BackgroundThe trend toward open science increases the pressure on authors to provide access to the source code and data they used to compute the results reported in their scientific papers. Since sharing materials reproducibly is challenging, several projects have developed solutions to support the release of executable analyses alongside articles.MethodsWe reviewed 11 applications that can assist researchers in adhering to reproducibility principles. The applications were found through a literature search and interactions with the reproducible research community. An application was included (...) in our analysis if it was actively maintained at the time the data for this paper was collected, supports the publication of executable code and data, is connected to the scholarly publication process. By investigating the software documentation and published articles, we compared the applications across 19 criteria, such as deployment options and features that support authors in creating and readers in studying executable papers.ResultsFrom the 11 applications, eight allow publishers to self-host the system for free, whereas three provide paid services. Authors can submit an executable analysis using Jupyter Notebooks or R Markdown documents. All approaches provide features to assist readers in studying the materials, e.g., one-click reproducible results or tools for manipulating the analysis parameters. Six applications allow for modifying materials after publication.ConclusionsThe applications support authors to publish reproducible research predominantly with literate programming. Concerning readers, most applications provide user interfaces to inspect and manipulate the computational analysis. The next step is to investigate the gaps identified in this review, such as the costs publishers have to expect when hosting an application, the consideration of sensitive data, and impacts on the review process. (shrink)

Text-generative AI-systems have become important semantic agents with ChatGPT. We conducted a series of experiments to learn what teachers’ conceptions of text-generative AI are in relation to philosophical texts. In our main experiment, using mixed methods, we had twenty-four high school students write philosophical essays, which we then randomized to essays with the same command from ChatGPT. We had ten prospective teachers assess these essays. They were able to tell whether it was an AI or student essay with 78.7 percent (...) accuracy, which is better than the Open AI Classifier. Interestingly, however, they used criteria like argumentative and logical flawlessness and neutrality. We concluded from this that they are using an inverted Turing test and are no longer looking for rationality in machines but for irrationality in humans. (shrink)

This 44-chapter volume tackles a quickly-evolving field of inquiry, mapping the existing discourse as part of a general attempt to place current developments in historical context; at the same time, breaking new ground in taking on novel subjects and pursuing fresh approaches. The term "A.I." is used to refer to a broad range of phenomena, from machine learning and data mining to artificial general intelligence. The recent advent of more sophisticated AI systems, which function with partial or full autonomy and (...) are capable of tasks which require learning and 'intelligence', presents difficult ethical questions, and has drawn concerns from many quarters about individual and societal welfare, democratic decision-making, moral agency, and the prevention of harm. This work ranges from explorations of normative constraints on specific applications of machine learning algorithms today-in everyday medical practice, for instance-to reflections on the (potential) status of AI as a form of consciousness with attendant rights and duties and, more generally still, on the conceptual terms and frameworks necessarily to understand tasks requiring intelligence, whether "human" or "A.I.". (shrink)

I show that the recent account of levels in neuroscience proposed by Craver and Bechtel is unsatisfactory since it fails to provide a plausible criterion for being at the same level and is incompatible with Craver and Bechtel’s account of downward causation. Furthermore, I argue that no distinct notion of levels is needed for analyzing explanations and causal issues in neuroscience: it is better to rely on more well-defined notions such as composition and scale. One outcome of this is that (...) apparent cases of downward causation can be analyzed away. (shrink)

This article introduces an “ordonomic” approach to corporate citizenship. We believe that ordonomics offers a conceptual framework for analyzing both the social structure and the semantics of moral commitments. We claim that such an analysis can provide theoretical guidance for the changing role of business in society, especially in regard to the expectation and trend that businesses take a political role and act as corporate citizens. The systematicraison d'êtreof corporate citizenship is that business firms can and—judged by the criterion of (...) prudent self-interest—“should” take on an active role in rule-finding discourses and rule-setting processes with the intent of realizing a win-win outcome of the economic game. We identify—and illustrate—four ways that corporate citizens can employ moral commitments as a factor of production to enhance their processes of economic value creation. (shrink)

