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)

A new computational methodology for executing calculations with infinite and infinitesimal quantities is described in this paper. It is based on the principle ‘The part is less than the whole’ introduced by Ancient Greeks and applied to all numbers (finite, infinite, and infinitesimal) and to all sets and processes (finite and infinite). It is shown that it becomes possible to write down finite, infinite, and infinitesimal numbers by a finite number of symbols as particular cases of a unique framework. The (...) new methodology has allowed us to introduce the Infinity Computer working with such numbers (its simulator has already been realized). Examples dealing with divergent series, infinite sets, and limits are given. (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)

In the chapter of Difference and Repetition entitled ‘Ideas and the synthesis of difference,’ Deleuze mobilizes mathematics to develop a ‘calculus of problems’ that is based on the mathematical philosophy of Albert Lautman. Deleuze explicates this process by referring to the operation of certain conceptual couples in the field of contemporary mathematics: most notably the continuous and the discontinuous, the infinite and the finite, and the global and the local. The two mathematical theories that Deleuze draws upon for this purpose (...) are the differential calculus and the theory of dynamical systems, and Galois’ theory of polynomial equations. For the purposes of this paper I will only treat the first of these, which is based on the idea that the singularities of vector fields determine the local trajectories of solution curves, or their ‘topological behaviour’. These singularities can be described in terms of the given mathematical problematic, that is for example, how to solve two divergent series in the same field, and in terms of the solutions, as the trajectories of the solution curves to the problem. What actually counts as a solution to a problem is determined by the specific characteristics of the problem itself, typically by the singularities of this problem and the way in which they are distributed in a system. Deleuze understands the differential calculus essentially as a ‘calculus of problems’, and the theory of dynamical systems as the qualitative and topological theory of problems, which, when connected together, are determinative of the complex logic of different/ciation. (DR 209). Deleuze develops the concept of a problematic idea from the differential calculus, and following Lautman considers the concept of genesis in mathematics to ‘play the role of model ... with respect to all other domains of incarnation’. While Lautman explicated the philosophical logic of the actualization of ideas within the framework of mathematics, Deleuze (along with Guattari) follows Lautman’s suggestion and explicates the operation of this logic within the framework of a multiplicity of domains, including for example philosophy, science and art in What is Philosophy?, and the variety of domains which characterise the plateaus in A Thousand Plateaus. While for Lautman, a mathematical problem is resolved by the development of a new mathematical theory, for Deleuze, it is the construction of a concept that offers a solution to a philosophical problem; even if this newly constructed concept is characteristic of, or modelled on the new mathematical theory. (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)

In this article, some classical paradoxes of infinity such as Galileo’s paradox, Hilbert’s paradox of the Grand Hotel, Thomson’s lamp paradox, and the rectangle paradox of Torricelli are considered. In addition, three paradoxes regarding divergent series and a new paradox dealing with multiplication of elements of an infinite set are also described. It is shown that the surprising counting system of an Amazonian tribe, Pirah ̃a, working with only three numerals (one, two, many) can help us to change (...) our perception of these paradoxes. A recently introduced methodology allowing one to work with finite, infinite, and infinitesimal numbers in a unique computational framework not only theoretically but also numerically is briefly described. This methodology is actively used nowadays in numerous applications in pure and applied mathematics and computer science as well as in teaching. It is shown in the article that this methodology also allows one to consider the paradoxes listed above in a new constructive light. (shrink)

A recently developed computational methodology for executing numerical calculations with infinities and infinitesimals is described in this paper. The approach developed has a pronounced applied character and is based on the principle “The part is less than the whole” introduced by the ancient Greeks. This principle is applied to all numbers (finite, infinite, and infinitesimal) and to all sets and processes (finite and infinite). The point of view on infinities and infinitesimals (and in general, on Mathematics) presented in this paper (...) uses strongly physical ideas emphasizing interrelations that hold between a mathematical object under observation and the tools used for this observation. It is shown how a new numeral system allowing one to express different infinite and infinitesimal quantities in a unique framework can be used for theoretical and computational purposes. Numerous examples dealing with infinite sets, divergent series, limits, and probability theory are given. (shrink)

This book presents a critical analysis of the semantic incommensurability thesis of Thomas Kuhn and Paul Feyerabend. In putting forward the thesis of incommensurability, Kuhn and Feyerabend drew attention to complex issues concerning the phenomenon of conceptual change in science. They raised serious problems about the semantic and logical relations between the content of theories which deploy unlike systems of concepts. Yet few of the more extreme claims associated with incommensurability stand scrutiny. The argument of this book is as follows. (...) The terms of theories with different concepts diverge semantically and the vocabularies of such theories may not be fully intertranslatable. Given the possibility of referential overlap between the terms of conceptually divergent theories, it does not follow that the content of such theories is incomparable. Nor, given the distinction between understanding a language and translation from one language into another, does it follow that the proponents of mutually untranslatable theories are unable to communicate. Neither is it the case that the shift between conceptually divergent theories involves a discontinuous transition between theories which have no common reference or that refer to distinct worlds of their own making. The semantic differences resulting from conceptual variance may be embraced within a thoroughly realist framework on which they are construed as diverse linguistic relations to a fixed and independent reality. -/- The book, which was originally published in 1994, has now been re-issued in the Routledge Revivals series. -/- . (shrink)

