The prime number theorem, established by Hadamard and de la Vallée Poussin independently in 1896, asserts that the density of primes in the positive integers is asymptotic to 1/ln x. Whereas their proofs made serious use of the methods of complex analysis, elementary proofs were provided by Selberg and Erdos in 1948. We describe a formally verified version of Selberg's proof, obtained using the Isabelle proof assistant.

1.1 Some examples of rule induction on permutations . . . . . . . 6 1.2 Ways of making new permutations . . . . . . . . . . . . . . . 7 1.3 Further results . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Removing elements . . . . . . . . . . (...) . . . . . . . . . . . . . . 8.. (shrink)

We are working on formalizing a proof of the prime number theorem using Isabelle/HOL. In support of this project we formalized a very general notion of O notation.

This paper examines the creation of what I have called “The Other Average Man” of nineteenth-century science. This other average man was created during the course of the career of the Belgian polymath Adolphe Quetelet and his development of physique sociale and the controversial l’homme moyen. Rather than discuss Quetelet’s abstract average man, which has received considerable attention, the paper focuses on the real average men that Quetelet imagined would do the work of providing data for physique sociale. To do (...) so, it investigates three moments in Quetelet’s administrative career in Belgium: his early life in Ghent and Brussels during the brief polity of the United Kingdom of the Netherlands, his remarkable transformation of the Académie Royale de Belgique in the 1820s, and an 1846 debate at the Academy on the possible determinism entailed by Quetelet’s statistical account of human behavior. These stories not only point to the creation of another average man in Quetelet’s social physics, but also demonstrate the importance of Belgium’s unique historical context for understanding one of nineteenth-century Europe’s most enduring contributions to the social sciences. (shrink)

Predictable polarization is everywhere: we can often predict how people’s opinions, including our own, will shift over time. Extant theories either neglect the fact that we can predict our own polarization, or explain it through irrational mechanisms. They needn’t. Empirical studies suggest that polarization is predictable when evidence is ambiguous, that is, when the rational response is not obvious. I show how Bayesians should model such ambiguity and then prove that—assuming rational updates are those which obey the value of evidence—ambiguity (...) is necessary and sufficient for the rationality of predictable polarization. The main theoretical result is that there can be a series of such updates, each of which is individually expected to make you more accurate, but which together will predictably polarize you. Polarization results from asymmetric increases in accuracy. This mechanism is not only theoretically possible, but empirically plausible. I argue that cognitive search—searching a cognitively accessible space for a particular item—often yields asymmetrically ambiguous evidence, I present an experiment supporting its polarizing effects, and I use simulations to show how it can explain two of the core causes of polarization: confirmation bias and the group polarization effect. (shrink)

Prediction-based accounts of language acquisition have the potential to explain several different effects in child language acquisition and adult language processing. However, evidence regarding the developmental predictions of such accounts is mixed. Here, we consider several predictions of these accounts in two large-scale developmental studies of syntactic priming of the English dative alternation. Study 1 was a cross-sectional study (N = 140) of children aged 3−9 years, in which we found strong evidence of abstract priming and the lexical boost, but (...) little evidence that either effect was moderated by age. We found weak evidence for a prime surprisal effect; however, exploratory analyses revealed a protracted developmental trajectory for verb-structure biases, providing an explanation as for why prime surprisal effects are more elusive in developmental populations. In a longitudinal study (N = 102) of children in tightly controlled age bands at 42, 48, and 54 months, we found priming effects emerged on trials with verb overlap early but did not observe clear evidence of priming on trials without verb overlap until 54 months. There was no evidence of a prime surprisal effect at any time point and none of the effects were moderated by age. The results relating to the emergence of the abstract priming and lexical boost effects are consistent with prediction-based models, while the absence of age-related effects appears to reflect the structure-specific challenges the dative presents to English-acquiring children. Overall, our complex pattern of findings demonstrates the value of developmental data sets in testing psycholinguistic theory. (shrink)

