We give a constructive proof of McNaughton's theorem stating that every piecewise linear function with integral coefficients is representable by some sentence in the infinite-valued calculus of Lukasiewicz. For the proof we only use Minkowski's convex body theorem and the rudiments of piecewise linear topology.

Simon Blackburn can be seen as challenging those committed to sui generis moral facts to explain the supervenience of the moral on the descriptive. We (like perhaps Derek Parfit) hold that normative facts in general are sui generis. We also hold that the normative supervenes on the descriptive, and we here endeavour to answer the generalization of Blackburn's challenge. In the course of pursuing this answer, we suggest that Frank Jackson's descriptivism rests on a conception of properties inappropriate to discussions (...) of normativity, and we see reason to reject descriptivism generally. We also discuss the views of David Brink, Jonathan Dancy and Bernard Williams in this area. (shrink)

This paper is a brief reponse to some of Douglas Portmore's criticisms of our version of the agent-relative/agent-neutral distinction.

Simon Blackburn can be seen as challenging those committed to sui generis moral facts to explain the supervenience of the moral on the descriptive. We hold that normative facts in general are sui generis. We also hold that the normative supervenes on the descriptive, and we here endeavour to answer the generalization of Blackburn's challenge. In the course of pursuing this answer, we suggest that Frank Jackson's descriptivism rests on a conception of properties inappropriate to discussions of normativity, and we (...) see reason to reject descriptivism generally. We also discuss the views of David Brink, Jonathan Dancy and Bernard Williams in this area. (shrink)

In this paper we defend a version of moral internalism and a cognitivist account of motivation against recent criticisms. The internalist thesis we espouse claims that, if an agent believes she has reason to A, then she is motivated to A. Discussion of counter-examples has been clouded by the absence of a clear account of the nature of motivation. While we can only begin to provide such an account in this paper, we do enough to show that our version of (...) internalism can be defended against putative counter-examples. All theories of motivation which take what motivates to be a psychological state run foul of the following plausible constraint: the reason why you ought to do an action and the reason why you do it can be the same. In our view, however, while what motivates is a reason (which is a fact) the state of being motivated is a cognitive stage, viz. the belief that one has reason to act. In cases where the agent's relevant beliefs are false, then she has no reason to act, but nontheless her action can be explained in other ways. (shrink)

In this article we argue that the complex connections between gender and fatness have not been fully examined, particularly in so far as they relate to men. We consider the role of early feminist literature in establishing the idea that the fear of fatness is fundamentally tied up with patriarchy and the ways this also underwrites more recent examinations of fatness and gender. Moreover, we assert that popular feminist scholarship has actively produced the assumption that weight is not only a (...) women's issue, but that it is tied up with the very construction of femininity. Through an examination of the cultural history of fatness we show that men have also been caught up in the drive to reshape the body over the last century. However, their concerns have remained largely hidden, framed as they often are in the lexicon of ‘fitness’ and ‘muscularity’. An examination of the limited published material on male concerns with fat reveals that for many men fatness is feminizing – and undermines normative forms of masculinity in threatening ways. We call for further research that considers both female and male experiences of fatness, given the limitations of approaches that focus merely on one or the other. (shrink)

This chapter analyses Butler's ethical theories, which are found primarily in Fifteen Sermons and A Dissertation of the Nature of Virtue. It covers his notions of superiority and authority, the supremacy of conscience, virtue, benevolence, and self-love.

McNaughton and Rawling's anti-reductionist intentions are to be welcomed, but are not well served by their continuing adherence to a neo-Humean notion of the 'descriptive'. Their too-willing acceptance of this notion is reflected in a denial of appropriate dialectical weight to considerations about the way 'pattern' disappears from the domain of value when we try to characterize the constituent features of the latter in non-evaluative terms. The need for a satisfactory account of the immanence of value in nature is real (...) enough, but such an account can be given without recourse to the problematic idea of a class of subvenient 'descriptive' properties. Likewise, McNaughton and Rawling's recognition of 'normative facts' is to be endorsed, but such facts are a more widespread and everyday phenomenon than they would have us think. (shrink)

The repentant offender has placed himself on the side of right, so to speak – he now stands with the victim against his own previous bad behaviour, which he now rejects. He’s a proper recipient for the gift of forgiveness. It can be morally appropriate to wipe the slate clean for him. But the unrepentant offender has undergone no such change. Why should we wipe the slate clean for such a person?

