This chapter presents the advantages of the use of functional regions of interest along with its specific concerns, and provides a reference to Karl J. Friston related to the subject. Functionally defined ROI help to test hypotheses about the cognitive functions of particular regions of the brain. fROI are useful for specifying brain locations and investigating separable components of the mind. The chapter provides an overview of the common and uncommon misconceptions about fROI related to assumptions of homogeneity, factorial designs (...) versus independent localizers, a summary measure, and the naming of fROI. (shrink)

The term ‘human nature’ can refer to different things in the world and fulfil different epistemic roles. Human nature can refer to a classificatory nature (classificatory criteria that determine the boundaries of, and membership in, a biological or social group called ‘human’), a descriptive nature (a bundle of properties describing the respective group’s life form), or an explanatory nature (a set of factors explaining that life form). This chapter will first introduce these three kinds of ‘human nature’, together with seven (...) reasons why we disagree about human nature. In the main, this chapter focuses on the explanatory concept of human nature, which is related to one of the seven reasons for disagreement, namely, the scientific authority inherent in the term ‘nature’. I will examine why, in a number of historical contexts, it was attractive to refer to ‘nature’ as an explanatory category, and why this usage has led to the continual contestation of the term within the sciences. The claim is that even if the contents of talk about ‘nature’ varied historically, the term’s pragmatic function of demarcation stayed the same. The term ‘nature’ conveys scientific authority over a territory; ‘human nature’ is a concept used to divide causes, as well as experts, and thereby conquer others who threaten to invade one’s epistemic territory. Analysing this demarcation, which has social as well as epistemic aspects, will help us to understand why the explanatory role has been important and why it is unlikely that people will ever agree on either the meaning or the importance of ‘human nature’ as an explanatory category. (shrink)

We discuss dividing lines (in model theory) and some test questions, mainly the universality spectrum. So there is much on conjectures, problems and old results, mainly of the author and also on some recent results.

I examine Bernard Lonergan's approach to the problem of evil. I look to determine whether his solution, which is based on the conjugate forms of faith, hope, and charity, and culminates in a heuristic where forgiveness plays an essential role in moving beyond the problem of evil is adequate. I examine the distinction between basic sin, moral evil, and physical evil as well as his claim that from the viewpoint of the unrestricted act of understanding the non-systematic vanishes.

In lieu of an abstract, here is a brief excerpt of the content:Philosophy and Rhetoric 37.1 (2004) 21-41 [Access article in PDF] Conquering Our Imagination: Thought Experiments and Enthymemes in Scientific Argument Nathan Crick Department of Communication University of Pittsburgh The dividing line between rhetoric and science has traditionally been drawn at the split between persuasion and logic. On the one side, rhetoric seeks to influence human beliefs and behavior through use of stylistic language that resonates with the experiences of (...) an audience; on the other, science endeavors to describe empirical phenomena through the use of logical propositions that can be understood wholly on their own terms. However, recent scholarship has blurred this border. For instance, in his research on Charles Darwin's rhetorical accomplishments, John Angus Campbell has sought to break down "the neopositivist Berlin Wall separating the context of discovery from the context of justification" that represents this traditional division (1990, 23). Claiming that scientific discovery and rhetorical invention are each "an aspect of a flexible logic of inquiry and presentation" (23), Campbell argues that "the social and theological ring of Darwin's language is not merely decorative or ameliorative, but is constitutive of the fabric of his thought" (5). In other words, Campbell insists there is something intrinsically valuable about Darwin's frequent use of colloquial language beyond its immediate rhetorical appeal—it also contributes something fundamental to scientific knowledge itself.This "something," according to Campbell, is the necessary connection between argument and audience that inspires scientific theorizing and culminates in the establishment of new scientific paradigms. Within the context of discovery, the potential rhetorical audience works as a motivating force in the invention of persuasive arguments. That is why, when Darwin's notebooks are closely examined, it can "be said that virtually every note Darwin penned... was written with an eye to a public, often in response to a nameable individual" (1990, 23). Then, within the context of justification, the actual rhetorical audience works to literally fill in the necessary gaps in any rhetorical argument. That is why Darwin, in order to [End Page 21] tap into this resource, "embedded his central insight in a preexisting common world of thought and feeling" (4). Finally, it is for both of these reasons that one cannot fully reconstruct Darwin's "core concept of his argument as a logical proposition shorn of its colloquial language and associations" (4). For Campbell, "the danger in setting aside Darwin's language is that we effectively remove half of the problem he addressed and disregard the intelligence required to address it—how to present a radical idea to a particular scientific and popular audience in a way that retains the persuasive force of the very tradition it destroys" (5).Campbell's claim that rhetoric is constitutive and cannot be boiled away through logical or reductive analysis asserts the centrality of both stylistic language and audience within the process of scientific argumentation. However, although it is clear that rhetoric has a role to play during revolutionary moments in the history of science, it is not as clear that contemporary audiences cannot go directly to the logical reconstructions of past theories without any significant loss of cognitive value. Thus, we must ask whether a scientific argument, when removed from its immediate persuasive context, can nonetheless be "shorn of its colloquial language and associations" in order to reveal its logical core. What, in other words, is the relationship between the logic of scientific argumentation, the rhetorical appeal of language, and the participation of an audience?This essay suggests that a tentative answer can be found by approaching the question through the concept of the "thoughtexperiment." Thought experiments are distinguished from traditional experiments by their explicitly hypothetical quality. Instead of seeking immediately verifiable empirical results, they are designed to invite an audience to visualize a set of initial conditions and then imagine what might happen in response to those conditions. Galileo, for instance, authored one of the most famous thought experiments when he speculated what would happen if two objects of different weights were tied together and dropped. Einstein tried to envision what we might see from a clear box... (shrink)

