This book deals with Colombeau solutions to Einstein field equations in general relativity: Gravitational singularities, distributional SAdS BH spacetime-induced vacuum dominance. This book covers key areas of Colombeau nonlinear generalized functions, distributional Riemannian, geometry, distributional schwarzschild geometry, Schwarzschild singularity, Schwarzschild horizon, smooth regularization, nonsmooth regularization, quantum fields, curved spacetime, vacuum fluctuations, vacuum dominance etc. This book contains various materials suitable for students, researchers and academicians of this area.

In contemporary mathematics, a Colombeau algebra of Colombeau generalized functions is an algebra of a certain kind containing the space of Schwartz distributions. While in classical distribution theory a general multiplication of distributions is not possible, Colombeau algebras provide a rigorous framework for this. Remark 1.1.1.Such a multiplication of distributions has been a long time mistakenly believed to be impossible because of Schwartz’ impossibility result, which basically states that there cannot be a differential algebra containing (...) the space of distributions and preserving the product of continuous functions. However, if one only wants to preserve the product of smooth functions instead such a construction becomes possible, as demonstrated first by J.F.Colombeau [1],[2]. As a mathematical tool, Colombeau algebras can be said to combine a treatment of singularities, differentiation and nonlinear operations in one framework, lifting the limitations of distribution theory. These algebras have found numerous applications in the fields of partial differential equations, geophysics, microlocal analysis and general relativity so far. (shrink)

This paper dealing with extension of the Einstein eld equations using apparatus of contemporary generalization of the classical Lorentzian geometry named in literature Colombeau distributional geometry, see for example [1], [2], [3], [4], [5], [6], [7] and [32]. The regularizations of singularities presented in some solutions of the Einstein equations is an important part of this approach. Any singularities present in some solutions of the Einstein equations recognized only in the sense of Colombeau generalized functions [1], (...) [2] and not classically. In this paper essentially new class Colombeau solutions to Einstein eld equations is obtained. The vacuum energy density of free scalar quantum field  with a distributional background spacetime also is considered. It has been widely believed that, except in very extreme situations, the influence of gravity on quantum fields should amount to just small, sub-dominant contributions. Here we argue that this belief is false by showing that there exist well-behaved spacetime evolutions where the vacuum energy density of free quantum fields is forced, by the very same background distributional spacetime such distributional BHs, to become dominant over any classical energy density component. This semiclassical gravity effect finds its roots in the singular behavior of quantum fields on curved spacetimes. In particular we obtain that the vacuum fluctuations have a singular behavior on BHs horizon. (shrink)

I present and defend the generalized selected effects theory (GSE) of function. According to GSE, the function of a trait consists in the activity that contributed to its bearer’s differential reproduction, or differential retention, within a population. Unlike the traditional selected effects (SE) theory, it does not require that the functional trait helped its bearer reproduce; differential retention is enough. Although the core theory has been presented previously, I go significantly beyond those presentations by providing a new argument for (...) GSE and defending it from a recent objection. I also sketch its implications for teleosemantics and philosophy of medicine. (shrink)

In this paper, I argue that what counts as the proper function of a trait is a matter of the de facto perspective that the biological system, itself, possesses on what counts as proper functioning for that trait. Unlike non-perspectival accounts, internal perspectivalism does not succumb to generality problems. But unlike external perspectivalism, internal perspectivalism can provide a fully naturalistic, mind-independent grounding of proper function and natural norms. The attribution of perspectives to biological systems is intended to be neither metaphorical (...) nor anthropomorphic: I do not mean to imply that such systems thereby must possess agency, cognition, intentions, concepts, or mental or psychological states. Instead, such systems provide the grounding for norms of performance when they internally enforce their own standard of (i.e., their own perspective on) what constitutes proper functioning or malfunctioning. By operating with a fixed, determinate level of generality, such systems provide the basis for an account of proper function that is immune to generality problems. (shrink)

This article outlines a method of collaboration that will manifest a high probability of cumulative and progressive results in science. The method will accomplish this through a division of labour grounded in the order of occurrence of human cognitional operations. The following article explores the possibility of a method known as functional specialization, distinct tasks presently operative in neuroscience. Functional specialization will enhance collaboration within a science as well as initiate implementation of generalized empirical method. Implementation of generalized (...) empirical method will be achieved through the focus of individual specialties on specific mental operations. (shrink)

In this paper, I identify a central problem for conceptual engineering: the problem of showing concept-users why they should recognise the authority of the concepts advocated by engineers. I argue that this authority problem cannot generally be solved by appealing to the increased precision, consistency, or other theoretical virtues of engineered concepts. Outside contexts in which we anyway already aim to realise theoretical virtues, solving the authority problem requires engineering to take a functional turn and attend to the functions (...) of concepts. But this then presents us with the problem of how to specify a concept’s function. I argue that extant solutions to this function specification problem are unsatisfactory for engineering purposes, because the functions they identify fail to reliably bestow authority on concepts, and hence fail to solve the authority problem. What is required is an authoritative notion of conceptual function: an account of the functions of concepts which simultaneously shows why concepts fulfilling such functions should be recognised as having authority. I offer an account that meets this combination of demands by specifying the functions of concepts in terms of how they tie in with our present concerns. (shrink)

