What does it look like when a group of scientists set out to re-envision an entire field of biology in symbolic and formal terms? I analyze the founding and articulation of Numerical Taxonomy between 1950 and 1970, the period when it set out a radical new approach to classification and founded a tradition of mathematics in systematic biology. I argue that introducing mathematics in a comprehensive way also requires re-organizing the daily work of scientists in the field. (...) class='Hi'>Numerical taxonomists sought to establish a mathematical method for classification that was universal to every type of organism, and I argue this intrinsically implicated them in a qualitative re-organization of the work of all systematists. I also discuss how Numerical Taxonomy’s re-organization of practice became entrenched across systematic biology even as opposing schools produced their own competing mathematical methods. In this way, the structure of the work process became more fundamental than the methodological theories that motivated it. (shrink)

People are increasingly exposed to conflicting health information and must navigate this information to make numerous decisions, such as which foods to consume, a process many find difficult. Although some consumers attribute these disagreements to aspects related to uncertainty and complexity of research, many use a narrower set of credibility-based explanations. Experts’ views on disagreements are underinvestigated and lack explicit identification and classification of the differences in causes for disagreement. Consequently, there is a gap in existing literature to understand the (...) range of reasons for these contradictions. Combining the findings from a literature study and expert interviews, a taxonomy of disagreements was developed. It identifies 10 types of disagreement classified under three dimensions: informant-, information- and uncertainty-related causes for disagreement. The taxonomy may assist with adoption of more effective strategies to deal with conflicting information and contributes to research and practice of science communication in the context of disagreement. (shrink)

We argue that the mathematization of science should be understood as a normative activity of advocating for a particular methodology with its own criteria for evaluating good research. As a case study, we examine the mathematization of taxonomic classification in systematic biology. We show how mathematization is a normative activity by contrasting its distinctive features in numerical taxonomy in the 1960s with an earlier reform advocated by Ernst Mayr starting in the 1940s. Both Mayr and the numerical (...) taxonomists sought to formalize the work of classification, but Mayr introduced a qualitative formalism based on human judgment for determining the taxonomic rank of populations, while the numerical taxonomists introduced a quantitative formalism based on automated procedures for computing classifications. The key contrast between Mayr and the numerical taxonomists is how they conceptualized the temporal structure of the workflow of classification, specifically where they allowed meta-level discourse about difficulties in producing the classification. (shrink)

Analytic theologians have proposed numerous “solutions” to the Logical Problem of the Trinity (LPT), mostly versions of Social Trinitarianism (ST) and Relative Identity Trinitarianism (RI). Both types of solution are controversial, but many hold out hope that further “Trinitarian theorizing” may yield some as yet unimagined, and somehow importantly different, solution to the LPT. I first give a precise definition of the LPT and of what would count as a solution to it. I then show how, though there are infinitely (...) many possible solutions, all solutions can be grouped together into a finite, exhaustive taxonomy, based precisely on those features which make them either controversial, heretical, or inconsistent. The taxonomy reveals why ST and RI have been the major proposed solutions, and also proves that there can be no importantly different, new solutions to the LPT. (shrink)

Abstract:Skepticism about grounding is the view that ground-theoretic concepts shouldn’t be used in meta­physical theorizing. Possible reasons for adopting this attitude are numerous: perhaps grounding is unintelligible; or perhaps it’s never instantiated; or perhaps it’s just too heterogeneous to be theor­­­­­etically useful. Unfortunately, as currently pursued the debate between grounding enthusiasts and skeptics is insufficiently structured. This paper’s purpose is to impose a measure of conceptual rigor on the debate by offering an opinionated taxonomy of views with a reasonable (...) claim to being “skeptical.” I argue that carving up logical space into pro- and anti-grounding views isn’t especially helpful; rather, we should recognize various degrees of ground-theoretic involvement depending on how inflationary our understanding of the theoretical term ‘ground’ is. (shrink)

As the digitization of information accelerates, the push to encode our surrounding numerically instead of linguistically increases. The role that language has traditionally played in the nomenclature of an integrative taxonomy is being replaced by the numeric identification of one or few quantitative characteristics. Nineteenth-century scientific systems of color identification divided, grouped, and named colors according to multiple characteristics. Now color identification relies on numeric values applied to spectrographic readings. This means of identification of color lacks the taxonomic rigor (...) of nineteenth century systems. Identifying color by numeric value instead of by grouping and naming them, strips color taxonomy of all but one quantitative aspect of a color. I use the case of color taxonomy to argue against a similar trend of numeric identification in the biological sciences. Unlike historically more integrative approaches to taxonomy in biology, genomic sequencing identifies one or few quantitative characteristics to encode an organism. If genomic sequencing becomes the primary means of identification in the biological sciences, just as in numeric systems of color identification, scientific taxonomy would suffer. Basing my analysis on theories of perception of division and on theories of language, I use the cases of color and species to argue for the advantages of an integrative taxonomic system of naming and categorizing over a method of identification, which encodes limited characteristics numerically. I hold that language is the most sophisticated tool for systematic taxonomy and that taxonomic nomenclature should be retained. (shrink)

