The human race has been socially organizing itself for probably about 1.8 million years. The first form of human organization was the hunter-gatherer, which was the form of organization in which man lived for about 99 % of his history. This mode of life caused humans to organize themselves into small groups and lead a nomadic life. The nomadic life ensured that these groups had no possessions and no wealth could be accumulated. In this manner, this form of human organization (...) ensured egalitarianism, a form of primitive communism. This changed dramatically with the development of agriculture in the so-called Neolithic Revolution in 10,000 BC. With the development of agriculture and the consequent development of technology, man became sedentary, the first towns were formed, and the class system made its appearance, that is, the separation between an administrative class and a productive class. The egalitarian and communist primitive society gave way to an increasingly centralized and hierarchical society. From network theory, they have been insisting for years on the benefits of the so-called scale-free networks, networks governed by certain privileged nodes called hubs. These networks are said to be slightly vulnerable and highly robust to errors. In this work, we perform a deep network analysis of a group of centralized-hierarchical networks and a group of decentralized-distributed networks. This work provides clear and compelling evidence that, contrary to what is maintained, decentralized-distributed networks are the least vulnerable and most robust networks, and are the networks that ensure an equitable and equal distribution of power and influence among their members. These results are analyzed in the context of network theory, and are discussed in relation to the theories of Jeremy Rifkin, Ernst Schumacher, Alexander Bogdanov and Aldous Huxley. (shrink)

Purpose. The article aims to provide practical recommendations for calculating natural frequencies in axisymmetric shells using finite element methods. It focuses on the need to develop a simplified model that can be used in any modern finite element software package. The study analyzes the impact of the simplified homogeneous model on the deviation and error of natural frequencies compared to real structures. Design / Method / Approach. The research is based on creating a simplified shell geometry by determining parameters (...) such as shell thickness and density. These parameters are derived under the condition of equivalence in the moment of inertia and mass of the cross-sectional element. These parameters can vary along the height of the shell. Findings. The natural frequencies of the experimental shell with complex geometry were calculated and compared with those of the simplified model. The deviations and errors in the calculated frequencies were determined. It was demonstrated that the simplified model allows the calculation of natural frequencies with a deviation of no more than 1% from the experimental model, while significantly reducing computation time and the required computer resources. Theoretical Implications. The research expands the understanding of challenges in calculating the natural frequencies of complex objects using finite element methods under limited computational resources. Practical Implications. Practical recommendations are provided for engineers and designers when performing modeling tasks in the mechanics of deformable solid bodies. Originality / Value. The article presents an original analysis of a real case where a simplified model was implemented to determine the natural harmonics of a liquid rocket engine nozzle, making it a valuable tool for studying complex structures. Research Limitations / Future Research. The study is limited to the analysis of determining the natural frequencies of axisymmetric shells and does not cover all possible geometric features. Future research may focus on developing simplified models based on the equivalence of stiffness and mass parameters. Article Type. Case study, practical article. (shrink)

Abstract Alzheimer's disease has spread insanely throughout the world. Early detection and intervention are essential to improve the chances of a positive outcome. This study presents a new method to predict a person's likelihood of developing Alzheimer's using a neural network model. The dataset includes 373 samples with 10 features, such as Group,M/F,Age,EDUC, SES,MMSE,CDR ,eTIV,nWBV,Oldpeak,ASF.. A four-layer neural network model (1 input, 2 hidden, 1 output) was trained on the dataset and achieved an accuracy of 98.10% and an average (...) class='Hi'>error of 0.01. This study provides a valuable tool for early detection and intervention of Alzheimer's, thus contributing to the field of health and medicine. (shrink)

In earlier work, I predicted that we would probably not be able to determine the colors of the dinosaurs. I lost this epistemic bet against science in dramatic fashion when scientists discovered that it is possible to draw inferences about dinosaur coloration based on the microstructure of fossil feathers (Vinther et al., 2008). This paper is an exercise in philosophical error analysis. I examine this episode with two questions in mind. First, does this case lend any support to (...) epistemic optimism about historical science? Second, under what conditions is it rational to make predictions about what questions scientists will or will not be able answer? In reply to the first question, I argue that the recent work on the colors of the dinosaurs matters less to the debate about the epistemology of historical science than it might seem. In reply to the second question, I argue that it is difficult to specify a policy that would rule out the failed bet without also being too conservative. (shrink)

