FOURTH EUROPEAN CONGRESS OF MATHEMATICS STOCKHOLM,SWEDEN JUNE27 ­ - JULY 2, 2004 Contributed papers L. Carleson’s celebrated theorem of 1965 [1] asserts the pointwise convergence of the partial Fourier sums of square integrable functions. The Fourier transform has a formulation on each of the Euclidean groups R , Z and Τ .Carleson’s original proof worked on Τ . Fefferman’s proof translates very easily to R . M´at´e [2] extended Carleson’s proof to Z . Each of the statements of the theorem (...) can be stated in terms of a maximal Fourier multiplier theorem [5]. Inequalities for such operators can be transferred between these three Euclidean groups, and was done P. Auscher and M.J. Carro [3]. But L. Carleson’s original proof and another proofs very long and very complicated. We give a very short and very “simple” proof of this fact. Our proof uses PNSA technique only, developed in part I, and does not uses complicated technical formations unavoidable by the using of purely standard approach to the present problems. In contradiction to Carleson’s method, which is based on profound properties of trigonometric series, the proposed approach is quite general and allows to research a wide class of analogous problems for the general orthogonal series. (shrink)

Carleson’s celebrated theorem of 1965 [1] asserts the pointwise convergence of the partial Fourier sums of square integrable functions. The Fourier transform has a formulation on each of the Euclidean groups R , Z andΤ .Carleson’s original proof worked on Τ . Fefferman’s proof translates very easily to R . M´at´e [2] extended Carleson’s proof to Z . Each of the statements of the theorem can be stated in terms of a maximal Fourier multiplier theorem [5]. Inequalities for such operators (...) can be transferred between these three Euclidean groups, and was done P. Auscher and M.J. Carro [3]. But L. Carleson’s original proof and another proofs very long and very complicated. We give a very short and very “simple” proof of this fact. Our proof uses PNSA technique only, developed in part I, and does not uses complicated technical formations unavoidable by the using of purely standard approach to the present problems. In contradiction to Carleson’s method, which is based on profound properties of trigonometric series, the proposed approach is quite general and allows to research a wide class of analogous problems for the general orthogonal series. (shrink)

In this perspective paper, I tried to explain that what will be the possible prospect of multiple functions in one and another through the chain rule of differentiation? The chain rule is a formula to compute the derivative of the functional composition of two or more functions. The chain rule provides us a technique for finding the derivative of composite functions, with the number of functions that make up the composition determining how many differentiation steps are necessary. The chain rule (...) in that what changes I noted, how it can be modified to reduce the differentiation process of multiple functions in one and another and implementing that process in the inverse of multiple functions in one and another, further proceedings them through the chain rule of differentiation with all prospects. Here I claim that the differentiation’s chain rule is not changed but the sequences of finding the derivative of multiple functions are changed. (shrink)

Abstract: The main aim of this work is to introduce acceleration methods called a Trigonometric acceleration methods which are of series of numerated methods. In general, these methods named as AL-Tememe’s acceleration methods of first kind to his discoverer ''Ali Hassan Mohammed''. These are very beneficial to acceleration the numerical results for definite integrations with continuous integrands which are of 2nd order main error, with respect to the accuracy and the number of the used subintervals and the fasting obtaining (...) results. Especially, for acceleration the results which are obviously obtained by trapezoidal and midpoint methods. Moreover, these methods could be enhancing the results of the ordinary differential equations numerically which are of 2nd order main error. (shrink)

This is an article about foundation of paralogical nonstandard analysis and its applications to the continuous function without a derivative presented by absolutely convergent trigonometrical series and another famous problems of trigonometrical and orthogonal series.

