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)

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.

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)

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)

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)

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)

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)

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)

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)

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)

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)

Attributions of certain speech-acts, like dog-whistling and wolf-crying, have an interesting complementary and antagonistic relationship that creates a kind of hostile dialectic and emergent divergence in political discourse. In the following, we will show how the wolf-cry and the dog-whistle are both epistemically difficult speech-acts to attribute, leading to asymmetric uncertainties in attribution. These uncertainties cause the attribution of wolf-cries and dog-whistles themselves to often be both reasonable but unconfirmable epistemic claims. Then, we will show how these patterns of (...) attributions can lead to a reciprocal dialectic of entrenched and self-amplifying dog-whistling versus wolf-crying, until an unhappy status quo is developed. This leads to a number of problems, including an epistemic standoff of standpoints, the attribution saturation of the political discourse, and a condition of self-defeating truth-seeking. Seemingly, the only surefire solution is a unanimous alleviation of such attributions, a standard that may seem insurmountable, though other options can be considered. (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.

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.

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)

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)

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)

The present research examined how nostalgia influences temporal self-appraisals and whether those appraisals relate to current mood. Across two studies, participants recalled either an ordinary or nostalgic memory and provided appraisals of their present and past selves. Participants who recalled nostalgic memories evaluated their past selves more positively than their present selves, whereas the reverse occurred for those who recalled ordinary memories. Those who recalled a positive future event also evaluated their future selves more positively than their present selves. Nostalgia (...) simultaneously enhanced positive mood by heightening favorable evaluations of past selves and diminished positive mood by heightening unfavorable evaluations of present selves. The current work supports a temporal-selves framework that allows for a more nuanced portrait of the nostalgic experience. (shrink)

This research looks at the various interpretations of "Mind" found in the Astika Darshanas, which cover the six main schools of Indian philosophy. At the same time, it looks into the profound East Asian Buddhist doctrine of One Mind as presented by Wonhyo, a great Korean Buddhist monk. This study seeks to identify the interesting similarities and differences that lie at the nexus of various philosophical domains by travelling through the complex landscape of different intellectual traditions. By using a comparative (...) approach, it aims to clarify the connections and distinguishing characteristics that form the conception of 'Mind' in both Korean Buddhist philosophy and the six schools of Indian philosophy, thereby advancing our understanding of the various philosophical currents that have influenced the intellectual fabric of these traditions. Focusing on the transmission and assimilation of Indian philosophical ideas into Buddhist philosophies, the research explores how these concepts were adapted and evolved as Buddhism spread across East Asian cultures. This research seeks to bridge these dissimilar contexts in order to reveal the interconnections of Indian and Korean philosophical traditions, contributing to a better understanding of the universal threads that connect these landscapes and highlighting the enduring resonance of fundamental concepts in the pursuit of enlightenment. (shrink)

Conceptual Metaphor Theory makes some strong claims against so-called Classical Theory which spans the accounts of metaphors from Aristotle to Davidson. Most of these theories, because of their traditional literal-metaphorical distinction, fail to take into account the phenomenon of conceptual metaphor. I argue that the underlying mechanism for explaining metaphor bears some striking resemblances among all of these theories. A mapping between two structures is always expressed. Conceptual Metaphor Theory insists, however, that the literal-metaphorical distinction of Classical Theories is empirically (...) wrong. I claim that this criticism is based rather on terminological decisions than on empirical issues. Conceptual Metaphor Theory focusses primarily on conventional metaphors and struggles to extend its mechanism to novel metaphors, whereas Classical Theories focus on novel metaphors and struggle to extend their mechanisms to conventional metaphors. Since all of these theories study metaphors from the synchronic point of view, they are unable to take into account any semantic change. A diachronic perspective is what we need here, one which would allow us to explain the role of metaphor in semantic change and the development of language in general. (shrink)