The ability to solve problems is a prerequisite in preparing mathematics preservice teachers. This study assessed preservice teachers’ problem-solving difficulties and performance, particularly in worded problems on number sense, measurement, geometry, algebra, and probability. Also, academic profile differences in the preservice teacher’s problem-solving performance and common errors were determined. A descriptive-comparative research design was employed with 158 random respondents. Data were gathered face-to-face during the first semester of the school year 2022-2023, and data were analyzed with the aid of jamovi (...) software, ensuring ethical measures. Overall findings revealed that the preservice teachers experienced average difficulty in solving problems. The low performance of the preservice teachers on the given problems was also demonstrated. Further analysis revealed a significant difference between the preservice teachers’ problem-solving performance based on their subject preference and program. Moreover, the error analysis revealed that the preservice teachers incurred comprehension errors in misrepresentation, misinterpretation, and miscalculation. These results will serve as a measure for policymakers and curriculum developers of the teacher education institution concerned to make relevant enhancements to the math courses offered in the elementary and secondary education programs. (shrink)

Reconstructability analysis (RA) decomposes wholes, namely data in the form either of set theoretic relations or multivariate probability distributions, into parts, namely relations or distributions involving subsets of variables. Data is modeled and compressed by variable-based decomposition, by more general state-based decomposition, or by the use of latent variables. Models, which specify the interdependencies among the variables, are selected to minimize error and complexity.

The conditional analysis of ability faces familiar counterexamples involving cases of volitional incapacity. An interesting response to the problem of volitional incapacity is to try to explain away the responses elicited by such counterexamples by distinguishing between what we are able to do and what we are able to bring ourselves to do. We argue that this error-theoretic response fails. Either it succeeds in solving the problem of volitional incapacity at the cost of making the conditional analysis (...) vulnerable to obvious counterexamples to its necessity. Or, it avoids the counterexamples to its necessity but fails to solve the problem of volitional incapacity. (shrink)

Moral error theory is comprised of two parts: a denial of the existence of objective values, and a claim about the ways in which we attempt to make reference to such objective values. John Mackie is sometimes presented as endorsing the view that we necessarily presuppose such objective values in our moral language and thought. In a series of recent papers, though, Victor Moberger (2017), Selim Berker (2019), and Michael Ridge (2020) point out that Mackie does not seem to (...) commit himself to this view. They argue that Mackie thinks this reference to objective values can, and perhaps should, be detached from our moral statements and judgments. In this paper, I argue that Moberger, Berker, and Ridge are right to point out that Mackie stops short of claiming a necessary connection between moral language and a commitment to objective values, but that he does not endorse the contrary claim either. Instead, Mackie stays neutral on the question whether it is possible to assert moral statements or make moral judgments without presupposing objective value. This is because he does not need to take a position on this matter. Mackie only engages with the conceptual analysis of moral language and thought to the extent required to achieve his argumentative goals: he wants to reject revisionary analyses of moral language and to refute the idea that we can assume moral truths to be in alignment with ordinary moral language. (shrink)

This paper outlines a quantitative theory of strongly semantic information (TSSI) based on truth-values rather than probability distributions. The main hypothesis supported in the paper is that the classic quantitative theory of weakly semantic information (TWSI), based on probability distributions, assumes that truth-values supervene on factual semantic information, yet this principle is too weak and generates a well-known semantic paradox, whereas TSSI, according to which factual semantic information encapsulates truth, can avoid the paradox and is more in line with the (...) standard conception of what generally counts as semantic information. After a brief introduction, section two outlines the semantic paradox implied by TWSI, analysing it in terms of an initial conflict between two requisites of a quantitative theory of semantic information. In section three, three criteria of semantic information equivalence are used to provide a taxonomy of quantitative approaches to semantic information and introduce TSSI. In section four, some further desiderata that should be fulfilled by a quantitative TSSI are explained. From section five to section seven, TSSI is developed on the basis of a calculus of truth-values and semantic discrepancy with respect to a given situation. In section eight, it is shown how TSSI succeeds in solving the paradox. Section nine summarises the main results of the paper and indicates some future developments. (shrink)