As the principle of natural selection is generalized to explain (adaptive) patterns of human behavior, it becomes less clear what the selective environment empirically refers to. While the environment and individual are relatively separable in the non-human biological context, they are highly entangled in the context of moral, social, and institutional evolution. This chapter brings attention to the problem of generalizing the selective environment, and argues that it is ontologically disunified and definable only through its explanatory function. What unifies (...) the selective environment is that it explains adaptation in a non-agential way, by screening off various forms of agency, whether divine, organismic, or human. This explanatory function of the selective environment helps avoid some sources of confusion when the theory of natural selection is applied to humanities and social sciences. (shrink)

Different cognitive functions recruit a number of different, often overlapping, areas of the brain. Theories in cognitive and computational neuroscience are beginning to take this kind of functional integration into account. The contributions to this special issue consider what functional integration tells us about various aspects of the mind such as perception, language, volition, agency, and reward. Here, I consider how and why functional integration may matter for the mind; I discuss a general theoretical framework, based on generative models, (...) that may unify many of the debates surrounding functional integration and the mind; and I briefly introduce each of the contributions. (shrink)

Millikan’s (1984. Language, Thought, and Other Biological Categories: New Foundations for Realism. MIT Press) selected effects theory of functions states that functions are effects for which the ancestors of a trait were selected for. As the function is an effect a thing’s ancestors produced, only things that are reproductions in some sense can have functions. Against this reproduction requirement, Garson (2019. What Biological Functions Are and Why They Matter. Cambridge University Press) argues that not only processes (...) of differential reproduction but also processes of differential persistence can lead to new functions. Since such “persistence functions” have the same explanatory power as traditional selected effects functions, selected effects theorists should include them in their theory. In this paper, I will defend Millikan’s theory against this argument. I will show that the proponents of the generalized theory have yet to provide a working notion of populations that avoids a liberality problem. Further, I will argue that persistence functions are at best a marginal case of functions due to their restricted explanatory power. (shrink)

Traditional inflationary approaches that specify the nature of truth are attractive in certain ways; yet, while many of these theories successfully explain why propositions in certain domains of discourse are true, they fail to adequately specify the nature of truth because they run up against counterexamples when attempting to generalize across all domains. One popular consequence is skepticism about the efficaciousness of inflationary approaches altogether. Yet, by recognizing that the failure to explain the truth of disparate propositions often stems from (...) inflationary approaches' allegiance to alethic monism, pluralist approaches are able to avoid this explanatory inadequacy and the resulting skepticism, though at the cost of inviting other conceptual difficulties. A novel approach, alethic functionalism, attempts to circumvent the problems faced by pluralist approaches while preserving their main insights. Unfortunately, it too generates additional problems---namely, with its suspect appropriation of the multiple realizability paradigm and its platitude-based strategy---that need to be dissolved before it can constitute an adequate inflationary approach to the nature of truth. (shrink)

Hilary Putnam once suggested that “the actual existence of sets as ‘intangible objects’ suffers… from a generalization of a problem first pointed out by Paul Benacerraf… are sets a kind of function or are functions a sort of set?” Sadly, he did not elaborate; my aim, here, is to do so on his behalf. There are well-known methods for treating sets as functions and functions as sets. But these do not raise any obvious philosophical or foundational puzzles. (...) For that, we first need to provide a full-fledged function theory. I supply such a theory: it axiomatizes the iterative notion of function in exactly the same sense that ZF axiomatizes the iterative notion of set. Indeed, this function theory is synonymous with ZF. It might seem that set theory and function theory present us with rival foundations for mathematics, since they postulate different ontologies. But appearances are deceptive. Set theory and function theory provide the very same judicial foundation for mathematics. They do not supply rival metaphysical foundations; indeed, if they supply metaphysical foundations at all, then they supply the very same metaphysical foundations. (shrink)

Much recent discussion has focused on the nature of artifacts, particularly on whether artifacts have essences. While the general consensus is that artifacts are at least intention-dependent, an equally common view is function essentialism about artifacts, the view that artifacts are essentially functional objects and that membership in an artifact kind is determined by a particular, shared function. This paper argues that function essentialism about artifacts is false. First, the two component conditions of function essentialism are given a clear and (...) precise formulation, after which counterexamples are offered to each. Second, ways to handle the counterexamples suggested by Randall Dipert and Simon Evnine are considered and rejected. Third, I then consider the prospects for restricting function essentialism to so-called technical artifacts, as Lynne Baker does, and argue that this, too, fails. This paper thereby consolidates the scattered literature on function essentialism and shows that, despite the seeming plausibility of the thesis, it should be rejected as an account of artifact essences. (shrink)

A common misunderstanding of the selected effects theory of function is that natural selection operating over an evolutionary time scale is the only functionbestowing process in the natural world. This construal of the selected effects theory conflicts with the existence and ubiquity of neurobiological functions that are evolutionary novel, such as structures underlying reading ability. This conflict has suggested to some that, while the selected effects theory may be relevant to some areas of evolutionary biology, its relevance to neuroscience (...) is marginal. This line of reasoning, however, neglects the fact that synapses, entire neurons, and potentially groups of neurons can undergo a type of selection analogous to natural selection operating over an evolutionary time scale. In the following, I argue that neural selection should be construed, by the selected effect theorist, as a distinct type of function-bestowing process in addition to natural selection. After explicating a generalized selected effects theory of function and distinguishing it from similar attempts to extend the selected effects theory, I do four things. First, I show how it allows one to identify neural selection as a distinct function-bestowing process, in contrast to other forms of neural structure formation such as neural construction. Second, I defend the view from one major criticism, and in so doing I clarify the content of the view. Third, I examine drug addiction to show the potential relevance of neural selection to neuroscientific and psychological research. Finally, I endorse a modest pluralism of function concepts within biology. (shrink)