The argument from inductive risk is considered to be one of the strongest challenges for value-free science. A great part of its appeal lies in the idea that even an ideal epistemic agent—the “perfect scientist” or “scientist qua scientist”—cannot escape inductive risk. In this paper, I scrutinize this ambition by stipulating an idealized Bayesian decision setting. I argue that inductive risk does not show that the “perfect scientist” must, descriptively speaking, make non-epistemic value-judgements, at least not in a way that (...) undermines the value-free ideal. However, the argument is more successful in showing that there are cases where the “perfect scientist” should, normatively speaking, use non-epistemic values. I also show that this is possible without creating problems of illegitimate prescription and wishful thinking. Thus, while inductive risk does not refute value-freedom completely, it still represents a powerful critique of value-free science. (shrink)

Moral philosophers and psychologists often assume that people judge morally lucky and morally unlucky agents differently, an assumption that stands at the heart of the Puzzle of Moral Luck. We examine whether the asymmetry is found for reflective intuitions regarding wrongness, blame, permissibility, and punishment judg- ments, whether people’s concrete, case-based judgments align with their explicit, abstract principles regarding moral luck, and what psychological mechanisms might drive the effect. Our experiments produce three findings: First, in within-subjects experiments favorable to reflective (...) deliberation, the vast majority of people judge a lucky and an unlucky agent as equally blameworthy, and their actions as equally wrong and permissible. The philosophical Puzzle of Moral Luck, and the challenge to the very possibility of systematic ethics it is frequently taken to engender, thus simply do not arise. Second, punishment judgments are significantly more outcome- dependent than wrongness, blame, and permissibility judgments. While this constitutes evidence in favor of current Dual Process Theories of moral judgment, the latter need to be qualified: punishment and blame judgments do not seem to be driven by the same process, as is commonly argued in the literature. Third, in between-subjects experiments, outcome has an effect on all four types of moral judgments. This effect is mediated by negligence ascriptions and can ultimately be explained as due to differing probability ascriptions across cases. (shrink)

In der 1970 gegr ndeten Reihe erscheinen Arbeiten, die philosophiehistorische Studien mit einem systematischen Ansatz oder systematische Studien mit philosophiehistorischen Rekonstruktionen verbinden. Neben deutschsprachigen werden auch englischsprachige Monographien ver ffentlicht. Gr ndungsherausgeber sind: Erhard Scheibe (Herausgeber bis 1991), G nther Patzig (bis 1999) und Wolfgang Wieland (bis 2003). Von 1990 bis 2007 wurde die Reihe von J rgen Mittelstra mitherausgegeben.

The current humanitarian use of drones is focused on two applications: disaster mapping and medical supply delivery. In response to the growing interest in drone deployment in the aid sector, we sought to develop a resource to support value sensitivity in humanitarian drone activities. Following a bottom-up approach encompassing a comprehensive literature review, two empirical studies, a review of guidance documents, and consultations with experts, this work illuminates the nature and scope of ethical challenges encountered by humanitarian organizations embarking upon (...) innovation programmes. The Framework for the Ethics Assessment of Humanitarian Drones (FEAHD) identifies five values and five key questions related to ethical considerations along the decision chain of humanitarian drone activities. It fills a gap between high-level, principle-based guidance related to humanitarian innovation, and detailed operation-oriented checklists for projects involving the use of drones. In this way, the FEAHD contributes to support value sensitivity in the humanitarian use of drones. (shrink)

I identify two reasons for believing in the objectivity of mathematical knowledge: apparent objectivity and applications in science. Focusing on arithmetic, I analyze platonism and cognitive nativism in terms of explaining these two reasons. After establishing that both theories run into difficulties, I present an alternative epistemological account that combines the theoretical frameworks of enculturation and cumulative cultural evolution. I show that this account can explain why arithmetical knowledge appears to be objective and has scientific applications. Finally, I will argue (...) that, while this account is compatible with platonist metaphysics, it does not require postulating mind-independent mathematical objects. (shrink)

In very general terms, an agent is a being with the capacity to act, and 'agency' denotes the exercise or manifestation of this capacity. The philosophy of action provides us with a standard conception and a standard theory of action. The former construes action in terms of intentionality, the latter explains the intentionality of action in terms of causation by the agent’s mental states and events. From this, we obtain a standard conception and a standard theory of agency. There are (...) alternative conceptions of agency, and it has been argued that the standard theory fails to capture agency. Further, it seems that genuine agency can be exhibited by beings that are not capable of intentional action, and it has been argued that agency can and should be explained without reference to causally efficacious mental states and events. Debates about the nature of agency have flourished over the past few decades in philosophy and in other areas of research. In philosophy, the nature of agency is an important issue in the philosophy of mind, the philosophy of psychology, the debates on free will and moral responsibility, in ethics, meta-ethics, and in the debates on the nature of reasons and practical rationality. For the most part, this entry focuses on conceptual and metaphysical questions concerning the nature of agency. In the final sections, it provides an overview of empirically informed accounts of the sense of agency and of various empirical challenges to the commonsense assumption that our reasons and our conscious intentions make a real difference to how we act. (shrink)