The availability of the defence of belief in consent under section 265(4) is a question of law, subject to review on appeal. The statutory provision is based on the common law rule that applies to all defences. Consideration of the defence when it is unavailable in law and failure to consider it when it is available are both incorrect. A judge is most likely to avoid error when ruling on availability of the defence if the ruling: (1) is grounded (...) on sound analysis of the substantive basis for the defence and its relationship to the principles of criminal responsibility; and (2) uses precise legal criteria to govern practical application of section 265(4) to the evidence in specific cases. The guidelines proposed in Part I are based on analyses of the substantive defence and culpable awareness and were developed to ensure that appropriate criteria are properly used when section 265(4) is applied. When a trial judge rules that the defence is available in law, the trier of fact must determine whether the defence is available on the facts as found, based on the evidence in the case. The model jury instructions proposed in Part II are designed to ensure that deliberations by the trier of fact are also guided and shaped by appropriate legal criteria. At both stages, the objective is to ground the deliberation process on fact, not fiction, and to regulate the exculpatory effect of the defence by using legal norms to exclude excuses based on extra-legal considerations such as sexual/racial fantasy, stereotype and myth, or community attitudes and custom. (shrink)

In the fifth version of our response-paper [26] to Imamura’s criticism, we recall that NonStandard Neutrosophic Logic was never used by neutrosophic community in no application, that the quarter of century old neutrosophic operators (1995-1998) criticized by Imamura were never utilized since they were improved shortly after but he omits to tell their development, and that in real world applications we need to convert/approximate the NonStandard Analysis hyperreals, monads and binads to tiny intervals with the desired accuracy – otherwise (...) they would be inapplicable. We point out several errors and false statements by Imamura [21] with respect to the inf/sup of nonstandard subsets, also Imamura’s “rigorous definition of neutrosophic logic” is wrong and the same for his definition of nonstandard unit interval, and we prove that there is not a total order on the set of hyperreals (because of the newly introduced Neutrosophic Hyperreals that are indeterminate), whence the Transfer Principle from R to R* is questionable. After his criticism, several response publications on theoretical nonstandard neutrosophics followed in the period 2018-2022. As such, I extended the NonStandard Analysis by adding the left monad closed to the right, right monad closed to the left, pierced binad (we introduced in 1998), and unpierced binad - all these in order to close the newly extended nonstandard space (R*) under nonstandard addition, nonstandard subtraction, nonstandard multiplication, nonstandard division, and nonstandard power operations [23, 24]. Improved definitions of NonStandard Unit Interval and NonStandard Neutrosophic Logic, together with NonStandard Neutrosophic Operators are presented. (shrink)

I give a pedagogical derivation of the Cramer-Rao Bound, which gives a lower bound on the variance of estimators used in statistical point estimation, commonly used to give numerical estimates of the systematic uncertainties in a measurement.

Background Analysis of aphasic narratives can be a challenge for clinicians. Previous studies have mainly employed measures that categorized speech samples at the word level. They included quantification of the use and misuse of different word classes, presence and absence of narrative contents and errors, paraphasias, and perseverations, as well as morphological structures and errors within a narrative. In other words, a great amount of research has been conducted in the aphasiology literature focusing on micro-linguistic structures of oral narratives. (...) Aspects of macro- linguistic structures, such as the analysis of content information by a speaker, consistency of using cohesive devices to present information within a narrative, and order of presenting information necessary to form a coherent discourse, have not been extensively investigated. The current investigation proposes a clinical analytic system to target three aspects of macro-linguistic structures in narratives among speakers with aphasia. Specifically, (1) the presence of search events (i.e., the mentioning of key events that allow the listener to understand; Capilouto, Wright, &Wagovich, 2006) within a narrative, (2) the sequence of the mentioned events, and (3) the informativeness (i.e., the fulfillment of lexical items that allow the user to understand what the event is detailing) of the event contents, were focused in the proposed framework. Method Ten controls transcripts from were selected from the AphasiaBank (MacWhinney, Fromm, Forbes, & Holland, 2011). Three narrative tasks, including sequential picture description of ‘Refused Umbrella’, procedural narrative of making a ‘Peanut Butter and Jelly Sandwich’, and telling of ‘Cinderella’ story, were used to establish normative data for the basis of analysis. Specifically, the Search Events (e) and Informative Words (i) used by at least 70% of the speakers were listed for each genre. The sequential order of mentioning the Search Events, i.e., common order of events in 90% of the speakers, (s.total) was determined. Twelve speakers with aphasia (nine fluent and three non-fluent) were recruited and administered the Western Aphasia Battery and Object and Action Naming Battery. Their performance in the above three discourse tasks were orthographically transcribed and analyzed using the following measures: e.total, e.matched with norm, e.missed, e.irrlevant, e.extra, s.total, i.pb&j, i.umbr, i.cind, and i.total. Three samples were randomly chosen to be re-analyzed for inter- and intra-rater reliability. Results Results of an independent t-test suggested significant differences between the fluent and non-fluent subjects in sequential order of Search Events for all genres (s.total) and i.total, suggesting sensitivity of this framework to differentiate between the two fluency groups. Results of Pearson product-moment correlations revealed significant relation between Informative Words and WAB spontaneous speech scores, AQ, as well as OAB scores, for both aphasic groups. The mean value of coefficients for intra-rater reliability (0.992), with significant correlations on e.match, e.miss, and e.extra, was higher than that of inter-rater reliability (0.897). Discussion Based on our preliminary results, this objective framework allowed clinical evaluation of impairment in macro-linguistic structures present in aphasic discourse. Further extension should involve more subjects encompassing a wider range of severity with different types of aphasia. (shrink)

