There are three main types of number used in modern, industrialized societies. Cardinals count sets (e.g., people, objects) and quantify elements of conventional scales (e.g., money, distance), ordinals index positions in ordered sequences (e.g., years, pages), and nominals serve as unique identifiers (e.g., telephone numbers, player numbers). Many studies that have cited number frequencies in support of claims about numerical cognition and mathematical cognition hinge on the assumption that most numbers analyzed are cardinal. This paper is the first to investigate (...) the relative frequencies of different number types, presenting a corpus analysis of morphologically unmarked numbers (not, e.g., “eighth” or “21st”) in which we manually annotated 3,600 concordances in the Corpus of Contemporary American English. Overall, cardinals are dominant—both pure cardinals (sets) and measurements (scales)—except in the range 1,000–10,000, which is dominated by ordinal years, like 1996 and 2004. Ordinals occur less often overall, and nominals even less so. Only for cardinals do round numbers, associated with approximation, dominate overall and increase with magnitude. In comparison with other registers, academic writing contains a lower proportion of measurements as well as a higher proportion of ordinals and, to some extent, nominals. In writing, pure cardinals and measurements are usually represented as number words, but measurements—especially larger, unround ones—are more likely to be numerals. Ordinals and nominals are mostly represented as numerals. Altogether, this paper reveals how numbers are used in American English, establishing an initial baseline for any analyses of number frequencies and shedding new light on the cognitive and psychological study of number. (shrink)

We present several generalizations of the well-known Kunen inconsistency that there is no nontrivial elementary embedding from the set-theoretic universe V to itself. For example, there is no elementary embedding from the universe V to a set-forcing extension V[G], or conversely from V[G] to V, or more generally from one set-forcing ground model of the universe to another, or between any two models that are eventually stationary correct, or from V to HOD, or conversely from HOD to V, or indeed (...) from any definable class to V, among many other possibilities we consider, including generic embeddings, definable embeddings and results not requiring the axiom of choice. We have aimed in this article for a unified presentation that weaves together some previously known unpublished or folklore results, several due to Woodin and others, along with our new contributions. (shrink)

Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, the view that there is more than one genuine deductive consequence relation, (...) a position which has profound implications for many linguists as well as for philosophers. We should not search for one true logic, since there are many. (shrink)

Consequence is at the heart of logic, and an account of consequence offers a vital tool in the evaluation of arguments. This text presents what the authors term as 'logical pluralism' arguing that the notion of logical consequence doesn't pin down one deductive consequence relation; it allows for many of them.

Motivated by contemporary debates concerning whether directors inappropriately deploy corporate funds for corporate political donations and the limited research into managerial influence on corporate political donations, we examine the impact of director influences from a network perspective. Using a sample of large listed Australian corporations and their political party donation activity during 2000–2007, we find that both the professional and non-professional networks of directors influence corporate political donations. We observe these influences in relation to donations at the federal and state (...) levels, and with respect to the choice of recipient political parties. (shrink)

The formulation and proof of Hume’s Law and several related inference barrier theses.

In this paper, we analyse the recent rapid growth of ‘binge’ drinking in the UK. This means the rapid consumption of large amounts of alcohol, especially by young people, leading to serious anti-social and criminal behaviour in urban centres. British soccer fans have often exhibited this kind of behaviour abroad, but it has become widespread amongst young people within Britain itself. Vomiting, collapsing in the street, shouting and chanting loudly, intimidating passers-by and fighting are now regular night-time features of many (...) British towns and cities. A particularly disturbing aspect is the huge rise in drunken and anti-social behaviour amongst young females. Increasingly, policy makers in the West are concerned about how not just to regulate but to alter social behaviour. Smoking and obesity are obvious examples, and in the UK ‘binge’ drinking has become a focus of acute policy concern. We show how a simple agent based model approach, combined with a limited amount of easily acquired information, can provide useful insights for policy makers in the context of behavioural regulation. We show that the hypothesis that the rise in binge drinking is a fashion-related phenomenon, with imitative behaviour spreading across social networks, is sufficient to account for the empirically observed patterns of binge drinking behaviour. The results show that a small world network, rather than a scale-free or random one, offers the best description of the data. (shrink)