The repentant offender has placed himself on the side of right, so to speak – he now stands with the victim against his own previous bad behaviour, which he now rejects. He’s a proper recipient for the gift of forgiveness. It can be morally appropriate to wipe the slate clean for him. But the unrepentant offender has undergone no such change. Why should we wipe the slate clean for such a person?

McNaughton and Rawling present a view on which practical reasons are facts, such as the fact that the rubbish bin is full. This is a non-normative fact, but it is a reason for you to do something, namely take the rubbish out. They see rationality as a matter of consistency. And they see duty as neither purely a matter of rationality nor of practical reason: on the one hand, the rational sociopath is immoral; but, on the other, morality does not (...) require that we always act on the weightiest moral reasons. McNaughton and Rawling criticize various forms of internalism, including Williams’s, and they tentatively propose a view of duty that is neither purely subjective in Prichard’s sense, nor purely objective. (shrink)

significant role for accomplishment thereby admits a ‘Trojan Horse’ (267).1 To abandon hedonism in favour of a conception of well-being that incorporates achievement is to take the first step down a slippery slope toward the collapse of the other two pillars of utilitarian morality: welfarism and consequentialism. We shall argue that Crisp’s arguments do not support these conclusions. We begin with welfarism. Crisp defines it thus: ‘Well-being is the only value. Everything good must be good for some being or beings’ (...) (264). The first part of this definition is potentially misleading, since it makes it sound as if welfarism adopts a monistic account of value, in which well-being is the only good thing. But well-being, as Crisp notes, when discussing hedonism, is best understood as consisting in a balance of good things over bad in one’s life. So understood, welfarism is silent on the issue of what things are good; it places a structural restriction on what kinds of things can be good: they must be things that are good for beings. It is a separate task to supply the content to fit this structure by determining what things are good, and welfarists differ in their answers: hedonists traditionally assert that pleasure alone is good; others add further items such as knowledge and virtue. Why is the thought that a person’s well-being depends importantly on what they accomplish a threat to welfarism? An accomplishment is judged both by its outcome or product and by the manner of the performance itself. But an activity or outcome is only an achievement if it is worthwhile, and whether it is worthwhile will depend on whether it exhibits what Crisp asserts to be ‘non-welfarist values’ (266), such as beauty, grace, importance, or style - excellences which welfarism, in Crisp’s view, cannot accommodate because they cannot be ‘cashed out in welfarist terms’, or ‘reduced to the value of well-being’ (266). Here Crisp rests his case, but it is worth trying to get clearer about the difficulties in order to see if the welfarist can meet them.. (shrink)

Scanlon suggests a buck-passing account of goodness. To say that something is good is not to give a reason to, say, favour it; rather it is to say that there are such reasons. When it comes to wrongness, however, Scanlon rejects a buck-passing account: to say that j ing is wrong is, on his view, to give a sufficient moral reason not to j. Philip Stratton-Lake 2003 argues that Scanlon can evade a redundancy objection against his (Scanlon’s) view of wrongness (...) by adopting a buck-passing account of wrongness. We argue that this manoeuvre does not succeed. Scanlon’s notion of wrongness rests on the idea of a reasonably rejectable principle. As Stratton-Lake points out, Scanlon offers two accounts, one in terms of permission, the other in terms of proscription. The permission account is tricky to formulate. Scanlon’s account (quoted in Stratton-Lake 2003: 71) might suggest any of the following four formulations (where the principles in question are principles ‘governing how one may act’ (Scanlon.. (shrink)

Lately, an increased interest in formal devices has led to an attempt on the part of some mathematicians to do without those aspects of mathematics which require intuition. One consequence of this movement has been a new conception of pure mathematics as a science of axiomatic systems. According to this conception, there is no reality beyond an axiomatic system which the statements of mathematics are about; the fact that a statement is a theorem in the system is all that (...) is of interest. This is a sort of nominalist position, since the contrary position seems to be committed to a belief in the existence of a domain of mathematical entities, which are just as suspect as the universale commonly discussed in metaphysical treatises. More often it is called formalism. (shrink)