Abstract:Qi has been both understood separately as substance and as field. This essay argues that qi in the Zhuangzi is both substance and field together. This qi field-substance is bidimensional where its vertical axis is that of substance and its horizontal axis that of field. This essay argues that the vertical dimension does not imply a substance dualism but a holism where qi differs in degrees of refinement; it argues that the horizontal dimension is composed of interrelated yinyang forces that (...) constitute an "empty" field. It also argues that at the center of this qi field-substance is the heart-mind and the body and, by drawing on rich resonances between the Zhuangzi and phenomenology, that human beings bring the fields of qi that they are situated in into certain coherences. (shrink)

The goal of this article is to motivate the idea of a social reason and demonstrate its usefulness in social theorizing. For example, in a society that values getting married young, the fact that one is young is a reason to get married. In racist and sexist societies, we have social reasons to be racist and sexist. Social reasons give rise to social requirements and obligations, where these requirements often conflict with prudential and moral requirements. My application of reasons to (...) social philosophy parallels Charles Mills' and Carole Pateman's applications of social contract theory to political philosophy. While they use social contract theory to make sense of patriarchy and white supremacy, I use the theory of normative reasons to make sense of social injustice. The theory of normative reasons meets non-ideal theory. (shrink)

A definition of emotion common to the affective sciences is an urgent desideratum. Lack of such a definition is a constant source of numerous misunderstandings and a series of mostly fruitless debates. There is little hope that there ever will be agreement on a common definition of emotion, given the sacred traditions of the disciplines involved and the egos of the scholars working in these disciplines. Our aim here is more modest. We propose a list of elements for a working (...) definition of emotion and discuss the justification for the inclusion of elements from our respective perspectives (philosophy and psychology). This working partial definition may at least serve as a litmus test to examine theories of emotion, old and new, across disciplinary boundaries. (shrink)

The potential for financial conflicts of interest (COIs) to damage the credibility of scientific research has become a significant social concern, especially in the wake of high-profile incidents involving the pharmaceutical, tobacco, fossil-fuel, and chemical industries. Scientists and policy makers have debated whether the presence of financial COIs should count as a reason for treating research with suspicion or whether research should instead be evaluated solely based on its scientific quality. This paper examines a recent proposal to develop criteria for (...) evaluating the credibility of research without considering its source of funding. It concludes that proposals of this sort are likely to be either ineffective or impractical in many cases. Nevertheless, this does not imply that all research funded by those with an interest in the outcome must be placed under a cloud of suspicion; there are conditions under which research is at much more serious risk of being corrupted than in other cases, and attention to these conditions can guide productive responses to financial COIs. (shrink)

Introducing analytic philosophy -- F.H. Bradley and monistic idealism -- G.E. Moore on idealism, the good, and common sense -- Gottlob Frege : logic and the philosophy of language -- Bertrand Russell on relations, descriptions, and knowledge -- E.E. Constance Jones on language and logic -- Ludwig Wittgenstein on language and philosophy -- Logical empiricism : meaning, metaphysics, and mathematics -- Susan Stebbing on logic, language, and analysis -- W.V.O Quine on analyticity and ontology -- Analytic philosophy since 1950.

Husserl seems to have devoted roughly equal amounts of energy and pages to the description of perception, judgement, and imagination. By “description,” he meant the analysis of the traits and components of mental states or acts and their objects. As his views changed over the years about the nature of intentionality and philosophy, the descriptive psychology of the Logical Investigations (1900/01) gave way to descriptive programmes in which the objects of perception and of judgement were conceived of in terms of (...) a new, analytic framework; in particular Husserl lost interest in describing the things and processes in the real world that are the objects of perception and judgement and so too in describing their relations to these acts. His new analytic framework, particularly as it applies to perception, has been thoroughly expounded and discussed in the literature. My aim here is to expound Husserl's first descriptions of perception within the framework of the Investigations and to incorporate as far as possible his later descriptive results to the extent that these are separable from his later turn to idealism. (shrink)