Rivka Weinberg advances an error theory of ultimate meaning with three parts: (1) a conceptual analysis, (2) the claim that the extension of the concept is empty, and (3) a proposed fitting response, namely being very, very sad. Weinberg’s conceptual analysis of ultimate meaning involves two features that jointly make it metaphysically impossible, namely (i) the separateness of activities and valued ends, and (ii) the bounded nature of human lives. Both are open to serious challenges. We offer (...) an internalist alternative to (i) and a relational alternative to (ii). We then draw out implications for (2) and conclude with reasons to be cheerful about the prospects of a meaningful life. (shrink)

In the fifth version of our reply article [26] to Imamura's critique, we recall that Neutrosophic Non-Standard Logic was never used by the neutrosophic community in any application, that the quarter-century old (1995-1998) neutrosophic operators criticized by Imamura were never used as they were improved soon after, but omits to talk about their development, and that in real-world applications we need to convert/approximate the hyperreals, monads and bi-nads of Non-Standard Analysis to tiny intervals with the desired precision; otherwise they (...) would be inapplicable. We pointed out several errors and false statements by Imamura [21] regarding the inf/sup of nonstandard subsets, also Imamura's "rigorous definition of neutrosophic logic" is incorrect, as is his definition of nonstandard unit interval, and we showed that there is no total order in Neutrosophic Computing and Machine Learning , Vol. 23, 2022 Florentin Smarandache, Definición mejorada de la lógica neutrosófica no estándar e introducción a los hiperreales neutrosóficos (Quinta versión) 2 the set of hyperreals (due to the recently introduced Neutrosophic Hyperreals which are indeterminate), so the Transfer Principle from R to R* is questionable. After his critique, several reply posts on non-standard theoretical neutrosophy followed in 2018-2022. As such, I extended the Nonstandard Analysis by adding the right-closed left monad, the left-closed right monad, the punctured binad (which we introduced in 1998), and the nonpunctured binad - all in order to close the newly extended nonstandard space (R*) under nonstandard addition, nonstandard subtraction, nonstandard multiplication, nonstandard division, and nonstandard power operations [23, 24]. Improved definitions of the Nonstandard Unitary Interval and Nonstandard Neutrosophic Logic are presented, along with Nonstandard Neutrosophic Operators. (shrink)

This paper tries to determine the philosophical nature of language, its functions, structure and content. It also explains the concept of natural language, ordinary and ideal language i.e. how there is a need of artificial perfect logical language without errors and unclearness in that language. This paper further shows the logical form of language with its syntactical, semantical, innate and acquired criteria for the evaluation of the languages. It deals with the analysis of language to clear what is unclear, (...) to know what is unknown, to make definite what is vague. In this paper I used the method; logical method for interpretation and argumentation, analytical method for simplification, and critical method to investigate the real domain of language. This paper does not deal with ordinary functions of the language but it deals with the conceptual and modular functions of the language. The fundamental aim of this written up is to determine the analytical approach of Wittgenstein to sketch the ‘language as a tool to discuss the state of affairs or facts of the worlds that is also what philosophy does. This paper describes the contributions of rationalism and empiricism in the field of knowing the truths of language. (shrink)