Sensations can occur in the absence of perception and yet be experienced ‘as if’ seen, heard, tasted, or otherwise perceived. Two concepts used to investigate types of these sensory-like mental phenomena (SLMP) are mental imagery and hallucinations. Mental imagery is used as a concept for investigating those SLMP that merely resemble perception in some way. Meanwhile, the concept of hallucinations is used to investigate those SLMP that are, in some sense, compellingly like perception. This may be a difference of degree. (...) Attempts to reliably differentiate between instances of each type of SLMP remain unresolved. Despite this, the concepts of mental imagery and hallucinations are each routinely used independently of the other. These uses are especially interesting in those published accounts of experiments where equivalent findings about the neuroanatomical correlates of SLMP are reported in support of diverging knowledge-claims about the role of SLMP in neurocognitive processes. This practice presents a puzzle. To examine one aspect of this puzzle, I compare the uses of these two scientific concepts in three ways: examining their roles in differentiating between types of SLMP; exploring how their respective historical developments intersect; and analysing their contributions in neuroimaging experiments. In presenting this series of comparative analyses, I will draw on three themes from historical, philosophical, and social studies of scientific practices: interest in material contributions to knowledge; accounts of how concepts are used in experiments; and explorations of the historical conditions within which current practices emerge. Building on this literature, my comparative analyses supports five related claims. My first claim is that the concepts of mental imagery and hallucinations are each used as independent tools in neuroimaging experiments. My second claim is that, as experimental tools, the concepts of mental imagery and hallucinations are each used for investigating discrete epistemic goals. My third claim is that there are implicit interdependent associations that structure the uses of these two concepts as tools for independently investigating these discrete epistemic goals in neuroimaging experiments. This third claim rests on my analyses of both past and present uses of each concept. Firstly, as seen in their intersecting histories, there are disciplined performances of using the concepts of mental imagery and hallucinations that carry-along shared associations about the mediating role of SLMP in thought. Secondly, these interdependent ‘mediator-view’ associations continue to structure the independent uses of each concept as a tool for investigating SLMP in pursuit of specific goals. Taking this further, my fourth claim is that recognising the structured uses of the concepts of mental imagery and hallucinations can help to account for how equivalent SLMP-neuro-correlates are generated in support of diverging knowledge-claims. Finally, my fifth claim is that the structured uses of these concepts as tools can contribute to experiments in ways analogous to, yet not equivalent with, the active contributions of material instruments. Bringing these claims together, I argue that the concepts of mental imagery and hallucinations operate as structured tools that can actively contribute to the knowledge generated by neuroimaging experiments. In presenting this argument I seek to demonstrate that examining the structured uses of concepts as tools can complement existing approaches to studying how the heterogeneous dynamics of experimental practices can come to contribute to scientific knowledge in unintended ways. (shrink)

The ancient Greeks already used to give ethnic names to their different scales, and observations on differences in music of the various nations always raised the interest of musicians and philosophers. Yet, it was only in the late nineteenth century that “comparative musicology” became an institutional science. An important role in this process was played by Carl Stumpf, a former pupil of Brentano’s who pioneered these researches in Berlin. Stumpf founded the Phonogrammarchiv to collect recordings of folk and extra-European music (...) and a dedicated journal, the Sammelbände für vergleichende Musikwissenschaft. Gifted in the field of science no less than in that of musicology, Stumpf developed an empirically-oriented approach to phenomenology, deeply divergent from Husserl’s and highly influential over the Berlin school of Gestalt psychology. A self-declared “outsider” among armchair philosophers, Stumpf experimentally investigated the perception of sounds and the origins of musical consonance. Developing the physiological studies of Ernst Weber on the sense of touch, Stumpf discovered that two sensations of tone, given at the same time, tend to mix in a certain degree. Musical consonance – he claimed – lays in this level of “tonal fusion”, not in the allegedly “natural” series of the harmonic partials of a vibrating chord, as suggested by the naturalists of all times from Pythagoras to Stumpf’s great contemporary Hermann Helmholtz. Accordingly, no musical system can claim for preponderance over the others: Stumpf’s researches in comparative musicology served to corroborate his theses on “tonal fusion” and the psychological foundations of consonance. Although Stumpf later revised and finally abandoned this theory, its permanent value lays in its opposition to dominant naturalistic approaches. The commitment for comparative musicology at the Berlin School is then no concession to a positivistic fashion for exoticism. The fundamentally Eurocentric stance of naturalistic theories of music is also fiercely contrasted by Stumpf’s pupil Erich Hornbostel, who suggests that music ought to be considered as culture, rather than as nature, and focuses attention on the eventually melting human cultures. The Berlin school flourished until the Nazis forced most of its exponents to emigration and, for tragically obvious reasons, heavily discouraged researches on these topics. (shrink)

