The idea that the form of a word reflects information about its meaning has its roots in Platonic philosophy, and has been experimentally investigated for concrete, sensory-based properties since the early 20th century. Here, we provide evidence for an abstract property of ‘boundedness’ that introduces a systematic, iconic bias on the phonological expectations of a novel lexicon. We show that this abstract property is general across events and objects. In Experiment 1, we show that subjects are systematically more likely to (...) associate sign language signs that end with a gestural boundary with telic verbs (denoting events with temporal boundaries, e.g., die, arrive) and with count nouns (denoting objects with spatial boundaries, e.g., ball, coin). In Experiments 2–3, we show that this iconic mapping acts on conceptual representations, not on grammatical features. Specifically, the mapping does not carry over to psychological nouns (e.g. people are not more likely to associate a gestural boundary with idea than with knowledge). Although these psychological nouns are still syntactically encoded as either count or mass, they do not denote objects that are conceived of as having spatial boundaries. The mapping bias thus breaks down. Experiments 4–5 replicate these findings with a new set of stimuli. Finally, in Experiments 6–11, we explore possible extensions to a similar bias for spoken language stimuli, with mixed results. Generally, the results here suggest that ‘boundedness’ of words' referents (in space or time) has a powerful effect on intuitions regarding the form that the words should take. (shrink)

We argue that the pictorial nature of certain constructions in signs and in gestures explains surprising properties of their syntax. In several sign languages, the standard word order (e.g. SVO) gets turned into SOV (with preverbal arguments) when the predicate is a classifier, a distinguished construction with highly iconic properties (e.g. Pavlič, 2016). In silent gestures, participants also prefer an SOV order in extensional constructions, irrespective of the word order of the language they speak (Goldin-Meadow et al., 2008). But in (...) silent gestures and in Brazilian Sign Language (Libras), intensional constructions can override these SOV preferences, yielding SVO instead (Schouwstra & de Swart, 2014; Napoli et al., 2017). This distinction was argued to be due to iconicity: arguments are expressed before the verb if they correspond to entities that are present before the action, otherwise they follow the verb. While agreeing with this intuition, we propose that the extensional/intensional distinction is neither empirically nor theoretically appropriate. In new data from American Sign Language, we replicate the distinction among extensional classifier predicates: for _x ate up the ball_, the ball is typically seen before the eating and a preposed object is preferred; but for _x spit out the ball_, the ball is typically seen after the spitting and a postposed object is preferred, although both _eat up_ and _spit out_ are used extensionally. We extend this finding to data involving pro-speech (= speech-replacing) gestures embedded in French sentences. We argue for a Visibility Generalization according to which arguments appear before the verb if their denotations are typically visible before the action, and we develop a new formal account within a pictorial semantics for visual animations (inspired by Greenberg and Abusch). It derives the observed word order preferences, it explains how the semantics of classifier predicates combines iconic and conventional properties, and it makes a more general point: sign language semantics combines logical semantics with pictorial semantics. (shrink)

Two experiments were designed to test the hypothesis that the nature of the remember–know instructions given to participants influences whether these responses reflect different memory states or different degrees of memory confidence. Participants studied words and nonwords, a variable that has been shown to dissociate confidence from remember–know judgments and were given a set of published remember–know instructions that either emphasized know judgments as highly confident or as less confident states of recognition. Experiment 1 replicated the standard finding showing that (...) remembering and knowing were differently influenced by the word–nonword variable, whereas confidence responses were not. By contrast, Experiment 2 showed a similar pattern of data for remember–know and sure–unsure responses, thus demonstrating the importance of the instructions for interpreting the relationship between remembering and knowing and confidence. (shrink)

Apocalyptic AI, the hope that we might one day upload our minds into machines and live forever in cyberspace, has become commonplace. This view now affects robotics and AI funding, play in online games, and philosophical and theological conversations about morality and human dignity.