As it has been shaped by improvements in its tools and methods, and by its discourse with critics, I describe how the astrological research program has advanced through three stages of modelling and design limitations. Single-factor tests (for example, the many Sun-sign–only experiments that have been published) are typically underdeterministic. Multi-factor tests, unless they are very well designed, can easily become overdeterministic. Chart-matching tests have been vulnerable to confirmation bias errors until the development of a machine-based, whole-chart matching protocol that (...) has objectively produced evidence of high effect-sizes. A meta-analysis of recent results shows the rapid advancement and how to further improve the results. The value of the program is not only to corroborate the taxonomic counterfactuals of astrological “cookbooks,” but to extend their explanatory reach by the comparison of astrological postulates and inferences with philosophies in other disciplines in terms of quantifiable processes and emergent effects. (shrink)

In fMRI research, the goal of correcting for multiple comparisons is to identify areas of activity that reflect true effects, and thus would be expected to replicate in future studies. Finding an appropriate balance between trying to minimize false positives (Type I error) while not being too stringent and omitting true effects (Type II error) can be challenging. Furthermore, the advantages and disadvantages of these types of errors may differ for different areas of study. In many areas of (...) social neuroscience that involve complex processes and considerable individual differences, such as the study of moral judgment, effects are typically smaller and statistical power weaker, leading to the suggestion that less stringent corrections that allow for more sensitivity may be beneficial, but also result in more false positives. Using moral judgment fMRI data, we evaluated four commonly used methods for multiple comparison correction implemented in SPM12 by examining which method produced the most precise overlap with results from a meta-analysis of relevant studies and with results from nonparametric permutation analyses. We found that voxel-wise thresholding with family-wise error correction based on Random Field Theory provides a more precise overlap (i.e., without omitting too few regions or encompassing too many additional regions) than either clusterwise thresholding, Bonferroni correction, or false discovery rate correction methods. (shrink)

This paper offers an analysis of the authoritatively normative concept PRACTICAL OUGHT that appeals to the constitutive norms for the activity of non-arbitrary selection. I argue that this analysis permits an attractive and substantive explanation of what the distinctive normative authority of this concept amounts to. I contrast my account with more familiar constitutivist theories, and briefly show how it answers ‘schmagency’-style objections to constitutivist explanations of normativity. Finally, I explain how the account offered here can be used (...) to help realists, error theorist, and fictionalists address central challenges to their views. (shrink)

Accurate statistical analysis of Fortnite gameplay data is essential for improving gaming strategies and performance. In this study, we present a novel approach to analyze Fortnite statistics using machine learning techniques. Our dataset comprises a wide range of gameplay metrics, including eliminations, assists, revives, accuracy, hits, headshots, distance traveled, materials gathered, materials used, damage taken, damage to players, damage to structures, and more. We collected this dataset to gain insights into Fortnite player performance and strategies. The proposed model employs (...) advanced machine learning algorithms and data preprocessing techniques. We aim to identify key performance indicators and influential factors that contribute to Fortnite success. By exploring patterns and relationships within the dataset, our model can provide valuable insights into gameplay optimization. Our research involves feature analysis to determine the most influential factors in predicting Fortnite performance. These factors include eliminations, assists, revives, accuracy, hits, headshots, distance traveled, materials gathered, materials used, damage taken, damage to players, damage to structures, and more. By understanding the impact of these factors, we aim to help Fortnite players enhance their skills and strategies. Through extensive training and validation of our machine learning model, we achieved remarkable results, with an accuracy rate of [Your Accuracy Rate]% and an average error of [Your Average Error]. This research not only provides valuable insights into Fortnite gameplay but also offers a foundation for future research in the field of esports analytics and performance optimization. (shrink)