When we ask what natural kinds are, there are two different things we might have in mind. The first, which I’ll call the taxonomy question, is what distinguishes a category which is a natural kind from an arbitrary class. The second, which I’ll call the ontology question, is what manner of stuff there is that realizes the category. Many philosophers have systematically conflated the two questions. The confusion is exhibited both by essentialists and by philosophers who pose their accounts (...) in terms of similarity. It also leads to misreading philosophers who do make the distinction. Distinguishing the questions allows for a more subtle understanding of both natural kinds and their underlying metaphysics. (shrink)

The goal of this paper is to develop a systematic taxonomy of cognitive artifacts, i.e., human-made, physical objects that functionally contribute to performing a cognitive task. First, I identify the target domain by conceptualizing the category of cognitive artifacts as a functional kind: a kind of artifact that is defined purely by its function. Next, on the basis of their informational properties, I develop a set of related subcategories in which cognitive artifacts with similar properties can be grouped. In (...) this taxonomy, I distinguish between three taxa, those of family, genus, and species. The family includes all cognitive artifacts without further specifying their informational properties. Two genera are then distinguished: representational and non-representational (or ecological) cognitive artifacts. These genera are further divided into species. In case of representational artifacts, these species are iconic, indexical, or symbolic. In case of ecological artifacts, these species are spatial or structural. Within species, token artifacts are identified. The proposed taxonomy is an important first step towards a better understanding of the range and variety of cognitive artifacts and is a helpful point of departure, both for conceptualizing how different artifacts augment or impair cognitive performance and how they transform and are integrated into our cognitive system and practices. (shrink)

A computational methodology called Grossone Infinity Computing introduced with the intention to allow one to work with infinities and infinitesimals numerically has been applied recently to a number of problems in numerical mathematics (optimization, numerical differentiation, numerical algorithms for solving ODEs, etc.). The possibility to use a specially developed computational device called the Infinity Computer (patented in USA and EU) for working with infinite and infinitesimal numbers numerically gives an additional advantage to this approach in comparison with (...) traditional methodologies studying infinities and infinitesimals only symbolically. The grossone methodology uses the Euclid’s Common Notion no. 5 ‘The whole is greater than the part’ and applies it to finite, infinite, and infinitesimal quantities and to finite and infinite sets and processes. It does not contradict Cantor’s and non-standard analysis views on infinity and can be considered as an applied development of their ideas. In this paper we consider infinite series and a particular attention is dedicated to divergent series with alternate signs. The Riemann series theorem states that conditionally convergent series can be rearranged in such a way that they either diverge or converge to an arbitrary real number. It is shown here that Riemann’s result is a consequence of the fact that symbol ∞ used traditionally does not allow us to express quantitatively the number of addends in the series, in other words, it just shows that the number of summands is infinite and does not allows us to count them. The usage of the grossone methodology allows us to see that (as it happens in the case where the number of addends is finite) rearrangements do not change the result for any sum with a fixed infinite number of summands. There are considered some traditional summation techniques such as Ramanujan summation producing results where to divergent series containing infinitely many positive integers negative results are assigned. It is shown that the careful counting of the number of addends in infinite series allows us to avoid this kind of results if grossone-based numerals are used. (shrink)

The emerging field of quantum mereology considers part-whole relations in quantum systems. Entangled quantum systems pose a peculiar problem in the field, since their total states are not reducible to that of their parts. While there exist several established proposals for modelling entangled systems, like monistic holism or relational holism, there is considerable unclarity, which further positions are available. Using the lambda operator and plural logic as formal tools, we review and develop conceivable models and evaluate their consistency and distinctness. (...) The main result is an exhaustive taxonomy of six distinct and precise models that both provide information about the mereological features as well as about the entangled property. The taxonomy is well-suited to serve as the basis for future systematic investigations. (shrink)

Kuhn's alleged taxonomic interpretation of incommensurability is grounded on an ill defined notion of untranslatability and is hence radically incomplete. To supplement it, I reconstruct Kuhn's taxonomic interpretation on the basis of a logical-semantic theory of taxonomy, a semantic theory of truth-value, and a truth-value conditional theory of cross-language communication. According to the reconstruction, two scientific languages are incommensurable when core sentences of one language, which have truth values when considered within its own context, lack truth values when considered (...) within the context of the other due to the unmatchable taxonomic structures underlying them. So constructed, Kuhn's mature interpretation of incommensurability does not depend upon the notion of truth-preserving translatability, but rather depends on the notion of truth-value-status-preserving cross-language communication. The reconstruction makes Kuhn's notion of incommensurability a well grounded, tenable and integrated notion.Author Keywords: Incommensurability; Thomas Kuhn; Taxonomic structures; Lexicons; Truth-value; Untranslatability; Cross-language communication. (shrink)

