This is a Turing Machine which computes the exponential function f(x,y) = xˆy. Instructions format and operation of this machine are intended to best reflect the basic conditions outlined by Alan Turing in his On Computable Numbers, with an Application to the Entscheidungsproblem (1936), using the simplest single-tape and single-symbol version, in essence due to Kleene (1952) and Carnielli & Epstein (2008). This machine is composed by four basic task machines: one which checks if exponent y is zero, (...) a second which checks if base x is zero, a third that is able to copy the base, and a fourth able to multiply multiple factors (in this case, factors will be all equal). They were conveniently separated in order to ease the reader's task to understand each step of its operation. We adopt the convention that a number n is represented by a string of n+1 symbols "1". Thus, an entry (x, y) will be represented by two respective strings of x+1 and y+1 symbols "1", separated by a single "0" (or a blank), and as an output, this machine will generate a string of (xˆy)+1 symbols "1". Some of the instructions are followed by a brief description of what's going on. (shrink)

In his book Reasons and Persons, Derek Parfit proposes the search for a self-consistent theory of population ethics, a theory capable of answering questions about the welfares of populations in a manner that satisfies all of our ethical intuitions, what he calls “Theory X.” But in the same work, Parfit offers what he sees as a major obstacle to that goal, the so-called “Repugnant Conclusion”, worrying whether the most well-off population is an increasingly large population. This problem, along with Roderick (...) Ninian Smart’s “Negative Utilitarianism” and Robert Nozick’s “Utility Monster” belong to a special class of ethical cases dealing with the mathematical limits of zero and infinity: trivial and unreal ethical solutions. These kinds of problems have plagued population ethics since Thomas Malthus first recognized the problem of exponential growth and its deleterious effects on personal wellbeing. In an attempt to answer Parfit, some, such as T. Sider, T. Hurka, and Y. Ng, have suggested formulations of marginal wellbeing without undermining core ethical principles. Other authors, like G. Arrhenius et al., have suggested that Parfit’s problem fundamentally undermines the possibility of a self-consistent population ethics. Here we will suggest that these problems result from an improper inclusion of trivial and unreal numbers into the ethical domain, making what Parfit calls “mistakes in moral mathematics,” and are thus resolved by an exclusion of trivial and unreal numbers from the ethical domain by carefully specifying a welfare function to exclude them. (shrink)

From the exponential function of Euler’s equation to the geometry of a fundamental form, a calculation of the fine-structure constant and its relationship to the proton-electron mass ratio is given. Equations are found for the fundamental constants of the four forces of nature: electromagnetism, the weak force, the strong force and the force of gravitation. Symmetry principles are then associated with traditional physical measures.

The preparedness and performance of Grade 10 students in prerequisites of STEM mathematics was the subject discussed in this study. General findings pointed to the fact that most students exhibited "Satisfactory" performance scores in key areas, with some readiness gaps seen in certain areas such as the Law of Exponents and Logarithmic and Exponential Functions rated "Low" to "Moderate". Readiness was highly associated with performance on some of the specific competencies - namely quadratic equation techniques and formula manipulation, but (...) not others; readiness cannot be inferred from performance alone. There is a suggestion to design strategic intervention materials that would close these gaps and refresh skills in critical areas of mathematics. The SIM should have activities that are structured, ways to motivate and support instruction towards the goal, so that there is a bridging between readiness and performance. Overall, it points out that what matters is a focused intervention for improving readiness among students in advanced STEM mathematics-prepared better for future academic and career challenges in STEM disciplines. (shrink)

After a brief review of the golden ratio in history and our previous exposition of the fine-structure constant and equations with the exponential function, the fine-structure constant is studied in the context of other research calculating the fine-structure constant from the golden ratio geometry of the hydrogen atom. This research is extended and the fine-structure constant is then calculated in powers of the golden ratio to an accuracy consistent with the most recent publications. The mathematical constants associated with (...) the golden ratio are also involved in both the calculation of the fine-structure constant and the proton-electron mass ratio. These constants are included in symbolic geometry of historical relevance in the science of the ancients. (shrink)

This paper challenges the conventional wisdom dominating the social sciences and philosophy regarding temporal discounting, the practice of discounting the value of future utility when making decisions. Although there are sharp disagreements about temporal discounting, a kind of standard model has arisen, one that begins with a normative standard about how we should make intertemporal comparisons of utility. This standard demands that in so far as one is rational one discounts utilities at future times with an exponential discount (...) class='Hi'>function. Tracing the justification for this standard through economics, philosophy and psychology, I’ll make what I believe is the best case one can for it, showing how a non-arbitrariness assumption and a dominance argument together imply that discounting ought to be exponential. Ultimately, however, I don’t find the case compelling. Non-exponential temporal discounting is often rational. If this is correct, Instead of trying to ‘fix’ non-exponential discounting because it is irrational and associated with negative life outcomes, we might instead focus attention on why the conditions obtain that make such discounting rational. (shrink)