The remember–know paradigm is one of the most widely used procedures to examine the subjective experience associated with memory retrieval. We examined how the terminology and instructions used to describe the experiences of remembering and knowing affected remember–know judgments. In Experiment 1 we found that using neutral terms, i.e., Type A memory and Type B memory, to describe the experiences of remembering and knowing reduced remember false alarms for younger and older adults as compared to using the terms Remember and (...) Know, thereby increasing overall memory accuracy in the neutral terminology condition. In Experiment 2 we found that using what we call source-specific remember–know instructions, which were intended to constrain remember judgments to recollective experiences arising only from the study context, reduced remember hits and false alarms, and increased know hits and false alarms. Based on these data and other considerations, we conclude that researchers should use neutral terminology and source-specific instructions to collect the most accurate reports of the experiences of remembering and knowing arising from the study context. (shrink)

The belief that computers will soon become transcendently intelligent and that human beings will “upload” their minds into machines has become ubiquitous in public discussions of robotics and artificial intelligence in Western cultures. Such beliefs are the result of pervasive Judaeo-Christian apocalyptic beliefs, and they have rapidly spread through modern pop and technological culture, including such varied and influential sources as Rolling Stone, the IEEE Spectrum, and official United States government reports. They have gained sufficient credibility to enable the construction (...) of Singularity University in California. While different approaches are possible (and, indeed, are common in Japan and possibly elsewhere), this particular vision of artificial intelligence and robotics has gained ground in the West through the influence of figures such as Hans Moravec and Ray Kurzweil. Because pop-science books help frame public discussion of new sciences and technologies for individuals, corporations, and governments alike, the integration of religious and technoscientific claims made by their authors should be clear and open for public and scientific debate. As we move forward into an increasingly robotic future, we should do so aware of the ways in which a group's religious environment can help set the tone for public acceptance and use of robotic technologies. (shrink)

Minding Time: A Philosophical and Theoretical Approach to the Psychology of Time offers an innovative philosophical account of the most fundamental kinds of time representation.

Mainstream psychological research has been characterized as androcentric in its construction of males as the norm. Does an androcentric bias also characterize the professional visibility of psychologists? We examined this issue for cognitive psychology, where the gender distribution in doctoral degrees has been roughly equal for several decades. Our investigation revealed that, across all indicators surveyed, male cognitive psychologists are more visible than their female counterparts: they are over-represented in professional society governance, as editors-in-chief of leading journals in the field, (...) as Fellows in professional societies, and as recipients of prestigious senior level awards. Taken together, our findings indicate that a gender parity in doctoral degrees in cognitive psychology does not translate into a parity in professional visibility. We discuss a variety of potential reasons for the observed gender gap and suggest that, without attention to gendered structures of status and power, as noted by Shields, existing gender hierarchies may persist and be reproduced. (shrink)

Video games and virtual worlds play substantial roles in contemporary transhumanism. Many transhumanists appreciate the freedom and power that accompany these digital landscapes and recognize that they can promote transhumanist ways of thinking beyond the borders of explicitly transhumanist groups. Video games and virtual worlds enable transcendence through their design and contribute to transhumanism through the options they enable and the influence they have. Because of their significant place in transhumanism, video games and virtual worlds are thus important to the (...) study of religion and science in the twenty‐first century. (shrink)

The use of remember–know judgments to assess subjective experience associated with memory retrieval, or as measures of recollection and familiarity processes, has been controversial. In the current study we had participants think aloud during study and provide verbal reports at test for remember–know and confidence judgments. Results indicated that the vast majority of remember judgments for studied items were associated with recollection from study , but this correspondence was less likely for high-confidence judgments . Instead, high-confidence judgments were more likely (...) than remember judgments to be associated with incorrect recollection and a lack of recollection. Know judgments were typically associated with a lack of recollection , but still included recollection from the study context . Thus, although remember judgments provided fairly accurate assessments of retrieval including contextual details, know judgments did not provide accurate assessments of retrieval lacking contextual details. (shrink)

Scholarship has grown increasingly nuanced in its grappling with the intersections of religion, science, and technology but requires a new paradigm. Contemporary approaches to specific technologies reveal a wide variety of perspectives but remain too often committed to typological classification. To be vigilant of our obligation to understand and reveal, scholars in the study of religion, science, and technology can adopt a hydra‐logical stance: we can recognize that there are cultural monsters possessing scientific, technological, and religious heads. These heads may (...) work with a common agenda or they might not. They might disagree, pulling their shared body back and forth in a public commotion that lays waste to their surroundings. They might see past one another or move in tandem—purposively or not. Evaluations of climate response and AI benefit from seeing how the various heads are inseparable: indeed, cutting one off simply promotes the growth of new heads. Methodological and analytical clarity, therefore, emerges in the transition from schemes of classification to the recognition of hydras. (shrink)