We find the claim that time is not real in both western and eastern philosophical traditions. In what follows I will call the view that time does not exist temporal error theory. Temporal error theory was made famous in western analytic philosophy in the early 1900s by John McTaggart (1908) and, in much the same tradition, temporal error theory was subsequently defended by Gödel (1949). The idea that time is not real, however, stretches back much further than that. It is (...) common to hear it said that according to Buddhist philosophy (as though that were a monolithic view) time is illusory. While it is not true that, in general, either contemporary or ancient Buddhist scholars have thought time to be illusory, there are certainly some schools of Buddhist thought, such as that of traditional Dzogchen practitioners, according to which there is no time. This paper is an attempt to set out a taxonomy of different views about what it takes for there to be time and, alongside that, a taxonomy of views about whether there is time or not, and if there is time what it is like. (shrink)

In this paper, we discern different types of possible relations. We focus on the distinction between internal and external relations and their various possible sub-types. In the first section, we present what is nowadays more or less the standard distinction between internal and external relations. In the second section, we make two contributions to the literature of internal relations: a new taxonomy of internal relations and a novel distinction between formal and material ontological relations. In the third section, we (...) discuss three distinctions among external relations, in particular the distinction between relata-specific and relata-unspecific relations. We argue that relata-specific external relations are a promising but incomplete solution to the vexed problem of Bradley’s relation regress. (shrink)

Criticism of big data has focused on showing that more is not necessarily better, in the sense that data may lose their value when taken out of context and aggregated together. The next step is to incorporate an awareness of pitfalls for aggregation into the design of data infrastructure and institutions. A common strategy minimizes aggregation errors by increasing the precision of our conventions for identifying and classifying data. As a counterpoint, we argue that there are pragmatic trade-offs between precision (...) and ambiguity that are key to designing effective solutions for generating big data about biodiversity. We focus on the importance of theory-dependence as a source of ambiguity in taxonomic nomenclature and hence a persistent challenge for implementing a single, long-term solution to storing and accessing meaningful sets of biological specimens. We argue that ambiguity does have a positive role to play in scientific progress as a tool for efficiently symbolizing multiple aspects of taxa and mediating between conflicting hypotheses about their nature. Pursuing a deeper understanding of the trade-offs and synthesis of precision and ambiguity as virtues of scientific language and communication systems then offers a productive next step for realizing sound, big biodiversity data services. (shrink)

Background If trials of therapeutic interventions are to serve society's interests, they must be of high methodological quality and must satisfy moral commitments to human subjects. The authors set out to develop a clinical - trials compendium in which standards for the ethical treatment of human subjects are integrated with standards for research methods. Methods The authors rank-ordered the world's nations and chose the 31 with >700 active trials as of 24 July 2008. Governmental and other authoritative entities of the (...) 31 countries were searched, and 1004 English-language documents containing ethical and/or methodological standards for clinical trials were identified. The authors extracted standards from 144 of those: 50 designated as ‘core’, 39 addressing trials of invasive procedures and a 5% sample of the remainder. As the integrating framework for the standards we developed a coherent taxonomy encompassing all elements of a trial's stages. Findings Review of the 144 documents yielded nearly 15 000 discrete standards. After duplicates were removed, 5903 substantive standards remained, distributed in the taxonomy as follows: initiation, 1401 standards, 8 divisions; design, 1869 standards, 16 divisions; conduct, 1473 standards, 8 divisions; analysing and reporting results, 997 standards, four divisions; and post-trial standards, 168 standards, 5 divisions. Conclusions The overwhelming number of source documents and standards uncovered in this study was not anticipated beforehand and confirms the extraordinary complexity of the clinical trials enterprise. This taxonomy of multinational ethical and methodological standards may help trialists and overseers improve the quality of clinical trials, particularly given the globalisation of clinical research. (shrink)

Humans and other animals have an evolved ability to detect discrete magnitudes in their environment. Does this observation support evolutionary debunking arguments against mathematical realism, as has been recently argued by Clarke-Doane, or does it bolster mathematical realism, as authors such as Joyce and Sinnott-Armstrong have assumed? To find out, we need to pay closer attention to the features of evolved numerical cognition. I provide a detailed examination of the functional properties of evolved numerical cognition, and propose that (...) they prima facie favor a realist account of numbers. (shrink)

The idea that there is a “Number Sense” (Dehaene, 1997) or “Core Knowledge” of number ensconced in a modular processing system (Carey, 2009) has gained popularity as the study of numerical cognition has matured. However, these claims are generally made with little, if any, detailed examination of which modular properties are instantiated in numerical processing. In this article, I aim to rectify this situation by detailing the modular properties on display in numerical cognitive processing. In the process, (...) I review literature from across the cognitive sciences and describe how the evidence reported in these works supports the hypothesis that numerical cognitive processing is modular. I outline the properties that would suffice for deeming a certain processing system a modular processing system. Subsequently, I use behavioral, neuropsychological, philosophical, and anthropological evidence to show that the number module is domain specific, informationally encapsulated, neurally localizable, subject to specific pathological breakdowns, mandatory, fast, and inaccessible at the person level; in other words, I use the evidence to demonstrate that some of our numerical capacity is housed in modular casing. (shrink)