Human creativity generates novel ideas to solve real-world problems. This thereby grants us the power to transform the surrounding world and extend our human attributes beyond what is currently possible. Creative ideas are not just new and unexpected, but are also successful in providing solutions that are useful, efficient and valuable. Thus, creativity optimizes the use of available resources and increases wealth. The origin of human creativity, however, is poorly understood, and semantic measures that could predict the success of generated (...) ideas are currently unknown. Here, we analyze a dataset of design problem-solving conversations in real-world settings by using 49 semantic measures based on WordNet 3.1 and demonstrate that a divergence of semantic similarity, an increased information content, and a decreased polysemy predict the success of generated ideas. The first feedback from clients also enhances information content and leads to a divergence of successful ideas in creative problem solving. These results advance cognitive science by identifying real-world processes in human problem solving that are relevant to the success of produced solutions and provide tools for real-time monitoring of problem solving, student training and skill acquisition. A selected subset of information content (IC Sánchez–Batet) and semantic similarity (Lin/Sánchez–Batet) measures, which are both statistically powerful and computationally fast, could support the development of technologies for computer-assisted enhancements of human creativity or for the implementation of creativity in machines endowed with general artificial intelligence. (shrink)

An artwork in one culture and form, say European classical music, cannot be evaluated in the context of another, say Hindustani music. While a person educated in the traditions of European music can rationally evaluate and discuss her response to a string quartet by Beethoven, her response to music in a foreign culture is merely subjective. She might "like" the latter, but her response is merely subjective. In this paper, I discuss the role of artforms: why response can be "objectively" (...) discussed within artforms, but is nonetheless subjective across them. My discussion falls into two parts. First, I offer a psychological account of aesthetic response to art: cultural learning stabilizes this response across individuals who are educated in an artform. Second, I offer a cultural-evolutionary account of the diversity of artforms, adapting Darwin's Principle of the Divergence of Character to explain the multiplicity of art forms. (shrink)

This article proposes a new interpretation of mutual information. We examine three extant interpretations of MI by reduction in doubt, by reduction in uncertainty, and by divergence. We argue that the first two are inconsistent with the epistemic value of information assumed in many applications of MI: the greater is the amount of information we acquire, the better is our epistemic position, other things being equal. The third interpretation is consistent with EVI, but it is faced with the problem (...) of measure sensitivity and fails to justify the use of MI in giving definitive answers to questions of information. We propose a fourth interpretation of MI by reduction in expected inaccuracy, where inaccuracy is measured by a strictly proper monotonic scoring rule. It is shown that the answers to questions of information given by MI are definitive whenever this interpretation is appropriate, and that it is appropriate in a wide range of applications with epistemic implications. _1_ Introduction _2_ Formal Analyses of the Three Interpretations _2.1_ Reduction in doubt _2.2_ Reduction in uncertainty _2.3_ Divergence _3_ Inconsistency with Epistemic Value of Information _4_ Problem of Measure Sensitivity _5_ Reduction in Expected Inaccuracy _6_ Resolution of the Problem of Measure Sensitivity _6.1_ Alternative measures of inaccuracy _6.2_ Resolution by strict propriety _6.3_ Range of applications _7_ Global Scoring Rules _8_ Conclusion. (shrink)

The paper discusses a posthuman reading of Merleau-Ponty’s later works and an application of the concept of flesh to the digital dimension. Whereas, in the Phenomenology of Perception, the world and other beings are seen from an egological and human perspective, in The Visible and the Invisible this perspective is reshaped. Human body is made of the same stuff of other bodies, and they constitute a common being, the flesh of the world. Merleau-Ponty sets out a path through flat ontology (...) and posthumanism, opposing human perspective as a privileged one. His posthuman turn passes through the concepts of reversibility and divergence. Humans are made of the same stuff as non-humans, so they reverse into one another, but, on the other hand, they are not reduced to an undifferentiated entity, because of their divergence. Merleau-Ponty’s problematizing perspective is here actualized and applied to the hybridization between human bodies and digital protheses. (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)

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)