Certain commentators on Russell's “no class” theory, in which apparent reference to classes or sets is eliminated using higher-order quantification, including W. V. Quine and (recently) Scott Soames, have doubted its success, noting the obscurity of Russell’s understanding of so-called “propositional functions”. These critics allege that realist readings of propositional functions fail to avoid commitment to classes or sets (or something equally problematic), and that nominalist readings fail to meet the demands placed on classes by mathematics. I show that Russell (...) did thoroughly explore these issues, and had good reasons for rejecting accounts of propositional functions as extra-linguistic entities. I argue in favor of a reading taking propositional functions to be nothing over and above open formulas which addresses many such worries, and in particular, does not interpret Russell as reducing classes to language. (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)

I clarify some of the details of the modal theory of function I outlined in Nanay (2010): (a) I explicate what it means that the function of a token biological trait is fixed by modal facts; (b) I address an objection to my trait type individuation argument against etiological function and (c) I examine the consequences of replacing the etiological theory of function with a modal theory for the prospects of using the concept of biological function to explain mental content.

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)

Function talk is a constant across different life sciences. From macro-evolution to genetics, functions are mentioned everywhere. For example, a limb’s function is to allow movement and RNA polymerases’ function is to transcribe DNA. Biochemistry is not immune from such a characterization; the biochemical world seems to be a chemical world embedded within biological processes. Specifically, biochemists commonly ascribe functions to biomolecules and classify them accordingly. This has been noticed in the recent philosophical literature on biochemical kinds. But while a (...) lot has been written on biological and psychological functions, little has been said explicitly about biochemical fuctions. Here, I explore functional attribution to biochemical molecules. I argue that if we accept this attribution, then biochemical functions are constituted by chemical dispositional properties that causally contribute to selected biological processes. In section 2, I discuss the controversy concerning the characterization of biochemical functions. In section 3, I consider whether a biological or a chemical under- standing of function can be applied to biochemical functions, illustrating the account with the example of vitamin B12. The result is that none of the theories on their own provides an adequate characterization. In section 4, I present an account of biochemical functions. In section 5, I assess this account taking into consideration common requirements for a theory of functions and an objection. (shrink)

What is the function of morality? On this question, something approaching a consensus has recently emerged. Impressed by developments in evolutionary theory, many philosophers now tell us that the function of morality is to reduce social tensions, and to thereby enable a society to efficiently promote the well-being of its members. In this paper, I subject this consensus to rigorous scrutiny, arguing that the functional hypothesis in question is not well supported. In particular, I attack the supposed evidential relation between (...) an evolutionary genealogy of morals and the functional hypothesis itself. I show that there are a great many functionally relevant discontinuities between our own culture and the culture within which morality allegedly emerged, and I argue that this seriously weakens the inference from morality’s evolutionary history to its present-day function. (shrink)

The functional approach to scientific progress has been mainly developed by Kuhn, Lakatos, Popper, Laudan, and more recently by Shan. The basic idea is that science progresses if key functions of science are fulfilled in a better way. This chapter defends the function approach. It begins with an overview of the two old versions of the functional approach by examining the work of Kuhn, Laudan, Popper, and Lakatos. It then argues for Shan’s new functional approach, in which scientific progress is (...) defined as an increase of usefulness of exemplary practices. (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)

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)

This article presents a distinct sense of ‘mechanism’, which I call the functional sense of mechanism. According to this sense, mechanisms serve functions, and this fact places substantive restrictions on the kinds of system activities ‘for which’ there can be a mechanism. On this view, there are no mechanisms for pathology; pathologies result from disrupting mechanisms for functions. Second, on this sense, natural selection is probably not a mechanism for evolution because it does not serve a function. After distinguishing this (...) sense fromsimilar explications of ‘mechanism’, I argue that it is ubiquitous in biology and has valuable epistemic benefits. (shrink)

Counting functions are shown to be complete by using a simpler argument than that used by Pelletier and Martin.