It is suggested that the relationship between visual attention and conscious visual experience can be simplified by distinguishing different aspects of both visual attention and visual experience. A set of principles is first proposed for any possible taxonomy of the processes involved in visual attention. A particular taxonomy is then put forward that describes five such processes, each with a distinct function and characteristic mode of operation. Based on these, three separate kinds—or possibly grades—of conscious visual experience can (...) be distinguished, each associated with a particular combination of attentional processes. (shrink)

Magicians use misdirection to prevent you from realizing the methods used to create a magical effect, thereby allowing you to experience an apparently impossible event. Magicians have acquired much knowledge about misdirection, and have suggested several taxonomies of misdirection. These describe many of the fundamental principles in misdirection, focusing on how misdirection is achieved by magicians. In this article we review the strengths and weaknesses of past taxonomies, and argue that a more natural way of making sense of misdirection is (...) to focus on the perceptual and cognitive mechanisms involved. Our psychologically-based taxonomy has three basic categories, corresponding to the types of psychological mechanisms affected: perception, memory, and reasoning. Each of these categories is then divided into subcategories based on the mechanisms that control these effects. This new taxonomy can help organize magicians' knowledge of misdirection in a meaningful way, and facilitate the dialog between magicians and scientists. (shrink)

The accepted narrative treats John Stuart Mill’s Kinds as the historical prototype for our natural kinds, but Mill actually employs two separate notions: Kinds and natural groups. Considering these, along with the accounts of Mill’s nineteenth-century interlocutors, forces us to recognize two distinct questions. First, what marks a natural kind as worthy of inclusion in taxonomy? Second, what exists in the world that makes a category meet that criterion? Mill’s two notions offer separate answers to the two questions: natural (...) groups for taxonomy and Kinds for ontology. This distinction is ignored in many contemporary debates about natural kinds and is obscured by the standard narrative that treats our natural kinds just as a development of Mill’s Kinds. (shrink)

In this paper we propose a formal theory of partitions (ways of dividing up or sorting or mapping reality) and we show how the theory can be applied in the geospatial domain. We characterize partitions at two levels: as systems of cells (theory A), and in terms of their projective relation to reality (theory B). We lay down conditions of well-formedness for partitions and we define what it means for partitions to project truly onto reality. We continue by classifying well-formed (...) partitions along three axes: (a) degree of correspondence between partition cells and objects in reality; (b) degree to which a partition represents the mereological structure of the domain it is projected onto; and (c) degree of completeness and exhaustiveness with which a partition represents reality. This classification is used to characterize three types of partitions that play an important role in spatial information science: cadastral partitions, categorical coverages, and the partitions involved in folk categorizations of the geospatial domain. (shrink)

In this chapter I shall bring to the fore the family resemblances of the different notions of the concept of ‘ways of thinking’ that I have introduced in the previous chapter. For example, I shall compare Hacking’s styles project with Daston and Galison’s study on objectivity as well as with other projects such as Fleck’s, Kuhn’s and Foucault’s. Thanks to these comparative analyses, I shall identify points where all these projects support one another. I shall also provide a model for (...) studying objectivity that incorporates the notions of Fleck, Foucault, Kuhn and Hacking. Used together, these notions provide a more profound understanding of how objectivity emerges. Furthermore, I shall propose a layered diagram that maps the differences between the notions of thought style, episteme, paradigm and style of reasoning. Finally I shall highlight two philosophical issues, relativism and contingency, connected with the concept of ‘ways of thinking’ in all its different notions. I shall argue that this issue is particularly controversial in the case of Hacking’s notion. (shrink)

This paper argues that the many and various conceptions of consciousness propounded by cognitive scientists and philosophers can all be understood as constituted with reference to four fundamental sorts of criterion: epistemic (concerned with kinds of consciousness), semantic (dealing with orders of consciousness), physiological (reflecting states of consciousness), and pragmatic (seeking to capture types of consciousness). The resulting four-fold taxonomy, intended to be exhaustive, suggests that all of the distinct varieties of consciousness currently encountered in cognitive neuroscience, the philosophy (...) of mind, clinical psychology, and other related fields ultimately refer to a unified natural process, analysed under four general aspects. The proposed taxonomy will, it is hoped, possess sufficient clarity to serve as a sound theoretical framework for further scientific studies, and to count as a significant step in the direction of a properly formulated unified concept of consciousness. (shrink)

Disgust has been a perennial feature of art from medieval visions of hell to postmodern travesties. The purpose of this chapter is to chart various ways in which disgust functions in artworks both in terms of content and style, canvassing cases in which the content and/or style is literally disgusting in contrast to cases where the disgust serves to characterize the content, often for moral or political or broader cultural purposes.