The neutral theory often is presented as a theory of "noise" or silent changes at an isolated "molecular level", relevant to marking the steady pace of divergence, but not to the origin of biological structure, function, or complexity. Nevertheless, precisely these issues can be addressed in neutral models, such as those elaborated here in regard to scrambled ciliate genes, gRNA-mediated RNA editing, the transition from self-splicing to spliceosomal splicing, and the retention of duplicate genes. All of these are instances of (...) a more general scheme of "constructive neutral evolution" that invokes biased variation, epistatic interactions, and excess capacities to account for a complex series of steps giving rise to novel structures or operations. The directional and constructive outcomes of these models are not due to neutral allele fixations per se, but to these other factors. Neutral models of this type may help to clarify the poorly understood role of non-selective factors in evolutionary innovation and directionality. (shrink)

Gilles Deleuze’s research during the 1980s focused on the 17th century German thinker G. W. Leibniz. In 1988, Deleuze published Le Pli, which forms part of a series of works on modern philosophy. This book displays Deleuze’s attention to the interpretations of contemporary commentators on modern philosophy, in this case, on Leibniz. In this context, there occurred a brief and important dialogue between Deleuze and Christiane Frémont, the French commentator and translator of Leibniz, with regard to their respective interpretations (...) of the great German philosopher. This article intends to give an account of the main topics present in that conversation. Firstly, we can say they involve 1) the problem of body and the Leibnizian vinculum substantiale, 2) the question of singularities, 3) the principle of economy and incompossibility, and 4) the Deleuzian concept of vice-diction. Our hypothesis in this study is that the readings made by both authors of the German thinker are mutually involved. It is essential, in order to support this hypothesis, to make precise the demarcations of relations between such readings. For this reason, our research will focus on Frémont’s study Singularités, individus et relations dans le système de Leibniz (2003) and on Deleuze’s work Le Pli (1988). We hope to determine the topics that emerge in the relationship, and to specify convergences and divergences of interpretation. (shrink)

Cabanis’ enucleation of the notion of instinct in his Rapports du physique et du moral de l’homme articulates through a critique of the use of this notion by Étienne Bonnot de Condillac, who would not have recognised the founding role of physiology in human perceptive and intellectual activity. An analysis of Cabanis’ criticism to Condillac and an investigation of the meaning attributed to the notion of instinct by both philosophers allow to individuate in this notion the expression of two different (...) types of materialism. The different position of Cabanis and Condillac on this notion, in fact, reflects the divergence on a series of notions – e.g. reflexion, sensitivity, habitus – which can be traced back to the different aims of their investigations. In addition to highlighting this basic divergence, this paper aims to bring out – especially referring to Condillac’s Logique – some points of contact, of which Cabanis seems not to have considered, concerning the conception of the human body as ‘organisation physique’. (shrink)

Pour traiter de la question singulière de la relation entre James et Renouvier à la lumière de cette préoccupation plus générale, nous choisirons ici une période un peu plus limitée que la carrière de James dans son ensemble : depuis ses premiers écrits jusqu’à la série d’articles de 1884-1885, qui allaient être si importants à la fois pour la psychologie et pour l’oeuvre philosophique, c’est-à-dire précisément jusqu’au point où les itinéraires philosophiques de James et de Renouvier commencent à diverger. Il (...) s’agit de voir en quoi la Critique philosophique est un cadre hospitalier pour le jeune James, mais aussi en quoi, dès la fin de cette période, des différends importants se font jour, sur la conscience notamment, ce qui donne lieu à une situation paradoxale où l’organe même qui a contribué à faire connaître James se retrouve à rebours de plusieurs de ses thèses importantes, avant la publication des Principles of Psychology (1890) et encore plus avant le Pragmatisme (1907). (shrink)

After two centuries, the Diltheyan idea of the incommensurability of the natural and social sciences remains hegemonic. Alternative visions have since been overlooked; in this regard, the Baden neo-Kantian school showed that any divergence concerns implied method and not the phenomenal object of studies. W. Windelband coined the terms “nomological” and “idiographic” to underline how each discipline can be explained as a science of both law and events. To begin, I will show how complex thinking can expand and institute a (...) general integrative frame that overcomes the assumed incommensurability. By “complex,” I mean an anti-reductionist approach to understanding and a consequent ability to reveal the phenomenal world in terms of nested self-organized systems. Social and natural systems are persistent coalescences of individual entities showing series of interduality such as unicity and multiplicity, top-down conservation and bottom-up inno- vation, constraint of law and freedom of agencies. The two instances are maintained together by the rejection of abstracted and isolated concepts and the embrace of a general principle of indeterminacy resolving the apparent contradiction within the parallelization of the extremes as two different moments of analyses rooted in the social and natural classical methods. This paper considers both a) the Positivist attempt in the XIX century to approach the study of social phenomena in terms of law and b) the emergence of a general social science embracing the principle of acasuality, adapted from the study of the subatomic phenomenal world in quantum theory. Finally, this paper sketches how complex methodology can address historical and social studies with system theory in order to overcome classical dualities such as determinism vs. freedom, social vs. individual, and top down conservation vs. bottom up innovation in the form of an integrative parallelization. (shrink)