Trust is a topic of longstanding philosophical interest. It is indispensable to every kind of coordinated human activity, from sport to scientific research. Even more, trust is necessary for the successful dissemination of knowledge, and by extension, for nearly any form of practical deliberation and planning. Without trust, we could achieve few of our goals and would know very little. Despite trust’s fundamental importance in human life, there is substantial philosophical disagreement about what trust is, and further, how trusting is (...) normatively constrained and best theorized about in relation to other things we value. This entry is divided into three sections, which explore key (and sometimes interconnected) ethical and epistemological themes in the philosophy of trust: (1) The Nature of Trust; (2) The Normativity of Trust, and (3) The Value of Trust. (shrink)

“Divide and conquer” might have been man’s motto in the pursuit of knowledge. Faced with the complexity of reality, he evolved a multiplicity of ‘sciences’, each of whose function is to deal with a particular aspect of this complexity. This very multiplicty of knowledge–types in turn gives rise to difficulties. There is always the danger of the “detotalisation of the totality”—to use Etienne Gilson’s phrase—one branch of knowledge may come to be identified with all knowledge, one ‘science’ may (...) be reduced to another, all because the relation of the various disciplines among themselves has not been sufficiently clarified. The problem then is to distinguish the different knowledge categories from one another, and to unite them in some order which will account for each one of them without however eliminating any. (shrink)

KANT ARGUES AT GREAT LENGTH in the Critique of Pure Reason that the existence of God cannot be demonstrated by means of theoretical reason. For after dividing all traditional theistic proofs into three different kinds—the ontological, the cosmological, and the physico-theological—Kant argues first that the cosmological and physico-theological implicitly assume the ontological argument and then that the ontological argument is necessarily fallacious. By restricting knowledge in this manner Kant notoriously makes room for faith, that is, in this case, for a (...) practical proof of the existence of God, which he develops in the Critique of Practical Reason. Kant’s reasons for rejecting theoretical proofs of the existence of God have received considerable attention. In particular, Kant’s objection to the ontological argument, namely that existence is not a real predicate, still seems relevant in contemporary philosophy of religion. What has not received much attention, however, is the relationship between Kant’s rejection of theistic proofs in his critical period and his views on the matter in his pre-critical period. For throughout his pre-critical period, but especially in his The Only Possible Argument in Support of a Demonstration of the Existence of God, Kant believes that there is a theoretical proof of the existence of God. One would naturally expect Kant’s criticisms of theistic proofs as developed in the “ideal of pure reason” to apply in straightforward ways to his earlier attempts at a theistic proof. However, Kant rejects the three traditional arguments in The Only Possible Argument just as he does in the first Critique. Further, his reason for rejecting the ontological argument in particular is identical to the one presented in the first Critique: “Existence is not a predicate or a determination of a thing.” Accordingly, Kant understood himself to be developing a theistic proof in The Only Possible Argument that is distinct from the three traditional arguments and is also not subject to the objections he raises against them. Given that Kant rejects all theoretical proofs of God’s existence in his critical period and given that he did not take his critical objections to the traditional proofs to apply to the theistic proof developed in The Only Possible Argument, what is his justification for rejecting his pre-critical argument for God’s existence? (shrink)