A primary aim of mind-wandering research has been to understand its influence on task performance. While this research has typically highlighted the costs of mind wandering, a handful of studies have suggested that mind wandering may be beneficial in certain situations. Perhaps the most-touted benefit is that mind wandering during a creative-incubation interval facilitates creative thinking. This finding has played a critical role in the development of accounts of the adaptive value of mind wandering and its functional role, as well (...) as potential mechanisms of mind wandering. Thus, a demonstration of the replicability of this important finding is warranted. Here, we attempted to conceptually replicate results of a highly cited laboratory-based experiment supporting this finding. However, across two studies (N = 443), we found no evidence for the claim that mind wandering during a creative-incubation interval facilitates a form of creativity associated with divergent thinking. We suggest that our failed conceptual replication stems from an inadequate characterization of mind wandering (task-unrelated thought), and that there are good reasons to think that task-unrelated thought is unlikely to be causally related to creativity. Our results cast doubt on the claim that task-unrelated thought during an incubation interval enhances divergent creativity while also offering some prescriptions for how future research might further elucidate the cognitive benefits of mind wandering. (shrink)

This article mainly aims to make an examination over the holy. It has been inquired into how something being ascribed holy can have a meaning in philosophy. As the article's research area, the differences in both opinion and execution which have later divided Christianity into two as Catholic and Orthodox Churches have been selected. The separation of these two churches under the subject titles such as Filioque controversy, the idea of First Among Equals (primas inter pares), and ritual of Transubstantiation (...) have also shaped how they perceived and thought the holy. With these divergences being investigated, it has been tried to present how much of a share these had in giving meaning for the holy. It has been labored to manifest the role of these two Churches' -which belong to and come from the same celestial tradition- divergences in the metamorphosis and paradigm shift that the holy underwent. For the last, through the Church Fathers' opinions and views which have been seen related to subject matter, with moving beyond the divergences, it has been searched whether there is a possibility of meeting on the common ground or not . (shrink)

Despite its pertinence to every field of study, no systematic theory exists for the exploration of the unknown world of new knowledge. In order to construct such a theory, this paper draws on the unique and highly refined principles of military strategy, in the process demonstrating the universal applicability of such principles and developing an effective analogy for the process of research. Such principles include diverging advance, converging attack, and selecting the superior and eliminating the inferior. In seeking further discoveries, (...) one should search for more possibilities, attack more aims, and confound the front line. The theory presented in this paper is also a means to further the unification of science. For no matter what the individuals look like, (soldiers, particles, cells, consumers, producers, stockholders, or concepts), what they pursue, (victory, negative action, viability, pleasure, profit, investment return, or knowledge), or what relationship exists between opponents, (hostile, mysterious, adaptive, reciprocal, cooperative, or explanatory), the result is always an unknown world in which individuals are exploring. It is reasonable to suppose that the exploration of the unknown world is a common property among individuals. (shrink)

In this chapter, I sketch a philosophical framework of shared and diverging worlds and cultural significance. Although the framework proposed is basically a psychologically informed, philosophical approach, it is explicitly aimed at being applicable for agent-based social simulations. The account consists of three parts: (1) a formal ontology of human worlds, (2) an analysis of the pre-semantic significance of the objects of human worlds, and (3) an account of what it means for agents to share a world (or to live (...) in diverging worlds). In this chapter, I will give a brief and concise summary of my account. At the end, I will briefly outline how the proposed framework might be put to use for multiagent social simulation of complex social interaction scenarios involving diverging (cultural) backgrounds. (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)