The author contends that classifying theories in the field of meta-ethics along a single dimension misses important nuances in each theory. With the increased sophistication and complexity of meta-ethical analyses in the modern era, the traditional cognitivist–non-cognitivist and realist–anti-realist categories no longer function adequately. The author categorizes the various meta-ethical theories along three dimensions. These dimensions focus on the linguistic analysis offered by each theory, its metaphysical commitments and its degree of normative tolerance.

Model-data symbiosis is the view that there is an interdependent and mutually beneficial relationship between data and models, whereby models are not only data-laden, but data are also model-laden or model filtered. In this paper I elaborate and defend the second, more controversial, component of the symbiosis view. In particular, I construct a preliminary taxonomy of the different ways in which theoretical and simulation models are used in the production of data sets. These include data conversion, data correction, data (...) interpolation, data scaling, data fusion, data assimilation, and synthetic data. Each is defined and briefly illustrated with an example from the geosciences. I argue that model-filtered data are typically more accurate and reliable than the so-called raw data, and hence beneficially serve the epistemic aims of science. By illuminating the methods by which raw data are turned into scientifically useful data sets, this taxonomy provides a foundation for developing a more adequate philosophy of data. (shrink)

The term attention has been used to mean so many different things that some have despaired of it being useful at all. This paper is devoted to bringing a modicum of order to the chaos through the time-honored device of categorization. The chief purpose of this paper is to introduce a comprehensive descriptive taxonomy of the nuanced ways the term attention may be employed. It is presented in table form, followed by elucidations and illustrations of each of its items. (...) But first, I offer reasons why a taxonomy of attention is needed and explore some of its possible benefits. After presenting the taxonomy, I sketch by way of example how it might be applied to two interesting questions: is the umbrella term attention still useful?; and, what is it that ties the subdefinitions of attention together yet distinguishes them from other kinds of cognition? (shrink)

The first aim of the paper is to show that under certain conditions generative syntax can be made suitable for Montague semantics, based on his type logic. One of the conditions is to make branching in the so-called X-bar syntax strictly binary, This makes it possible to provide an adequate semantics for Noun Phrases by taking them as referring to sets of collections of sets of entities ( type <ett,t>) rather than to sets of sets of entities (ett).

I will begin by proposing a taxonomy of taxonomic positions regarding the mind–brain: localism, globalism, revisionism, and contextualism, and will go on to focus on the last position. Although some versions of contextualism have been defended by various researchers, they largely limit themselves to a version of neural contextualism: different brain regions perform different functions in different neural contexts. I will defend what I call “environmental-etiological contextualism,” according to which the psychological functions carried out by various neural regions can (...) only be identified and individuated against an environmental context or with reference to a causal history. While this idea may seem innocuous enough, it has important implications for a structure-to-function mapping in the mind and brain sciences. It entails that the same neural structures can subserve different psychological functions in different contexts, leading to crosscutting psycho-neural mappings. I will try to illustrate how this can occur with reference to recent research on episodic memory. (shrink)

A set of parameters for classifying composition operations is introduced. These parameters determine whether a composition operation is 1) universal, 2) determinate, 3) whether there is a difference between possible and actual compositions, 4) whether there can be singleton compositions, 5) whether they give rise to a hierarchy, and 6) whether components of compositions can be repeated. Philosophical implications of these parameters (in particular in relation to set theory) and mereology are discussed.

This study aimed to assess the effectiveness of remedial instruction in improving the numeracy skills of Grade 7 students at Malbug National High School during the school year 2023-2024. Adopting a quasi-experimental research design, the research focused on Grade 7 students at Malbug National High School, Cawayan East District, Masbate Province Division, Philippines, identified as non-numerates, employing pre-tests and post-tests as essential research tools. The independent variable was the remedial instruction in numeracy, while the dependent variable was students' numeracy performance (...) measured through pre-tests and post-tests. Before the intervention, the pre-test numeracy performance exhibited a varied distribution of students across different score ranges. A majority fell into the "Needs Major Support" category, emphasizing the necessity for targeted interventions. The post-test results, however, revealed a remarkable improvement, with 87.88% of initially non-numerate students achieving scores in the "Transforming" range. A thorough statistical examination validated a notable disparity in the scores obtained before and after the instructional intervention, substantiating the favorable influence of remedial instruction. The calculated t-value of 19.594, exceeding the critical t-value, led to rejecting the null hypothesis. In conclusion, the study emphasizes the need for tailored interventions based on the initial deficiency in numeracy skills. The post-test results underscored the success of remedial instruction in fostering substantial growth. The study recommends sustaining the remedial program, implementing periodic assessments, providing teacher training, involving parents in students' development, allocating adequate resources, and further research in other schools to strengthen findings. (shrink)