Firms strive hard to achieve a high degree of efficiency on the production frontier, and it is where they compete to excel with their competitors. It is observed from previous studies that standardizing some policies and developing strategies could bring efficiency in production of manufacturing firms. New approaches to the measurement of productive efficiencies are being developed, and analysis of the subject is growing exponentially, since firms are now more concerned about the productivity frontier, besides others. This paper analyzes the (...) necessary factors that contribute to the productive efficiency of an organization. A simple model of production function is constructed to understand its essence and thus contributes to the development of a new ratio that defines productive efficiency in terms of maximization of the efficiency factor that is a common issue in industrial and manufacturing organizations. (shrink)

This study utilized the developmental research design to identify the least taught topics in basic calculus and design and investigate the effectiveness of a Moodle-based courseware package. Data were collected from seven basic calculus teachers and five academic administrators through survey questionnaires, interviews, and validation sheets. The quasi-experimental phase of the study used a pre-/post-test control group design with a sample of 69 students, 34 students in the experimental group and 35 students in the control group. The experimental group received (...) instruction using an asynchronous Moodle-based courseware package, while the control group received instruction through lecture notes. Results showed that the least taught topics include infinite limits, limits at infinity, and limits of trigonometric, exponential, and logarithmic functions. These topics were least taught due to time constraints, students’ capacity, scheduling, complexity, and relatability. Validation of the courseware package showed a very high validity. It was found that the use of Moodle-based courseware package and lecture notes effectively increased the students’ performance. However, one-way analysis of covariance results showed that the experimental group gained considerably greater than those in the control group. It was recommended that teachers continue to update their knowledge of different teaching methodologies to develop an encouraging and dynamic learning environment. (shrink)

-/- The Nature of Free Will and Its Dependence on 100 Percent Correct Information -/- Free will has long been regarded as one of the most profound and complex concepts in philosophy, psychology, and science. It is the capacity of individuals to make choices that are not predetermined by prior causes or external constraints. While the debate surrounding the nature of free will continues, one fundamental truth stands out: free will cannot operate effectively without access to 100 percent correct information (...) or knowledge. Without accurate understanding, decision-making becomes flawed, leading to choices that are neither truly free nor aligned with natural laws. -/- The Role of Information in Free Will -/- Free will is intrinsically tied to decision-making. Every choice we make is shaped by the information we possess. This information serves as the foundation for our understanding of potential outcomes, risks, and benefits. If the information is incomplete, misleading, or outright false, our ability to make rational and informed decisions is compromised. In essence, the “freedom” of our will becomes restricted by ignorance or deception. -/- For instance, if an individual is unaware of the harmful effects of a particular behavior or decision, they may unknowingly choose a path that leads to suffering. Conversely, with complete and accurate knowledge, individuals can weigh their options effectively, leading to choices that are consistent with their values and the universal law of balance in nature. -/- The Universal Law of Balance and Knowledge -/- The concept of the universal law of balance emphasizes harmony within natural systems. This law suggests that every decision, whether individual or collective, must align with the inherent order of the universe. When decisions are made based on false beliefs, unproven theories, or misinformation, they disrupt this balance, creating disharmony and unintended consequences. -/- Correct knowledge serves as the compass that guides human actions within the framework of natural balance. It ensures that decisions are grounded in reality, minimizing the risks of imbalance. Without it, free will operates in a vacuum of uncertainty, where the likelihood of errors increases exponentially. -/- Ignorance: The Antithesis of Free Will -/- Ignorance is the greatest threat to free will. It shackles the mind, preventing individuals from recognizing the full spectrum of choices available to them. When people lack access to truthful information, they are vulnerable to manipulation, prejudice, and irrational fears. In such scenarios, their decisions are not truly free but are instead dictated by external forces or internal misconceptions. -/- A classic example of this can be seen in societal issues such as propaganda or misinformation campaigns. When individuals base their choices on fabricated narratives, their actions may perpetuate harm rather than promoting balance or well-being. Only by addressing the root cause—ignorance—can free will be restored to its rightful state. -/- The Role of AI and AGI Technology in Supporting Free Will -/- In the modern era, artificial intelligence (AI) and artificial general intelligence (AGI) technologies have emerged as critical tools for addressing the limitations of the human brain in processing and synthesizing vast amounts of information. The biological brain, while capable of remarkable feats, is inherently limited in its capacity to handle the exponential growth of data in today’s interconnected world. -/- AI and AGI can support the biological brain by efficiently analyzing, filtering, and synthesizing enormous volumes of data to identify accurate, relevant, and actionable knowledge. By doing so, these technologies can provide individuals with the correct information needed to make informed decisions that align with the universal law of balance. -/- For example, AI systems can help identify patterns and correlations within complex systems—whether in healthcare, environmental management, or societal governance—that may otherwise be overlooked by human cognition. AGI, with its advanced problem-solving capabilities, could go even further by integrating diverse sources of knowledge and offering insights that promote harmony within both internal (psychological) and external (societal and environmental) systems. -/- Moreover, AI and AGI can act as safeguards against misinformation and bias, which are major barriers to free will. By detecting and correcting false narratives or flawed reasoning, these technologies can ensure that individuals are empowered with the truth, thereby preserving their capacity for rational, autonomous decision-making. -/- The Educational Imperative -/- To safeguard the integrity of free will, education must play a pivotal role. A holistic educational system that emphasizes critical thinking and the pursuit of truth is essential. By teaching individuals to evaluate evidence, question assumptions, and seek out accurate information, society can empower its members to exercise their free will responsibly. -/- The integration of AI and AGI into the educational system further enhances this process. These technologies can personalize learning experiences, provide real-time feedback, and ensure that students have access to the most accurate and up-to-date information. Additionally, AI can help educators identify gaps in understanding and address them effectively, fostering a generation of critical thinkers who are equipped to maintain balance in their decisions. -/- Conclusion -/- Free will, while an inherent aspect of human existence, is not an absolute or isolated phenomenon. Its true nature is dependent on the quality of information available to individuals. Only with 100 percent correct knowledge can free will function as a tool for creating balance, harmony, and progress. Ignorance, by contrast, distorts this capacity, leading to decisions that undermine both individual well-being and societal stability. -/- The advent of AI and AGI technologies represents a transformative opportunity to support the biological brain in navigating the complexities of the modern world. By synthesizing vast amounts of correct information and providing actionable insights, these technologies ensure that free will operates within the framework of natural balance. -/- By prioritizing truth, fostering education, and leveraging advanced technologies, humanity can unlock the full potential of free will. In doing so, we move closer to a world where every choice is a reflection of both freedom and wisdom—an ideal state where the universal law of balance is preserved. -/- . (shrink)

