We prove almost sure exponential stability for the disease-free equilibrium of a stochastic differential equations model of an SIR epidemic with vaccination. The model allows for vertical transmission. The stochastic perturbation is associated with the force of infection and is such that the total population size remains constant in time. We prove almost sure positivity of solutions. The main result concerns especially the smaller values of the diffusion parameter, and describes the stability in terms of an analogue $$\mathcal{R}_\sigma$$ of the (...) basic reproduction number $$\mathcal{R}_0$$ of the underlying deterministic model, with $$\mathcal{R}_\sigma \le \mathcal{R}_0$$. We prove that the disease-free equilibrium is almost sure exponentially stable if $$\mathcal{R}_\sigma <1$$. (shrink)

Religion and the external world -- Projection, religion, and the external world -- The senses, reason and the imagination -- Realism, meaning and justification : the external world and religious belief -- Modality, projection and realism -- 'Our profound ignorance' : causal realism, and the failure to detect necessity -- Spreading the mind : projection, necessity and realism -- Into the labyrinth : persons, modality, and Hume's undoing -- Value, projection, and realism -- Gilding : projection, value and secondary qualities (...) -- The gold : good, evil, belief and desire -- The golden : relational values, realism and a moral sense. (shrink)

Theism, according to David O'Connor, has in recent centuries been on trial for its life, the charge being that the existence of so much evil in the world is incompatible with belief in a benevolent creator. But this trial, he claims is incapable of producing a reasoned verdict.

Between 1787, and the end of his life in 1832, Bentham turned his attention to the development and application of economic ideas and principles within the general structure of his legislative project. For seventeen years this interest was manifested through a number of books and pamphlets, most of which remained in manuscript form, that develop a distinctive approach to economic questions. Although Bentham was influenced by Adam Smith's An Inquiry into the Nature and Causes of the Wealth of Nations, he (...) neither adopted a Smithian vocabulary for addressing questions of economic principle and policy, nor did he accept many of the distinctive features of Smith's economic theory. One consequence of this was that Bentham played almost no part in the development of the emerging science of political economy in the early nineteenth century. The standard histories of economics all emphasize how little he contributed to the mainstream of late eighteenth and early nineteenth-century debate by concentrating attention on his utilitarianism and the psychology of hedonism on which it is premised. Others have argued that the calculating nature of his theory of practical reason reduced the whole legislative project to a crude attempt to apply economics to all aspects of social and political life. Put at its simplest this argument amounts to the erroneous claim that Bentham's science of legislation is reducible to the science of political economy. A different but equally dangerous error would be to argue that because Bentham's conception of the science of legislation comprehends all the basic forms of social relationships, there can be no science of political economy as there is no autonomous sphere of activity governed by the principles of economics. This approach is no doubt attractive from an historical point of view given that the major premise of this argument is true, and that many of Bentham's ‘economic’ arguments are couched in terms of his theory of legislation. Yet it fails to account for the undoubted importance of political economy within Bentham's writings, not just on finance, economic policy, colonies and preventive police, but also in other aspects of his utilitarian public policy such as prison reform, pauper management, and even constitutional reform. All of these works reflect a conception of political economy in its broadest terms. However, this conception of political economy differs in many respects from that of Bentham's contemporaries, and for this reason Bentham's distinctive approach to problems of economics and political economy has largely been misunderstood. (shrink)

This essay explores a variety of important Chinese conceptions of the actual and ideal relationship between human beings and the rest of the natural world. It presents views from the earliest period of historical China, the latter part of the Shang dynasty (ca. 1200–1050 bce), and from representative thinkers of other periods, extending down to the last imperial era, the Qing dynasty (1644–1911 ce). There is a fairly clear line of development from the earliest period, when the Chinese saw the (...) natural realm as chaotic, dangerous and largely inscrutable, to a later view of the world as well ordered, inclined toward human good and more open to understanding. This later view was first expressed during the “Eastern Zhou” (770–221 bce), and reached a mature and systematic form in the following Han dynasty (206 bce–220 ce). Subsequent periods saw remarkable variation in the specific features of this view but its general form – a belief in a well ordered and manageable world, inclined toward human good and open to human understanding – remained dominant throughout subsequent Chinese history. (shrink)