Guy Fletcher has written an excellent and much needed book about prudence—lucid, thoughtful, and, to my mind, persuasive. He is well acquainted with all the contemporary literature on his topic, and his treatment of the contributions of others is fair, sympathetic, and helpful. While the discussion becomes increasingly subtle and complex, Fletcher remains admirably clear throughout. Signposts and reminders help the reader, as do outlines and summaries. He follows the excellent ‘rule of three’ as taught (I am informed) to prospective (...) preachers: first you tell them what you are going to tell them; then you tell them; and then you tell them what you have just told them. In all these respects, this book is exemplary.His topic is the nature of prudential discourse, i.e., thought and talk about what benefits or harms someone, and about what someone prudentially ought to do, has reason to do, needs to do, etc. While much has been written about what makes one's life go well, or whether ‘morality and self-interest can be reconciled’, little, he claims, has been written about these meta-prudential questions, and it is this omission he seeks to rectify (p. 1). But is this project, Fletcher asks, really necessary? After all, isn’t it obvious that prudential discourse is normative in the way that moral discourse is? And since philosophers have written extensively about meta-normative issues, the matter has already been more than adequately discussed. Fletcher's response is that while many philosophers think that the answer to the question whether prudential discourse is normative is obvious; unfortunately, they do not agree about what the obvious answer is. (shrink)

Joseph Butler's Fifteen Sermons is a classic and widely influential work of moral philosophy. Its topics include the role of conscience in human nature, self-love and egoism, compassion, resentment and forgiveness, love of our neighbour and of God. It is here presented with introduction, annotation, and other selected writings by Butler.

I wish from my Heart, I could avoid concluding, that since Morality, according to your Opinion as well as mine, is determin'd merely by Sentiment, it regards only human Nature & human Life. … If Morality were determin'd by Reason, that is the same to all rational Beings: But nothing but Experience can assure us, that the Sentiments are the same. What Experience have we with regard to superior Beings? How can we ascribe to them any Sentiments at all? They (...) have implanted those Sentiments in us for the Conduct of Life like our bodily Sensations, which they possess not themselves. When we ask whether morality ‘regards only human nature and human life’ we might be concerned with one of two kinds of question. We may be asking what kinds of being could share our moral point of view. What is the potential scope of the community of moral agents and assessors? Is the moral point of view essentially a human point of view? Could we, or should we, adopt a wider standpoint which would leave room for a significant moral dialogue with non-human moral agents, if there are any? Alternatively, we could be asking whether only human beings should be the objects of moral concern or whether we should widen the circle of concern to include other kinds of being. We may make the same point using a helpful device of Cora Diamond's. We may be concerned with what should replace x or with what should replace y in the formula: We x s assess together conduct and character in so far as it affects ourselves and our fellow y s. (shrink)

This is an analytical study of organizational transformation, values that must be present and operationalized for organizations to successfully change, and the role that leadership has in facilitat ing that change. Specifically, using De Geus' model of living and economic companies and taking input from key theorists such as Senge, Quinn, Bolman and Deal, and others, this study examines and analyzes the values and guiding principles that facilitate an organization's ability to transform, quali ties the leadership must possess and how (...) leadership must function as catalysts to facilitate and ener gize successful, positive change. (shrink)

A layman's guide to the mechanics of Gödel's proof together with a lucid discussion of the issues which it raises. Includes an essay discussing the significance of Gödel's work in the light of Wittgenstein's criticisms.

Iris Murdoch has long been known as one of the most deeply insightful and morally passionate novelists of our time. This attention has often eclipsed Murdoch's sophisticated and influential work as a philosopher, which has had a wide-ranging impact on thinkers in moral philosophy as well as religious ethics and political theory. Yet it has never been the subject of a book-length study in its own right. Picturing the Human seeks to fill this gap. In this groundbreaking book, author Maria (...) Antonaccio presents the first systematic and comprehensive treatment of Murdoch's moral philosophy. Unlike literary critical studies of her novels, it offers a general philosophical framework for assessing Murdoch's thought as a whole. Antonaccio also suggests a new interpretive method for reading Murdoch's philosophy and outlines the significance of her thought in the context of current debates in ethics. This vital study will appeal to those interested in moral philosophy, religious ethics, and literary criticism, and grants those who have long loved Murdoch's novels a closer look at her remarkable philosophy. (shrink)