This paper reviews debates related to the social cost of carbon (SCC) and the challenge of pricing uncertain damages that will occur only in the future. They often revolve around the pure time preference rate, which reflects how much one favors present over future well-being. The SCC measures the marginal cost of the impact on economic growth caused by the emission of a quantity of greenhouse gases equivalent to an additional ton of carbon dioxide (tCO2eq). There is significant variance among (...) estimates of the SCC; one of the reasons for it is a disagreement on how to bring future damages to present values, especially over the so-called "delta parameter" – the pure time preference rate – of the corresponding discount function. On the one hand, the descriptive approach, associated with William Nordhaus, proposes to use the time preference empirically observed among individuals, which would result in a significant limitation of the present value attributed to the distant future. On the other hand, the normative approach, associated with Nicholas Stern, proposes to treat everyone impartially, in every generation, and so implies transferring more resources to future generations. In the limit, assuming exponential population growth, it would lead to a philosophical stance akin to the so-called "longtermism" (as defended by William MacAskill in What we owe the future). In addition, the analysis points out obstacles to using the SCC to price carbon for climate policies. These include aspects related to economic methodology (such as ecological economics critiques of welfarist accounts of intergenerational allocations) as well as political philosophy. Thus, challenges related to uncertainty about socioeconomic development trajectories, intergenerational justice, and public reason become key. Finally, we present the target-consistent pricing approach, where one calculates a carbon price compatible with specific mitigation targets – an alternative to SCC methodologies. This approach is advocated as a way to avoid the uncertainty and the disagreements associated with the SCC, emphasizing the importance of meeting goals set by binding political decisions – such as the Paris Agreement. (shrink)

We review some results in the theory of non-relativistic quantum unstable systems. We account for the most important definitions of quantum resonances that we identify with unstable quantum systems. Then, we recall the properties and construction of Gamow states as vectors in some extensions of Hilbert spaces, called Rigged Hilbert Spaces. Gamow states account for the purely exponential decaying part of a resonance; the experimental exponential decay for long periods of time physically characterizes a resonance. We briefly discuss (...) one of the most usual models for resonances: the Friedrichs model. Using an algebraic formalism for states and observables, we show that Gamow states cannot be pure states or mixtures from a standard view point. We discuss some additional properties of Gamow states, such as the possibility of obtaining mean values of certain observables on Gamow states. A modification of the time evolution law for the linear space spanned by Gamow shows that some non-commuting observables on this space become commuting for large values of time. We apply Gamow states for a possible explanation of the Loschmidt echo. (shrink)