Existing social disparities in the United States are inconsistent with Lincoln’s promise of democracy; therefore, there is a need for a critical conceptualization of the first principles that undergird American democracy and the genesis of democratic social change in America. This study aimed to construct a grounded theory that provides an understanding of the process of American democratic social change. The result was the construction of two frameworks: the demoralization process that triggers social change, and a formal grounded theory that (...) could explain democratic social change endeavors across different domains and levels of analysis. This democratic social change grounded theory answers the research question: How do the principles of the American founding documents provide an understanding of the process of American democratic social change? (shrink)

This paper provides a sorely-needed evaluation of the view that mathematical explanations in science explain by unifying. Illustrating with some novel examples, I argue that the view is misguided. For believers in mathematical explanations in science, my discussion rules out one way of spelling out how they work, bringing us one step closer to the right way. For non-believers, it contributes to a divide-and-conquer strategy for showing that there are no such explanations in science. My discussion also undermines (...) the appeal to unifying power in support of the enhanced indispensability argument. (shrink)

In this paper, I compile some reasons for resisting Stainton's analysis of sub-sentential speech. My resistance stems from considerations about the intentions and expectations of those who communicate using sub-sentential speech. I challenge Stainton's reasons for thinking that some sub-sentential utterances have the status of full-fledged speech acts and argue that they turn out to be degenerate speech acts. After offering my own analysis of sub-sentential speech, I recommend that by revisiting the divide and conquer strategy Stainton dismisses (...) for handling the alleged cases of genuine sub-sentential speech, we can resist radical forms of contextualism suggested by his analysis. En este texto recopilo algunas razones para oponerse al análisis del habla suboracional que plantea Stainton. Mi oposición surge de consideraciones en torno a las intenciones y expectativas de quienes se comunican usando el habla suboracional. Pongo en duda las razones que aduce Stainton para pensar que algunas proferencias suboracionales tienen el estatus de actos de habla en toda la extensión de la palabra y arguyo que resultan ser actos de habla degenerados. Después de ofrecer mi propio análisis del habla suboracional, recomiendo que, retomando la estrategia "divide y vencerás" que Stainton descarta para manejar los presuntos casos de habla suboracional genuina, podemos oponernos a las formas radicales de contextualismo que su análisis sugiere. (shrink)

Design and analysis of algorithms can be a difficult subject for students due to its sometimes-abstract nature and its use of a wide variety of mathematical tools. Here the author, an experienced and successful textbook writer, makes the subject as straightforward as possible in an up-to-date textbook incorporating various new developments appropriate for an introductory course. This text presents the main techniques of algorithm design, namely, divide-and-conquer algorithms, greedy algorithms, dynamic programming algorithms, and backtracking. Graph algorithms are studied (...) in detail, and a careful treatment of the theory of NP-completeness is presented. In addition, the text includes useful introductory material on mathematical background including order notation, algorithm analysis and reductions, and basic data structures. This will serve as a useful review and reference for students who have covered this material in a previous course. Features The first three chapters provide a mathematical review, basic algorithm analysis, and data structures. Detailed pseudocode descriptions of the algorithms along with illustrative algorithms are included. Proofs of correctness of algorithms are included when appropriate. The book presents a suitable amount of mathematical rigor. After reading and understanding the material in this book, students will be able to apply the basic design principles to various real-world problems that they may encounter in their future professional careers. (shrink)

This book initiates a discussion among scholars in rhetoric and hermeneutics in many areas of the humanities. Twenty leading thinkers explore the ways these two powerful disciplines inform each other and influence a wide variety of intellectual fields. Walter Jost and Michael J. Hyde organize pivotal topics in rhetoric and hermeneutics with originality and coherence, dividing their book into four sections: Locating the Disciplines; Inventions and Applications; Arguments and Narratives; and Civic Discourse and Critical Theory. For readers across the humanities, (...) the book demonstrates the usefulness of rhetorical and hermeneutic approaches in literary, philosophical, legal, religious, and political thinking. (shrink)

