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)

Local connectedness functions for (κ, 1)-simplified morasses, localisations of the coupling function c studied in [M96, §1], are defined and their elementary properties discussed. Several different, useful, canonical ways of arriving at the functions are examined. This analysis is then used to give explicit formulae for generalisations of the local distance functions which were defined recursively in [K00], leading to simple proofs of the principal properties of those functions. It is then extended to the properties of local connectedness functions (...) in the context of κ-M-proper forcing for sucessor κ. The functions are shown to enjoy substantial strengthenings of the properties (particularly the ∆-properties) hitherto proved for both c and for Todorcevic’s ρ-functions in the special case κ = ω1. A couple of examples of the use of local connectedness functions in consort with κ-M-proper forcing are then given. (shrink)

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.

In the foundations of Fechner's psychophysics, the concept of “functional relation” plays a highly relevant role in three different respects: (1) in respect to the principles of measurement, (2) in respect to the mind-body problem, and (3) in respect to the concept of a law of nature. In all three cases, it is important to explain the difference between a functional dependency of a variable upon another and a causal relationship between two (or more) variables. In all three respects, Ernst (...) Mach developed Fechner's ideas further and tried to extend the lessons he had learned from using the concept of a functional relation in psychophysics to the whole of science. For all three cases, I explain why they are still relevant for psychophysics and philosophy today. (shrink)

This study examined the relationship between individual differences in executive functions (EF; assessed by measures of working memory, Stroop, trail making, and verbal fluency) and ability to down-regulate and up-regulate responses to emotionally evocative film clips. To ensure a wide range of EF, 48 participants with diverse neurodegenerative disorders and 21 older neurologically normal ageing participants were included. Participants were exposed to three different movie clips that were designed to elicit a mix of disgust and amusement. While watching the films (...) they were either instructed to watch, down-regulate, and up-regulate their visible emotional responses. Heart rate and facial behaviours were monitored throughout. Emotion regulatory ability was operationalised as changes in heart rate and facial behaviour in the down- and up-regulation conditions, controlling for responses in the watch condition. Results indicated that higher verbal fluency scores were related to greater ability to regulate emotion in both the down-regulation and up-regulation conditions. This finding remained significant even after controlling for age and general cognitive functioning. No relationships were found between emotion regulation and the other EF measures. We believe these results derive from differences among EF measures, with verbal-fluency performance best capturing the complex sequence of controlled planning, activation, and monitoring required for successful emotion regulation. These findings contribute to our understanding of emotion–cognition interaction, suggesting a link between emotion-regulatory abilities and individual differences in complex executive functions. (shrink)

Justin Garson has recently argued that proper functions are proximal activities of traits selected by phylogenetic or ontogenetic selection processes, and that traits are dysfunctional only if they cannot perform their proper functions for constitutional reasons. We partially agree with Garson, but reject the view that functions are proximal activities, as well as his account of dysfunctions. Instead, we propose our own theory that biological functions are selected dispositions and that a trait is dysfunctional in virtue of not having the (...) dispositions for which it was selected. This account can explain both defects (or dysfunctions in Garson’s sense) and dysfunctions due to environmental factors. Moreover, it offers a neat way to explain the graduality of dysfunction. (shrink)

The variety MBA of monadic bounded algebras consists of Boolean algebras with a distinguished element E, thought of as an existence predicate, and an operator ∃ reflecting the properties of the existential quantifier in free logic. This variety is generated by a certain class FMBA of algebras isomorphic to ones whose elements are propositional functions. We show that FMBA is characterised by the disjunction of the equations ∃E = 1 and ∃E = 0. We also define a weaker notion of (...) "relatively functional" algebra, and show that every member of MBA is isomorphic to a relatively functional one. (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)

The objective of this paper is to present a new theory of synaptic function in the nervous system. The basis for this theory is the experimental demonstration that a nerve impulse assumes five different forms as it advances through the synaptic region, and that five basic mathematical operations have been identified as being involved in the transformation of one form into another form. As a result of these data, the synaptic region is regarded as a functional unit where information (...) coming to it is unpacked, processed, stored, and retrieved for transit to another synaptic region or effector site. The data also suggests that a nerve impulse is a bolus of energy, therefore, without substance; that it contains information coded in its shape or form; that it is precisely described mathematically. Furthermore, the data suggests synaptic regions process these nerve impulses by applying mathematical operations to them; that function in the synaptic region is highly stereotyped (programmed); that chemical substances are associated with the mathematical operations. The basic approach of this theory is to regard a significant portion of the nervous system as an interface between the external universe and man himself. As an interface, the nervous system receives and processes information from both the external universe and man himself in a programmed manner. The interface functions by converting the information it receives into a bolus of energy, the nerve impulse, then processes the bolus by converting it into numbers or functions and applying mathematical operation to it. (shrink)