The visibility of transhumanism in pop culture reveals its dramatic advance in twenty-first-century life. The more widespread the movement becomes, the more important it is to consider how transhumanism might be made relevant to global humanity. This article orients technological progress by drawing transhumanism into conversation with minjung theology from Korea. Minjung theology offers global tech culture—and its pursuit of technological salvation—an ethical foundation through attention to Han (an emotion specific to those who suffer from individual, sociopolitical, economic, and cultural (...) oppression but have been unable to express it adequately) and the lived reality of those who are often excluded from benefits of technological society. Working in the other direction, transhumanist perspectives on technology offer minjung theology an opportunity to expand its reach through the development of a transcendent theological perspective. (shrink)

This is an introduction to the Symposium on Artificial Intelligence and Apocalypticism, which resulted from a conference hosted by the Centre for the Critical Study of Apocalyptic and Millenarian Movements (CenSAMM) in Bedford, UK. The introduction provides a brief history of scholarly work in the intersections of apocalypticism and artificial intelligence and of the emergence of CenSAMM from a millenarian religious community, the Panacea Society. It concludes by pointing toward the contributions of the symposium's essays.

This monograph addresses the question of the increasing irrelevance of philosophy, which has seen scientists as well as philosophers concluding that philosophy is dead and has dissolved into the sciences. It seeks to answer the question of whether or not philosophy can still be fruitful and what kind of philosophy can be such. The author argues that from its very beginning philosophy has focused on knowledge and methods for acquiring knowledge. This view, however, has generally been abandoned in the last (...) century with the belief that, unlike the sciences, philosophy makes no observations or experiments and requires only thought. Thus, in order for philosophy to once again be relevant, it needs to return to its roots and focus on knowledge as well as methods for acquiring knowledge. Accordingly, this book deals with several questions about knowledge that are essential to this view of philosophy, including mathematical knowledge. Coverage examines such issues as the nature of knowledge; plausibility and common sense; knowledge as problem solving; modeling scientific knowledge; mathematical objects, definitions, diagrams; mathematics and reality; and more. This monograph presents a new approach to philosophy, epistemology, and the philosophy of mathematics. It will appeal to graduate students and researchers with interests in the role of knowledge, the analytic method, models of science, and mathematics and reality. (shrink)

Ayudha Puja, a South Indian festival translated as “worship of the machines,” is a dramatic example of how religion and science intertwine in political life. Across South India, but especially in the state of Karnataka, scientists and engineers celebrate the festival in offices, laboratories, and workshops by attending a puja led by a priest. Although the festival is noteworthy in many ways, one of its most immediate valences is political. In this article, we argue that Ayudha Puja normalizes Brahminical Hinduism (...) within scientific culture through the inclusion of non-Hindus and through scientists' description of the festival as “cultural” rather than “religious.”. (shrink)

Many of the computing systems programmed using Machine Learning are opaque: it is difficult to know why they do what they do or how they work. Explainable Artificial Intelligence aims to develop analytic techniques that render opaque computing systems transparent, but lacks a normative framework with which to evaluate these techniques’ explanatory successes. The aim of the present discussion is to develop such a framework, paying particular attention to different stakeholders’ distinct explanatory requirements. Building on an analysis of “opacity” from (...) philosophy of science, this framework is modeled after accounts of explanation in cognitive science. The framework distinguishes between the explanation-seeking questions that are likely to be asked by different stakeholders, and specifies the general ways in which these questions should be answered so as to allow these stakeholders to perform their roles in the Machine Learning ecosystem. By applying the normative framework to recently developed techniques such as input heatmapping, feature-detector visualization, and diagnostic classification, it is possible to determine whether and to what extent techniques from Explainable Artificial Intelligence can be used to render opaque computing systems transparent and, thus, whether they can be used to solve the Black Box Problem. (shrink)

In his new book, Carlos Alberto Torres, an internationally renowned critical theorist of education, explores the early writings of Paulo Freire whose ideas have had a tremendous and long-lasting impact on the world of pedagogy and politics. Torres analyzes Freire's works, from the 1960s and 1970s, before Freire gained worldwide recognition for his Pedagogy of the Oppressed. Offering an in-depth look into the formative thinking of Freire, Torres identifies how his ideas produced frameworks for educating global citizens, building community and (...) mutual respect, creating social responsibility, instilling an appreciation for diversity, promoting multiple literacies, and social justice education. This volume is the result of more than 3 decades of research with access to Freire's personal library and the archives of the Paulo Freire Institute, as well as the author's extensive conversations with Paulo Freire over two decades--Dr. Torres was Freire's adviser during his tenure as Secretary of Education in the Municipality of São Paulo, Brazil, 1989-1991. (shrink)