A proper function of an entity is a beneficial effect that helps explain the persistence of the entity. Proper functions thereby arise through feedback mechanisms with beneficial effects as inputs and persistence as outputs. We continue to make assertions because they benefit speakers by benefiting speakers. Hearers benefit from true information. Speakers benefit by influencing hearer belief. If hearers do not benefit, they will not form beliefs in response to assertions. Speakers can then only maintain influence by providing true information, (...) often enough. The function of assertion is then inducing true hearer belief. When interests conflict, however, some mechanism must ensure that speakers provide true information often enough, instead of deceiving, or providing information regardless of quality. In humans, a core mechanism stabilizing true assertion involves social norms for truth telling. We tell the truth partly because we prescribe and enforce telling the truth. (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)

Objective Manic and depressive phases of bipolar disorder (BD) show opposite psychomotor symptoms. Neuronally, these may depend on altered relationships between sensorimotor network (SMN) and subcortical structures. The study aimed to investigate the functional relationships of SMN with substantia nigra (SN) and raphe nuclei (RN) via subcortical-cortical loops, and their alteration in bipolar mania and depression, as characterized by psychomotor excitation and inhibition. -/- Method In this resting-state functional magnetic resonance imaging (fMRI) study on healthy (n = 67) and BD (...) patients (n = 100), (1) functional connectivity (FC) between thalamus and SMN was calculated and correlated with FC from SN or RN to basal ganglia (BG)/thalamus in healthy; (2) using an a-priori-driven approach, thalamus-SMN FC, SN-BG/thalamus FC, and RN-BG/thalamus FC were compared between healthy and BD, focusing on manic (n = 34) and inhibited depressed (n = 21) patients. -/- Results (1) In healthy, the thalamus-SMN FC showed a quadratic correlation with SN-BG/thalamus FC and a linear negative correlation with RN-BG/thalamus FC. Accordingly, the SN-related FC appears to enable the thalamus-SMN coupling, while the RN-related FC affects it favoring anti-correlation. (2) In BD, mania showed an increase in thalamus-SMN FC toward positive values (ie, thalamus-SMN abnormal coupling) paralleled by reduction of RN-BG/thalamus FC. By contrast, inhibited depression showed a decrease in thalamus-SMN FC toward around-zero values (ie, thalamus-SMN disconnection) paralleled by reduction of SN-BG/thalamus FC (and RN-BG/thalamus FC). The results were replicated in independent HC and BD datasets. -/- Conclusions These findings suggest an abnormal relationship of SMN with neurotransmitters-related areas via subcortical-cortical loops in mania and inhibited depression, finally resulting in psychomotor alterations. (shrink)

Various prominent theories of pain assume that it is pain’s biological function to inform organisms about damage to their bodies. I argue that this is a mistake. First, there is no biological evidence to support the notion that pain was originally selected for its informative capacities, nor that it currently contributes to the fitness of organisms in this specific capacity. Second, neurological evidence indicates that modulating mechanisms in the nociceptive system systematically prevent pain from serving a primarily informative role. These (...) considerations threaten to undermine standard perceptual and representational accounts of pain. (shrink)

What is the biological function of perception? I hold perception, especially visual perception in humans, has the biological function of accurately representing the environment. Tyler Burge argues this cannot be so in Origins of Objectivity (Oxford, 2010), for accuracy is a semantical relationship and not, as such, a practical matter. Burge also provides a supporting example. I rebut the argument and the example. Accuracy is sometimes also a practical matter if accuracy partly explains how perception contributes to survival and reproduction.

This is a short overview of the biological functions debate in philosophy. While it was fairly comprehensive when it was written, my short book ​A Critical Overview of Biological Functions has largely supplanted it as a definitive and up-to-date overview of the debate, both because the book takes into account new developments since then, and because the length of the book allowed me to go into substantially more detail about existing views.