Place is central to many research projects in the social sciences, but it is often taken by researchers as a given. Recently, discourse analysts have devoted more attention to the construction of place in interaction. We focus on one aspect of this construction, the process of drawing inferences from place categories and place names, in transcripts of oral history interviews. We apply membership categorization analysis to descriptions of house types and houses, showing how some categories are presented as being shared (...) and recognizable, and how inferences are projected. Then we apply a similar approach to the ways inferences are drawn from place names, focusing especially on proximity. Participants’ categories can be investigated by examining the ways they are used in question–answer pairs, and in the construction of turns using elaborations, contrasting pairs, negatives and qualifications. This analysis shows the work these place references do for the participants, for instance, in categorizing themselves and others and giving accounts for behaviour. (shrink)

This volume is based on the talks given at the Workshop on Infinity and Truth held at the Institute for Mathematical Sciences, National University of Singapore, from 25 to 29 July 2011. The chapters are by leading experts in mathematical and philosophical logic that examine various aspects of the foundations of mathematics. The theme of the volume focuses on two basic foundational questions: (i) What is the nature of mathematical truth and how does one resolve questions that are formally unsolvable (...) within the Zermelo Fraenkel Set Theory with the Axiom of Choice, and (ii) Do the discoveries in mathematics provide evidence favoring one philosophical view over others? These issues are discussed from the vantage point of recent progresses in foundational studies. The final chapter features questions proposed by the participants of the Workshop that will drive foundational research. The wide range of topics covered here will be of benefit to students, researchers and mathematicians interested in the foundations of mathematics. (shrink)

We respond to Swinburne’s reply to our critique of his argument for the Resurrection by defending the relevance of our counterexamples to his claim that God does not permit grand deception. We reaffirm and clarify our charge that Swinburne ignores two crucial items of Negative Natural Theology (NNT)—that God has an exceptionally weak tendency to raise the dead and that even people with exemplary public records sometimes sin. We show, accordingly, that our total evidence makes it highly probable that Jesus (...) was not sinless, incarnate, or resurrected and that God has permitted massive deception regarding these defining Christian dogmas. (shrink)

Reading Nietzsche, now available in English for the first time, is a group of essays that grew out of this monumental work.

In this paper we argue the need to introduce the philosophical tradition of the examined life into the workplace in a systematic way and show how it can be done. We set out seven key philosophical areas and selected questions for managers to pose about their organisations. We conclude with a case study, which examines one of our key questions ‘What is real?’. We also provide some recommended reading for managers seeking an introduction to philosophy and to explore the seven (...) areas. (shrink)

We prove the following result which is due to the third author. Let [Formula: see text]. If [Formula: see text] determinacy and [Formula: see text] determinacy both hold true and there is no [Formula: see text]-definable [Formula: see text]-sequence of pairwise distinct reals, then [Formula: see text] exists and is [Formula: see text]-iterable. The proof yields that [Formula: see text] determinacy implies that [Formula: see text] exists and is [Formula: see text]-iterable for all reals [Formula: see text]. A consequence is (...) the Determinacy Transfer Theorem for arbitrary [Formula: see text], namely the statement that [Formula: see text] determinacy implies [Formula: see text] determinacy. (shrink)

(2013). A review of “Smith, Nicholas J. J., Logic: The Laws of Truth. Australasian Journal of Philosophy: Vol. 91, No. 3, pp. 629-629. doi: 10.1080/00048402.2013.794849.

We prove the following result which is due to the third author. Let [Formula: see text]. If [Formula: see text] determinacy and [Formula: see text] determinacy both hold true and there is no [Formula: see text]-definable [Formula: see text]-sequence of pairwise distinct reals, then [Formula: see text] exists and is [Formula: see text]-iterable. The proof yields that [Formula: see text] determinacy implies that [Formula: see text] exists and is [Formula: see text]-iterable for all reals [Formula: see text]. A consequence is (...) the Determinacy Transfer Theorem for arbitrary [Formula: see text], namely the statement that [Formula: see text] determinacy implies [Formula: see text] determinacy. (shrink)