Technical achievement in laboratories requires millennia–old ritual formulations; the methodological expectations and presuppositions of scientists stem not only from investigations of the last three centuries but also from the ritual knowledge making that has governed human religion. Laboratory research is a form of human ritual open to interpretation in the manner of religious ritual. The experiments of the laboratory are fact–gathering ventures, but the integration of that knowledge into our general understanding of a universe of information networks is the process (...) of knowledge making, and it is the highest achievement of all rituals, be they religious or scientific. Ritual theory offers insight into the nature of scientific experimentation. (shrink)

This paper extends earlier work by its authors on formal aspects of the processes of contracting a theory to eliminate a proposition and revising a theory to introduce a proposition. In the course of the earlier work, Gardenfors developed general postulates of a more or less equational nature for such processes, whilst Alchourron and Makinson studied the particular case of contraction functions that are maximal, in the sense of yielding a maximal subset of the theory (or alternatively, of one of (...) its axiomatic bases), that fails to imply the proposition being eliminated. In the present paper, the authors study a broader class, including contraction functions that may be less than maximal. Specifically, they investigate "partial meet contraction functions", which are defined to yield the intersection of some nonempty family of maximal subsets of the theory that fail to imply the proposition being eliminated. Basic properties of these functions are established: it is shown in particular that they satisfy the Gardenfors postulates, and moreover that they are sufficiently general to provide a representation theorem for those postulates. Some special classes of partial meet contraction functions, notably those that are "relational" and "transitively relational", are studied in detail, and their connections with certain "supplementary postulates" of Gardenfors investigated, with a further representation theorem established. (shrink)

v. 1. Ensino secundário e médio -- v. 2. Estudos sobre o ensino primário -- Planejamento educacional e contribuições à educação do futuro.

. In this essay I point toward the difficulties inherent in ontological objectivity and seek to restore our truth claims to validity through a relational ontology and the dynamic of coimplication in signals and noise. Theological examination of art and science points toward similarities between art, religion, and science. All three have often focused upon a “metaphysics of presence,” the desire for absolute presence of the object . If we accept a relational ontology, however, we must accept that the revelation (...) of presence is always simultaneously a concealment. This helps explain technoscientific achievement without recourse to a philosophically flawed objectivity. Twentieth‐century information theory shows the impossibility of a “pure signal.” By accepting that signal and noise are permanently interconnected, we begin to see how noise makes signal possible and even how noise becomes signal . Information theory thus underscores important similarities and leads toward new approaches in aesthetics, Christian theology, and scientific research. By comparing art, religion, and science, I argue that rejecting a metaphysics of presence without rejecting presence itself allows human beings to know the world. Although religion, science, and art often seek the absolute presence of their objects, they function better without. (shrink)

The study examined whether test awareness contributes to age effects in priming. Younger and older adults were given two priming tests . Awareness was assessed using both a standard post-test questionnaire and an on-line measure. Results from the on-line awareness condition showed that, relative to older adults, younger adults showed higher levels of priming and awareness, and a stronger relationship between the two, suggesting that awareness could account for age differences in priming. In contrast, in the post-test questionnaire condition, there (...) was no age effect in word-stem completion or category production priming, despite the fact that awareness was greater in younger than older adults in the word-stem completion test and that category production priming was dependent on awareness in both age groups. These results suggest that awareness may mediate age effects in priming, but only under conditions of relatively high levels of awareness. (shrink)

Dans le cadre de la réflexion sur l’héritage philosophique des messianismes, Jacques Derrida pense la « messianicité » comme structure universelle et quasi a priori de l’expérience, tandis que Gérard Bensussan, en croisant l’œuvre derridienne, appelle « temps messianique » l’événement interruptif qui met en cause le devenir historique. Tous deux accordent un rôle majeur à la tradition juive, au-delà de toute appartenance religieuse et au-delà d’une simple sécularisation, encore qu’avec bien des différences. La lecture de cette question chez les (...) deux philosophes entend reconstruire le dialogue entre leurs positions respectives. Elle montre en fin de compte que la réflexion de Derrida s’achève sur une indécision apparente au sujet du rapport entre messianicité et messianismes, tandis que Bensussan signale cette aporie et indique la nécessité de situer le temps messianique au-delà dans la tradition du messianisme juif. (shrink)