The basic human ability to treat quantitative information can be divided into two parts. With proto-arithmetical ability, based on the core cognitive abilities for subitizing and estimation, numerosities can be treated in a limited and/or approximate manner. With arithmetical ability, numerosities are processed (counted, operated on) systematically in a discrete, linear, and unbounded manner. In this paper, I study the theory of enculturation as presented by Menary (2015) as a possible explanation of how we make the move from the proto-arithmetical (...) ability to arithmetic proper. I argue that enculturation based on neural reuse provides a theoretically sound and fruitful framework for explaining this development. However, I show that a comprehensive explanation must be based on valid theoretical distinctions and involve several stages in the development of arithmetical knowledge. I provide an account that meets these challenges and thus leads to a better understanding of the subject of enculturation. (shrink)

Like all causal theories in philosophy, the causal theory of action is plagued by the problem of deviant causal chains. I have proposed a solution on the basis of the assumption that mental states and events are causally efficacious in virtue of their contents. This solution has been questioned by Torbjörn Tännsjö (2009). First, I will reply to the objection, and then I will discuss Tännsjö’s alternative.

Intellectual humility is an interesting but underexplored disposition. The claim “I am (intellectually) humble” seems paradoxical in that someone who has the disposition in question would not typically volunteer it. There is an explanatory gap between the meaning of the sentence and the meaning the speaker expresses by uttering it. We therefore suggest analyzing intellectual humility semantically, using a psycholexical approach that focuses on both synonyms and antonyms of ‘intellectual humility’. We present a thesaurus-based method to map the semantic space (...) of intellectual humility as a heuristic to support philosophical and psychological analysis of this disposition. We find three semantic clusters that compose intellectual humility: the sensible self, the discreet self, and the inquisitive self; likewise, we find three clusters that compose its contraries: the overrated self, the underrated other, and the underrated self. (shrink)

Beck presents an outline of the procedure of bootstrapping of integer concepts, with the purpose of explicating the account of Carey. According to that theory, integer concepts are acquired through a process of inductive and analogous reasoning based on the object tracking system, which allows individuating objects in a parallel fashion. Discussing the bootstrapping theory, Beck dismisses what he calls the "deviant-interpretation challenge"—the possibility that the bootstrapped integer sequence does not follow a linear progression after some point—as being general to (...) any account of inductive learning. While the account of Carey and Beck focuses on the OTS, in this paper I want to reconsider the importance of another empirically well-established cognitive core system for treating numerosities, namely the approximate number system. Since the ANS-based account offers a potential alternative for integer concept acquisition, I show that it provides a good reason to revisit the deviant-interpretation challenge. Finally, I will present a hybrid OTS-ANS model as the foundation of integer concept acquisition and the framework of enculturation as a solution to the challenge. (shrink)

The principles of biomedical ethics – autonomy, non-maleficence, beneficence, and justice – are of paradigmatic importance for framing ethical problems in medicine and for teaching ethics to medical students and professionals. In order to underline this significance, Tom L. Beauchamp and James F. Childress base the principles in the common morality, i.e. they claim that the principles represent basic moral values shared by all persons committed to morality and are thus grounded in human moral psychology. We empirically investigated the relationship (...) of the principles to other moral and non-moral values that provide orientations in medicine. By way of comparison, we performed a similar analysis for the business & finance domain. (shrink)