There are many things—call them ‘experts’—that you should defer to in forming your opinions. The trouble is, many experts are modest: they’re less than certain that they are worthy of deference. When this happens, the standard theories of deference break down: the most popular (“Reflection”-style) principles collapse to inconsistency, while their most popular (“New-Reflection”-style) variants allow you to defer to someone while regarding them as an anti-expert. We propose a middle way: deferring to someone involves preferring to make any decision (...) using their opinions instead of your own. In a slogan, deferring opinions is deferring decisions. Generalizing the proposal of Dorst (2020a), we first formulate a new principle that shows exactly how your opinions must relate to an expert’s for this to be so. We then build off the results of Levinstein (2019) and Campbell-Moore (2020) to show that this principle is also equivalent to the constraint that you must always expect the expert’s estimates to be more accurate than your own. Finally, we characterize the conditions an expert’s opinions must meet to be worthy of deference in this sense, showing how they sit naturally between the too-strong constraints of Reflection and the too-weak constraints of New Reflection. (shrink)

Assertions are the centre of gravity in social epistemology. They are the vehicles we use to exchange information within scientific groups and society as a whole. It is therefore essential to determine under which conditions we are permitted to make an assertion. In this paper we argue and provide empirical evidence for the view that the norm of assertion is justified belief: truth or even knowledge are not required. Our results challenge the knowledge account advocated by, e.g. Williamson (1996), in (...) general, and more specifically, put into question several studies conducted by Turri (2013, 2016) that support a knowledge norm of assertion. Instead, the justified belief account championed by, e.g. Douven (2006), seems to prevail. (shrink)

Phenomenal Conservatism (the view that an appearance that p gives one prima facie justification for believing that p) is a promising, and popular, internalist theory of epistemic justification. Despite its popularity, it faces numerous objections and challenges. For instance, epistemologists have argued that Phenomenal Conservatism is incompatible with Bayesianism, is afflicted by bootstrapping and cognitive penetration problems, does not guarantee that epistemic justification is a stable property, does not provide an account of defeat, and is not a complete theory of (...) epistemic justification. This book shows that Phenomenal Conservatism is actually immune to some of these problems, though not all of them. Accordingly, it explores the prospects of integrating Phenomenal Conservatism with Explanationism (the view that epistemic justification is a matter of explanatory relations between one’s evidence and propositions supported by that evidence). The resulting theory, Phenomenal Explanationism, has advantages over Phenomenal Conservatism and Explanationism taken on their own. Phenomenal Explanationism is a highly unified, comprehensive internalist theory of epistemic justification that delivers on the promises of Phenomenal Conservatism while avoiding its pitfalls. (shrink)

An important and engaging book on a key argument in contemporary debates about free will and moral responsibility.

Twenty philosophers offer new essays examining the form of reasoning known as inference to the best explanation - widely used in science and in our everyday lives, yet still controversial. Best Explanations represents the state of the art when it comes to understanding, criticizing, and defending this form of reasoning.

Introduction -- Organization, society and politics -- An Aristotelian perspective -- The politics -- The public good -- The rhetoric -- Talk and texts -- The Nichomachean ethics -- Decision making and ethics -- The Poetics -- Bolshevism to ballet in three steps -- What is "public interest"?: a case study -- Where do we go from here?

This paper presents the results of two corpus studies investigating the discourse surrounding conspiracy theories and genuine theories. The results of these studies show that conspiracy theories lack the epistemic and scientific standing characteristic of theories more generally. Instead, our findings indicate that conspiracy theories are spread in a manner that resembles the dissemination of rumors and falsehoods. Based on these empirical results, we argue that it is time for both re-engineering conspiracy theory and for relabeling "conspiracy theory". We propose (...) relabelling conspiracy theories as either "conspiracy stories" or "conspiracy narratives" to more accurately convey their true nature. (shrink)

ABSTRACTAndrew Bacon, Matti Eklund, and Patrick Greenough have individually proposed objections to the project in my book, Replacing Truth. Briefly, the book outlines a conceptual engineering project – our defective concept of truth is replaced for certain purposes with a team of concepts that can do some of the jobs we thought truth could do. Here, I respond to their objections and develop the views expressed in Replacing Truth in various ways.