Selgelid and Koplin’s article ‘Kidney Sales and the Burden of Proof’ (K&S 2019) presents a series of detailed and persuasive arguments, intended to demolish my own arguments against the prohibition of organ selling. And perhaps they might succeed, if the case described by the authors were anything like the one I actually make. However, notwithstanding the extensive quotations and the detailed explanations of the way I supposedly argue, this account of my position comprehensively mistakes both the conclusions I reach (...) and the arguments I give for them. -/- I know that there are around many misconceptions about my views on this subject, but I have always hoped they could not survive a reading of what I had actually written. I have just—after a gap of many years—looked again at the two most recent of the texts Koplin and Selgelid refer to, and it goes without saying that I can see various things I could now do better; but I do still find these misinterpretations hard to understand. And since anyone with nothing to go on but this article would reasonably conclude that the original texts were not worth reading, I am grateful to the editors for the opportunity to try to set the record straight. -/- I presume not many readers would be interested in a detailed comparative commentary on the texts, showing where this account gets my intentions wrong. I shall try instead to explain how what I do mean—and what I think I say—diverges from what is said here, and then go on to a brief outline of what my arguments and conclusions really are. I hope this may also give some sense of why, for all the opposition I have encountered since I was first drawn into this debate, I persist in thinking that the work I have been doing is important not only for this topic but for analysis in practical ethics more generally. (shrink)

A new computational methodology allowing one to work in a new way with infinities and infinitesimals is presented in this paper. The new approach, among other things, gives the possibility to calculate the number of elements of certain infinite sets, avoids indeterminate forms and various kinds of divergences. This methodology has been used by the author as a starting point in developing a new kind of computer – the Infinity Computer – able to execute computations and to store in its (...) memory not only finite numbers but also infinite and infinitesimal ones. (shrink)

Biologists, historians of biology, and philosophers of biology often ask what is it to be an individual, really. This book does not answer that question. Instead, it answers a much more interesting one: How do biologists individuate individuals? In answering that question, the authors explore why biologists individuate individuals, in what ways, and for what purposes. The cross-disciplinary, dialogical approach to answering metaphysical questions that is pursued in the volume may seem strange to metaphysicians who are not biologically focused, but (...) it is adroitly achieved by the editors. Scott Lidgard (a paleontologist and marine ecologist) and Lynn K. Nyhart (a historian of biology) orchestrate a dialogue among historians of biology, philosophers of biology, and practicing biologists over 10 chapters. These are followed by three reflective commentaries written to frame the different disciplinary perspectives and to highlight the historical, biological, and philosophical themes across the chapters. The result is a volume—in structure and in content—that has much to be generously commended. Biological individuality is a hotly discussed topic, but it is also part of a series of long-standing arguments within both the history and philosophy of biology (HPB) and metaphysics. Notable and fervent debates have centered on evolution and the units of selection, predominantly on Michael T. Ghiselin’s and David L. Hull’s notion of species as individuals, Peter Godfrey-Smith’s Darwinian individuals, and Ellen Clarke’s individuating mechanisms. Lately, it has encompassed non-Darwinian individuals, symbiotic associations like Thomas Pradeu’s immunological individuals, and John Dupré and Maureen A. O’Malley’s metabolic individuals.2 The present volume is curated in a way to introduce the reader to new research in HPB that articulates these debates as well as to introduce and engage in the study of further notions of biological individuality. But its aim is more than an introduction. As the subtitle suggests, it is also intended to give the reader insight into the working together of biologists, historians of biology, and philosophers of biology in figuring out how the notion of biological individuality is instantiated. As such, the problem-centered dialogue that results does more than talk through biological individuality. It shows how the different and often divergent goals of the authors’ disciplines shape not only how they think about individuality but how they communicate this thinking in reciprocal collaboration with others in different disciplines. … cont’d…. (shrink)

The thesis of instrumental convergence holds that a wide range of ends have common means: for instance, self preservation, desire preservation, self improvement, and resource acquisition. Bostrom contends that instrumental convergence gives us reason to think that "the default outcome of the creation of machine superintelligence is existential catastrophe". I use the tools of decision theory to investigate whether this thesis is true. I find that, even if intrinsic desires are randomly selected, instrumental rationality induces biases towards certain kinds of (...) choices. Firstly, a bias towards choices which leave less up to chance. Secondly, a bias towards desire preservation, in line with Bostrom's conjecture. And thirdly, a bias towards choices which afford more choices later on. I do not find biases towards any other of the convergent instrumental means on Bostrom's list. I conclude that the biases induced by instrumental rationality at best weakly support Bostrom's conclusion that machine superintelligence is likely to lead to existential catastrophe. (shrink)