Numerous research groups are now utilizing Basic Formal Ontology as an upper-level framework to assist in the organization and integration of biomedical information. This paper provides elucidation of the three existing BFO subcategories of realizable entity, namely function, role, and disposition. It proposes one further sub-category of tendency, and considers the merits of recognizing two sub-categories of function for domain ontologies, namely, artifactual and biological function. The motivation is to help advance the coherent ontological treatment of functions, roles, and (...) dispositions, to help provide the potential for more detailed classification, and to shed light on BFO’s general make-up and use. (shrink)

Recently, Piccinini and Craver have stated three theses concerning the relations between functional analysis and mechanistic explanation in cognitive sciences: No Distinctness: functional analysis and mechanistic explanation are explanations of the same kind; Integration: functional analysis is a kind of mechanistic explanation; and Subordination: functional analyses are unsatisfactory sketches of mechanisms. In this paper, I argue, first, that functional analysis and mechanistic explanations are sub-kinds of explanation by scientific (idealized) models. From that point of view, we must take into account (...) the tradeoff between the representational/explanatory goals of generality and precision that govern the practice of model-building. In some modeling scenarios, it is rational to maximize explanatory generality at the expense of mechanistic precision. This tradeoff allows me to put forward a problem for the mechanist position. If mechanistic modeling endorses generality as a valuable goal, then Subordination should be rejected. If mechanists reject generality as a goal, then Integration is false. I suggest that mechanists should accept that functional analysis can offer acceptable explanations of cognitive phenomena. (shrink)

An important method for finding the optimal solution for linear and nonlinear models is the graphical method, which is used if the linear or nonlinear mathematical model contains one, two, or three variables. The models that contain only two variables are among the most models for which the optimal solution has been obtained graphically, whether these models are linear or non-linear in references and research that are concerned with the science of operations research, when the data of the (...) issue under study is classical data. In this research, we will present a study through, which we present the graphical method for solving Neutrosophical nonlinear models in the following case: A nonlinear programming issue, the objective function is a nonlinear function, and the constraints are linear functions. Note that we can use the same method if (i) the objective function follower is a linear follower and the constraints are nonlinear; (ii) the objective function is a non-linear follower and the constraints are non-linear. In the three cases, the nonlinear models are neutrosophic, and as we know, the mathematical model is a nonlinear model if any of the components of the objective function or the constraints are nonlinear expressions, and the nonlinear expressions may be in both. At the left end of the constraints are neutrosophic values, at least one or all of them. Then, the possible solutions to the neutrosophic nonlinear programming problem are the set of rays that fulfills all the constraints. As for the region of possible solutions, it is the region that contains all the rays that fulfill the constraints. The optimal solution is the beam that fulfills all constraints and at which the function reaches a maximum or minimum value, depending on the nature of the issue under study (noting that it is not necessary to be alone). (shrink)

The notion of function is indispensable to our understanding of distinctions such as that between being broken and being in working order (for artifacts) and between being diseased and being healthy (for organisms). A clear account of the ontology of functions and functioning is thus an important desideratum for any top-level ontology intended for application to domains such as engineering or medicine. The benefit of using top-level ontologies in applied ontology can only be realized when each of the categories (...) identified and defined by a top-level ontology is integrated with the others in a coherent fashion. Basic Formal Ontology (BFO) has from the beginning included function as one of its categories, exploiting a version of the etiological account of function that is framed at a level of generality sufficient to accommodate both biological and artifactual functions. This account has been subjected to a series of criticisms and refinements. We here articulate BFO’s account of function, provide some reasons for favoring it over competing views, and defend it against objections. (shrink)

Modern health care relies extensively on the use of technologies for assessing and treating patients, so it is important to be certain that health care technologies perform their professed functions in an effective and safe manner. Philosophers of technology have developed methods to assign and evaluate the functions of technological products, the major elements of which are described in the ICE theory. This paper questions whether the standard of evidence advocated by the ICE theory is adequate for ascribing (...) and assessing technologies employed in health care. The paper proposes that the general problem with the standard of evidence embodied in the ICE theory is too permissive for assessing medical technologies, in that it does not take into account the relative benefit and harm of medical technologies in ensuring safe functional performance in patients. The paper illustrates how evidence-based medicine has demonstrated the value of clinical research methods, including observational studies, randomized and non-randomized clinical trials, and formal techniques, such as meta-analysis, to measure therapeutic effectiveness. I argue, therefore, that evidence from clinical research studies should take precedence over the testimonial evidence and other types of non-clinical evidence, in providing justification for health technologies. (shrink)