The standard interpretation of quantum mechanics and a standard interpretation of the awareness of pain have a common feature: Both postulate the existence of an irresolvable duality. Whereas many physicists claim that all particles exhibit particle and wave properties, many philosophers working on pain argue that our awareness of pain is paradoxical, exhibiting both perceptual and introspective characteristics. In this chapter, we offer a pessimistic take on the putative paradox of pain. Specifically, we attempt to resolve the supposed paradox by (...) undermining the reasons offered for accepting the introspective side of the dualism. (shrink)

Do people tend to be overconfident? Many think so. They’ve run studies on whether people are calibrated: whether their average confidence in their opinions matches the proportion of those opinions that are true. Under certain conditions, people are systematically ‘over-calibrated’—for example, of the opinions they’re 80% confident in, only 60% are true. From this empirical over-calibration, it’s inferred that people are irrationally overconfident. My question: When and why is this inference warranted? Answering it requires articulating a general connection between being (...) rational and being right—something extant studies have not done. I show how to do so using the notion of deference. This provides a theoretical foundation for calibration research, but also reveals a flaw: the connection between being rational and being right is much weaker than is standardly assumed, since rational people can often be expected to be miscalibrated. Thus we can’t test whether people are overconfident by simply testing whether they are over-calibrated; instead, we must try to predict the rational deviations from calibration, and then compare those predictions to people’s performance. I show how this can be done—and that doing so complicates the interpretation of robust empirical effects. (shrink)

This interview took place through email during October-November, 2019. Michael: It’s a real pleasure to engage you in conversation. You were a foundation member of PESA and someone who in the pre-I...

What is essential to language? Two thinkers active in Vienna in the 1930's, Karl Bühler and Ludwig Wittgenstein, gave apparently incompatible answers to this question. I compare what Wittgenstein says about language and reference at the beginning of his Philosophical Investigations with some aspects of the descriptive analysis of language worked out by Bühler between 1907 and 1934, a systematic development of the philosophies of mind and language of such heirs of Brentano as Martinak, Marty, Meinong, Landgrebe and Husserl. Y (...) a-Uil quelque chose qui est essentiel au langage? Deux penseurs actifs à Vienne dans les années trente, Karl Bühler et Ludwig Wittgenstein, donnent à cette question des réponses qui sont apparemment incompatibles. Je compare ce que Wittgenstein dit du langage et de la référence au début de ses Investigations Philosophiques avec quelques aspects de l'analyse descriptive élaborée par Bühler entre 1907 et 1934, un développement systématique des philosophies de l'esprit et du langage des héritiers de Brentano tels que Martinak, Marty, Meinong, Landgrebe et Husserl. (shrink)

Although there has been a recent swell of interest in theories of truth that attempt solutions to the liar paradox and the other paradoxes affecting our concept of truth, many of these theories have been criticized for generating new paradoxes, called revenge paradoxes. The criticism is that the theories of truth in question are inadequate because they only work for languages lacking in the resources to generate revenge paradoxes. Theorists facing these objections offer a range of replies, and the matter (...) seems now to be at a standoff. I aim, first, to bolster the revenge objections by considering a relation, internalizability, between languages and theories of truth. A theory of truth is internalizable for a language iff there is an extension of that language in which the theory is expressible and for which the theory provides an accurate and complete assignment of semantic values. There are good reasons to think that acceptable theories of truth are internalizable for any language. With this internalizability requirement in hand, I argue that properly formulated revenge objections are decisive and that the replies to them are inadequate. Second, I show that the internalizability requirement can be met by a certain theory of truth. The central claim of this theory is that truth is an inconsistent concept and should be replaced with a pair of consistent concepts that can then be used to provide a semantics for our truth predicates. This theory is compatible with classical logic, does not give rise to revenge paradoxes of any kind, and satisfies the internalizability requirement. (shrink)