In computer science, an algorithm is an unambiguous specification of how to solve a class of problems. Algorithms can perform calculation, data processing and automated reasoning tasks. As an effective method, an algorithm can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function. Starting from an initial state and initial input (perhaps empty), the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states, (...) eventually producing "output" and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input. This book introduces a set of concepts in solving problems computationally such as Growth of Functions; Backtracking; Divide and Conquer; Greedy Algorithms; Dynamic Programming; Elementary Graph Algorithms; Minimal Spanning Tree; Single-Source Shortest Paths; All Pairs Shortest Paths; Flow Networks; Polynomial Multiplication, to ways of solving NP-Complete Problems, supported with comprehensive, and detailed problems and solutions, making it an ideal resource to those studying computer science, computer engineering and information technology. (shrink)

Rather than set out an overarching view or take a stand on the debunking of morality tout court, in what follows I’ll explore a divide and conquer strategy. First, I will briefly sketch a debunking argument that, instead of targeting all of morality or human moral nature, has a more narrow focus—namely, the intuitive moral authority of disgust. The argument concludes that as vivid and compelling as they can be while one is in their grip, feelings of disgust (...) should be granted no power to justify moral judgments. Importantly, the argument is grounded in empirical advances concerning the character of the emotion itself. Next, I will step back and consider the argument’s general form. I then point to arguments that others have made that seem to share this form and selective focus, and comment on what such arguments do and do not presuppose. Finally, I locate the selective strategy with respect to other approaches moral debunking. (shrink)

A best-seller in its French edition, the construction of this book is original and its success in the French market demonstrates its appeal. It is based on three principles: 1. An organization of the chapters by families of algorithms : exhaustive search, divide and conquer, etc. At the contrary, there is no chapter only devoted to a systematic exposure of, say, algorithms on strings. Some of these will be found in different chapters. 2. For each family of algorithms, (...) an introduction is given to the mathematical principles and the issues of a rigorous design, with one or two pedagogical examples. 3. For its most part, the book details 150 problems, spanning on seven families of algorithms. For each problem, a precise and progressive statement is given. More important, a complete solution is detailed, with respect to the design principles that have been presented ; often, some classical errors are pointed at. Roughly speaking, two thirds of the book are devoted to the detailed rational construction of the solutions. (shrink)

The strategy of divide and conquer is usually an excellent one, but it all depends on how you do the carving. Chalmer's attempt to sort the "easy" problems of consciousness from the "really hard" problem is not, I think, a useful contribution to research, but a major misdirector of attention, an illusion-generator. How could this be? Let me describe two somewhat similar strategic proposals, and compare them to Chalmers' recommendation.

We can hardly know for certain how strongly a scholarly discipline like history is able to affect politics and society, popular views and morals. Whatever its impact, it's influence also varies from epoch to epoch. During a few decades of the nineteenth century, historians were overwhelmed by so many questions and by such high expectations that there existed a large public space for them that they merely had to occupy. At other times, they have had to conquer this space (...) first if they wanted to gain continued attention.To be sure, a differentiation has to be introduced: any society has particular interests, e.g., in parts of its more recent past or in events that society sees as having something like a “mythical quality” about then, events that represent a major divide, that are deeply imprinted on that society's memory, that have attained a special role through tradition. There is, of course, always a space commanding wider public attention for these aspects. However, they are no more than small specks on the large canvas of history. (shrink)

The strategy of divide and conquer is usually an excellent one, but it all depends on how you do the carving. Chalmer's attempt to sort the "easy" problems of consciousness from the "really hard" problem is not, I think, a useful contribution to research, but a major misdirector of attention, an illusion-generator. How could this be? Let me describe two somewhat similar strategic proposals, and compare them to Chalmers' recommendation.

This paper will argue that there is no such thing as introspective access to judgments and decisions. It won't challenge the existence of introspective access to perceptual and imagistic states, nor to emotional feelings and bodily sensations. On the contrary, the model presented in Section 2 presumes such access. Hence introspection is here divided into two categories: introspection of propositional attitude events, on the one hand, and introspection of broadly perceptual events, on the other. I shall assume that the latter (...) exists while arguing that the former doesn't (or not in the case of judgments and decisions, at least). Section 1 makes some preliminary points and distinctions, and outlines the scope of the argument. Section 2 presents and motivates the general model of introspection that predicts a divided result. Section 3 provides independent evidence for the conclusion that judgments and decisions aren't introspectable. Section 4 then replies to a number of objections to the argument, the most important of which is made from the perspective of so-called "dual systems theories" of belief formation and decision making. The upshot is a limited form of eliminativism about introspection, in respect of at least two core categories of propositional attitude. (shrink)