From the first co-operative trust school at Reddish Vale in Manchester in 2006, the following decade would witness a remarkable growth of ‘co-operative schools’ in England, which at one point numbered over 850. This paper outlines the key development of democratic education by the co-operative schools network. It explains the approach to democracy and explores the way values were put into practice. At the heart of co-operativism lay a tension between engaging with technical everyday reforms and utopian transformative visions of (...) an educational future. A new arena of debate and practice was established with considerable importance for our understanding of democratic education within the mainstream. (shrink)

We give a fairly complete account which first shows that the solution to the inner model problem for one supercompact cardinal will yield an ultimate version ofLand then shows that the various current approaches to inner model theory must be fundamentally altered to provide that solution.

We investigate both iteration hypotheses and extender models at the level of one supercompact cardinal. The HOD Conjecture is introduced and shown to be a key conjecture both for the Inner Model Program and for understanding the limits of the large cardinal hierarchy. We show that if the HOD Conjecture is true then this provides strong evidence for the existence of an ultimate version of Gödel's constructible universe L. Whether or not this "ultimate" L exists is now arguably the central (...) issue for the Inner Model Program. (shrink)

Something has been going wrong on many college campuses in the last few years. Speakers are shouted down. Students and professors say they are walking on eggshells and are afraid to speak honestly. Rates of anxiety, depression, and suicide are rising--on campus as well as nationally. How did this happen? First Amendment expert Greg Lukianoff and social psychologist Jonathan Haidt show how the new problems on campus have their origins in three terrible ideas that have become increasingly woven into (...) American childhood and education: What doesn't kill you makes you weaker; always trust your feelings; and life is a battle between good people and evil people. These three Great Untruths contradict basic psychological principles about well-being and ancient wisdom from many cultures. Embracing these untruths--and the resulting culture of safetyism--interferes with young people's social, emotional, and intellectual development. It makes it harder for them to become autonomous adults who are able to navigate the bumpy road of life. Lukianoff and Haidt investigate the many social trends that have intersected to promote the spread of these untruths. They explore changes in childhood such as the rise of fearful parenting, the decline of unsupervised, child-directed play, and the new world of social media that has engulfed teenagers in the last decade. They examine changes on campus, including the corporatization of universities and the emergence of new ideas about identity and justice. They situate the conflicts on campus within the context of America's rapidly rising political polarization and dysfunction. This is a book for anyone who is confused by what is happening on college campuses today, or has children, or is concerned about the growing inability of Americans to live, work, and cooperate across party lines. (shrink)

The results of this paper concern the effective cardinal structure of the subsets of [ω1]<ω1, the set of all countable subsets of ω1. The main results include dichotomy theorems and theorems which show that the effective cardinal structure is complicated.

We investigate large cardinal axioms beyond the level of ω-huge in context of the universality of the suitable extender models of [Suitable Extender Models I, J. Math. Log.10 101–339]. We show that there is an analog of ADℝ at the level of ω-huge, more precisely the construction of the minimum model of ADℝ generalizes to the level of Vλ+1. This allows us to formulate the indicated generalization of ADℝ and then to prove that if the axiom holds in V at (...) a proper class of λ then in every suitable extender model, the axiom holds at a proper class of λ. (shrink)

This paper concerns a key point of decision in Donald Davidson's early work in philosophy of language — a fateful decision that set him and the discourse in the area on the path of truth-theoretic semantics. The decision of moment is the one Davidson makes when, in the face of a certain barrier, he gives up on the idea of constructing an explicit meaning theory that would parallel Tarski's recursive way with truth theory. For Davidson there was little choice: he (...) tells us he does not see how to deal with the difficulty except in the radical way he proposes. But there is a way to give such a meaning theory — a meaning theory proper which, using classical logic only, meets a meaning-theoretic analogue of Convention T, satisfies Davidson’s three key desiderata for a theory of meaning, reflects linguistic competence, and avoids quantifying over meanings. The meaning theory sketched here uses Tarskian strategies, as Davidson proposed, but differs from Davidson's approach in not going by way of a truth theory for the target language. (shrink)