If there is to be any progress in the debate about what sort of positive moral status Kant can give the emotions, we need a taxonomy of the terms Kant uses for these concepts. It used to be thought that Kant had little room for emotions in his ethics. In the past three decades, Marcia Baron, Paul Guyer, Barbara Herman, Nancy Sherman, Allen Wood and others have argued otherwise. Contrary to what a cursory reading of the Groundwork may indicate, (...) Kant thinks the emotions play an important role in the moral life. I want to extend the work of Baron, Guyer, Herman, Sherman and Wood in three ways. First, I will set out in a diagram Kant's taxonomy of feelings and emotions. Agreement on such a taxonomy should make it easier to evaluate debates about Kant and the emotions. Second, I will focus on a certain subclass of emotions – reason-caused affects – that have previously received little attention, even from these Kant scholars. Third, these scholars base much of their defence of Kant on his later works – especially the Metaphysics of Morals and the Anthropology – but Kant's fairly rich taxonomy of the emotions, including reason-caused affects, is clearly in place at least as early as the Critique of Judgment . I believe that the Critique of Judgment is an importantly ignored resource for understanding the moral role of the emotions for Kant. The third Critique makes positive, philosophically interesting claims about the emotions and morality. Kant emphasizes certain roles for emotions in this work that he develops to the same extent nowhere else. Nevertheless, the Critique of Judgment goes all but unmentioned by many who write on these issues. In what follows, I will defend as many of my claims as possible using the third Critique. (shrink)

In a recent paper in Astrophysics and Space Science Vol. 364 no. 11 (2019), S. Ershkov & D. Leschenko presented a new solving procedure for Euler-Poisson equations for solving momentum equations of the CR3BP near libration points for uniformly rotating planets having inclined orbits in the solar system with respect to the orbit of the Earth. The system of equations of the CR3BP has been explored with regard to the existence of an analytic way of presentation of the approximated solution (...) in the vicinity of libration points. A new and elegant ansatz has been suggested in their publication whereby, in solving, the momentum equation is reduced to a system two coupled Riccati ODEs. In this paper, we presented a numerical solution of such coupled Riccati ODEs using Mathematica software package. (shrink)

“Pick a card, any card. This has to be a completely free choice.” the magician tells you. But is it really? Although we like to think that we are using our free will to make our decisions, research in psychology has shown that many of our behaviours are automatic and unconsciously influenced by external stimuli (Ariely, 2008; Bargh & Chartrand, 1999; Newell & Shanks, 2014; Nisbett & Wilson, 1977), and that we are often oblivious to the cognitive mechanisms that underpin (...) our decision (Wegner, 2002, 2003). Magicians have exploited this illusory sense of agency for a long time, and have developed a wide range of techniques to influence and control spectators’ choices of such things as card, word, or number (Annemann, 1933; Banachek, 2002a; Jones, 1994; Turner, 2015). These techniques are instances of what is called forcing. -/- Many forces are extremely effective, illustrating various weaknesses in our sense of control over decisions and their outcomes. Researchers have started to investigate them in various ways (Kuhn, Pailh s, & Lan, 2020; Olson, Amlani, Raz, & Rensink, 2015; Pailhes & Kuhn, 2020b, 2020c; Shalom et al., 2013) and are beginning to obtain valuable insights into decision-making processes as well as a better understanding of the cognitive mechanisms that lead people to experience an illusory sense of free will and of agency. -/- Although magicians have acquired large amounts of knowledge in covertly controlling people’s choices, much of this knowledge is only discussed in the context of individual magic tricks, or in books that are not readily accessible to non-magicans. As we and others have argued elsewhere (Ekroll, Sayim, & Wagemans, 2017; Kuhn, 2019; Kuhn, Amlani, & Rensink, 2008; Kuhn, Caffaratti, Teszka, & Rensink, 2014; Macknik et al., 2008; Olson et al., 2015; Olson, Landry, Appourchaux, & Raz, 2016; Shalom et al., 2013; Thomas, Didierjean, Maquestiaux, & Gygax, 2015), a particularly effective way of making this knowledge more available is via the creation of taxonomies centered around psychological mechanisms (Rensink & Kuhn, 2015). For example, the psychologically based taxonomy of misdirection (Kuhn et al., 2014) helps draw links between misdirection and formal theories of perception and cognition. -/- Our aim here is to apply a similar process to the knowledge magicians have about forcing. The present paper develops a psychologically based taxonomy of forcing techniques with two goals in mind. Firstly, it should help uncover the various psychological mechanisms that underlie forcing techniques. Secondly, it should facilitate knowledge transfer between magicians and psychologists. Among other things, this knowledge will allow researchers to gain new insights into the mechanisms underlying decision-making, and the feeling of free will and of agency over choice. We start by defining the magician’s force and then look at some of the past classifications of forcing. (shrink)

The term “Gettier Case” is a technical term frequently applied to a wide array of thought experiments in contemporary epistemology. What do these cases have in common? It is said that they all involve a justified true belief which, intuitively, is not knowledge, due to a form of luck called “Gettiering.” While this very broad characterization suffices for some purposes, it masks radical diversity. We argue that the extent of this diversity merits abandoning the notion of a “Gettier case” in (...) a favour of more finely grained terminology. We propose such terminology, and use it to effectively sort the myriad Gettier cases from the theoretical literature in a way that charts deep fault lines in ordinary judgments about knowledge. (shrink)