Dispositionalists try to provide an account of modality—possibility, necessity, and the counterfactual conditional—in terms of dispositions. But there may be a tension between dispositionalist accounts of possibility on the one hand, and of counterfactuals on the other. Dispositionalists about possibility must hold that there are no impossible dispositions, i.e., dispositions with metaphysically impossible stimulus and/or manifestation conditions; dispositionalist accounts of counterfactuals, if they allow for non-vacuous counterpossibles, require that there are such impossible dispositions. I argue, first, that there are in (...) fact no impossible dispositions; and second, that the dispositionalist can nevertheless acknowledge the non-vacuity of some counterpossibles. The strategy in the second part is one of ‘divide and conquer’ that is not confined to the dispositionalist: it consists in arguing that counterpossibles, when non-vacuous, are read epistemically and are therefore outside the purview of a dispositional account. (shrink)

When encountering a set of alternatives displayed in the form of a list, the decision maker usually determines a particular alternative, after which she stops checking the remaining ones, and chooses an alternative from those observed so far. We present a framework in which both decision problems are explicitly modeled, and axiomatically characterize a ‘divide-and-choose’ rule which unifies successive choice and satisficing choice.

We obtain a chain condition for dividing in an arbitrary theory and a new and shorter proof of a chain condition result of Shelah for simple theories.

Is human nature something that the natural and social sciences aim to describe, or is it a pernicious fiction? What role, if any, does ”human nature’ play in directing and informing scientific work? Can we talk about human nature without invoking---either implicitly or explicitly---a contrast with human culture? It might be tempting to think that the respectability of ”human nature’ is an issue that divides natural and social scientists along disciplinary boundaries, but the truth is more complex. The contributors to (...) this collection take very different stances with regard to the idea of human nature. They come from the fields of psychology, the philosophy of science, social and biological anthropology, evolutionary theory, and the study of animal cognition. Some of them are ”human nature’ enthusiasts, some are sceptics, and some say that human nature is a concept with many faces, each of which plays a role in its own investigative niche. Some want to eliminate the notion altogether, some think it unproblematic, others want to retain it with reforming modifications. Some say that human nature is a target for investigation that the human sciences cannot do without, others argue that the term does far more harm than good. The diverse perspectives articulated in this book help to explain why we disagree about human nature, and what, if anything, might resolve that disagreement. Introduction Tim Lewens 1 Doubling Down on the Nomological Notion of Human Nature Edouard Machery 2 Trait Bin and Trait Cluster Accounts of Human Nature Grant Ramsey 3 A Developmental Systems Account of Human Nature Karola Stotz and Paul Griffiths 4 Human Nature, Natural Pedagogy, and Evolutionary Causal Essentialism Cecilia Heyes 5 Human Nature John Dupré 6 Sceptical Reflections on Human Nature Kim Sterelny 7 The Social Construction of Human Nature Kevin N. Laland and Gillian R. Brown 8 The Use and Non-Use of the Human Nature Concept by Evolutionary Biologists Peter J. Richerson 9 Human Ontogenies as Historical Processes Christina Toren 10 Divide and Conquer Maria Kronfeldner. (shrink)

Much debate has ensued regarding the challenge to scientific realism provided by consideration of certain problematic episodes of theory change in the history of science. This paper contends that there is an interesting case which has been overlooked in this debate, namely the prediction of the positron by Dirac from his ‘hole’ theory, and its subsequent replacement by a theory which failed to contain a central, and essential, theoretical posit: the ‘Dirac sea’ of negative energy electrons. Accounting for this case (...) with the ‘divide and conquer’ strategy of contemporary scientific realism proves particularly troublesome, even for the structural realist. (shrink)

The term ‘ellipsis’ can be used to refer to a variety of phenomena: syntactic, semantic, and pragmatic. In this article, I discuss the recent comprehensive survey by Stainton 2006 of these kinds of ellipsis with respect to the analysis of nonsententials and try to show that despite his trenchant criticisms and insightful proposal, some of the criticisms can be evaded and the insights incorporated into a semantic ellipsis analysis, making a ‘divide-and-conquer’ strategy to the properties of nonsententials feasible (...) after all. -/- Editor's comment: To find the contribution, please go to item 16 of the URL, which contains the full text. Professor Merchant has permitted this. (shrink)