In cognitive science, the concept of dissociation has been central to the functional individuation and decomposition of cognitive systems. Setting aside debates about the legitimacy of inferring the existence of dissociable systems from ‘behavioural’ dissociation data, the main idea behind the dissociation approach is that two cognitive systems are dissociable, and thus viewed as distinct, if each can be damaged, or impaired, without affecting the other system’s functions. In this article, I propose a notion of functional independence that does (...) not require dissociability, and describe an approach to the functional decomposition and modelling of cognitive systems that complements the dissociation approach. I show that highly integrated cognitive and neurocognitive systems can be decomposed into non-dissociable but functionally independent components, and argue that this approach can provide a general account of cognitive specialization in terms of a stable structure–function relationship. 1 Introduction2 Functional Independence without Dissociability3 FI Systems and Cognitive Architecture4 FI Systems and Cognitive Specialization. (shrink)

It is argued that medical science requires a classificatory system that (a) puts functions in the taxonomic center and (b) does justice ontologically to the difference between the processes which are the realizations of functions and the objects which are their bearers. We propose formulae for constructing such a system and describe some of its benefits. The arguments are general enough to be of interest to all the life sciences.

It is generally argued that if the wave-function in the de Broglie–Bohm theory is a physical field, it must be a field in configuration space. Nevertheless, it is possible to interpret the wave-function as a multi-field in three-dimensional space. This approach hasn’t received the attention yet it really deserves. The aim of this paper is threefold: first, we show that the wave-function is naturally and straightforwardly construed as a multi-field; second, we show why this interpretation is superior to other interpretations (...) discussed in the literature; third, we clarify common misconceptions. (shrink)

There’s a general assumption that teleology and function do not exist in inanimate nature. Throughout biology, it is generally taken as granted that teleology (or teleonomy) and functions are not only unique to life, but perhaps even a defining quality of life. For many, it’s obvious that rocks, water, and the like, are not teleological, nor could they possibly have stand-alone functions. This idea - that teleology and function are unique to life - is the target of this (...) paper. I begin with an overview of McShea’s field theoretic account of teleology. I start with the field theoretic account because it presents a promising analysis of teleological systems. It is promising because, in not making any assumptions about life’s special status in teleological systems, it avoids counterexamples that have problematized other accounts. I then consider some of the prominent efforts that have been made to attempt to avoid ascribing functions or teleology to some form of inanimate nature. In my assessment, none of the efforts are successful. I conclude by offering mineral evolution as a case study to show how inanimate nature can be both teleological and functional. The evolution of mineral species reveals that teleology and function extend to inanimate nature, and that teleology and function come in degrees. (shrink)

Discussions of the functions of biological traits generally take the notion of a trait for granted. Defining this notion is a non-trivial problem. Different approaches to function place different constraints on adequate accounts of the notion of a trait. Accounts of function based on engineering-style analyses allow trait boundaries to be a matter of human interest. Accounts of function based on natural selection have typically been taken to require trait boundaries that are objectively real. After canvassing problems raised by (...) each approach, I conclude with some facts that satisfactory notions of trait must respect. (shrink)

It is argued that medical science requires a classificatory system that (a) puts functions in the taxonomic center and (b) does justice ontologically to the difference between the processes which are the realizations of functions and the objects which are their bearers. We propose formulae for constructing such a system and describe some of its benefits. The arguments are general enough to be of interest to all the life sciences.

Confirmation bias is one of the most widely discussed epistemically problematic cognitions, challenging reliable belief formation and the correction of inaccurate views. Given its problematic nature, it remains unclear why the bias evolved and is still with us today. To offer an explanation, several philosophers and scientists have argued that the bias is in fact adaptive. I critically discuss three recent proposals of this kind before developing a novel alternative, what I call the ‘reality-matching account’. According to the account, confirmation (...) bias evolved because it helps us influence people and social structures so that they come to match our beliefs about them. This can result in significant developmental and epistemic benefits for us and other people, ensuring that over time we don’t become epistemically disconnected from social reality but can navigate it more easily. While that might not be the only evolved function of confirmation bias, it is an important one that has so far been neglected in the theorizing on the bias. (shrink)

A distinction is drawn among predicates, open sentences (or open formulas), and general terms, including general-term phrases. Attaching a copula, perhaps together with an article, to a general term yields a predicate. Predicates can also be obtained through lambda-abstraction on an open sentence. The issue of designation and semantic content for each type of general expression is investigated. It is argued that the designatum of a general term is a universal, e.g., a kind, whereas the designatum of a predicate is (...) a class (or its characteristic function) and the designatum of an open sentence is a truth-value. Predicates and open sentences are therefore typically non-rigid designators. It is argued further that certain general terms, including phrases, are invariably rigid designators, whereas certain others (general definite descriptions) are typically non-rigid. Suitable semantic contents for predicates, open sentences, and general terms are proposed. Consequences for the thesis of compositionality are drawn. (shrink)