Abstract : A measurement result is never absolutely accurate: it is affected by an unknown “measurement error” which characterizes the discrepancy between the obtained value and the “true value” of the quantity intended to be measured. As a consequence, to be acceptable a measurement result cannot take the form of a unique numerical value, but has to be accompanied by an indication of its “measurement uncertainty”, which enunciates a state of doubt. What, though, is the value of measurement uncertainty? (...) What is its numerical value: how does one calculate it? What is its epistemic value: how one should interpret a measurement result? Firstly, we describe the statistical models that scientists make use of in contemporary metrology to perform an uncertainty analysis, and we show that the issue of the interpretation of probabilities is vigorously debated. This debate brings out epistemological issues about the nature and function of physical measurements, metrologists insisting in particular on the subjective aspect of measurement. Secondly, we examine the philosophical elaboration of metrologists in their technical works, where they criticize the use of the notion of “true value” of a physical quantity. We then challenge this elaboration and defend such a notion. The third part turns to a specific use of measurement uncertainty in order to address our thematic from the perspective of precision physics, considering the activity of the adjustments of physical constants. In the course of this activity, physicists have developed a dynamic conception of the accuracy of their measurement results, oriented towards a future progress of knowledge, and underlining the epistemic virtues of a never-ending process of identification and correction of measurement errors. (shrink)

The statistical technique of analysis of variance is often used by biologists as a measure of causal factors’ relative strength or importance. I argue that it is a tool ill suited to this purpose, on several grounds. I suggest a superior alternative, and outline some implications. I finish with a diagnosis of the source of error – an unwitting inheritance of bad philosophy that now requires the remedy of better philosophy.

Corcoran, J. 2005. Counterexamples and proexamples. Bulletin of Symbolic Logic 11(2005) 460. -/- John Corcoran, Counterexamples and Proexamples. Philosophy, University at Buffalo, Buffalo, NY 14260-4150 E-mail: [email protected] Every perfect number that is not even is a counterexample for the universal proposition that every perfect number is even. Conversely, every counterexample for the proposition “every perfect number is even” is a perfect number that is not even. Every perfect number that is odd is a proexample for the existential proposition that some (...) perfect number is odd. Conversely, every proexample for the proposition “some perfect number is odd” is a perfect number that is odd. As trivial these remarks may seem, they can not be taken for granted, even in mathematical and logical texts designed to introduce their respective subjects. One well-reviewed book on counterexamples in analysis says that in order to demonstrate that a universal proposition is false it is necessary and sufficient to construct a counterexample. It is easy to see that it is not necessary to construct a counterexample to demonstrate that the proposition “every true proposition is known to be true” is false–necessity fails. Moreover the mere construction of an object that happens to be a counterexample does not by itself demonstrate that it is a counterexample–sufficiency fails. In order to demonstrate that a universal proposition is false it is neither necessary nor sufficient to construct a counterexample. Likewise, of course, in order to demonstrate that an existential proposition is true it is neither necessary nor sufficient to construct a proexample. This article defines the above relational concepts of counterexample and of proexample, it discusses their surprising history and philosophy, it gives many examples of uses of these and related concepts in the literature and it discusses some of the many errors that have been made as a result of overlooking the challenging subtlety of the proper use of these two basic and indispensable concepts. (shrink)

Social norms are commonly understood as rules that dictate which behaviors are appropriate, permissible, or obligatory in different situations for members of a given community. Many researchers have sought to explain the ubiquity of social norms in human life in terms of the psychological mechanisms underlying their acquisition, conformity, and enforcement. Existing theories of the psychology of social norms appeal to a variety of constructs, from prediction-error minimization, to reinforcement learning, to shared intentionality, to domain-specific adaptations for norm acquisition. (...) In this paper, we propose a novel methodological and conceptual framework for the cognitive science of social norms that we call normative pluralism. We begin with an analysis of the explanatory aims of the cognitive science of social norms. From this analysis, we derive a recommendation for a reformed conception of its explanandum: a minimally psychological construct that we call normative regularities. Our central empirical proposal is that the psychological underpinnings of social norms are most likely realized by a heterogeneous set of cognitive, motivational, and ecological mechanisms that vary between norms and between individuals, rather than by a single type of process or distinctive norm system. This pluralistic approach, we suggest, offers a methodologically sound point of departure for a fruitful and rigorous science of social norms. (shrink)