In the debate over the moral status of nonsentient organisms, biocentrists argue that all living things, including nonsentient ones, have interests of their own. They often defend this claim by arguing that living organisms are goal-directed, functionally organized systems. This argument for ascribing interests has faced a serious challenge that is sometimes called the Problem of Scope. Critics have argued that ascribing interests on the basis of functional organization would have implausible implications regarding the scope of the argument, such as (...) ascribing interests to inanimate artifacts and machines. In this paper, I argue that much of the recent discussion on the Problem of Scope is based on an uncharitable interpretation of the argument for ascribing interests, which presupposes a reductionist account of functions. I assess this version of the argument, and explain why it cannot succeed. I then consider an alternative interpretation of the argument, which starts from a non-reductionist account of functions. I argue that this version of the argument avoids the Problem of Scope, while acknowledging that it has limitations of its own. (shrink)

The evolutionary theory of artefact proper function holds that an artefact’s proper function is that effect which explains the reproduction of past instances of the artefact type. This theory has many sources but received its clearest presentation in Beth Preston’s essay “Why Is a Wing Like a Spoon?”. More recently, Preston has raised an objection to the theory, based on the phenomenon of ‘phantom functions’: these are functions that an artefact type is unable to perform, but which nonetheless (...) apparently constitute its proper function. Deflecting qi energy, for example, is the proper function of feng shui mirrors, even though no feng shui mirror is able to do this. Preston concludes that the existence of phantom functions refutes the evolutionary theory of artefact proper function. In this paper, the evolutionary theory is defended, by arguing that it can adequately account for phantom function cases. (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)

A study of what Descartes calls émotions in his Passions of the Soul suggests that, rather than just a theory of passions—as Descartes himself explicitly claims to be proposing—he was in practice putting forward a more comprehensive theory of passions-émotions, a unified theory which would be closer to what today should properly be called Descartes’ theory of emotions. I try here to make explicit the grounds of this unity by showing that émotions both fit within the functional account Descartes attributes (...) to what he calls passions; and complement the intentionality of passions by expanding it to new objects. In order to show this I offer also a tentative distinction, functionally and intentionally, between passions and émotions in general, on one hand, and, on the other, between the two apparent types of émotions Descartes refers to in the treatise—interior or internal [intérieure] and intellectual [intellectuelle] émotions. (shrink)

This book, originally published in French, examines the philosophical debates on functions over the last forty years and proposes new ways of analysis. Pervasive throughout the life sciences, the concept of function has the air of an epistemological scandal: ascribing a function to a biological structure or process amounts to suggesting that it is explained by its effects. This book confronts the debates on function with the use of the notion in a wide range of disciplines, such (...) as biology, psychology, and medicine. It also raises the question of whether this notion, which is as old in the history of technology as it is in the life sciences, has the same meaning in these two domains. (shrink)

In this paper I defend an etiological theory of biological functions (according to which the proper function of a trait is the effect for which it was selected by natural selection) against three objections which have been influential. I argue, contrary to Millikan, that it is wrong to base our defense of the theory on a rejection of conceptual analysis, for conceptual analysis does have an important role in philosophy of science. I also argue that biology requires a normative (...) notion of a "proper function", and that a normative notion is not ahistorical. (shrink)

This 2001 book offers an examination of functional explanation as it is used in biology and the social sciences, and focuses on the kinds of philosophical presuppositions that such explanations carry with them. It tackles such questions as: why are some things explained functionally while others are not? What do the functional explanations tell us about how these objects are conceptualized? What do we commit ourselves to when we give and take functional explanations in the life sciences and the social (...) sciences? McLaughlin gives a critical review of the debate on functional explanation in the philosophy of science. He discusses the history of the philosophical question of teleology, and provides a comprehensive review of the post-war literature on functional explanation. What Functions Explain provides a sophisticated and detailed Aristotelian analysis of our concept of natural functions, and offers a positive contribution to the ongoing debate on the topic. (shrink)

As well known, the exact sciences served Kant as a model of metaphysical cognition. There is also an opposite relation between science and metaphysics, however, namely the teleology of reason, as expressed at the end of the Critique of Pure Reason. There, Kant claims that the sciences are ultimately subordinate to the essential ends of humanity “through the mediation of a rational cognition from mere concepts”, i. e., metaphysical cognition.