This topic focuses on the problems that arise in providing medical care to the population during armed conflict or martial law. Under such conditions, hospitals, clinics, and other healthcare facilities have to work in challenging circumstances with limited resources and reduced security for medical personnel. This topic explores such issues as how martial law affects the work of medical institutions, what problems arise in providing medical care to the population in war, how war affects the health of the people, and (...) what consequences it may have in the long term. Research in this area will help to understand how to organize better and prepare medical facilities to work in war conditions and ensure high-quality medical care to the population in emergencies. The methods used to write this article were analysis, synthesis, generalization, explanation, and data qualification. The primary and fundamental sources for writing an article may vary depending on the topic, but generally, the following sources can be recommended. Academic studies: these can be scholarly articles, monographs, dissertations, conference papers, and other materials related to the topic of your article. These sources can help you find information about the latest research in the field and allow you to see the approaches and methodologies used in the studies. Official sources: These can be legal documents, reports, regulations, guidelines, and other materials issued by government agencies, ministries, and other departments. These sources can help you understand the rules and regulations governing your article's topic. Expert reviews: these can be interviews with experts in the field, articles, and other materials written by well-known specialists. These sources can help you understand the views and opinions of well-known experts on the issues related to your paper. (shrink)

A general framework for translating various logical systems is presented, including a set of partial unary operators of affirmation and negation. Despite its usual reading, affirmation is not redundant in any domain of values and whenever it does not behave like a full mapping. After depicting the process of partial functions, a number of logics are translated through a variety of affirmations and a unique pair of negations. This relies upon two preconditions: a deconstruction of truth-values as ordered and (...) structured objects, unlike its mainstream presentation as a simple object; a redefinition of the Principle of Bivalence as a set of four independent properties, such that its definition does not equate with normality. (shrink)

A hard choice is a situation in which an agent is unable to make a justifiable choice from a given menu of alternatives. Our objective is to present a systematic treatment of the axiomatic structure of such situations. To do so, we draw on and contribute to the study of choice functions that can be indecisive, i.e., that may fail to select a non-empty set for some menus. In this more general framework, we present new characterizations of two well-known (...) choice rules, the maximally dominant choice rule and the top-cycle choice rule. Together with existing results, this yields an understanding of the circumstances in which hard choices arise. (shrink)

In his landmark article for this journal, Francis Mechner (2018) presents a novel analysis of the confluence of unique combinations of variables accounting for aesthetic experiences, a phenomenon he calls synergetics. He proposes that artists, musicians, and writers use novel devices to capitalize on those effects. In my response to Mechner's fascinating article, I question the generality of such synergetic experiences to a wide array of audience members. I also question whether the evolutionary basis for aesthetic creativity accounts for the (...) ubiquity of aesthetic activity, as Mechner suggests. I do share Mechner’s emphasis on the importance of culturally nesting aesthetic contributions. But I suggest understanding aesthetic activities across cultures and subcultures requires additional mechanisms serving important bridging functions. I explore dispositional analysis, drawing on both Wittgenstein’s aesthetic language games and derived stimulus relationships. The behavioral functions of aesthetic experiences are those playing roles in cultural contingencies: motivational events, antecedent stimulus events, and consequences of aesthetic activities. Two kinds of aesthetic responses are discussed: 1) aesthetic creative responses by artists, writers or musicians, and 2) responses of audience members to those creations. These resulting aesthetic stimuli may play critical roles in cultural metacontingencies. (shrink)

Diagnoses in medicine are often taken to serve as explanations of patients’ symptoms and signs. This article examines how they do so. I begin by arguing that although some instances of diagnostic explanation can be formulated as covering law arguments, they are explanatory neither in virtue of their argumentative structures nor in virtue of general regularities between diagnoses and clinical presentations. I then consider the theory that medical diagnoses explain symptoms and signs by identifying their actual causes in particular cases. (...) While I take this to be largely correct, I argue that for a diagnosis to function as a satisfactory causal explanation of a patient’s symptoms and signs, it also needs to be supplemented by understanding the mechanisms by which the identified cause produces the symptoms and signs. This mechanistic understanding comes not from the diagnosis itself, but rather from the theoretical framework within which the physician operates. (shrink)

Even when brain scans fail to detect a striate lesion, functional evidence for blindsight can be adduced. In the aftermath of an automobile accident, JK became blind. Results of ophthalmic exams indicated that the blindness must be cortical. Nevertheless, multiple MRI scans failed to detect structural damage to the striate cortex. Prior to the accident JK had been an athlete; after the accident he retained some athletic abilities, arousing suspicions that he might be engaged in fraud. His residual athletic abilities—e.g., (...) hitting a handball or baseball, or catching a Frisbee—coupled with his experienced blindness, suggested blindsight. But due to the apparent absence of striate lesions, we designed a series of tasks for temporal and spatial dimensions in an attempt to detect functional evidence of his disability. Indeed, test results revealed compelling neural evidence that comport with his subjective reports. This spatiotemporal task-related method that includes contrasts with healthy controls, and detailed understanding of the patient's conscious experience, can be generalized for clinical, scientific and forensic investigations of blindsight. -/- . (shrink)

This paper argues for the general proper functionalist view that epistemic warrant consists in the normal functioning of the belief-forming process when the process has forming true beliefs reliably as an etiological function. Such a process is reliable in normal conditions when functioning normally. This paper applies this view to so-called testimony-based beliefs. It argues that when a hearer forms a comprehension-based belief that P (a belief based on taking another to have asserted that P) through the exercise of a (...) reliable competence to comprehend and filter assertive speech acts, then the hearer's belief is prima facie warranted. The paper discusses the psychology of comprehension, the function of assertion, and the evolution of filtering mechanisms, especially coherence checking. (shrink)