Within collective epistemology, there is a class of theories that understand the epistemic status of collective attitude ascriptions, such as ‘the college union knows that the industrial action is going to plan’, or ‘the jury justifiedly believes that the suspect is guilty’, as saying that a sufficient subset of group member attitudes have the relevant epistemic status. In this paper, I will demonstrate that these summativist approaches to collective epistemology are incompatible with epistemic permissivism, the doctrine that a single body (...) of evidence may rationalize multiple doxastic attitudes. In particular, I will make use of epistemic permissivism to provide a general recipe for generating so-called divergence cases, which demonstrate situations in which rationality requires group-level and member-level attitudes to diverge. I will call this class of cases permissive divergence cases. While other divergence cases have been discussed in the literature, permissive divergence cases prove themselves to be less susceptible to many of the worries raised against their competitors, while being directly built on an often-defended epistemological thesis. (shrink)

Public participation in scientific research has gained prominence in many scientific fields, but the theory of participatory research is still limited. In this paper, we suggest that the divergence of values and goals between academic researchers and public participants in research is key to analyzing the different forms this research takes. We examine two existing characterizations of participatory research: one in terms of public participants' role in the research, the other in terms of the virtues of the research. In our (...) view, each of these captures an important feature of participatory research but is, on its own, limited in what features it takes into account. We introduce an expanded conception of norms of collaboration that extends to both academic researchers and public participants. We suggest that satisfying these norms requires consideration of the two groups' possibly divergent values and goals, and that a broad characterization of participatory research that starts from participants' values and goals can motivate both public participants’ role in the research and the virtues of the research. The resulting framework clarifies the similarities and differences among participatory projects and can help guide the responsible design of such projects. (shrink)

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

In this paper, Taylor series is used to solve neutrosophic multi-objective programming problem (NMOPP). In the proposed approach, the truth membership, Indeterminacy membership, falsity membership functions associated with each objective of multi-objective programming problems are transformed into a single objective linear programming problem by using a first order Taylor polynomial series. Finally, to illustrate the efficiency of the proposed method, a numerical experiment for supplier selection is given as an application of Taylor series method for solving neutrosophic (...) multi-objective programming problem at end of this paper. (shrink)

We report the results of an exploratory study that examines the judgments of climate scientists, climate policy experts, astrophysicists, and non-experts (N = 3367) about the factors that contribute to the creation and persistence of disagreement within climate science and astrophysics and about how one should respond to expert disagreement. We found that, as compared to non-experts, climate experts believe that within climate science (i) there is less disagreement about climate change, (ii) methodological factors play less of a role in (...) generating disagreements, (iii) fewer personal or institutional biases influence climate research, and (iv) there is more agreement about which methods should be used to examine relevant phenomena we also observed that the uniquely American political context predicted experts’ judgments about some of these factors. We also found that, in regard to disagreements concerning cosmic ray physics, and commensurate with the greater inherent uncertainty and data lacunae in their field, astrophysicists working on cosmic rays were generally more willing to acknowledge expert disagreement, more open to the idea that a set of data can have multiple valid interpretations, and generally less quick to dismiss someone articulating a non-standard view as non-expert, than climate scientists were in regard to climate science. (shrink)

Vagueness does not necessarily come in with vague predicates, nor need it be expressed by them , but undoubtedly 'vague predicates' are traditionally in the focus of main stream discussions of vagueness. In her current modal logic presentation and discussion of the Sorites paradox Susanne Bobzien[1] lists among the properties of a Sorites series a rather weak modal tolerance principle governing the 'grey zone' containing the borderline cases of the Sorites series, which later proves crucial for her solution (...) of the Sorites paradox by use of epistemic interpreted modal operators in 1st order modal logic. We suggest (for different research interest) instead a non-modal description of the switch in the grey zone (respecting tolerance), by resort to similarity sequences, thus getting tangent to two other areas of research in the field. Let's say -any way- the Sorites paradox vanishes, the Sorites series does not. (shrink)

Recent research on infant and animal imitation and on mirror neuron systems has
brought imitation back in focus in psychology and cognitive science. This topic has
always been important for philosophical hermeneutics as well, focusing on theory and
method of understanding. Unfortunately, relations between the scientific and the
hermeneutic approaches to imitation and understanding have scarcely been investigated,
to the loss of both disciplines. In contrast to the cognitive scientific emphasis on
sharing and convergence of representations, the hermeneutic analysis emphasizes the
indeterminacy and openness of action understanding (...) due to preunderstanding, action
configuration, and the processual nature of understanding. This article discusses empirical
evidence in support of these aspects and concludes that hermeneutics can
contribute to the scientific investigation of imitation and understanding. Since, conversely,
some grounding—and constraining—aspects of hermeneutics may be derived
from cognitive science, both should be integrated in a multilevel explanation of
imitation and understanding. This holds also for explanations that are largely based on
mirror neuron systems, since these appear to be sensitive to developmental and
experiential factors, too. (shrink)