Scientists often diverge widely when choosing between research programs. This can seem to be rooted in disagreements about which of several theories, competing to address shared questions or phenomena, is currently the most epistemically or explanatorily valuable—i.e. most successful. But many such cases are actually more directly rooted in differing judgments of pursuit-worthiness, concerning which theory will be best down the line, or which addresses the most significant data or questions. Using case studies from 16th-century astronomy and 20th-century geology and (...) biology, I argue that divergent theory choice is thus often driven by considerations of scientific process, even where direct epistemic or explanatory evaluation of its final products appears more relevant. Broadly following Kuhn’s analysis of theoretical virtues, I suggest that widely shared criteria for pursuit-worthiness function as imprecise, mutually-conflicting values. However, even Kuhn and others sensitive to pragmatic dimensions of theory ‘acceptance’, including the virtue of fruitfulness, still commonly understate the role of pursuit-worthiness—especially by exaggerating the impact of more present-oriented virtues, or failing to stress how ‘competing’ theories excel at addressing different questions or data. This framework clarifies the nature of the choice and competition involved in theory choice, and the role of alternative theoretical virtues. (shrink)

Despite their divergent metaphysical assumptions, Reformed and evolutionary epistemologists have converged on the notion of proper basicality. Where Reformed epistemologists appeal to God, who has designed the mind in such a way that it successfully aims at the truth, evolutionary epistemologists appeal to natural selection as a mechanism that favors truth-preserving cognitive capacities. This paper investigates whether Reformed and evolutionary epistemological accounts of theistic belief are compatible. We will argue that their chief incompatibility lies in the noetic effects of sin (...) and what may be termed the noetic effects of evolution, systematic tendencies wherein human cognitive faculties go awry. We propose a reconceptualization of the noetic effects of sin to mitigate this tension. (shrink)

A patient is diagnosed with the persistent vegetative state (PVS) when they show no evidence of the awareness of the self or the environment for an extended period of time. The chance of recovery of any mental function or the ability to interact in a meaningful way is low. Though rare, the condition, considering its nature as a state outwith the realm of the conscious, coupled with the trauma experienced by the patient's kin as well as health care staff confronted (...) with painful decisions regarding the patient's care, has attracted a considerable amount of discussion within the bioethics community. At present, there is a wealth of literature that discusses the relevant neurology, that elucidates the plethora of ethical challenges in understanding and dealing with the condition, and that analyses the real-world cases which have prominently featured in the mainstream media as a result of emotionally charged, divergent views concerning the provision of care to the patient. However, there is scarcely anything in the published scholarly literature that proposes concrete and practically actionable solutions to the now widely recognized moral conundrums. The present article describes a step in that direction. I start from the very foundations, laying out a sentientist approach which serves as the basis for the consequent moral decision-making, and then proceed to systematically identify and deconstruct the different cases of discord, using the aforementioned foundations as the basis for their resolution. A major intellectual contribution concerns the fluidity of the duty of care which I argue is demanded by the sentientist focus. The said duty is shown initially to have for its object the patient, which depending on the circumstances, can change to the patient's kin, or the health care staff themselves. In conclusion, the proposed framework represents the first comprehensive proposal regarding the decision-making processes involved in the deliberation on the provision of life sustaining treatment to a patient in a PVS. (shrink)

It is common to distinguish two great families of representation. Symbolic representations include logical and mathematical symbols, words, and complex linguistic expressions. Iconic representations include dials, diagrams, maps, pictures, 3-dimensional models, and depictive gestures. This essay describes and motivates a new way of distinguishing iconic from symbolic representation. It locates the difference not in the signs themselves, nor in the contents they express, but in the semantic rules by which signs are associated with contents. The two kinds of rule have (...) divergent forms, occupying opposite poles on a spectrum of naturalness. Symbolic rules are composed entirely of primitive juxtapositions of sign types with contents, while iconic rules determine contents entirely by uniform natural relations with sign types. This distinction is marked explicitly in the formal semantics of familiar sign systems, both for atomic first-order representations, like words, pixel colors, and dials, and for complex second-order representations, like sentences, diagrams, and pictures. (shrink)

Many widely divergent accounts of luck have been offered or employed in discussing an equally wide range of philosophical topics. We should, then, expect to find some unified philosophical conception of luck of which moral luck, epistemic luck, and luck egalitarianism are species. One of the attempts to provide such an account is that offered by Duncan Pritchard, which he refers to as the modal account. This view commits us to calling an event lucky when it obtains in this world, (...) but fails to obtain in a wide class of nearby possible worlds. In support of this account, Pritchard argues that a theory of luck ought to capture the fact that luck comes in degrees and that luck is closely associated with risk. I argue against this claim by suggesting that an understanding of luck grounded in considerations of probability is better able to satisfy these demands, and that the probability theory better explains exemplary cases of luck like those brought up by Pritchard. (shrink)