This paper examines Hume’s ‘Title Principle’ and its role in a response to one of the ‘manifest contradictions’ he identifies in the conclusion to Book I of A Treatise on Human Nature. This ‘contradiction’ is a tension between two ‘equally natural and necessary’ principles of the imagination, our causal inferences and our propensity to believe in the continued and distinct existence of objects. The problem is that the consistent application of causal reason undercuts any grounds with have for the belief (...) in continued and distinct existence, and yet that belief is as ‘natural and necessary’ as our propensity to infer effects from causes. The TP appears to offer a way to resolve this ‘contradiction’. It statesWhere reason is lively, and mixes itself with some propensity, it ought to be assented to. Where it does not, it never can have any title to operate upon us.’ In brief, if it can be shown that the causal inferences that undermine the belief in external world are not ‘lively’ nor mixed with some propensity’ then we have grounds for think that they have no normative authority. This is in part a response to another ‘manifest contradiction’, namely the apparently self-undermining nature of reason. In this paper I examine the nature and grounds of the TP and its relation to these ‘manifest contradictions’. (shrink)

In his paper ‘Has the Ontological Argument Been Refuted?’, 97–110) William F. Vallicella argues that my attempt to show that the Ontological Argument begs the question is unsuccessful. 1 I believe he is wrong about this, but before endeavouring to vindicate my position I must first make clear what precisely is the point at issue between us. The Ontological Argument is not a single argument, but a family of arguments. Newly devised formulations of the argument are frequently put forward by (...) philosophers in an effort to avoid difficulties that have been pointed out in previous versions. As a consequence there is no possibility of a conclusive proof that every form of the argument embodies the same fallacy. Nevertheless, one can, I believe, prove that all the standard versions of the argument embody a certain fallacy and that, given the nature of the argument, it is therefore unlikely that the argument can be formulated in such a way as to avoid this difficulty. What I tried to show in my paper is that the six best-known versions of the argument all beg the question and that they do so at the same point in the argument, namely when it is asserted that it is possible that an absolutely perfect being exists. It is difficult to see how an ontological argument could be formulated without including this claim as one of its premises, since the distinguishing badge of the argument is the inference from the possibility of an absolutely perfect being to its actuality. It must be unlikely then, if my criticism of these six versions is correct, that there is any way of formulating the argument that avoids this fallacy. (shrink)

I want to deal in this essay with the group of philosophers that G.E.M. Anscombe includes under the term ‘modern moral philosophy’ in her essay by that name. The stars of this group are Hobbes, Hume, Adam Smith, Mill, Sidgwick, Moore. I mean to include as well generally the last hundred years of emotivists, utilitarians, and those theorists who have emphasized universalizability in its various versions. For reasons which I hope will soon become clear, I will refer to this broad (...) group as the ‘atomistic tradition.’ I will be assuming, though not often saying, that the most forthright and thorough spokesman of the tradition is David Hume who, in his purely skeptical moments, was so atomistic and extensionalist that he even denied personal identity over time. Anything less than that is not purely atomistic. (shrink)

What lies at the heart of physical inquiry? What are the foundational ideas and working assumptions that inform the enterprise of natural science? What principles guide research? How do scientists decide whether they are building theories in the right direction? Is there a right direction? Do physical theories actually approximate an objective reality, or are they simply useful summaries, mnemonics for experimental results? This book is Nobel Prize winner Jim Peebles's contribution to such big, classic debates in the philosophy of (...) science, drawing on a lifetime of experience as a leading physicist and taking the development of physical cosmology as a "worked example." He begins with a consideration of the history of thought about the nature of the physical sciences since Einstein, culminating in a succinct statement of what he sees as the fundamental working assumptions of physics. Then, through a careful examination of the development of the general theory of relativity, Einstein's cosmological principle, the big bang theory, and our current model of the universe, he makes the argument that physical theories ultimately are useful approximations to an objective reality whose nature science is discovering. An essential reflection on and interrogation of the nature and practice of science by a giant in the field, The Whole Truth will be illuminating reading for cosmologists, physicists, and historians, philosophers, and sociologists of science alike. (shrink)