On Kripke’s intended definition, a term designates an object x rigidly if the term designates x with respect to every possible world in which x exists and does not designate anything else with respect to worlds in which x does not exist. Kripke evidently holds in Naming and Necessity, hereafter N&N (pp. 117–144, passim, and especially at 134, 139–140), that certain general terms – including natural-kind terms like ‘‘water’’ and ‘‘tiger’’, phenomenon terms like ‘‘heat’’ and ‘‘hot’’, and color terms like (...) ‘‘blue’’ – are rigid designators solely as a matter of philosophical semantics (independently of empirical, extra-linguistic facts). As a consequence, Kripke argues, identity statements involving these general terms are like identity statements involving proper names (e.g., ‘‘Clark Kent=Superman’’) in that, solely as a matter of philosophical semantics, they express necessary truths if they are true at all. But whereas it is reasonably clear what it is for a (first-order) singular term to designate, Kripke does not explicitly say what it is for a general term to designate. General terms are standardly treated in modern logic as predicates, usually monadic predicates. There are very forceful reasons – due independently to Church and Godel, and ultimately to Frege – for taking predicates to designate their semantic extensions. But insofar as the extension of the general term ‘‘tiger’’ is the class of actual tigers (or its characteristic function), it is clear that the term does not rigidly designate its extension, since the class of tigers in one possible world may differ from the class of tigers in another. What, then, is it for ‘‘tiger’’ to be rigid? (shrink)

The meaning of the wave function and its evolution are investigated. First, we argue that the wave function in quantum mechanics is a description of random discontinuous motion of particles, and the modulus square of the wave function gives the probability density of the particles being in certain locations in space. Next, we show that the linear non-relativistic evolution of the wave function of an isolated system obeys the free Schrödinger equation due to the requirements of spacetime translation invariance and (...) relativistic invariance. Thirdly, we argue that the random discontinuous motion of particles may lead to a stochastic, nonlinear collapse evolution of the wave function. A discrete model of energy-conserved wavefunction collapse is proposed and shown consistent with existing experiments and our macroscopic experience. Besides, we also give a critical analysis of the de Broglie-Bohm theory, the many-worlds interpretation and other dynamical collapse theories, and briefly discuss the issues of unifying quantum mechanics and relativity. (shrink)

We defend a functionalist approach to emotion that begins by focusing on emotions as central states with causal connections to behavior and to other cognitive states. The approach brackets the conscious experience of emotion, lists plausible features that emotions exhibit, and argues that alternative schemes are unpromising candidates. We conclude with the benefits of our approach: one can study emotions in animals; one can look in the brain for the implementation of specific features; and one ends up with an architecture (...) of the mind in which emotions are fully accommodated through their relations to the rest of cognition. Our article focuses on arguing for this general approach; as such, it is an essay in the philosophy of emotion rather than in the psychology or neuroscience of emotion. (shrink)

We introduce a new type of pluralism about biological function that, in contrast to existing, demonstrates a practical integration among the term’s different meanings. In particular, we show how to generalize Sandra Mitchell’s notion of integrative pluralism to circumstances where multiple epistemic tools of the same type are jointly necessary to solve scientific problems. We argue that the multiple definitions of biological function operate jointly in this way based on how biologists explain the evolution of protein function. To clarify how (...) our account relates to existing views, we introduce a general typology for monist and pluralist accounts along with standardized criteria for judging which is best supported by evidence. (shrink)

Although it has been given qualified approval by a number of philosophers of education, the so-called ‘therapeutic turn’ in education has been the subject of criticism by several commentators on post-compulsory and adult learning over the last few years. A key feature of this alleged development in recent educational policy is said to be the replacement of the traditional goals of knowledge and understanding with personal and social objectives concerned with enhancing and developing confidence and self-esteem in learners. After offering (...) some critical observations on these developments, I suggest that there are some educationally justifiable goals underpinning what has been described as a therapeutic turn. Whilst accepting that ‘self-esteem’ and cognate concepts cannot provide a general end or universal aim of education, the therapeutic function is more valuable and significant than is generally acknowledged. This claim is justified by an examination of the concept of ‘mindfulness’ that, it is argued, can be an immensely powerful and valuable notion, which is integrally connected with the centrally transformative and developmental nature of learning and educational activity at all levels. (shrink)