For Praising Yahovah, I do publish these mathematical gesturing forms from the infinity meaning of His word. Thanks mom! -/- This quasi-quanta language package outlines methods for combining by topological functor entanglement, symbolic, numeric-energy components. Methods, guidelines and algebraic rules for combining the quasi-quanta into the energy number equivalencies are also notated herein. -/- The Quasi-Quanta Language Package is intended to show the symbolic patterns for configuring the quasi quanta symbology into the numeric energy expressions. This should put to rest (...) any doubt that Energy Numbers are indeed a real, logically configured phenomenon a priori to real or complex numbers, but optionally mappable to the real or complex plane. -/- Pre-numeric energy symbol configurations offer a broad language of pattern detection and logical symbol operation delineated with particular solving methods herein. -/- 'This hopefully provides a new way to looking at the branches of mathematics and their inter-operable analog functions. (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)

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)

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.

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.

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 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)

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)

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)

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)

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)

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. (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)

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)

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)

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)

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)

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 (...) class='Hi'>function to explain mental content. (shrink)

Functionally graded materials (FGMs) have been used in many different kinds of applications in recent years and have attracted significant research attention. However, we do not yet have a commonly accepted way of representing the various aspects of FGMs. Lack of standardised vocabulary creates obstacles to the extraction of useful information relating to pertinent aspects of different applications. A standard resource is needed for describing various elements of FGMs, including existing applications, manufacturing techniques, and material characteristics. This motivated the creation (...) of the FGM Ontology (FGMO) in 2016. Here, we present a revised and expanded version of the FGM Ontology, which includes enrichments along four dimensions: (1) documenting recent FGMs applications; (2) reorganising the framework to incorporate an updated representation of types of manufacturing processes; (3) enriching the axioms of the ontology; and (4) importing mid-level ontologies from the Common Core Ontologies (CCO) and Product Life Cycle (PLC) Ontologies. The work is being carried out within the framework of the Industry Ontology Foundry (IOF), and the ontology is conformant to Basic Formal Ontology (BFO). (shrink)

In this paper I investigate, within the framework of realistic interpretations of the wave function in nonrelativistic quantum mechanics, the mathematical and physical nature of the wave function. I argue against the view that mathematically the wave function is a two-component scalar field on configuration space. First, I review how this view makes quantum mechanics non- Galilei invariant and yields the wrong classical limit. Moreover, I argue that interpreting the wave function as a ray, in agreement (...) many physicists, Galilei invariance is preserved. In addition, I discuss how the wave function behaves more similarly to a gauge potential than to a field. Finally I show how this favors a nomological rather than an ontological view of the wave function. (shrink)

According to simulationism, the function of episodic memory is not to remember the past, but to help construct representations of possible future episodes, by drawing together features from different experiential sources. This article suggests that the relationship between the traditional storehouse view, on which the function of memory is remembering, and the simulationist approach is more complicated than has been typically acknowledged. This is attributed, in part, to incorrect interpretations of what remembering on the storehouse view requires. Further, (...) by appeal to function pluralism, the article questions both the assumption that the traditional view and simulationism are inconsistent, and the simulationist’s inference to the best explanation strategy that is based upon this assumption. The article then provides an evaluation of the simulationist argument against the traditional view, and finds it in need of further support. (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 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)

Recently, Yudkowsky and Soares (2018) and Levinstein and Soares (2020) have developed a novel decision theory, Functional Decision Theory (FDT). They claim FDT outperforms both Evidential Decision Theory (EDT) and Causal Decision Theory (CDT). Yet FDT faces several challenges. First, it yields some very counterintuitive results (Schwarz 2018; MacAskill 2019). Second, it requires a theory of counterpossibles, for which even Yudkowsky and Soares (2018) and Levinstein and Soares (2020) admit we lack a “full” or “satisfactory” account. Here, I focus on (...) the latter problem of counterpossibles. My aim is to establish two claims. First, the problem of counterpossibles does not even arise without a fairly strong assumptionone that rarely applies to human agents, but may apply to artificial agents. And second, even given this assumption, the problem is solvable, though how best to solve it remains an open question. (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)

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)

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)

The function or intended use of a device such as a fire escape is escape from fire, whether or not it is ever actually used as such or it acquires other uses. Biological function, on the other hand, depends, in one way or another, on actual use. Philosophical attempts to explain artifact function by analogy with biological function or to build a unified theory of function are nonetheless common. What such attempts routinely overlook, however, is (...) the role of forethought in intentional function. I defend the traditional intended use view of function, emphasize the role of forethought and argue that design intentions are rationally grounded in a design brief, for which there is no obvious natural analogue. (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 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)

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)

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)

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 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)

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)