‘What is characteristic of every mental activity’, according to Brentano, is ‘the reference to something as an object. In this respect every mental activity seems to be something relational.’ But what sort of a relation, if any, is our cognitive access to the world? This question – which we shall call Brentano’s question – throws a new light on many of the traditional problems of epistemology. The paper defends a view of perceptual acts as real relations of a subject to (...) an object. To make this view coherent, a theory of different types of relations is developed, resting on ideas on formal ontology put forward by Husserl in his Logical Investigations and on the theory of relations sketched in Smith's "Acta cum fundamentis in re". The theory is applied to the notion of a Cambridge change, which proves to have an unforeseen relevance to our understanding of perception. (shrink)

Niche construction is the process whereby organisms, through their activities and choices, modify their own and each other’s niches. By transforming natural-selection pressures, niche construction generates feedback in evolution at various different levels. Niche-constructing species play important ecological roles by creating habitats and resources used by other species and thereby affecting the flow of energy and matter through ecosystems—a process often referred to as “ecosystem engineering.” An important emphasis of niche construction theory (NCT) is that acquired characters play an evolutionary (...) role through transforming selective environments. This is particularly relevant to human evolution, where our species has engaged in extensive environmental modification through cultural practices. Humans can construct developmental environments that feed back to affect how individuals learn and develop and the diseases to which they are exposed. Here we provide an introduction to NCT and illustrate some of its more important implications for the human sciences. (shrink)

ABSTRACT In a series of papers read to the Cambridge Philosophical Society through the 1820s, the Cambridge mathematician George Peacock laid the foundation for a natural history of arithmetic that would tell a story of human progress from counting to modern arithmetic. The trajectory of that history, Peacock argued, established algebraic analysis as a form of universal reasoning that used empirically warranted operations of mind to think with symbols on paper. The science of counting would suggest arithmetic, arithmetic would suggest (...) arithmetical algebra, and, finally, arithmetical algebra would suggest symbolic algebra. This philosophy of suggestion provided the foundation for Peacock's “principle of equivalent forms,” which justified the practice of nineteenth-century English symbolic algebra. Peacock's philosophy of suggestion owed a considerable debt to the early Cambridge Philosophical Society culture of natural history. The aim of this essay is to show how that culture of natural history was constitutively significant to the practice of nineteenth-century English algebra. (shrink)

Suppose that realism about values is true, that there are objects and states of affairs which are intrinsically valuable, that some objects and states of affairs are intrinsically more valuable than others and that some objects and states of affairs are intrinsically valuable for Sam, and others for Maria.