Cartesians and Lichtenbergians have diverging views of the deliverances of introspection. According to the Cartesians, a rational subject, competent with the relevant concepts, can come to know that he or she thinks – hence, that he or she exists – on the sole basis of his or her introspective awareness of his or her conscious thinking. According to the Lichtenbergians, this is not possible. This paper offers a defence of the Lichtenbergian position using Peacocke and Campbell's recent exchange on Descartes'scogitoas (...) a framework for discussion. A thought-experiment will be presented involving two communities with radically different conceptions of the metaphysics of the self. The purpose of the thought-experiment is to suggest that a substantive metaphysical thesis, whose truth cannot be a priori known, is presupposed by any justified transition from one's introspective awareness of a certain mental activity to the self-ascription of that activity. (shrink)

Amidst the broad divergence in opinion of philosophers and scientists at understanding reality that has lent character to the historical epochs of the Philosophical enterprise, the crucial realization has always been, of the necessity of Epistemology in our entire program of making inquiry into ‘What Is’. This realization seems born out of the erstwhile problem of knowing. Epistemology, which investigates the nature, sources, limitations and validating of knowledge, offers a striking challenge here. Since we have no direct access to (...) our world around us, outside of the subjective experience offered us by our senses, we are handicapped at making comparisons of our beliefs with a concrete world, out there, or with elements of the world. Our statements about the world seem to stand alone, buffeted against the intimidating tide of possible contradicting circumstances. Our putative claims to knowledge, therefore, face the exigency of justification. Ayer, expressing the urgency of resolving this persisting lacuna, provides an alternative criterion of knowing, as ‘having the right to be sure’. Thus, it is this deep-seated concern that has evolved, over time, to become the primary thrust of the project of Epistemology, raising the controversy over which, of Epistemology or Metaphysics, is to be accorded the prime status of first philosophy. However, Aquinas is wise to build his epistemological premise on a firm metaphysical support, clarifying the needed development from being to knowledge. For, being has to first exist to constitute the object of perception, belief, and knowledge. Accordingly, our exposition of Aquinas’ epistemology will first take a cursory look at the theoretical and historical background to Aquinas’ Philosophy, before offering a general characterization of his theory of knowledge. Then, the paper will discuss his concept of sense perception as a basis for all knowing, followed closely by an analysis of cognition and Scientia. (shrink)

Formal models of appearance and reality have proved fruitful for investigating structural properties of perceptual knowledge. This paper applies the same approach to epistemic justification. Our central goal is to give a simple account of The Preface, in which justified belief fails to agglomerate. Following recent work by a number of authors, we understand knowledge in terms of normality. An agent knows p iff p is true throughout all relevant normal worlds. To model The Preface, we appeal to the normality (...) of error. Sometimes, it is more normal for reality and appearance to diverge than to match. We show that this simple idea has dramatic consequences for the theory of knowledge and justification. Among other things, we argue that a proper treatment of The Preface requires a departure from the internalist idea that epistemic justification supervenes on the appearances and the widespread idea that one knows most when free from error. (shrink)

Mystical religious experiences typically purport to engage with the transcendent and often claim to involve encounters with spiritual entities or a detachment from the material world. Daoism diverges from this paradigm. This paper examines Daoist mystical experiences of bodily transformations and explores their epistemological implications. Specifically, we defend the justificatory power of Daoist somatic experiences against the disanalogy objection. The disanalogy objection posits that mystical experiences, in contrast to sense perceptions, are not socially verifiable and thereby lack prima facie epistemic (...) value. We argue that some Daoist mystical bodily states, being essentially spatiotemporal, are exempt from this challenge. This leads to a broader understanding of mysticism and offers a partial resolution to the disanalogy objection. (shrink)