The file on this site provides the slides for a lecture given in Hangzhou in May 2018, and the lecture itself is available at the URL beginning 'sms' in the set of links provided in connection with this item. -/- It is commonly assumed that regular physics underpins biology. Here it is proposed, in a synthesis of ideas by various authors, that in reality structures and mechanisms of a biological character underpin the world studied by physicists, in principle supplying detail (...) in the domain that according to regular physics is of an indeterminate character. In regular physics mathematical equations are primary, but this constraint leads to problems with reconciling theory and reality. Biology on the other hand typically does not characterise nature in quantitative terms, instead investigating in detail important complex interrelationships between parts, leading to an understanding of the systems concerned that is in some respects beyond that which prevails in regular physics. It makes contact with quantum physics in various ways, for example in that both involve interactions between observer and observed, an insight that explains what is special about processes involving observation, justifying in the quantum physics context the replacement of the unphysical many-worlds picture by one involving collapse. The link with biology furthermore clarifies Wheeler’s suggestion that a multiplicity of observations can lead to the ‘fabrication of form’, including the insight that this process depends on very specific ‘structures with power’ related to the 'semiotic scaffolding' of the application of sign theory to biology known as biosemiotics. -/- The observer-observed 'circle' of Wheeler and Yardley is a special case of a more general phenomenon, oppositional dynamics, related to the 'intra-action' of Barad's Agential Realism, involving cooperating systems such as mind and matter, abstract and concrete, observer and observed, that preserve their identities while interacting with one another in such a way as to act as a unit. A third system may also be involved, the mediating system of Peirce linking the two together. Such a situation of changing connections and separations may plausibly lead in the future to an understanding of how complex systems are able to evolve to produce 'life, the universe and everything'. -/- (Added 1 July 2018) The general structure proposed here as an alternative to a mathematics-based physics can be usefully characterised by relating it to different disciplines and the specialised concepts utilised therein. In theoretical physics, the test for the correctness of a theory typically involves numerical predictions, corresponding to which theories are expressed in terms of equations, that is to say assertions that two quantities have identical values. Equations have a lesser significance in biology which typically talks in terms of functional mechanisms, dependent for example on details of chemistry and concepts such as genes, natural selection, signals and geometrical or topologically motivated concepts such as the interconnections between systems and the unfolding of DNA. Biosemiotics adds to this the concept of signs and their interpretation, implying novel concepts such as semiotic scaffolding and the semiosphere, code duality, and appreciation of the different types of signs, including symbols and their capacity for abstraction and use in language systems. Circular Theory adds to this picture, as do the ideas of Barad, considerations such as the idea of oppositional dynamics. The proposals in this lecture can be regarded as the idea that concepts such as those deriving from biosemiotics have more general applicability than just conventional biology and may apply, in some circumstances, to nonlinear systems generally, including the domain new to science hypothesised to underlie the phenomena of present-day physics. -/- The task then has to be to restore the mathematical aspect presumed, in this picture, not to be fundamental as it is in conventional theory. Deacon has invoked a complex sequence of evolutionary steps to account for the emergence over time of human language systems, and correspondingly mathematical behaviour can be subsumed under the general evolutionary mechanisms of biosemiotics (cf. also the proposals of Davis and Hersh regarding the nature of mathematics), so that the mathematical behaviour of physical systems is consistent with the proposed scheme. In conclusion, it is suggested that theoretical physicists should cease expecting to find some universal mathematical ‘theory of everything’, and focus instead on understanding in more detail complex systems exhibiting behaviour of a biological character, extending existing understanding. This may in time provide a more fruitful understanding of the natural world than does the regular approach. The essential concepts have an observational basis from both biology and the little-known discipline of cymatics (a discipline concerned with the remarkable patterns that specific waveforms can give rise to), while again computer simulations also offer promise in providing insight into the complex behaviours involved in the above proposals. -/- References -/- Jesper Hoffmeyer, Semiotic Scaffolding of Living Systems. Commens, a Digital Companion to C. S. Peirce (on Commens web site). Terrence Deacon, The Symbolic Species, W.W. Norton & Co. Karen Barad, Meeting the Universe Halfway: Quantum Physics and the Entanglement of Matter and Meaning, Duke University Press. Philip Davis and Reuben Hersh, The Mathematical Experience, Penguin. Ilexa Yardley, Circular Theory. (shrink)

This paper presents a new reconstruction of Wittgenstein’s famous (and controversial) rule-following arguments. Two are the novel features offered by our reconstruction. In the first place, we propose a shift of the central focus of the discussion, from the general semantics and the philosophy of mind to the philosophy of mathematics and the rejection of the notion of a function. The second new feature is positive: we argue that Wittgenstein offers us a new alternative notion of a rule (to replace (...) the rejected functions), a notion reminiscent of Category Theory’s notion of a morphism. (shrink)

In this book, for the first time, authors try to introduce the concept of linguistic variables as a continuum of linguistic terms/elements/words in par or similar to a real continuum. For instance, we have the linguistic variable, say the heights of people, then we place the heights in the linguistic continuum [shortest, tallest] unlike the real continuum (–∞, ∞) where both –∞ or +∞ is only a non-included symbols of the real continuum, but in case of the linguistic continuum we (...) generally include the ends or to be more mathematical say it is a closed interval, where shortest denotes the shortest height of a person, maybe the born infant who is very short from usual and the tallest will denote the tallest one usually very tall; however this linguistic continuum [shortest, tallest] in the real continuum will be the closed interval say [1 foot, 8 feet] or [1, 8] the measurement in terms of feet. So, the real interval is a subinterval with which we have associated the real continuum in terms of qualifying unit feet and inches in this case. (shrink)

Are there different sizes of infinity? That is, are there infinite sets of different sizes? This is one of the most natural questions that one can ask about the infinite. But it is of course generally taken to be settled by mathematical results, such as Cantor’s theorem, to the effect that there are infinite sets without bijections between them. These results settle the question, given an almost universally accepted principle relating size to the existence of functions. The principle is: (...) for any sets A and B, if A is the same size as B, then there is a bijection from A to B. The aim of the paper, however, is to argue that this question is in fact wide open: to argue that we are not in a position to know the answer, because we are not in one to know the principle. The aim, that is, is to argue that for all we know there is only one size of infinity. (shrink)