ABSTRACT In this paper we study consequence relations on the set of many sided sequents over a propositional language. We deal with the consequence relations axiomatized by the sequent calculi defined in [2] and associated with arbitrary finite algebras. These consequence relations are examples of what we call Gentzen systems. We define a semantics for these systems and prove a Strong Completeness Theorem, which is an extension of the Completeness Theorem for provable sequents stated in [2]. For the (...) special case of the finite linear MV-algebras, the Strong Completeness Theorem was proved in [10], as a consequence of McNaughton's Theorem. The main tool to prove this result for arbitrary algebras is the deduction-detachment theorem for Gentzen systems. (shrink)

This paper critically engages Philip Mirowki's essay, "The scientific dimensions of social knowledge and their distant echoes in 20th-century American philosophy of science." It argues that although the cold war context of anti-democratic elitism best suited for making decisions about engaging in nuclear war may seem to be politically and ideologically motivated, in fact we need to carefully consider the arguments underlying the new rational choice based political philosophies of the post-WWII era typified by Arrow's impossibility theorem. A distrust (...) of democratic decision-making principles may be developed by social scientists whose leanings may be toward the left or right side of the spectrum of political practices. (shrink)

In 1931 the mathematical logician Kurt Godel published a revolutionary paper that challenged certain basic assumptions underpinning mathematics and logic. A colleague of Albert Einstein, his theorem proved that mathematics was partly based on propositions not provable within the mathematical system and had radical implications that have echoed throughout many fields. A gripping combination of science and accessibility, Godel’s Proof by Nagel and Newman is for both mathematicians and the idly curious, offering those with a taste for logic and (...) philosophy the chance to satisfy their intellectual curiosity. (shrink)

Arrow’s axiomatic foundation of social choice theory can be understood as an application of Tarski’s methodology of the deductive sciences—which is closely related to the latter’s foundational contribution to model theory. In this note we show in a model-theoretic framework how Arrow’s use of von Neumann and Morgenstern’s concept of winning coalitions allows to exploit the algebraic structures involved in preference aggregation; this approach entails an alternative indirect ultrafilter proof for Arrow’s dictatorship result. This link also connects Arrow’s seminal result (...) to key developments and concepts in the history of model theory, notably ultraproducts and preservation results. (shrink)

A new approach to quantum theory is proposed in this paper. The basis is taken to be theoretical variables, variables that may be accessible or inaccessible, i.e., it may be possible or impossible for an observer to assign arbitrarily sharp numerical values to them. In an epistemic process, the accessible variables are just ideal observations connected to an observer or to some communicating observers. Group actions are defined on these variables, and group representation theory is the basis for developing the (...) Hilbert space formalism here. Operators corresponding to accessible theoretical variables are derived, and in the discrete case, it is proved that the possible physical values are the eigenvalues of these operators. The focus of the paper is some mathematical theorems paving the ground for the proposed foundation of quantum theory. It is shown here that the groups and transformations needed in this approach can be constructed explicitly in the case where the accessible variables are finite-dimensional. This simplifies the theory considerably: To reproduce the Hilbert space formulation, it is enough to assume the existence of two complementary variables. The interpretation inferred from the proposed foundation here may be called a general epistemic interpretation of quantum theory. A special case of this interpretation is QBism; it also has a relationship to several other interpretations. (shrink)

Halin in 1965 proved that if a graph has [Formula: see text] many pairwise disjoint rays for each [Formula: see text] then it has infinitely many pairwise disjoint rays. We analyze the complexity of this and other similar results in terms of computable and proof theoretic complexity. The statement of Halin’s theorem and the construction proving it seem very much like standard versions of compactness arguments such as König’s Lemma. Those results, while not computable, are relatively simple. They only (...) use arithmetic procedures or, equivalently, finitely many iterations of the Turing jump. We show that several Halin-type theorems are much more complicated. They are among the theorems of hyperarithmetic analysis. Such theorems imply the ability to iterate the Turing jump along any computable well ordering. Several important logical principles in this class have been extensively studied beginning with work of Kreisel, H. Friedman, Steel and others in the 1960s and 1970s. Until now, only one purely mathematical example was known. Our work provides many more and so answers Question 30 of Montalbán’s Open Questions in Reverse Mathematics in 2011. Some of these theorems including ones in Halin in 1965 are also shown to have unusual proof theoretic strength as well. (shrink)