Margaret Macdonald was at the institutional heart of analytic philosophy in Britain in the mid-twentieth century. Yet, her views on the nature of philosophical theories diverge quite considerably from those of many of her contemporaries. In this paper, I focus on her 1953 article ‘Linguistic Philosophy and Perception’, a provocative paper in which Macdonald argues that the value of philosophical theories is more akin to that of poetry or art than science or mathematics. I do so for two reasons. First, (...) because it reveals just how far Macdonald’s meta- philosophical views diverged from those of many of her contemporaries. Second, because the discussion in LPP pre-empts recent literature on the nature of philosophical inquiry and the efficacy of philosophical arguments. Indeed, Macdonald’s paper is just as likely to provoke discussion today as it was in the 1950s. (shrink)

In his analysis of “the essential tension between tradition and innovation” Thomas S. Kuhn focused on the apparent paradox that, on the one hand, normal research is a highly convergent activity based upon a settled consensus, but, on the other hand, the ultimate effect of this tradition-bound work has invariably been to change the tradition. Kuhn argued that, on the one hand, without the possibility of divergent thought, fundamental innovation would be precluded. On the other hand, without a strong emphasis (...) on convergent thought, science would become a mess created by continuous theory changes and scientific progress would again be precluded. On Kuhn’s view, both convergent and divergent thought are therefore equally necessary for the progress of science. In this paper, I shall argue that a similar fundamental tension exists between the demands we see for novel insights of an interdisciplinary nature and the need for established intellectual doctrines founded in the classical disciplines. First, I shall revisit Kuhn’s analysis of the essential tension between tradition and innovation. Next, I shall argue that the tension inherent in interdisciplinary research between, on the one hand, intellectual independence and critical scrutiny and, on the other hand, epistemic dependence and trust is a complement to Kuhn’s essential tension within mono-disciplinary science between convergent and divergent thought. (shrink)

In this paper, I argue that the method of transparency --determining whether I believe that p by considering whether p -- does not explain our privileged access to our own beliefs. Looking outward to determine whether one believes that p leads to the formation of a judgment about whether p, which one can then self-attribute. But use of this process does not constitute genuine privileged access to whether one judges that p. And looking outward will not provide for access to (...) dispositional beliefs, which are arguably more central examples of belief than occurrent judgments. First, one’s dispositional beliefs as to whether p may diverge from the occurrent judgments generated by the method of transparency. Second, even in cases where these are reliably linked — e.g., in which one’s judgment that p derives from one’s dispositional belief that p — using the judgment to self-attribute the dispositional belief requires an ‘inward’ gaze. (shrink)

The article recapitulates what logic is about traditionally and works out two roles it has been playing in philosophy: the role of an instrument and of a philosophical discipline in its own right. Using Tarski’s philosophical-logical work as case study, it develops a logical reconstructionist methodology of philosophical logic that extends and refines Rudolf Carnap’s account of explication and rational reconstruction. The methodology overlaps with, but also partially diverges from, contemporary anti-exceptionalism about logic.

Augmented reality (AR) technologies function to ‘augment’ normal perception by superimposing virtual objects onto an agent’s visual field. The philosophy of augmented reality is a small but growing subfield within the philosophy of technology. Existing work in this subfield includes research on the phenomenology of augmented experiences, the metaphysics of virtual objects, and different ethical issues associated with AR systems, including (but not limited to) issues of privacy, property rights, ownership, trust, and informed consent. This paper addresses some epistemological issues (...) posed by AR systems. I focus on a near-future version of AR technology called the Real-World Web, which promises to radically transform the nature of our relationship to digital information by mixing the virtual with the physical. I argue that the Real-World Web (RWW) threatens to exacerbate three existing epistemic problems in the digital age: the problem of digital distraction, the problem of digital deception, and the problem of digital divergence. The RWW is poised to present new versions of these problems in the form of what I call the augmented attention economy, augmented skepticism, and the problem of other augmented minds. The paper draws on a range of empirical research on AR and offers a phenomenological analysis of virtual objects as perceptual affordances to help ground and guide the speculative nature of the discussion. It also considers a few policy-based and designed-based proposals to mitigate the epistemic threats posed by AR technology. (shrink)