Migration is a recurrent phenomenon of human history because it is a successful adaptive strategy of human beings. Although migration today is not of a greater magnitude than in the past, it attracts a great deal of media and academia attention. The present wave of non-Western immigrants into the United States and Europe caused, apart from myriad economic, social and political problems, an ideological dispute between globalism and right-wing populism. Both ideological approaches attract many zealots who spread extreme opinions and (...) poison the whole political life. Using the scholastic method, I examined some opposing points of view of globalists and right-wing populists on several topics regarding non-Western immigration: border control, illegal immigration, limitations of legal immigration, refugee relocation quotas and cultural integration of immigrants. The globalists’ and right-wing populists’ theses and arguments were checked in regard with established authorities, available factual data and human reason. Highlighting some important topics relating to immigration problem and weighing the main arguments used by globalists and right-wing populists, I also indicate several points of compromise that could help people to moderate their political opinions. (shrink)

A Série Investigação Filosófica, uma iniciativa do Núcleo de Ensino e Pesquisa em Filosofia do Departamento de Filosofia da UFPel e do Grupo de Pesquisa Investigação Filosófica do Departamento de Filosofia da UNIFAP, sob o selo editorial do NEPFil online e da Editora da Universidade Federal de Pelotas, com auxílio financeiro da John Templeton Foundation, tem por objetivo precípuo a publicação da tradução para a língua portuguesa de textos selecionados a partir de diversas plataformas internacionalmente reconhecidas, tal como a Stanford (...) Encyclopedia of Philosophy, por exemplo. O objetivo geral da série é disponibilizar materiais bibliográficos relevantes tanto para a utilização enquanto material didático quanto para a própria investigação filosófica. (shrink)

The cosmological constant problem arises because the magnitude of vacuum energy density predicted by quantum eld theory is about 120 orders of magnitude larger than the value implied by cosmological observations of accelerating cosmic expansion. We pointed out that the fractal nature of the quantum space-time with negative Hausdor - Colombeau dimensions can resolve this tension. The canonical Quantum Field Theory is widely believed to break down at some fundamental high-energy cuto  and therefore the quantum uctuations in the vacuum (...) can be treated classically seriously only up to this high-energy cuto . In this paper we argue that Quantum Field Theory in fractal space-time with negative Hausdor -Colombeau dimensions gives high-energy cuto on natural way. We argue that there exists hidden physical mechanism which cancel divergences in canonical QED4;QCD4; Higher-Derivative - Quantum-Gravity, etc. In fact we argue that corresponding supermassive Pauli-Villars ghost elds really exists. It means that there exists the ghost-driven acceleration of the univers hidden in cosmological constant. In order to obtain desired physical result we apply the canonical Pauli-Villars regularization up to : This would t in the observed value of the dark energy needed to explain the accelerated expansion of the universe if we choose highly symmetric masses distribution between standard matter and ghost matter below that scale ;i.e., fs:m () . (shrink)

We attribute three major insights to Hegel: first, an understanding of the real numbers as the paradigmatic kind of number ; second, a recognition that a quantitative relation has three elements, which is embedded in his conception of measure; and third, a recognition of the phenomenon of divergence of measures such as in second-order or continuous phase transitions in which correlation length diverges. For ease of exposition, we will refer to these three insights as the R First Theory, Tripartite Relations, (...) and Divergence of Measures. Given the constraints of space, we emphasize the first and the third in this paper. (shrink)

Structured around Charles S. Peirce's three-fold categorical scheme, this article proposes a comparative study of Ayn Rand and Peirce's realist views in general metaphysics. Rand's stance is seen as diverging with Peirce's argument from asymptotic representation but converging with arguments from brute relation and neutral category. It is argued that, by dismissing traditional subject-object dualisms, Rand and Peirce both propose iconoclastic construals of what it means to be real, dismissals made all the more noteworthy by the fact each chose to (...) ground them in indissoluble triads of self-evident first principles. (shrink)

Recent research on infant and animal imitation and on mirror neuron systems has brought imitation back in focus in psychology and cognitive science. This topic has always been important for philosophical hermeneutics as well, focusing on theory and method of understanding. Unfortunately, relations between the scientific and the hermeneutic approaches to imitation and understanding have scarcely been investigated, to the loss of both disciplines. In contrast to the cognitive scientific emphasis on sharing and convergence of representations, the hermeneutic analysis emphasizes (...) the indeterminacy and openness of action understanding due to preunderstanding, action configuration, and the processual nature of understanding. This article discusses empirical evidence in support of these aspects and concludes that hermeneutics can contribute to the scientific investigation of imitation and understanding. Since, conversely, some grounding—and constraining—aspects of hermeneutics may be derived from cognitive science, both should be integrated in a multilevel explanation of imitation and understanding. This holds also for explanations that are largely based on mirror neuron systems, since these appear to be sensitive to developmental and experiential factors, too. (shrink)