Dualism holds that some mental events are fundamental and non-physical. I develop a prima facie plausible causal argument for dualism. The argument has several significant implications. First, it constitutes a new way of arguing for dualism. Second, it provides dualists with a parity response to causal arguments for physicalism. Third, it transforms the dialectical role of epiphenomenalism. Fourth, it refutes the view that causal considerations prima facie support physicalism but not dualism. After developing the causal argument for dualism and drawing (...) out these implications, I subject the argument to a battery of objections. Some prompt revisions to the argument. Others reveal limitations in scope. It falls out of the discussion that the causal argument for dualism is best used against physicalism as a keystone in a divide and conquer strategy. (shrink)

This article traces the origins of Kenneth Wilson's conception of effective field theories (EFTs) in the 1960s. I argue that what really made the difference in Wilson's path to his first prototype of EFT are his long-standing pragmatic aspirations and methodological commitments. Wilson's primary interest was to work on mathematically interesting physical problems and he thought that progress could be made by treating them as if they could be analyzed in principle by a sufficiently powerful computer. The first point explains (...) why he had no qualms about twisting the structure of field theories; the second why he divided the state-space of a toy model field theory into continuous slices by following a standard divide-and-conquer algorithmic strategy instead of working directly with a fully discretized and finite theory. I also show how Wilson's prototype bears the mark of these aspirations and commitments and clear up a few striking ironies along the way. (shrink)

Although the map of technology ethics is expanding, the growing subdomains within it may raise misgivings. In a recent and very interesting article, Sætra and Danaher have argued that the current dynamic of sub-specialization is harmful to the ethics of technology. In this commentary, we offer three reasons to diminish their concern about ethical proliferation. We argue first that the problem of demarcation is weakened if we attend to other sub-disciplines of technology ethics not mentioned by these authors. We claim (...) secondly that the logic of sub-specializations is less problematic if one does adopt mixed models (combining internalist and externalist approaches) in applied ethics. We finally reject that clarity and distinction are necessary conditions for defining sub-fields within ethics of technology, defending the porosity and constructive nature of ethical disciplines. (shrink)

For Augustin Thierry, rewriting the story of the past was, until 1830, explicitly a way of making the future, and after 1830, implicitly a way of justifying the present. In subverting traditional historiography perceived as a legitimation of royal authority Thierry did not follow the Enlightenment strategy of opposing history and reason. Writing after 1789, he discovered reason in history. Constant and the Saint-Simonians had already distinguished two ages of history an age of conquest or violence, and an age, just (...) beginning, of commerce and reason but these appeared as discontinuous. Thierry's aim, especially after 1830, was to reveal history as a continuous, providential unfolding of reason, culminating in the bourgeois nation state. The violence of history was thus to be subsumed by reason. Historiographically, narrative and commentary were not to be discontinuous, as in Enlightenment historiography; meaning was to emerge instead from the narrative itself. Correspondingly, the historian's role was to be construed as a mediating, not a constructive one. The historian is the mouthpiece of history, as the bourgeois, the true hero of history, uniting in himself conquered and conqueror, re-presents what in history was divided the nation. In neither case is control to be viewed as a mark of division or violence; historian and hero are alike agents or representatives of totality . Violence reasserts itself thematically, however, in the stark, unresolved opposition of conquered and conqueror, subject and lord, female and male, victim and executioner, which structures Thierry's most successful historical narratives. (shrink)

We show that any countable model of a model complete theory has an elementary extension with a “pseudofinite-like” quasi-dimension that detects dividing.

Not long ago I was called by my brother’s doctor. He wanted to know if I would accept his judgment that the respirator for my brother should be turned off. Vince, age 81, had contracted West Nile virus, normally treated successfully in 99% of cases, but often lethal in 1%. My brother was in that 1%, with a fast onset of the disease and a no less rapid decline into a coma, all in one day. There was no pain or (...) suffering. His doctor called me one month later for my decision. I had no hesitation in agreeing with him—despite knowing that some patients do come out of seemingly irreversible comas later, even much later, than that—a low probability, but not a certainty. But my brother had lived a long and... (shrink)

Abstract.We obtain a chain condition for dividing in an arbitrary theory and a new and shorter proof of a chain condition result of Shelah for simple theories.