This paper argues that proper functions are proximal functions. In other words, it rejects the notion that there are distal biological functions – strictly speaking, distal functions are not functions at all, but simply beneficial effects normally associated with a trait performing its function. Once we rule out distal functions, two further positions become available: dysfunctions are simply failures of proper function, and pathological conditions are dysfunctions. Although elegant and seemingly intuitive, this simple view has had surprisingly little uptake in (...) the literature. Indeed, our position departs from that of almost every theorist who has engaged with the issue at any depth. We start by presenting three arguments for the position that proper functions are proximal: one from the specificity of functions, one from their relation to intervention, and one from their relation to pathology. We then consider two case studies evidencing the trouble that accepting distal functions causes for philosophical reflection on the nature of pathological conditions. Finally, we anticipate and respond to three objections: that there can be failure of function without dysfunction; that our account is unacceptably revisionary in respect of normal function-talk; and that our thesis over-generalises from a narrow set of cases. (shrink)

Functional diversity holds the promise of understanding ecosystems in ways unattainable by taxonomic diversity studies. Underlying this promise is the intuition that investigating the diversity of what organisms actually do—i.e. their functional traits—within ecosystems will generate more reliable insights into the ways these ecosystems behave, compared to considering only species diversity. But this promise also rests on several conceptual and methodological—i.e. epistemic—assumptions that cut across various theories and domains of ecology. These assumptions should be clearly addressed, notably for the sake (...) of an effective comparison and integration across domains, and for assessing whether or not to use functional diversity approaches for developing ecological management strategies. The objective of this contribution is to identify and critically analyze the most salient of these assumptions. To this aim, we provide an “epistemic roadmap” that pinpoints these assumptions along a set of historical, conceptual, empirical, theoretical, and normative dimensions. (shrink)

Epistemic warrant consists in the normal functioning of the belief-forming process when the process has forming true beliefs reliably as an etiological function. Evolution by natural selection is the most familiar source of etiological functions. . What then of learning? What then of Swampman? Though functions require history, natural selection is not the only source. Self-repair and trial-and-error learning are both sources. Warrant requires history, but not necessarily that much.

In the region where some cat sits, there are many very cat-like items that are proper parts of the cat (or otherwise mereologically overlap the cat) , but which we are inclined to think are not themselves cats, e.g. all of Tibbles minus the tail. The question is, how can something be so cat-like without itself being a cat. Some have tried to answer this “Problem of the Many” (a problem that arises for many different kinds of things we regularly (...) encounter, including desks, persons, rocks, and clouds) by relying on a mereological maximality principle, according to which, something cannot be a member of a kind K if it is a large proper part of, or otherwise greatly mereologically overlaps, a K. It has been shown, however, that a maximality constraint of this type, i.e. one that restricts mereological overlap, is open to strong objections. Inspired by the insights of, especially, Sutton and Madden, I develop a type of functional-maximality principle that avoids these objections (and has other merits), and thereby provides a better answer to the Problem of the Many. (shrink)

Our perceptual systems are not stagnant but can learn from experience. Why is this so? That is, what is the function of perceptual learning? I consider two answers to this question: The Offloading View, which says that the function of perceptual learning is to offload tasks from cognition onto perception, thereby freeing up cognitive resources (Connolly, 2019) and the Perceptual View, which says that the function of perceptual learning is to improve the functioning of perception. I argue that the Perceptual (...) View better explains data from infants and animals, and better accounts for learned tasks that only perception could perform. (shrink)

In ‘A modal theory of function’, I gave an argument against all existing theories of function and outlined a new theory. Karen Neander and Alex Rosenberg argue against both my negative and my positive claim. My aim here is not merely to defend my account from their objections, but to (a) very briefly point out that the new account of etiological function they propose in response to my criticism cannot avoid the circularity worry either and, more importantly, to (b) highlight, (...) and attempt to make precise, an important feature of my modal theory that may have been understated in the original paper – that function attributions depend on the explanatory project at hand. (shrink)

The function of a trait token is usually defined in terms of some properties of other (past, present, future) tokens of the same trait type. I argue that this strategy is problematic, as trait types are (at least partly) individuated by their functional properties, which would lead to circularity. In order to avoid this problem, I suggest a way to define the function of a trait token in terms of the properties of the very same trait token. To able to (...) allow for the possibility of malfunctioning, some of these properties need to be modal ones: a function of a trait is to do F just in case its doing F would contribute to the inclusive fitness of the organism whose trait it is. Function attributions have modal force. Finally, I explore whether and how this theory of biological function could be modified to cover artifact function. (shrink)