In the latter half of the twentieth century, philosophers of science have argued (implicitly and explicitly) that epistemically rational individuals might compose epistemically irrational groups and that, conversely, epistemically rational groups might be composed of epistemically irrational individuals. We call the conjunction of these two claims the Independence Thesis, as they together imply that methodological prescriptions for scientific communities and those for individual scientists might be logically independent of one another. We develop a formal model of scientific inquiry, define four (...) criteria for individual and group epistemic rationality, and then prove that the four definitions diverge, in the sense that individuals will be judged rational when groups are not and vice versa. We conclude by explaining implications of the inconsistency thesis for (i) descriptive history and sociology of science and (ii) normative prescriptions for scientific communities. (shrink)

The extent to which individuals with a variety of cultural backgrounds differ in empathic responsiveness is unknown. This article describes the differences in trait empathy in one independent and one interdependent society (i.e., the US and Iran, respectively). The analysis of data collected from self-reported questionnaires answered by 326 adults indicated a significant difference in the cognitive component of empathy concerning participants’ affiliation to either egocentric or socio-centric society: Iranian participants with interdependent cultural norms, reported higher cognitive empathy compared to (...) American participants who share independent cultural norms. In line with previous studies, gender differences were observed in all subscales of questionnaires, except the Empathy Quotient (EQ). Female participants demonstrated more empathy than males in both samples. Implications for understanding the cross-cultural differences of various components of empathy are discussed. (shrink)

This paper presents what the authors call the ‘divergence problem’ regarding choosing between different future possibilities. As is discussed in the first half, the central issue of the problem is the difficulty of temporally locating the ‘active cause’ on the modal divergent diagram. In the second half of this paper, we discuss the ‘second-person freedom’ which is, strictly, neither compatibilist negative freedom nor incompatibilist positive freedom. The divergence problem leads us to two hypothetical views (i.e. the view of single-line (...) determination and that of one-off chance), and these views bring humans closer to the afree side – i.e. outside of the contrast between being free and being unfree. The afree side is greatly different from the ordinary human side. This paper tries to secure the second-person freedom as a substitute for the ordinary human freedom while preventing the divergence problem from arising. (shrink)

The special composition question asks, roughly, under what conditions composition occurs. The common sense view is that composition only occurs among some things and that all and only ‘ordinary objects’ exist. Peter van Inwagen has marshaled a devastating argument against this view. The common sense view appears to commit one to giving what van Inwagen calls a ‘series-style answer’ to the special composition question, but van Inwagen argues that series-style answers are impossible because they are inconsistent with the (...) transitivity of parthood. In what follows I answer this objection in addition to other, less troubling objections raised by van Inwagen. (shrink)

In the past decade, policy-makers in science have been concerned with harmonizing research integrity standards across Europe. These standards are encapsulated in the European Code of Conduct for Research Integrity. Yet, almost every European country today has its own national-level code of conduct for research integrity. In this study we document in detail how national-level codes diverge on almost all aspects concerning research integrity – except for what constitutes egregious misconduct. Besides allowing for potentially unfair responses to joint misconduct by (...) international collaborations, we argue that the divergences raise questions about the envisaged self-regulatory function of the codes of conduct. (shrink)

In this paper I provide a comparative analysis of Augustine's and Paul Tillich's doctrines of Original Sin. I argue that Augustine's doctrine is deeply flawed in ways corrected for by Tillich.

Abstract: Lotteries have long been a source of fascination and intrigue, offering the tantalizing prospect of unexpected fortunes. In this research paper, we delve into the world of lottery predictions, employing cutting-edge AI techniques to unlock the secrets of lottery outcomes. Our dataset, obtained from Kaggle, comprises historical lottery draws, and our goal is to develop predictive models that can anticipate future winning numbers. This study explores the use of deep learning and time series analysis to achieve this elusive (...) feat. Through rigorous experimentation and data-driven approaches, we seek to determine the viability of AI in the realm of lottery predictions. Our findings reveal both the promise and limitations of AI in this context, shedding light on the complexities of lottery data and the potential need for quantum computing as a last resort. (shrink)

This article presents a simple derivation of optimization models for reaction networks leading to a generalized form of the mass-action law, and compares the formal structure of Minimum Information Divergence, Quadratic Programming and Kirchhoff type network models. These optimization models are used in related articles to develop and illustrate the operation of ontology alignment algorithms and to discuss closely connected issues concerning the epistemological and statistical significance of sharp or precise hypotheses in empirical science.