Linnebo in 2018 argues that abstract objects like numbers are “thin” because they are only required to be referents of singular terms in abstraction principles, such as Hume's principle. As the specification of existence claims made by analytic truths (the abstraction principles), their existence does not make any substantial demands of the world; however, as Linnebo notes, there is a potential counter-argument concerning infinite regress against introducing objects this way. Against this, he argues that vicious regress is avoided in the (...) account of arithmetic based on Hume's principle because we are specifying numbers in terms of the concept of equinumerosity, or its ordinal equivalent. But far from being only a matter for philosophy, this implies a distinct empirical prediction: in cognitive development, the principle of equinumerosity is primary to number concepts. However, by analysing and expanding on the bootstrapping theory of Carey in 2009, I argue in this paper that there are good reasons to think that the development could be the other way around: possessing numerosity concepts may precede grasping the principle of equinumerosity. I propose that this analysis of early numerical cognition can also help us understand what numbers as thin objects are like, moving away from Platonist interpretations. (shrink)

Are our beliefs justified only relatively to a specific culture or society? Is it possible to give reasons for the superiority of our scientific, epistemic methods? Markus Seidel sets out to answer these questions in his critique of epistemic relativism. Focusing on the work of the most prominent, explicitly relativist position in the sociology of scientific knowledge – so-called 'Edinburgh relativism' or the 'Strong Programme' –, he scrutinizes the key arguments for epistemic relativism from a philosophical perspective: underdetermination and (...) norm-circularity. His main negative result is that these arguments fall short of establishing epistemic relativism. -/- Despite arguing for epistemic absolutism, Seidel aims to provide an account of non-relative justification that nevertheless integrates the basic, correct intuition of the epistemic relativist. His main positive result is that the epistemic absolutist can very well accept the idea that people using different standards of justification can be equally justified in holding their beliefs: Rational disagreement, he maintains, is perfectly possible. -/- The book provides a detailed critique of relativism in the sociology of scientific knowledge and beyond. With its constructive part it aims at making conciliatory steps in a highly embittered discussion between sociology and philosophy of science. (shrink)

The idea of levels of organization plays a central role in the philosophy of the life sciences. In this article, I first examine the explanatory goals that have motivated accounts of levels of organization. I then show that the most state-of-the-art and scientifically plausible account of levels of organization, the account of levels of mechanism proposed by Bechtel and Craver, is fundamentally problematic. Finally, I argue that the explanatory goals can be reached by adopting a deflationary approach, where levels of (...) organization give way to more well-defined and fundamental notions, such as scale and composition. (shrink)

Metaphysics and science have a long but troubled relationship. In the twentieth century the Logical Positivists argued metaphysics was irrelevant and that philosophy should be guided by science. However, metaphysics and science attempt to answer many of the same, fundamental questions: What are laws of nature? What is causation? What are natural kinds? -/- In this book, Markus Schrenk examines and explains the central questions and problems in the metaphysics of science. He reviews the development of the field from (...) the early modern period through to the latest research, systematically assessing key topics including -/- dispositions, counterfactual conditionals, laws of nature, causation, natural kinds, essence, necessity. -/- With the addition of chapter summaries and annotated further reading, Metaphysics of Science is a much-needed, clear and informative survey of this exciting area of philosophical research. It is essential reading for students and scholars of philosophy of science and metaphysics. (shrink)

Zeit und Zeitlichkeit erscheinen für die Natur und die Existenz des Menschen grundlegend und fordern zugleich sein Denken wesentlich heraus. Das gilt in besonderer Weise für die Epoche des Mittelalters, in der sich Philosophen und Theologen, sowohl in Christentum als auch Islam, intensiv mit dem Thema auseinandergesetzt haben. Das daraus hervorgegangene, vielfältige und interessante Material ist oft als Gefüge aus naturphilosophischen, ethischen und religiösen Komponenten zu charakterisieren und eröffnet überraschende Einblicke - gerade in vergleichender Perspektive. Zu diesem Zweck wurden in (...) der vorliegenden Studie die zwei Denker al-Gazali ( 1111 Tus) und Meister Eckhart ( 1328 Avignon?) ausgewählt und gegenübergestellt. Nach der historischen bzw. ideengeschichtlichen Kontextualisierung beider werden im Detailzugriff auf die Texte die wichtigsten Punkte zu den jeweiligen Zeit- und Ewigkeitsvorstellungen herausgearbeitet und die Kategorien zu ihrer Gruppierung gebildet. Schliesslich werden im Vergleich die Gemeinsamkeiten und Unterschiede benannt. Die zwei Hauptthesen, denen die Arbeit dabei folgt, sind erstens die relative Ähnlichkeit der Referenzautoren, deren Zeitvorstellungen und spiritueller Ausrichtung. Und zweitens daran anknüpfend die Annahme, dass bei intellektueller und lebenspraktischer Vertiefung der Religion kulturelle und religionsspezifische Unterschiede in den Hinter- und universale Motive in den Vordergrund rücken."-- Back cover. (shrink)