A common kind of explanation in cognitive neuroscience might be called function-theoretic: with some target cognitive capacity in view, the theorist hypothesizes that the system computes a well-defined function (in the mathematical sense) and explains how computing this function constitutes the exercise of the cognitive capacity (in the system's normal environment). Recently, proponents of the so-called ‘new mechanist’ approach in philosophy of science have argued that a model of a cognitive capacity is explanatory only to the extent that it reveals (...) the causal structure of the mechanism underlying the capacity. If they are right, then a cognitive model that resists a transparent mapping to known neural mechanisms fails to be explanatory. I argue that a function-theoretic characterization of a cognitive capacity can be genuinely explanatory even absent an account of how the capacity is realized in neural hardware. (shrink)

In this paper, the sine, cosine and cotangent similarity measures of interval rough neutrosophic sets is proposed. Some properties of the proposed measures are discussed. We have proposed multi attribute decision making approaches based on proposed similarity measures. To demonstrate the applicability, a numerical example is solved.

Representations are not only used in our folk-psychological explanations of behaviour, but are also fruitfully postulated, for example, in cognitive science. The mainstream view in cognitive science maintains that our mind is a representational system. This popular view requires an understanding of the nature of the entities they are postulating. Teleosemantic theories face this challenge, unpacking the normativity in the relation of representation by appealing to the teleological function of the representing state. It has been argued that, if intentionality is (...) to be explained in teleological terms, then the function of a state cannot depend on its phylogenetical history, given the metaphysical possibility of a duplicate of an intentional being that lacks an evolutionary history. In this paper, I present a method to produce, according to our current knowledge in genetic engineering, human-like individuals who are not the product of natural selection in the required sense. This variation will be used to shed light on the main replies that have been offered in the literature to the Swampman thought experiment. I argue that these replies are not satisfactory: representations should better not depend on natural selection. I conclude that a non-etiological notion of function is to be preferred for characterizing the relation of representation. (shrink)

The etiological account of teleological function is beset by several difficulties, which I propose to solve by grafting onto the etiological theory a subordinated goal-contribution clause. This approach enables us to ascribe neither too many teleofunctions nor too few; to give a unitary, one-clause analysis that works just as well for teleological functions derived from Darwinian evolution, as for those derived from human intention; and finally, to save the etiological theory from falsification, by explaining how, in spite of appearances, the (...) theory can allow for evolutionary function loss. (shrink)

A central dispute in understanding Frege’s philosophy concerns how the sense of a complex expression relates to the senses of its component expressions. According to one reading, the sense of a complex expression is a whole built from the senses of the component expressions. On this interpretation, Frege is an early proponent of structured propositions. A rival reading says that senses compose by functional application: the sense of a complex expression is the value of the function denoted by its functional (...) component for the arguments denoted by its remaining components. I argue that two non-negotiable Fregean theses entail that senses compose by functional application. One thesis is that referents compose by functional application. The other thesis is that an expression in an indirect context refers to its customary sense. (shrink)

Trigonometry serves as an important precursor to calculus as well as college level courses. However, a possible factor that affects students from learning is teachers’ strategies in teaching. Several studies reveal that cooperative learning such as study group can increase achievement of students in mathematics. This study focused on the effects of study groups on the grade 9 students’ achievement in trigonometric problems. It sought to identify the achievement of the students in problem solving before and after the interventions (...) and to compare the interventions, the group taught with study groups and taught with the existing method. The study used true experimental design particularly pretest-posttest control group design. The study was analyzed through frequency count and percentage of scores, Wilcoxon rank test, and t-test for independents samples. The subjects of the study were the Grade 9 students in a public high school in Nueva Vizcaya, Philippines. The results revealed that majority of the students’ achievements increased. Moreover, the intervention with a study group and the existing method can improve the students’ performance in solving trigonometric problems. Furthermore, the result suggests that study group method was more effective than the existing method. (shrink)