One reason that many of the philosophical debates about free will might seem intractable is that di erent participants in those debates use various terms in ways that not only don't line up, but might even contradict each other. For instance, it is widely accepted to understand libertarianism as\the conjunction of incompatibilism [the thesis that free will is incompatible with the truth of determinism] and the thesis that we have free will" (van Inwagen (1983), 13f; see also Kane (2001), 17; (...) Pereboom (2006), xiv). However, for van Inwagen's later reservations about the use of the term `libertarianism', see van Inwagen (2008), relevant pages). This makes perplexing a number of views that have the name `libertarian compatibilism' (see Vihvelin (2000) and Arvan (2013)) as on the standard use of the terms involved, the name appears to involve a contradiction. Even the meaning and usage of the term `free will' is itself contested. Manuel Vargas writes that \`free will' is a term of both ordinary and technical discourse" (Vargas (2013), 325). However, it is not clear if the ordinary use of the term always tracks the technical use. But in an in uential paper on \How to Think about About the Problem of Free Will," Peter van Inwagen claims that \the phrase `free will' . . . hardly exists except as a philosophical term of art. Its non- philosophical uses are pretty much con ned to the phrase `of his/her own free will' which means `uncoerced"' (van Inwagen (2008), 320 footnote 1). To many of us, a look at the philosophical and literatures of the past millennium suggest a use that need not be a technical notion, even if it is often used in a technical way. No matter how this debate about the `ordinary use' of the phrase turns out, recognizing that `free will' gets used in di erent ways and being careful in such usage is important in order to avoid what Chalmers has called `merely verbal disputes' (Chalmers (2011)). For this reason, we want to be very clear in how we understand and de ne free will. There seem to be at least two di erent fundamental notions of what free will is in the contemporary literature. The rst of these, which seems to have garnered the most attention in the last century, works under the assumption that for a person to rightly be said to have free will, she must have the ability 1 to do otherwise than what she does, in fact, do. Under this view I could be said to have freely chosen to drive to work only if I also could have freely chosen, for example, to bike to work or to skip work altogether. This approach to free will is referred to as a `leeway-based approach' (cite my book) or an `alternative- possiblities approach' (see Sartorio (2016).) In contrast, a smaller percentage of the extant literature focuses primarily on the issues of `source,' `ultimacy,' and `origination'. This second approach doesn't focus immediately on the presence or absence of alternative possibilities. On this approach, I freely choose to drive to work only if I am the source of my choice and there is nothing outside of me from which the choice is ultimately derived. In what follows, we refer to the rst of these conceptions|the conception that free will is primarily a matter of having alternative possibilities|as the `leeway- based' conception. Similarly, we will refer to the second of these conceptions| that free will is primarily a matter of our being the source of our choices in a particular way|as the `sourcehood' conception. (John Fischer and Carolina Sartorio refers to sourcehood views as `actual sequence' views; see Fischer (2006) and Sartorio (2016)). Both of these notions can be seen in the following passage taken from Robert Kane: We believe we have free will when we view ourselves as agents ca- pable of in uencing the world in various ways. Open alternatives, or alternative possibilities, seem to lie before us. We reason and deliberate among them and choose. We feel (1) it is `up to us' what we choose and how we act; and this means we could have chosen or acted otherwise. As Aristotle noted: when acting is `up to us,' so is not acting. This `up-to-us-ness' also suggests (2) the ultimate control of our actions lies in us and not outside us in factors beyond our control (Kane (2005), 6). In the next two sections, I look in greater detail at each of these two approaches to the nature of free will, and how they each seek to approach what it means for an action to be `up to us'. I also show how the di erences between these two conceptions cut across the debate about what Kane refers to as the Com- patibility Question: \Is free will compatible with determinism?" (Kane (1996), 13). Along the way, I also brie y point out a number of ways how which of these conceptions is at work shapes how one engages various arguments and other issues regarding. (shrink)

This book aims to develop certain aspects of Gottlob Frege’s theory of meaning, especially those relevant to intensional logic. It offers a new interpretation of the nature of senses, and attempts to devise a logical calculus for the theory of sense and reference that captures as closely as possible the views of the historical Frege. (The approach is contrasted with the less historically-minded Logic of Sense and Denotation of Alonzo Church.) Comparisons of Frege’s theory with those of Russell and others (...) are given. It is in the end shown that developing Frege’s theory in these ways reveals serious problems hitherto largely unnoticed, including those possibly rendering a Fregean intensional logic inconsistent even if his naïve class theory is excluded. (shrink)

Generic statements (‘Tigers have stripes’) are pervasive and early-emerging modes of generalization with a distinctive linguistic profile. Previous experimental work found that generics display a unique asymmetry between their acceptance conditions and the implications that are typically drawn from them. This paper presents evidence against the hypothesis that only generics display an asymmetry. Correcting for limitations of previous designs, we found a generalized asymmetry effect across generics, various kinds of explicitly quantified statements (‘most’, ‘some’, ‘typically’, ‘usually’), and variations in types (...) of predicated properties (striking vs. neutral). We discuss implications of these results for our understanding of the source of asymmetry effects and whether and in which ways these effects might introduce biased beliefs into social networks. (shrink)

Therapy for metaphysics -- Concepts, rules, and the spirit of recognition -- Meaning and meanings -- Reference and presence -- Truth and correspondence -- Emancipating theology.

Ways into the Logic of Alexander of Aphrodisias is intended to give an overview of the logic of Alexander of Aphrodisias (fl. early third century A D). Since ...