This article evaluates alternative models for explaining human behavior. In particular, it compares the resourceful, evaluative, maximizing model (REMM) with the economic (or money maximizing) model of human behavior. The theoretical framework is developed to enhance our understanding of "individual value creation" and to seek an economically rational explanation to: Why Warren Buffett is giving his money away to charity? The article develops a framework of biological, material, and immaterial sources of value. The article additionally extends the existing REMM and (...) finds several economically rational reasons for him to give away his money including the present value of help and goodwill, gained control, and lowered transaction costs. (shrink)

Recent years have seen an explosion of empirical data concerning arithmetical cognition. In this paper that data is taken to be philosophically important and an outline for an empirically feasible epistemological theory of arithmetic is presented. The epistemological theory is based on the empirically well-supported hypothesis that our arithmetical ability is built on a protoarithmetical ability to categorize observations in terms of quantities that we have already as infants and share with many nonhuman animals. It is argued here that arithmetical (...) knowledge developed in such a way cannot be totally conceptual in the sense relevant to the philosophy of arithmetic, but neither can arithmetic understood to be empirical. Rather, we need to develop a contextual a priori notion of arithmetical knowledge that preserves the special mathematical characteristics without ignoring the roots of arithmetical cognition. Such a contextual a priori theory is shown not to require any ontologically problematic assumptions, in addition to fitting well within a standard framework of general epistemology. (shrink)

This paper concerns anti-Humean intuitions about connections in nature. It argues for the existence of a de re link that is not necessity.Some anti-Humeans tacitly assume that metaphysical necessity can be used for all sorts of anti-Humean desires. Metaphysical necessity is thought to stick together whatever would be loose and separate in a Hume world, as if it were a kind of universal superglue.I argue that this is not feasible. Metaphysical necessity might connect synchronically co-existent properties—kinds and their essential features, (...) for example—but it is difficult to see how it could also serve as the binding force for successions of events. That is, metaphysical necessity seems not to be fit for diachronic, causal affairs in which causal laws, causation, or dispositions are involved. A different anti-Humean connection in nature has to do that job.My arguments focus mainly on a debate which has been the battleground for Humean vs. anti-Humean intuitions for many decades—namely, the analysis of dispositional predicates—yet I believe (but do not argue here) that the arguments generalise to causation and causal laws straightforwardly. (shrink)

In this paper I study the development of arithmetical cognition with the focus on metaphorical thinking. In an approach developing on Lakoff and Núñez, I propose one particular conceptual metaphor, the Process → Object Metaphor, as a key element in understanding the development of mathematical thinking.

This paper proposes and defends an account of what it is to act for reasons. In the first part, I will discuss the desire-belief and the deliberative model of acting for reasons. I will argue that we can avoid the weaknesses and retain the strengths of both views, if we pursue an alternative according to which acting for reasons involves taking something as a reason. In the main part, I will develop an account of what it is to take something (...) as a reason for action. On the basis of this, I will then offer a new account of what it is to act for reasons. (shrink)

Previous research in Explainable Artificial Intelligence (XAI) suggests that a main aim of explainability approaches is to satisfy specific interests, goals, expectations, needs, and demands regarding artificial systems (we call these “stakeholders' desiderata”) in a variety of contexts. However, the literature on XAI is vast, spreads out across multiple largely disconnected disciplines, and it often remains unclear how explainability approaches are supposed to achieve the goal of satisfying stakeholders' desiderata. This paper discusses the main classes of stakeholders calling for explainability (...) of artificial systems and reviews their desiderata. We provide a model that explicitly spells out the main concepts and relations necessary to consider and investigate when evaluating, adjusting, choosing, and developing explainability approaches that aim to satisfy stakeholders' desiderata. This model can serve researchers from the variety of different disciplines involved in XAI as a common ground. It emphasizes where there is interdisciplinary potential in the evaluation and the development of explainability approaches. (shrink)