There is an under-appreciated tradition of genealogical explanation that is centrally concerned with social functions. I shall refer to it as the tradition of pragmatic genealogy. It runs from David Hume (T, 3.2.2) and the early Friedrich Nietzsche (TL) through E. J. Craig (1990, 1993) to Bernard Williams (2002) and Miranda Fricker (2007). These pragmatic genealogists start out with a description of an avowedly fictional “state of nature” and end up ascribing social functions to particular building blocks of our practices (...) – such as the fact that we use a certain concept, or live by a certain virtue – which we did not necessarily expect to have such a function at all. That the seemingly archaic device of a fictional state-of-nature story should be a helpful way to get at the functions of our actual practices must seem a mystifying proposal, however; I shall therefore endeavor to demystify it in what follows. My aim in this chapter is twofold. First, by delineating the framework of pragmatic genealogy and contrasting it with superficially similar methods, I argue that pragmatic genealogies are best interpreted as dynamic models whose point is to reveal the function – and non-coincidentally often the social function – of certain practices. Second, by buttressing this framework with something it notably lacks, namely an account of the type of functionality it operates with, I argue that both the type of functional commitment and the depth of factual obligation incurred by a pragmatic genealogy depend on what we use the method for: the dynamic models of pragmatic genealogy can be used merely as heuristic devices helping us spot functional patterns, or more ambitiously as arguments grounding our ascriptions of functionality to actual practices, or even more ambitiously as bases for functional explanations of the resilience or the persistence of practices. By bringing these distinctions into view, we gain the ability to distinguish strengths and weaknesses of the method’s application from strengths and weaknesses of the method itself. (shrink)

Humans possess two nonverbal systems capable of representing numbers, both limited in their representational power: the first one represents numbers in an approximate fashion, and the second one conveys information about small numbers only. Conception of exact large numbers has therefore been thought to arise from the manipulation of exact numerical symbols. Here, we focus on two fundamental properties of the exact numbers as prerequisites to the concept of EXACT NUMBERS : the fact that all numbers can be generated by (...) a successor function and the fact that equality between numbers can be defined in an exact fashion. We discuss some recent findings assessing how speakers of Munduruc (an Amazonian language), and young Western children (3-4 years old) understand these fundamental properties of numbers. (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)

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)

The Spohnian paradigm of ranking functions is in many respects like an order-of-magnitude reverse of subjective probability theory. Unlike probabilities, however, ranking functions are only indirectly—via a pointwise ranking function on the underlying set of possibilities W —defined on a field of propositions A over W. This research note shows under which conditions ranking functions on a field of propositions A over W and rankings on a language L are induced by pointwise ranking functions on W and the set of (...) models for L, ModL, respectively. (shrink)

The debate on the notion of function has been historically dominated by dispositional and etiological accounts, but recently a third contender has gained prominence: the organizational account. This original theory of function is intended to offer an alternative account based on the notion of self-maintaining system. However, there is a set of cases where organizational accounts seem to generate counterintuitive results. These cases involve cross-generational traits, that is, traits that do not contribute in any relevant way to the self-maintenance of (...) the organism carrying them, but instead have very important effects on organisms that belong to the next generation. We argue that any plausible solution to the problem of cross-generational traits shows that the organizational account just is a version of the etiological theory and, furthermore, that it does not provide any substantive advantage over standard etiological theories of function. (shrink)

We give a new and elementary construction of primitive positive decomposition of higher arity relations into binary relations on finite domains. Such decompositions come up in applications to constraint satisfaction problems, clone theory and relational databases. The construction exploits functional completeness of 2-input functions in many-valued logic by interpreting relations as graphs of partially defined multivalued ‘functions’. The ‘functions’ are then composed from ordinary functions in the usual sense. The construction is computationally effective and relies on well-developed methods of functional (...) decomposition, but reduces relations only to ternary relations. An additional construction then decomposes ternary into binary relations, also effectively, by converting certain disjunctions into existential quantifications. The result gives a uniform proof of Peirce’s reduction thesis on finite domains, and shows that the graph of any Sheffer function composes all relations there. (shrink)