It has been known for long time that most of the existing cosmology models have singularity problem. Cosmological singularity has been a consequence of excessive symmetry of flow, such as “Hubble’s law”. More realistic one is suggested, based on Newtonian cosmology model but here we include the vertical-rotational effect of the whole Universe. We review a Riccati-type equation obtained by Nurgaliev, and solve the equation numerically with Mathematica. It is our hope that the new proposed method can be verified with (...) observation data. (shrink)

In this survey, a recent computational methodology paying a special attention to the separation of mathematical objects from numeral systems involved in their representation is described. It has been introduced with the intention to allow one to work with infinities and infinitesimals numerically in a unique computational framework in all the situations requiring these notions. The methodology does not contradict Cantor’s and non-standard analysis views and is based on the Euclid’s Common Notion no. 5 “The whole is greater than the (...) part” applied to all quantities (finite, infinite, and infinitesimal) and to all sets and processes (finite and infinite). The methodology uses a computational device called the Infinity Computer (patented in USA and EU) working numerically (recall that traditional theories work with infinities and infinitesimals only symbolically) with infinite and infinitesimal numbers that can be written in a positional numeral system with an infinite radix. It is argued that numeral systems involved in computations limit our capabilities to compute and lead to ambiguities in theoretical assertions, as well. The introduced methodology gives the possibility to use the same numeral system for measuring infinite sets, working with divergent series, probability, fractals, optimization problems, numerical differentiation, ODEs, etc. (recall that traditionally different numerals lemniscate; Aleph zero, etc. are used in different situations related to infinity). Numerous numerical examples and theoretical illustrations are given. The accuracy of the achieved results is continuously compared with those obtained by traditional tools used to work with infinities and infinitesimals. In particular, it is shown that the new approach allows one to observe mathematical objects involved in the Hypotheses of Continuum and the Riemann zeta function with a higher accuracy than it is done by traditional tools. It is stressed that the hardness of both problems is not related to their nature but is a consequence of the weakness of traditional numeral systems used to study them. It is shown that the introduced methodology and numeral system change our perception of the mathematical objects studied in the two problems. (shrink)

Numerical identity is the non-relational sameness of an object to itself. It is concerned with understanding how entities undergo change and maintain their identity. In substance metaphysics, an entity is considered a substance with an essence and such an essence is the source of its power. However, such a framework fails to explain the sense in which an entity is still the entity it was, amidst changes. Those who claim that essence is unaffected by existence are faced with challenge (...) of exploring the epistemic access to such an essence, which is questionable at best. Process metaphysics is a strong candidate for a theory that can ontologically explain regularity and change without appeal to essence. Process and its interactions is the main category. Every process is an emergent organization of constitutive interactions and is individuated on the basis of its interactive powers, that is, the ways in which it interacts with the world around it. Interactions are situated adaptation to changes. In this way, changes are crucial within process metaphysics and are included in the starting point of its investigation. What seems to the naked eyes as one-ness/singularity is a complex process where an organization of interactions is emerging from moment to moment by continually adapting to the changes around and within it. The question of numerical identity over time becomes valid only within substance metaphysics which has no space to accommodate change, due to its allegiance to essence. (shrink)

In this paper I study the development of arithmetical cognition with the focus on metaphorical thinking. In an approach developing on Lakoff and Núñez, I propose one particular conceptual metaphor, the Process → Object Metaphor, as a key element in understanding the development of mathematical thinking.

Following a hypothesis by Marciak-Kozlowska, 2011, we consider one-dimensional Schumann wave transfer phenomena. Numerical solution of that equation was obtained by the help of Mathematica.

Through a selective historical, theoretical, and critical survey of the uses of the concept of scaffolding over the past 30 years, this chapter traces the development of the concept across developmental psychology, educational theory, and cognitive anthropology, and its place in the interdisciplinary field of distributed cognition from the 1990s. Offering a big-picture overview of the uses of the notion of scaffolding, it suggests three ways to taxonomise forms of scaffolding, and addresses the possible criticism that the metaphor of scaffolding (...) retains an overly individualist vision of cognition. The chapter is aimed at a broad interdisciplinary audience interested in processes of learning, teaching, and apprenticeship as they apply to the study of memory. (shrink)

Four perspectives on numerical origins are examined. The nativist model sees numbers as an aspect of numerosity, the biologically endowed ability to appreciate quantity that humans share with other species. The linguistic model sees numbers as a function of language. The embodied model sees numbers as conceptual metaphors informed by physical experience and expressed in language. Finally, the extended model sees numbers as conceptual outcomes of a cognitive system that includes material forms as constitutive components. If numerical origins (...) are to be found, each perspective must address one or more critical questions that will require working across discipline boundaries. (shrink)

Four perspectives on numerical origins are examined. The nativist model sees numbers as an aspect of numerosity, the biologically endowed ability to appreciate quantity that humans share with other species. The linguistic model sees numbers as a function of language. The embodied model sees numbers as conceptual metaphors informed by physical experience and expressed in language. Finally, the extended model sees numbers as conceptual outcomes of a cognitive system that includes material forms as constitutive components. If numerical origins (...) are to be found, each perspective must address one or more critical questions that will require working across discipline boundaries. (shrink)

In this paper, I propose a general taxonomy of different forms of eliminativism. In order to do so, I begin by exploring eliminativism from a broad perspective, providing a comparative picture of eliminativist projects in different domains. This exploration shows that eliminativism is a label used for a family of related types of eliminativist arguments and claims. The proposed taxonomy is an attempt to systematise those arguments and claims.