We characterize a type of functional explanation that addresses why a homologous trait originating deep in the evolutionary history of a group remains widespread and largely unchanged across the group’s lineages. We argue that biologists regularly provide this type of explanation when they attribute conserved functions to phenotypic and genetic traits. The concept of conserved function applies broadly to many biological domains, and we illustrate its importance using examples of molecular sequence alignments at the intersection of evolution and cell (...) biology. We use these examples to show how the study of conserved functions can integrate knowledge of a trait’s causal effects on fitness and its history of natural selection without invoking adaptation. We also show how conserved function provides a novel basis for addressing objections against evolutionary functions raised by Robert Cummins. (shrink)

Recently something close to a consensus about the best way to naturalize the notion of biological function appears to be emerging. Nonetheless, teleological notions in biology remain controversial. In this paper we provide a naturalistic analysis for the notion of natural design. Many authors assume that natural design should be assimilated directly to function. Others find the notion problematic because it suggests that evolution is a directed process. We argue that both of these views are mistaken. Our naturalistic (...) account does not simply equate design with function. We argue that the distinction between function and design is important for understanding the evolution of the physical and behavioral traits of organisms. (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)

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)

The paper examines the interplays between logic and politics in the Polish School of Logic starting from 1914. The Polish School of Logic flourished between 1920 and 1939. Philosophically, it was influenced by Kazimierz Twardowski (1866–1938). For Twardowski logic is fundamental for every kind of human activity, professional and private and this means that every argument should be formulated and proceed by correct inferential rules. These rules involve semiotics, formal logic and methodology of science. The paper shows how this position (...) was shared by Twardowski’s students, including Jan Łukasiewicz, Stanisław Leśniewski, Kazimierz Ajdukiewicz and Tadeusz Kotrabiński, as well as by the next generation of logicians and philosophers and especially by Alfred Tarski. These authors considered logic, philosophy and science as completely neutral with respect to politics and ideology but they also considered logical skills as indispensable in political activities. (shrink)

It is argued that the many-worlds interpretation is by far the best interpretation of quantum mechanics. The key points of this view are viewing the wave functions of worlds in three dimensions and understanding probability through self-locating uncertainty.

But what are functions? Here, 15 leading scholars of philosophy of psychology and philosophy of biology present new essays on functions.

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)

Functional language is ubiquitous in ecology, mainly in the researches about biodiversity and ecosystem function. However, it has not been adequately investigated by ecologists or philosophers of ecology. In the contemporary philosophy of ecology we can recognize a kind of implicit consensus about this issue: while the etiological approaches cannot offer a good concept of function in ecology, Cummins’ systemic approach can. Here we propose to go beyond this implicit consensus, because we think these approaches are not adequate (...) for ecology. We argue that a sound epistemological framework to function in ecology is to be found in organizational approaches. In this line, we define function in ecology as a precise effect of a given constraint on the ecosystem flow of matter and energy performed by a given item of biodiversity, within a closure of constraints. We elaborate on this definition by developing a case study of a bromeliad ecosystem. (shrink)

The etiological approach to ‘proper functions’ in biology can be strengthened by relating it to Robert Cummins' general treatment of function ascription. The proper functions of a biological trait are the functions it is assigned in a Cummins-style functional explanation of the fitness of ancestors. These functions figure in selective explanations of the trait. It is also argued that some recent etiological theories include inaccurate accounts of selective explanation in biology. Finally, a generalization of the notion of selective explanation (...) allows an analysis of the proper functions of human artifacts. (shrink)

Wave function realism is an interpretative framework for quantum theories which recommends taking the central ontology of these theories to consist of the quantum wave function, understood as a field on a high-dimensional space. This paper presents and evaluates three standard arguments for wave function realism, and clarifies the sort of ontological framework these arguments support.

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)

In this book the notion of MOD functions are defined on MOD planes. This new concept of MOD functions behaves in a very different way. Even very simple functions like y = nx has several zeros in MOD planes where as they are nice single line graphs with only (0, 0) as the only zero. Further polynomials in MOD planes do not in general follows the usual or classical laws of differentiation or integration.