The paper develops an account of minimal traces devoid of representational content and exploits an analogy to a predictive processing framework of perception. As perception can be regarded as a prediction of the present on the basis of sparse sensory inputs without any representational content, episodic memory can be conceived of as a “prediction of the past” on the basis of a minimal trace, i.e., an informationally sparse, merely causal link to a previous experience. The resulting notion of episodic memory (...) will be validated as a natural kind distinct from imagination. This trace minimalist view contrasts with two theory camps dominating the philosophical debate on memory. On one side, we face versions of the Causal Theory that hold on to the idea that episodic remembering requires a memory trace that causally links the event of remembering to the event of experience and carries over representational content from the content of experience to the content of remembering. The Causal Theory, however, fails to account for the epistemic generativity of episodic memory and is psychologically and information-theoretically implausible. On the other side, a new camp of simulationists is currently forming up. Motivated by empirical and conceptual deficits of the Causal Theory, they reject not only the necessity of preserving representational content, but also the necessity of a causal link between experience and memory. They argue that remembering is nothing but a peculiar form of imagination, peculiar only in that it has been reliably produced and is directed towards an episode of one’s personal past. Albeit sharing their criticism of the Causal Theory and, in particular, rejecting its demand for an intermediary carrier of representational content, the paper argues that a causal connection to experience is still necessary to fulfill even the minimal requirements of past-directedness and reliability. (shrink)

This paper offers a critique of sustainability reporting and, in particular, a critique of the modern disconnect between the practice of sustainability reporting and what we consider to be the urgent issue of our era: sustaining the life-supporting ecological systems on which humanity and other species depend. Tracing the history of such reporting developments, we identify and isolate the concept of the ‘triple bottom line’ (TBL) as a core and dominant idea that continues to pervade business reporting, and business engagement (...) with sustainability. Incorporating an entity’s economic, environmental and social performance indicators into its management and reporting processes, we argue, has become synonymous with corporate sustainability; in the process, concern for ecology has become sidelined. Moreover, this process has become reinforced and institutionalised through SustainAbility’s biennial benchmarking reports, KPMG’s triennial surveys of practice, initiatives by the accountancy profession and, particularly, the Global Reporting Initiative (GRI)’s sustainability reporting guidelines. We argue that the TBL and the GRI are insufficient conditions for organizations contributing to the sustaining of the Earth’s ecology. Paradoxically, they may reinforce business-as-usual and greater levels of un-sustainability. (shrink)

Robustness is often presented as a guideline for distinguishing the true or real from mere appearances or artifacts. Most of recent discussions of robustness have focused on the kind of derivational robustness analysis introduced by Levins, while the related but distinct idea of robustness as multiple accessibility, defended by Wimsatt, has received less attention. In this paper, I argue that the latter kind of robustness, when properly understood, can provide justification for ontological commitments. The idea is that we are justified (...) in believing that things studied by science are real insofar as we have robust evidence for them. I develop and analyze this idea in detail, and based on concrete examples show that it plays an important role in science. Finally, I demonstrate how robustness can be used to clarify the debate on scientific realism and to formulate new arguments. (shrink)

This article aims to classify those reducts of expansions of (Q, <) by unary predicates which eliminate quantifiers, and in particular to show that, up to interdefinability, there are only finitely many for a given language. Equivalently, we wish to classify the closed subgroups of Sym(Q) containing the group of all automorphisms of (Q, <) fixing setwise certain subsets. This goal is achieved for expansions by convex predicates, yielding expansions by constants as a special case, and for the expansion by (...) a dense, co-dense predicate. Partial results are obtained in the general setting of several dense predicates. (shrink)

Why would we want to develop artificial human-like arithmetical intelligence, when computers already outperform humans in arithmetical calculations? Aside from arithmetic consisting of much more than mere calculations, one suggested reason is that AI research can help us explain the development of human arithmetical cognition. Here I argue that this question needs to be studied already in the context of basic, non-symbolic, numerical cognition. Analyzing recent machine learning research on artificial neural networks, I show how AI studies could potentially shed (...) light on the development of human numerical abilities, from the proto-arithmetical abilities of subitizing and estimating to counting procedures. Although the current results are far from conclusive and much more work is needed, I argue that AI research should be included in the interdisciplinary toolbox when we try to explain the development and character of numerical cognition and arithmetical intelligence. This makes it relevant also for the epistemology of mathematics. (shrink)