An ethnographic approach to the South Indian festival Ayudha Puja reveals that the celebration plays a role in the construction of scientific communities. Ayudha Puja has the ability to absorb westerners, non-Hindus, and non-Brahmins into Indian science and engineering communities and is thus widely practiced in South Indian industry and academia. The practice of Ayudha Puja thus parallels what M. N. Srinivas labels “Sanskritization.” Within India, the process of Sanskritization refers to the adoption of high-caste habits and diet by upwardly (...) mobile lower-caste communities. While not actually an example of Sanskritization, participation in Ayudha Puja is analogous to that process: by joining a Hindu rite within the scientific and professional workspace, outsiders become part of local laboratory, department, or office culture. Such practices reveal the need for scholars to investigate scientific community building outside the domain of how scientists reveal new facts about the world. (shrink)

The received view of dynamical explanation is that dynamical cognitive science seeks to provide covering law explanations of cognitive phenomena. By analyzing three prominent examples of dynamicist research, I show that the received view is misleading: some dynamical explanations are mechanistic explanations, and in this way resemble computational and connectionist explanations. Interestingly, these dynamical explanations invoke the mathematical framework of dynamical systems theory to describe mechanisms far more complex and distributed than the ones typically considered by philosophers. Therefore, contemporary dynamicist (...) research reveals the need for a more sophisticated account of mechanistic explanation. (shrink)

Models developed using machine learning are increasingly prevalent in scientific research. At the same time, these models are notoriously opaque. Explainable AI aims to mitigate the impact of opacity by rendering opaque models transparent. More than being just the solution to a problem, however, Explainable AI can also play an invaluable role in scientific exploration. This paper describes how post-hoc analytic techniques from Explainable AI can be used to refine target phenomena in medical science, to identify starting points for future (...) investigations of causal relationships, and to generate possible explanations of target phenomena in cognitive science. In this way, this paper describes how Explainable AI—over and above machine learning itself—contributes to the efficiency and scope of data-driven scientific research. (shrink)

The definitive account of Aristotle's life and school This definitive biography shows that Aristotle's philosophy is best understood on the basis of a firm knowledge of his life and of the school he founded. First published in Italian, and now translated, updated, and expanded for English readers, this concise chronological narrative is the most authoritative account of Aristotle's life and his Lyceum available in any language. Gathering, distilling, and analyzing all the evidence and previous scholarship, Carlo Natali, one of (...) the world's leading Aristotle scholars, provides a masterful synthesis that is accessible to students yet filled with evidence and original interpretations that specialists will find informative and provocative. Cutting through the controversy and confusion that have surrounded Aristotle's biography, Natali tells the story of Aristotle's eventful life and sheds new light on his role in the foundation of the Lyceum. Natali offers the most detailed and persuasive argument yet for the view that the school, an important institution of higher learning and scientific research, was designed to foster a new intellectual way of life among Aristotle's followers, helping them fulfill an aristocratic ideal of the best way to use the leisure they enjoyed. Drawing a wealth of connections between Aristotle's life and thinking, Natali demonstrates how the two are mutually illuminating. For this edition, ancient texts have been freshly translated on the basis of the most recent critical editions; indexes have been added, including a comprehensive index of sources and an index to previous scholarship; and scholarship that has appeared since the book's original publication has been incorporated. (shrink)

Franz Brentano is not usually associated with mathematics. Generally, only Brentano’s discussion of the continuum and his critique of the mathematical accounts of it is treated in the literature. It is this detailed critique which suggests that Brentano had more than a superficial familiarity with mathematics. Indeed, considering the authors and works quoted in his lectures, Brentano appears well-informed and quite interested in the mathematical research of his time. I specifically address his lectures here as there is much less to (...) be found about mathematics in his published works. Besides Brentano’s own work, it is quite remarkable to see that practically all of his better-known students sooner or later produced a work on the philosophy of mathematics. This also encourages the supposition not just of a common interest in the matter, but of a common theoretical core. All this prompts the question: Can we speak of a Brentanist philosophy of mathematics? (shrink)