In their response to our article (Keestra and Cowley, 2009), Hacker and Bennett charge us with failing to understand the project of their book Philosophical Foundations of Neuroscience (PFN; Bennett and Hacker, 2003) and do this by discussing foundationalism, linguistic conservatism and the passivity of perception. In this rebuttal we explore disagreements that explain the alleged errors. First, we reiterate our substantial disagreement with Bennett and Hacker (B&H) regarding their assumption that, even regarding much debated concepts like ‘consciousness’, we can (...) assume conceptual consensus within a community of competent speakers. Instead, we emphasize variability and divergence between individuals and groups in such contexts. Second, we plead for modesty in conceptual analysis, including the use of conceptual ambiguities as heuristics for the investigation of explanatory mechanisms. Third, we elucidate our proposal by discussing the interdependence of perception and action, which in some cases appear to be problematic for PFN. Fourth, we discuss why our view of conceptual innovation is different from B&H’s, as we plead for linking explanatory ingredients with conceptual analysis. We end by repeating our particular agreement with their mereological principle, even though we present different reasons: psychological concepts should not be applied to mere components or operations of explanatory mechanisms, for which another vocabulary should be developed. (shrink)

The semantic analysis of conditional sentences does not entirely align with their morphosyntactic structure. I substantiate this hypothesis with instances from both Czech and English that extend beyond conventional textbook examples. I also highlight that logicians and philosophers often make terminological errors when they disregard the insights from linguistic disciplines. Despite the early analytic philosophy’s emphasis on terminological precision, the practical application falls significantly short of this ideal. I firmly believe that a proper understanding of the morphosyntax and semantics (...) of conditional sentences is a prerequisite for their classification and analysis. In our pursuit of a comprehensive exploration of conditional clauses, we must also grapple with methodological challenges that delve into the very core of the philosophy of language. The primary issue revolves around the fact that two out of the three a priori methods in philosophy rely heavily on the analysis of conditional sentences: thought experiments and modal metaphysics. (shrink)

This article provides an analysis of Johannes Clauberg’s intentions in writing his Logica vetus et nova (1654, 1658). Announced before his adherence to Cartesianism, his Logica was eventually developed in order to provide Cartesian philosophy with a Scholastic form, embodying a complete methodology for the academic disciplines based on Descartes’ rules and a medicina mentis against philosophical prejudices. However, this was not its only function: thanks to the rules for the interpretation of philosophical texts it encompassed, Clauberg’s Logica was (...) meant to provide a general hermeneutics designed to put an end to the quarrels raised by the dissemination of Cartesianism. Such quarrels, according to Clauberg, were caused by the misinterpretation of Descartes’ texts in Revius’ Methodi cartesianae consideratio theologica (1648) and Statera philosophiae cartesianae (1650) and in Lentulus’ Nova Renati Descartes sapientia (1651), which criticized the apparent lack of a logical theory in Descartes’ philosophy and its supposed inconsistencies. Clauberg answers their criticisms by giving a clear account of Descartes’ logical theory and by undermining the interpretative criteria they assumed, in light of a general theory of error. Polemics over Cartesian philosophy, in this way, favored the development of a comprehensive Cartesian methodology for academic disciplines and of the first hermeneutics for philosophical texts. (shrink)

Preregistration has been proposed as a useful method for making a publicly verifiable distinction between confirmatory hypothesis tests, which involve planned tests of ante hoc hypotheses, and exploratory hypothesis tests, which involve unplanned tests of post hoc hypotheses. This distinction is thought to be important because it has been proposed that confirmatory hypothesis tests provide more compelling results (less uncertain, less tentative, less open to bias) than exploratory hypothesis tests. In this article, we challenge this proposition and argue that there (...) are several advantages of exploratory hypothesis tests that can make their results more compelling than those of confirmatory hypothesis tests. We also consider some potential disadvantages of exploratory hypothesis tests and conclude that their advantages can outweigh the disadvantages. We conclude that exploratory hypothesis tests avoid researcher commitment and researcher prophecy biases, reduce the probability of data fraud, are more appropriate in the context of unplanned deviations, facilitate inference to the best explanation, and allow peer reviewers to make additional contributions at the data analysis stage. In contrast, confirmatory hypothesis tests may lead to an inappropriate level of confidence in research conclusions, less appropriate analyses in the context of unplanned deviations, and greater bias and errors in theoretical inferences. (shrink)