Questions concerning free will are intertwined with issues in almost every area of philosophy, from metaphysics to philosophy of mind to moral philosophy, and are also informed by work in different areas of science. Free will is also a perennial concern of serious thinkers in theology and in non-western traditions. Because free will can be approached from so many different perspectives and has implications for so many debates, a comprehensive survey needs to encompass an enormous range of approaches. This book (...) is the first to draw together leading experts on every aspect of free will, from those who are central to the current philosophical debates, to non-western perspectives, to scientific contributions and to those who know the rich history of the subject. Its 61 chapters, commissioned especially for this volume from the world’s leading researchers, are framed by a General Introduction and briefer introductions for each of the six sections. A list of References, an annotated Suggested Reading list, and a short list of Related Topics are included at the end of each chapter. (shrink)

Canada has recently published a new Clinical Practice Guideline on the diagnosis and management of brain death. It states that consent is not necessary to carry out the interventions required to make the diagnosis. A supporting article not only sets out the arguments for this but also contends that ‘UK laws similarly carve out an exception, excusing clinicians from a prima facie duty to get consent’. This is supplemented by the claim that recent court decisions in the UK similarly confirm (...) that consent is not required, referencing two judgements inBattersbee. We disagree with the authors’ interpretation of the law on consent in the UK and argue that there is nothing inBattersbeeto support the conclusion that consent to testing is not necessary. Where there is a disagreement about testing for brain death in the UK, court authorisation is required. (shrink)

ABSTRACT In a series of papers read to the Cambridge Philosophical Society through the 1820s, the Cambridge mathematician George Peacock laid the foundation for a natural history of arithmetic that would tell a story of human progress from counting to modern arithmetic. The trajectory of that history, Peacock argued, established algebraic analysis as a form of universal reasoning that used empirically warranted operations of mind to think with symbols on paper. The science of counting would suggest arithmetic, arithmetic would suggest (...) arithmetical algebra, and, finally, arithmetical algebra would suggest symbolic algebra. This philosophy of suggestion provided the foundation for Peacock's “principle of equivalent forms,” which justified the practice of nineteenth-century English symbolic algebra. Peacock's philosophy of suggestion owed a considerable debt to the early Cambridge Philosophical Society culture of natural history. The aim of this essay is to show how that culture of natural history was constitutively significant to the practice of nineteenth-century English algebra. (shrink)

There is growing interest in understanding and eliciting division of labor within groups of scientists. This paper illustrates the need for this division of labor through a historical example, and a formal model is presented to better analyze situations of this type. Analysis of this model reveals that a division of labor can be maintained in two different ways: by limiting information or by endowing the scientists with extreme beliefs. If both features are present however, cognitive diversity is maintained indefinitely, (...) and as a result agents fail to converge to the truth. Beyond the mechanisms for creating diversity suggested here, this shows that the real epistemic goal is not diversity but transient diversity. (shrink)

Existentialism claims that there is no human reality except in action: pragmatism argues that meaning and truth are given only in practice. Wittgenstein calls for attention to forms of life, Marxism calls for attention to doing, and feminism calls for attention to the body. What do these tell us about ritual acts and their connection to spirit and to truth in Christianity and other world religions? Religious rituals have a special status as virtually pure forms of belief in action. Thinking (...) Through Rituals asks how philosophical tools like existentialism and Marxism can help us to understand the thought behind actions such as tasting the Christian host, joining in ceremony and speaking sacred words. Thinking Through Rituals proposes a new philosophical understanding of rituals as mental strategies giving access to knowledge of the world, in opposition to traditional approaches which see rituals as forms of social organization and control. Covering areas including the body, pilgrimage,initiation, sacrifice and art, this is an exciting look at the relationship between doing and meaning which is implied by ritual practice, but most fully explained by philosophical theory. (shrink)

This paper details the content and structure of the folk concept of life, and discusses its relevance for scientific research on life. In four empirical studies, we investigate which features of life are considered salient, universal, central, and necessary. Functionings, such as nutrition and reproduction, but not material composition, turn out to be salient features commonly associated with living beings (Study 1). By contrast, being made of cells is considered a universal feature of living species (Study 2), a central aspect (...) of life (Study 3), and our best candidate for being necessary for life (Study 4). These results are best explained by the hypothesis that people take life to be a natural kind subject to scientific scrutiny. (shrink)