In a context of pervasive digitalization of the social world, both before and during the COVID-19 pandemic, the field of education has undergone major changes with the development of digital practices and settings. However, the physical presence of the subjects and the body remain something primordial and irreplaceable in traditional educational processes. Thus, it is often assumed that virtuality is opposed to the corporeal reality of the subjects involved in teaching, learning and studying. In this paper we aim to critically (...) challenge this assumption by addressing the phenomenon of virtuality in a more original sense: as a fundamental dimension of corporeality itself. Drawing on Merleau-Ponty’s phenomenological insights, we argue that the experience of the virtual is inherently embodied and fully real. We understand corporeality and virtuality as entangled and multidimensional phenomena. At the same time, this leads us to rethink the digital as only one possible medium in which virtuality can appear as inherent to embodied experience. We develop our phenomenological approach in three instances. First, we question and bracket two common assumptions about corporeality. From our critical perspective, assumptions about a disembodied digitality and a devirtualized corporeality represent extremes within which educational discourses currently move. Second, we address the inherent virtuality of embodied experience. We outline the heuristic concept of the virtual body to describe corporeality and virtuality as entangled and multidimensional phenomena that encompass extension, intercorporeality and intermediality. Finally, we make some remarks on the relationships of corporeality and virtuality considering the challenges of digital education. (shrink)

In the last few decades there has been a revival of interest in diagrams in mathematics. But the revival, at least at its origin, has been motivated by adherence to the view that the method of mathematics is the axiomatic method, and specifically by the attempt to fit diagrams into the axiomatic method, translating particular diagrams into statements and inference rules of a formal system. This approach does not deal with diagrams qua diagrams, and is incapable of accounting for the (...) role diagrams play as means of discovery and understanding. Alternatively, this paper purports to show that the view that the method of mathematics is the analytic method is capable of dealing with diagrams qua diagrams, and of accounting for such role. (shrink)

Bayesian reverse-engineering is a research strategy for developing three-level explanations of behavior and cognition. Starting from a computational-level analysis of behavior and cognition as optimal probabilistic inference, Bayesian reverse-engineers apply numerous tweaks and heuristics to formulate testable hypotheses at the algorithmic and implementational levels. In so doing, they exploit recent technological advances in Bayesian artificial intelligence, machine learning, and statistics, but also consider established principles from cognitive psychology and neuroscience. Although these tweaks and heuristics are highly pragmatic in character and (...) are often deployed unsystematically, Bayesian reverse-engineering avoids several important worries that have been raised about the explanatory credentials of Bayesian cognitive science: the worry that the lower levels of analysis are being ignored altogether; the challenge that the mathematical models being developed are unfalsifiable; and the charge that the terms ‘optimal’ and ‘rational’ have lost their customary normative force. But while Bayesian reverse-engineering is therefore a viable and productive research strategy, it is also no fool-proof recipe for explanatory success. (shrink)

The philosophy of mathematics of the last few decades is commonly distinguished into mainstream and maverick, to which a ‘third way’ has been recently added, the philosophy of mathematical practice. In this paper the limitations of these trends in the philosophy of mathematics are pointed out, and it is argued that they are due to the fact that all of them are based on a top-down approach, that is, an approach which explains the nature of mathematics in terms of some (...) general unproven assumption. As an alternative, a bottom-up approach is proposed, which explains the nature of mathematics in terms of the activity of real individuals and interactions between them. This involves distinguishing between mathematics as a discipline and the mathematics embodied in organisms as a result of biological evolution, which however, while being distinguished, are not opposed. Moreover, it requires a view of mathematical proof, mathematical definition and mathematical objects which is alternative to the top-down approach. (shrink)

The philosophical conception of mechanistic explanation is grounded on a limited number of canonical examples. These examples provide an overly narrow view of contemporary scientific practice, because they do not reflect the extent to which the heuristic strategies and descriptive practices that contribute to mechanistic explanation have evolved beyond the well-known methods of decomposition, localization, and pictorial representation. Recent examples from evolutionary robotics and network approaches to biology and neuroscience demonstrate the increasingly important role played by computer simulations and mathematical (...) representations in the epistemic practices of mechanism discovery and mechanism description. These examples also indicate that the scope of mechanistic explanation must be re-examined: With new and increasingly powerful methods of discovery and description comes the possibility of describing mechanisms far more complex than traditionally assumed. (shrink)

The terms of a mathematical problem become precise and concise if they are expressed in an appropriate notation, therefore notations are useful to mathematics. But are notations only useful, or also essential? According to prevailing view, they are not essential. Contrary to this view, this paper argues that notations are essential to mathematics, because they may play a crucial role in mathematical discovery. Specifically, since notations may consist of symbolic notations, diagrammatic notations, or a mix of symbolic and diagrammatic notations, (...) notations may play a crucial role in mathematical discovery in different ways. Some examples are given to illustrate these ways. (shrink)