Several of Thomas Aquinas's proofs for the existence of God rely on the claim that causal series cannot proceed in infinitum. I argue that Aquinas has good reason to hold this claim given his conception of causation. Because he holds that effects are ontologically dependent on their causes, he holds that the relevant causal series are wholly derivative: the later members of such series serve as causes only insofar as they have been caused by and are effects (...) of the earlier members. Because the intermediate causes in such series possess causal powers only by deriving them from all the preceding causes, they need a first and non-derivative cause to serve as the source of their causal powers. (shrink)

This essay is my review of the classic TV series, Route 66. It was a classic “buddy movie,” with two young men who tour the country in a gorgeous 1956 Chevy Corvette, staying in various towns and working at various blue-collar jobs. The acting was generally superb, and the scripts were mainly written by the fine script writer Stirling Silliphant, and produced by the famous producer Herbert Leonard. I suggest that this 50-year-old series tells us a lot about (...) cultural change in America during that time. I suggest also that it helps demonstrate that the charge made by a famous cultural critic of the time—Newton Minow, who was Chairman of the Federal Communications Corporation from 1961 to 1963—that this period of commercial TV was a “vast wasteland” was not merely arrogantly elitist, but was in fact patently false. The 1950s and early 1960s saw many amazingly good series in a wide variety of genres. (shrink)

Rambo (2008) marked the return of Sylvester Stallone's iconic action hero. What is most striking about the fourth film (as the response from reviewers testifies), is its graphic violence. My intention here is to critically engage with Rambo (2008) as rewriting the series' established aesthetic of violence. My overarching aim is to highlight how the popular press has sought to read the 2008 version of Rambo according to the discursive narratives surrounding Stallone's 1980s action films. The negative response to (...) Rambo, I argue, stems from relying on critical patterns that do not fit the film itself. (shrink)

This text aims to theoretically think on the performative work devel-oped in the region of Belém, Pará, as attempts to understand its modes of subjectivation related to the narratives of Amazonian culture and identities of the ancestral past that molds the present of the islands around the city, more specifically the Island of Cotijuba. Experiencing these liveliness territories, I absorb myself to comprehend both the imagetic production of this research and the potentialities that emerge when connected through the intentional intervention (...) of the narrative. (shrink)

At the end of the nineteenth century, Ludwig Edinger completed the first comparative survey of the microscopic anatomy of vertebrate brains. He is regarded as the founder of the field of comparative neuroanatomy. Modern commentators have misunderstood him to have espoused an anti-Darwinian linear view of brain evolution, harkening to the metaphysics of the scala naturae. This understanding arises, in part, from an increasingly contested view of nineteenth-century morphology in Germany. Edinger did espouse a progressionist, though not strictly linear, view (...) of forebrain evolution, but his work also provided carefully documented evidence that brain stem structures vary in complexity independently from one another and across species in a manner that is not compatible with linear progress. This led Edinger to reject progressionism for all brain structures other than the forebrain roof, based on reasoning not too dissimilar from those his successors used to dismiss it for the forebrain roof. (shrink)

Este livro marca o início da Série Investigação Filosófica. Uma série de livros de traduções de textos de plataformas internacionalmente reconhecidas, que possa servir tanto como material didático para os professores das diferentes subáreas e níveis da Filosofia quanto como material de estudo para o desenvolvimento pesquisas relevantes na área. Nós, professores, sabemos o quão difícil é encontrar bons materiais em português para indicarmos. E há uma certa deficiência na graduação brasileira de filosofia, principalmente em localizações menos favorecidas, com relação (...) ao conhecimento de outras línguas, como o inglês e o francês. Tentamos, então, suprir essa deficiência, ao introduzirmos traduções de textos importantes ao público de língua portuguesa, sem nenhuma finalidade comercial e meramente pela glória da filosofia. O presente volume é constituído de três traduções de verbetes importantes sobre lógica, da Enciclopédia de Filosofia da Stanford: (1) A Lógica de Aristóteles, (2) Lógica Clássica, (3) Lógica Modal. (shrink)

How can McTaggart's A-series notion of time be incorporated into physics while retaining the B-series notion? It may be the A-series 'now' can be construed as ontologically private. How is that modeled? Could a definition of a combined AB-series entropy help with the Past Hypothesis problem? What if the increase in entropy as a system goes from earlier times to later times is canceled by the decrease in entropy as a system goes from future, to present, (...) to past? (shrink)

The Berlin Group was an equal partner with the Vienna Circle as a school of scientific philosophy, albeit one that pursued an itinerary of its own. But while the latter presented its defining projects in readily discernible terms and became immediately popular, the Berlin Group, whose project was at least as sig-nificant as that of its Austrian counterpart, remained largely unrecognized. The task of this chapter is to distinguish the Berliners’ work from that of the Vienna Circle and to bring (...) to light its impact in the history of scientific philosophy. (shrink)

Philosophers of biology have worked extensively on how we ought best to interpret the probabilities which arise throughout evolutionary theory. In spite of this substantial work, however, much of the debate has remained persistently intractable. I offer the example of Bayesian models of divergence time estimation as a case study in how we might bring further resources from the biological literature to bear on these debates. These models offer us an example in which a number of different sources of uncertainty (...) are combined to produce an estimate for a complex, unobservable quantity. These models have been carefully analyzed in recent biological work, which has determined the relationship between these sources of uncertainty, both quantitatively and qualitatively. I suggest here that this case shows us the limitations of univocal analyses of probability in evolution, as well as the simple dichotomy between “subjective” and “objective” probabilities, and I conclude by gesturing toward ways in which we might introduce more sophisticated interpretive taxonomies of probability as a path toward advancing debates on probability in the life sciences. (shrink)