A century after the discovery of quantum mechanics, the meaning of quantum mechanics still remains elusive. This is largely due to the puzzling nature of the wave function, the central object in quantum mechanics. If we are realists about quantum mechanics, how should we understand the wave function? What does it represent? What is its physical meaning? Answering these questions would improve our understanding of what it means to be a realist about quantum mechanics. In this survey article, I review (...) and compare several realist interpretations of the wave function. They fall into three categories: ontological interpretations, nomological interpretations, and the sui generis interpretation. For simplicity, I will focus on non-relativistic quantum mechanics. (shrink)

This paper reconstructs the function argument of Aristotle’s Eudemian Ethics 2.1. The argument seeks to define happiness through the method of division; shows that the highest good is better than all four of the goods of the soul, not only two, as commentators have thought; and unlike the Nicomachean argument, makes the highest good definitionally independent of the human function.

Nietzsche talks about shame [scham*, schmach*, schand*] in all of his published and authorized works, from The Birth of Tragedy to Ecce Homo. He refers to shame in over one hundred passages – at least five times as often as he refers to resentment/ressentiment. Yet the scholarly literature on Nietzsche and shame includes just a handful of publications, while the literature on Nietzsche and resentment includes over a thousand. Arguably, this disproportionate engagement has been driven by the fact that English (...) translations of Nietzsche’s writings systematically italicize and transliterate ‘ressentiment’ rather than treating it as the normal word it is. In any case, this chapter aims to fill the gap in the secondary literature by using digital humanities methods to systematically investigate the functions of shame in Nietzsche’s writings. I argue that Nietzsche is ambivalent about shame, depending on the function that it serves. There are four main functions. First, in a society of near-equals, it regulates interactions and incentives in ways that preserve game-theoretic equilibria. Second and relatedly, Nietzsche associates the capacity to experience nuanced and appropriate feelings of shame – and to anticipate them in others – with the pathos of distance, a virtue that he associates with nobility. Third, when shame is directed towards fixed aspects of human nature, it transforms those aspects into vices; by contrast, when it is directed towards malleable aspects of human nature, it may foster self-improvement and virtue. Nietzsche frequently laments the way that shame targets immutable aspects of ourselves. Finally and relatedly, Nietzsche casts counter-shame on those who would direct first-order shame on fixed aspects of human nature, as well as a paradoxical form of uplifting shame on their victims. If this is right, then Nietzsche does not offer a univocal verdict on shame. Instead, like many other emotions and emotional capacities, shame is inescapable, complex, and function-relative. (shrink)

A common kind of explanation in cognitive neuroscience might be called functiontheoretic: with some target cognitive capacity in view, the theorist hypothesizes that the system computes a well-defined function (in the mathematical sense) and explains how computing this function constitutes (in the system’s normal environment) the exercise of the cognitive capacity. Recently, proponents of the so-called ‘new mechanist’ approach in philosophy of science have argued that a model of a cognitive capacity is explanatory only to the extent that it reveals (...) the causal structure of the mechanism underlying the capacity. If they are right, then a cognitive model that resists a transparent mapping to known neural mechanisms fails to be explanatory. I argue that a functiontheoretic characterization of a cognitive capacity can be genuinely explanatory even absent an account of how the capacity is realized in neural hardware. (shrink)

Deception has recently received a significant amount of attention. One of main reasons is that it lies at the intersection of various areas of research, such as the evolution of cooperation, animal communication, ethics or epistemology. This essay focuses on the biological approach to deception and argues that standard definitions put forward by most biologists and philosophers are inadequate. We provide a functional account of deception which solves the problems of extant accounts in virtue of two characteristics: deceptive states have (...) the function of causing a misinformative states and they do not necessarily provide direct benefits to the deceivers and losses to the targets. (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)

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)

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)