It has been long known that a year after Schrödinger published his equation, Madelung also published a hydrodynamics version of Schrödinger equation. Quantum diffusion is studied via dissipative Madelung hydrodynamics. Initially the wave packet spreads ballistically, than passes for an instant through normal diffusion and later tends asymptotically to a sub‐diffusive law. In this paper we will review two different approaches, including Madelung hydrodynamics and also Bohm potential. Madelung formulation leads to diffusion interpretation, which after a generalization yields to Ermakov (...) equation. Since Ermakov equation cannot be solved analytically, then we try to find out its solution with Mathematica package. It is our hope that these methods can be verified and compared with experimental data. But we admit that more researches are needed to fill all the missing details. (shrink)

In a recent paper, Chunghyoung Lee argues that, because zygotes are developmentally plastic, they cannot be numerically identical to the singletons into which they develop, thereby undermining conceptionism. In this short paper, I respond to Lee. I argue, first, that, on the most popular theories of personal identity, zygotic plasticity does not undermine conceptionism, and, second, that, even overlooking this first issue, Lee’s plasticity argument is problematic. My goal in all of this is not to take a stand in the (...) abortion debate, which I remain silent on here, but, rather, to push for the conclusion that transitivity fails when we are talking about numerical identity of non-abstract objects. (shrink)

Traditional computers work with finite numbers. Situations where the usage of infinite or infinitesimal quantities is required are studied mainly theoretically. In this paper, a recently introduced computational methodology (that is not related to the non-standard analysis) is used to work with finite, infinite, and infinitesimal numbers numerically. This can be done on a new kind of a computer – the Infinity Computer – able to work with all these types of numbers. The new computational tools both give possibilities to (...) execute computations of a new type and open new horizons for creating new mathematical models where a computational usage of infinite and/or infinitesimal numbers can be useful. A number of numerical examples showing the potential of the new approach and dealing with divergent series, limits, probability theory, linear algebra, and calculation of volumes of objects consisting of parts of different dimensions are given. (shrink)

The goal of this paper consists of developing a new (more physical and numerical in comparison with standard and non-standard analysis approaches) point of view on Calculus with functions assuming infinite and infinitesimal values. It uses recently introduced infinite and infinitesimal numbers being in accordance with the principle ‘The part is less than the whole’ observed in the physical world around us. These numbers have a strong practical advantage with respect to traditional approaches: they are representable at a new (...) kind of a computer – the Infinity Computer – able to work numerically with all of them. An introduction to the theory of physical and mathematical continuity and differentiation (including subdifferentials) for functions assuming finite, infinite, and infinitesimal values over finite, infinite, and infinitesimal domains is developed in the paper. This theory allows one to work with derivatives that can assume not only finite but infinite and infinitesimal values, as well. It is emphasized that the newly introduced notion of the physical continuity allows one to see the same mathematical object as a continuous or a discrete one, in dependence on the wish of the researcher, i.e., as it happens in the physical world where the same object can be viewed as a continuous or a discrete in dependence on the instrument of the observation used by the researcher. Connections between pure mathematical concepts and their computational realizations are continuously emphasized through the text. Numerous examples are given. (shrink)

Aquinas, Ockham, and Burdan all claim that a person can be numerically identical over time, despite changes in size, shape, and color. How can we reconcile this with the Indiscernibility of Identicals, the principle that numerical identity implies indiscernibility across time? Almost all contemporary metaphysicians regard the Indiscernibility of Identicals as axiomatic. But I will argue that Aquinas, Ockham, and Burdan would reject it, perhaps in favor of a principle restricted to indiscernibility at a time.

Phenomenological psychology has emphasized that experience as it is immediately "given" to the experiencing individual is an appropriate subject matter for psychological investigation. Consideration of the methodological implications of this stance suggests that certain text analytic and cluster analytic methods could be used to discern the identifying properties of different types of experience. We present results of a study in which textual analysis was used to identify recurrent properties of participants' verbal accounts of their experience, cluster analysis was used to (...) classify participants' accounts according to the similarity of their profiles of properties, and the resulting clusters were examined for their more or less characteristic prpoerties. Using these methods, three distinct types of experience of a Renaissance painting were identified and described. This demonstration of numerically aided phenomenological methods indicates the compatibility of rigorous and sensitive descriptions of experiential accounts. (shrink)