Loïc Wacquant argues for a radicalization of the habitus concept provided by Pierre Bourdieu, suggesting that habitus is a site and mode for conducting research, not simply an explanatory or theoretical mechanism. Taking seriously this call to examine skills and communities of practice through apprenticeship, however, requires that the theoretical account of habitus be subject to empirical testing. Moreover, enquiry into communities of practice, especially the subtle psychological, behavioural and even neurological consequences of skill acquisition, means that claims about the (...) habitus can be scrutinized by fields such as psychology, neurology and even human biology. Habitus as a truly open path of inquiry will demand, not wholly novel concepts, but a recognition of when claims about practice are simultaneously testable, and falsifiable, by other forms of empirical enquiry, including the human sciences. (shrink)

Charles Travis and Hans-Georg Gadamer both affirm radical contextualism, the view that natural language is ineliminably context-sensitive. However, they offer different accounts of the role linguistic meaning plays in determining the contents of utterances. I discuss the differences between Travis's and Gadamer's views of meaning and offer an argument in favour of the latter. I argue that Travis's view assumes a principled distinction between literal and figurative speech that is at odds with his wider contextualist commitments. By contrast, Gadamer's view, (...) on which meaning is ‘fundamentally metaphorical,’ makes no such assumption and thus avoids the difficulty. (shrink)

This article underlines and draws attention to critical insights Esposito makes regarding the prospects of rethinking community in a globalized world. Alongside Agamben and Nancy, Esposito challenges the property prejudice found in mainstream models of community. In identity politics, collective identity is converted into a form of communal property. Borders, sovereign territories, and exclusive rights are fiercely defended in the name of communal property. Esposito responds to this problem by developing what I call a “deontological communal contract” where being and (...) ethics are prioritized over having and economics. I examine this new perspective on community in relation to mainstream models found in contemporary and classical social theory. (shrink)

In an attempt to address the theoretical gap between linguistics and philosophy, a group of semanticists, calling itself the Generic Group, has worked to develop a common view of genericity. Their research has resulted in this book, which consists of a substantive introduction and eleven original articles on important aspects of the interpretation of generic expressions. The introduction provides a clear overview of the issues and synthesizes the major analytical approaches to them. Taken together, the papers that follow reflect the (...) current state of the art in the semantics of generics, and afford insight into various generic phenomena. (shrink)

Collagen fibrils are some of the most‐abundant and important extracellular structures in our bodies, yet we are unsure of their shape and size. This is largely due to an inherent difficulty in isolating them from their surrounding tissues. Echinoderms have collagenous tissues that are similar to ours in many ways, yet they can be manipulated to easily relinquish their collagen fibrils, providing an excellent opportunity to study native fibrillar structure. In the early 1990s, they were found to defy the commonly (...) accepted fibrillar model of the time in that they were much shorter, they were shaped like double‐ended spindles, and their centers exhibited a reversal in molecular polarity. Realization of these features helped to reform the questions that were being asked about vertebrate fibrils, shifting the focus toward shape and size. Since then, researchers working with both groups (echinoderms and vertebrates) have worked together to find the structure of native fibrils. This information will be fundamental in understanding what holds collagenous tissues together at the fibrillar level, and could have important implications for people with Ehlers‐Danlos syndrome. BioEssays 29:645–653, 2007. © 2007 Wiley Periodicals, Inc. (shrink)

I am grateful to Catharine Abell and Jonathan Gilmore for their comments and for the opportunity to think again about some important questions. Before I respond.

Technological progress may eventually produce sophisticated robots with human-like traits that result in humans forming meaningful relationships with them. Such relationships would likely lead to a demand for human–artificial intelligence matrimony. U.S. Supreme Court decisions that expanded the definition of marriage to include interracial and same-sex couples, as well as those that have not extended marriage to polygamous relationships, provide guidance regarding the criteria that human–AI would have to meet to successfully assert a right to marry. Ultimately, robots will have (...) to possess certain characteristics of personhood to marry, including the capacity to contract and to engage in an intimate relationship. Alternatively, if AIs can simulate these abilities sufficiently, we may believe that they have these capacities. Even if AIs genuinely possess the capabilities necessary to enter into a marriage, it is social acceptance of intelligent non-humans as life partners that will likely influence legal development is this realm rather than personhood criteria. However, AIs are likely to face bias due to their “artificial” rather than biological nature. Yet, Peter Singer’s influential argument regarding speciesism in the context of animal rights implies that AIs with specific human-like qualities cannot be justifiably denied certain rights. (shrink)