The material interpretation of conditionals is commonly recognized as involving some paradoxical results. I here argue that the truth functional approach to natural language is the reason for the inadequacy of this material interpretation, since the truth or falsity of some pair of statements ‘p’ and ‘q’ cannot per se be decisive for the truth or falsity of a conditional relation ‘if p then q’. This inadequacy also affects the ability of the overall formal system to establish whether or not (...) arguments involving conditionals are valid. I also demonstrate that the Paradox of Indicative Conditionals does not actually involve a paradox, but instead contains some paralogistic elements that make it appear to be a paradox. The discussion of the paradox in this paper further reveals that the material interpretation of conditionals adversely affects the treatment of disjunctions. -/- Much has been said about these matters in the literature that point in the same direction. However, there seems to be some reluctance against fully complying with the arguments against the truth functional account of conditionals, since many of the alternative accounts rely on the material conditional, or at least on an understanding of the conditional as a function of antecedent and consequent in a similar sense as the material conditional. My argument against truth functionality indicates that it may in general involve similar problems to treat conditionals as such functions, whether one deals with theories of truth, assertability or probability. (shrink)

In this paper, we generalize the definition of Neutrosophic sets and present a method for extending crisp functions on Neutrosophic sets and study some properties of such extended functions.

Magnetic levitation system is operated primarily based at the principle of magnetic attraction and repulsion to levitate the passengers and the train. However, magnetic levitation trains are rather nonlinear and open loop unstable which makes it hard to govern. In this paper, investigation, design and control of a nonlinear Maglev train based on NARMA-L2, model reference and predictive controllers. The response of the Maglev train with the proposed controllers for the precise role of a Magnetic levitation machine have (...) been as compared for a step input signal. The simulation consequences prove that the Maglev teach system with NARMA-L2 controller suggests the quality performance in adjusting the precise function of the system and the device improves the experience consolation and street managing criteria. (shrink)

Magnetic levitation system is operated primarily based at the principle of magnetic attraction and repulsion to levitate the passengers and the train. However, magnetic levitation trains are rather nonlinear and open loop unstable which makes it hard to govern. In this paper, investigation, design and control of a nonlinear Maglev train based on NARMA-L2, model reference and predictive controllers. The response of the Maglev train with the proposed controllers for the precise role of a Magnetic levitation machine have (...) been as compared for a step input signal. The simulation consequences prove that the Maglev teach system with NARMA-L2 controller suggests the quality performance in adjusting the precise function of the system and the device improves the experience consolation and street managing criteria. (shrink)

Extant literature suggests a positive correlation between social trust (also called generalized trust) and life satisfaction. However, the psychological pathways underlying this relationship can be complex. Using the Bayesian Mindsponge Framework (BMF), we examined the influence of social trust in a high-violence environment. Employing Bayesian analysis on a sample of 1237 adults in Cali, Colombia, we found that in a linear relationship, generalized trust is positively associated with life satisfaction. However, in a model including the interactions between trust (...) and education level as well as between trust and socioeconomic status, generalized trust is found to be negatively associated with life satisfaction. In this non-linear relationship, both education level and socioeconomic status have moderating effects against the negative association between generalized trust and life satisfaction. In other words, less educated people living in worse socioeconomic conditions are more likely to have lower life satisfaction when they have higher levels of social trust. In contrast, highly educated people living in better socioeconomic conditions are more likely to have higher life satisfaction when they have higher levels of social trust. Due to the facilitating function of trust in information processing, lowering the rigor of the filtering system in a high-violence social environment will likely put an individual at risk. Based on our findings, we suggest that policymakers should consider the impacts of social contexts when advocating for increasing social trust. We also recommend that researchers carefully examine the psychological mechanism underlying an observed association before making suggestions for policymaking. (shrink)

We argue that the extant evidence for Stoic logic provides all the elements required for a variable-free theory of multiple generality, including a number of remarkably modern features that straddle logic and semantics, such as the understanding of one- and two-place predicates as functions, the canonical formulation of universals as quantified conditionals, a straightforward relation between elements of propositional and first-order logic, and the roles of anaphora and rigid order in the regimented sentences that express multiply general propositions. We (...) consider and reinterpret some ancient texts that have been neglected in the context of Stoic universal and existential propositions and offer new explanations of some puzzling features in Stoic logic. Our results confirm that Stoic logic surpasses Aristotle’s with regard to multiple generality, and are a reminder that focusing on multiple generality through the lens of Frege-inspired variable-binding quantifier theory may hamper our understanding and appreciation of pre-Fregean theories of multiple generality. (shrink)

Epistemic rationality is typically taken to be immodest at least in this sense: a rational epistemic state should always take itself to be doing at least as well, epistemically and by its own light, than any alternative epistemic state. If epistemic states are probability functions and their alternatives are other probability functions defined over the same collection of proposition, we can capture the relevant sense of immodesty by claiming that epistemic utility functions are (strictly) proper. In this (...) paper I examine what happens if we allow for the alternatives to an epistemic state to include probability functions with different domains. I first prove an impossibility result: on minimal assumptions, I show that there is no way of vindicating strong immodesty principles to the effect that any probability function should take itself to be doing at least as well than any alternative probability function, regardless of its domain. I then consider alternative, weaker generalizations of the traditional immodesty principle and prove some characterization results for some classes of epistemic utility functions satisfying each of the relevant principles. (shrink)