Philosophers of evolutionary biology favor the so-called etiological concept of function according to which the function of a trait is its evolutionary purpose, defined as the effect for which that trait was favored by natural selection. We term this the selected effect (SE) analysis of function. An alternative account of function was introduced by Robert Cummins in a non-evolutionary and non-purposive context. Cummins''s account has received attention but little support from philosophers of biology. This paper will (...) show that a similar non-purposive concept of function, which we term causal role (CR) function, is crucial to certain research programs in evolutionary biology, and that philosophical criticisms of Cummins''s concept are ineffective in this scientific context. Specifically, we demonstrate that CR functions are a vital and ineliminable part of research in comparative and functional anatomy, and that biological categories used by anatomists are not defined by the application of SE functional analysis. Causal role functions are non-historically defined, but may themselves be used in an historical analysis. Furthermore, we show that a philosophical insistence on the primary of SE functions places practicing biologists in an untenable position, as such functions can rarely be demonstrated (in contrast to CR functions). Biologists who study the form and function of organismal design recognize that it is virtually impossible to identify the past action of selection on any particular structure retrospectively, a requirement for recognizing SE functions. (shrink)

“Functional finance” is an economic theory within the Post Keynesian school of thought. Especially in the form of Modern Monetary Theory (MMT), it has begun to have two big but opposite effects on the debate over Universal Basic Income (UBI). Some people state MMT in an exaggerated way that implies the government can spend all it wants on UBI or anything else without ever raising taxes or borrowing money as if government spending had no limits of any kind. Other people (...) refer to MMT while arguing that any effort to maintain a livable level of UBI is unsustainable. This article discusses the functional finance implications for the cost and sustainability of UBI, arguing that neither of those exaggerated implications are correct. MMT doesn’t free us for the concern for how to support UBI with taxes, but neither does it give reason to believe UBI is any less sustainable. (shrink)

In an important and timely book, Anneli Jefferson outlines a view according to which a given mental disorder is a brain disorder if it is a (harmful) mental dysfunction realised by a brain dysfunction. Prima facie, Jefferson’s book is a study in the metaphysics of dysfunction: how does mental dysfunction relate to brain dysfunction, and what does this imply for the status of mental disorders and brain disorders? In what follows, I shall argue that Jefferson’s contribution to this debate is (...) better understood as a conceptual explication of how psychiatrists, some philosophers, scientists and clinicians in the field (broadly construed) think of the label ‘brain disorder’. I infer this on the basis that Jefferson’s thesis would not follow from any serious, well-worked out theory of proper function. Despite initial appearances, Jefferson’s book about brain dysfunction is not about function at all. (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)

We sketch a novel and improved version of Boorse’s biostatistical theory of functions. Roughly, our theory maintains that (i) functions are non-negligible contributions to survival or inclusive fitness (when a trait contributes to survival or inclusive fitness); (ii) situations appropriate for the performance of a function are typical situations in which a trait contributes to survival or inclusive fitness; (iii) appropriate rates of functioning are rates that make adequate contributions to survival or inclusive fitness (in situations appropriate for the (...) performance of that function); and (iv) dysfunction is the inability to perform a function at an appropriate rate in appropriate situations. Based on our theory, we sketch solutions to three problems that have afflicted Boorse’s theory of function, namely, Kingma’s ([2010]) problem of the situation-specificity of functions, the problem of multi-functional traits, and the problem of how to distinguish between appropriate and inappropriate rates of functioning. (shrink)

Perceptions "present" objects as red, as round, etc.-- in general as possessing some property. This is the "perceptual content" of the title, And the article attempts to answer the following question: what is a materialistically adequate basis for assigning content to what are, after all, neurophysiological states of biological organisms? The thesis is that a state is a perception that presents its object as "F" if the "biological function" of the state is to detect the presence of objects that (...) are "F". The theory contrasts with causal/informational theories, and with internalist theories, for example those which assign content on the basis of introspected feel. Its advantages are that it permits perceptual error while at the same time allowing content to be expressed in terms of external properties. The argument of the paper is illustrated throughout by examples from biology and computational psychology. (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)

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)

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)

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)

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)

Ned Block, John Campbell; Functional Role and Truth Conditions, Proceedings of the Aristotelian Society, Volume 88, Issue 1, 1 June 1988, Pages 273–292, https:/.

This paper argues that a minimal notion of function and a notion of normal-proper function are used in explaining how bodies and brains operate. Neither is Cummins’ notion, as originally defined, and yet his is often taken to be the clearly relevant notion for such an explanatory context. This paper also explains how adverting to normal-proper functions, even if these are selected functions, can play a significant scientific role in the operational explanations of complex systems that physiologists and (...) neurophysiologists provide, despite a lack of relevant causal efficacy on the part of such functions. (shrink)