This book introduces an important group of logics that have come to be known under the umbrella term 'susbstructural'. Substructural logics have independently led to significant developments in philosophy, computing and linguistics. _An Introduction to Substrucural Logics_ is the first book to systematically survey the new results and the significant impact that this class of logics has had on a wide range of fields.The following topics are covered: * Proof Theory * Propositional Structures * Frames * Decidability * Coda Both (...) students and professors of philosophy, computing, linguistics, and mathematics will find this to be an important addition to their reading. (shrink)

Longevity is valuable. Most of us would agree that it’s bad to die when you could go on living, and death’s badness has to do with the value your life would have if it continued. Most of us would also agree that it’s bad if life expectancy in a country is low, it’s bad if there is high infant mortality and it’s bad if there is a wide mortality gap between different groups in a population. But how can we make (...) such judgments more precise? How should we evaluate the harm of mortality in a population? Although philosophers have written a lot about the harm of death for individuals, very little work has been done on the harm of mortality for populations. In this article, I take the first steps towards developing a theory of the harm of population mortality. Even these first steps, I argue, lead to surprising results. (shrink)

Developments in Non-Invasive Prenatal Testing (NIPT) and cell-free fetal DNA analysis raise the possibility that antenatal services may soon be able to support couples in non-invasively testing for, and diagnosing, an unprecedented range of genetic disorders and traits coded within their unborn child’s genome. Inevitably, this has prompted debate within the bioethics literature about what screening options should be offered to couples for the purpose of reproductive choice. In relation to this problem, the European Society of Human Genetics (ESHG) and (...) American Society of Human Genetics (ASHG) tentatively recommend that any expansion of this type of screening, as facilitated by NIPT, should be limited to serious congenital and childhood disorders. In support of this recommendation, the ESHG and ASHG cite considerations of distribution justice. Notably, however, an account of justice in the organization and provision of this type of screening which might substantiate this recommendation has yet to be developed. This paper attempts to redress this oversight through an investigation of Norman Daniels’ theory of Just health: meeting health needs fairly. In line with this aim, the paper examines what special moral importance (for Just health) screening for the purpose of reproductive choice might have where concerning serious congenital and childhood disorders in particular. The paper concludes that screening for reproductive choice where concerning serious congenital and childhood disorders may be important for providing women with fair opportunity to protect their health (by either having or not having an affected child). (shrink)

Our topic is the notion of logical consequence: the link between premises and conclusions, the glue that holds together deductively valid argument. How can we understand this relation between premises and conclusions? It seems that any account begs questions. Painting with very broad brushtrokes, we can sketch the landscape of disagreement like this: “Realists” prefer an analysis of logical consequence in terms of the preservation of truth [29]. “Anti-realists” take this to be unhelpful and o:er alternative analyses. Some, like Dummett, (...) look to preservation of warrant to assert [9, 36]. Others, like Brandom [5], take inference as primitive, and analyse other notions in terms of it. There is plenty of disagreement on the “realist” side of the fence too. It is one thing to argue that logical consequence involves preservation of truth. It is another to explain how far truth must be preserved. Is the preservation essentially modal (in all circumstances [25]) or analytic (vouchsafed by.. (shrink)

The literature on values in science struggles with questions about how to describe and manage the role of values in scientific research. We argue that progress can be made by shifting this literature’s current emphasis. Rather than arguing about how non-epistemic values can or should figure into scientific assessment, we suggest analyzing how scientific assessment can accommodate non-epistemic values. For scientific assessment to do so, it arguably needs to incorporate goals that have been traditionally characterized as non-epistemic. Building on this (...) insight, we show how the adequacy-for-purpose framework recently developed for assessing scientific models can provide a general framework for describing scientific assessment so that it goes beyond purely epistemic considerations. Adopting this framework has significant advantages and opens the possibility of effecting a partial rapprochement between critics and proponents of the value-free ideal. (shrink)