I develop and defend a sense-datum theory of perception. My theory follows the spirit of classic sense-datum theories: I argue that what it is to have a perceptual experience is to be acquainted with some sense-data, where sense-data are private particulars that have all the properties they appear to have, that are common to both perception and hallucination, that constitute the phenomenal characters of perceptual experiences, and that may be aptly described as pictures in-side one’s head. But my theory also (...) diverges from conventional sense-datum theories in some key respects: on my view, (1) sense-data are first-person presentations of neural states, (2) the sensational qualities of sense-data differ in kind from the sensible qualities of external objects, and (3) sense-data are the vehicles in virtue of which we perceive, rather than the objects that we perceive. I argue that this package of claims is appropriately labeled ‘sense-datum theory’, and that the resultant view ought to be a live contender in contemporary philosophy of perception. (shrink)

Artificial Intelligence (AI) is already having a major impact on society. As a result, many organizations have launched a wide range of initiatives to establish ethical principles for the adoption of socially beneficial AI. Unfortunately, the sheer volume of proposed principles threatens to overwhelm and confuse. How might this problem of ‘principle proliferation’ be solved? In this paper, we report the results of a fine-grained analysis of several of the highest-profile sets of ethical principles for AI. We assess whether these (...) principles converge upon a set of agreed-upon principles, or diverge, with significant disagreement over what constitutes ‘ethical AI.’ Our analysis finds a high degree of overlap among the sets of principles we analyze. We then identify an overarching framework consisting of five core principles for ethical AI. Four of them are core principles commonly used in bioethics: beneficence, non-maleficence, autonomy, and justice. On the basis of our comparative analysis, we argue that a new principle is needed in addition: explicability, understood as incorporating both the epistemological sense of intelligibility (as an answer to the question ‘how does it work?’) and in the ethical sense of accountability (as an answer to the question: ‘who is responsible for the way it works?’). In the ensuing discussion, we note the limitations and assess the implications of this ethical framework for future efforts to create laws, rules, technical standards, and best practices for ethical AI in a wide range of contexts. (shrink)

McCarthy et al.’s proposal gains much of its plausibility by relying on a superficial treatment of justice, human dignity, sin, and the common good within the Christian tradition. Upon closer inspection of what these terms mean within the context of Christianity, it becomes clear that despite using the same phrases (e.g., a commitment to “protecting vulnerable populations,” the goal of “promoting justice,” etc.) contemporary secular bioethical goals are often deeply at odds with goals of Christian bioethics. So, while the authors (...) are right that there is room for dialogue (and even agreement) concerning general moral principles, the process of specification and application of these principles will often be heavily influenced by competing ethical traditions. Such divergent influences will often frustrate cooperative ventures between secular and religious bioethical projects. Thus, when put into action, McCarthy et al.’s proposal will—at best—produce a divided kingdom; one that cannot hope to stand. (shrink)

Algorithms are used across a wide range of societal sectors such as banking, administration, and healthcare to make predictions that impact on our lives. While the predictions can be incredibly accurate about our present and future behavior, there is an important question about how these algorithms in fact represent human identity. In this paper, we explore this question and argue that machine learning algorithms represent human identity in terms of what we shall call the statistical individual. This statisticalized representation of (...) individuals, we shall argue, differs significantly from our ordinary conception of human identity, which is tightly intertwined with considerations about biological, psychological, and narrative continuity—as witnessed by our most well-established philosophical views on personal identity. Indeed, algorithmic representations of individuals give no special attention to biological, psychological, and narrative continuity and instead rely on predictive properties that significantly exceed and diverge from those that we would ordinarily take to be relevant for questions about how we are. (shrink)