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)

We show the intimate relationship between McNaughton Theorem and the Chinese Remaindner Theorem for MV-algebras. We develop a very short and simple proof of McNaughton Theorem. The arguing is elementary and right out of the definitions. We exhibit the theorem as just an instance of the Chinese theorem. Since the variety of MV-algebras is arithmetic, the Chinese theorem holds for MV-algebras. However, to make this paper self-contained and entirely elementary, we include a (...) simple proof of this theorem inspired in Ferraioli and Lettieri (Math Logic Q 1:27–43, 2011). (shrink)

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.

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)

In recent years the distinction between agent-relative and agent-neutral reasons has been taken by many to play a key role in distinguishing deontology from consequentialism. It is central to all universalist consequentialist theories that value is determined impersonally; the real value of any state of affairs does not depend on the point of view of the agent. No reference, therefore, to the agent or to his or her position in the world need enter into a consequentialist understanding of what makes (...) an action right or wrong or morally permissible. Consequentialism thus provides an agent-neutral account of both the right and the good. (shrink)

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.

In this paper, the principal objections to unconditional forgiveness are canvassed, primarily that it fails to take wrongdoing seriously enough, and that it displays a lack of self-respect. It is argued that these objections stem from a mistaken understanding of what forgiveness actually involves, including the erroneous view that forgiveness involves some degree of condoning of the offence, and is incompatible with blaming the offender or punishing him. Two positive reasons for endorsing unconditional forgiveness are considered: respect for persons and (...) human solidarity; and it is argued that the latter provides more plausible grounds for it than the former. (shrink)

This book introduces the reader to ethics by examining a current and important debate. During the last fifty years the orthodox position in ethics has been a broadly non-cognitivist one: since there are no moral facts, moral remarks are best understood, not as attempting to describe the world, but as having some other function - such as expressing the attitudes or preferences of the speaker. In recent years this position has been increasingly challenged by moral realists who maintain that there (...) are moral facts; there is a truth of the matter in ethics, which is independent of our views, and which we seek to discover. Unfortunately much of this interesting debate found in the work of McDowell, Wiggins, Putnam, Blackburn and others is not easily accessible to undergraduates. McNaughton presents many of the major issues in ethics by way of a clear exposition of both sides of this argument and assumes no prior knowledge of philosophy. Topics discussed include: moral observation, moral motivation, amoralism and wickedness, moral weakness, cultural relativism and utilitarianism. The book concludes that a convincing case can be made out for a radical form of moral realism in which moral virtue is found, not in the following of correct moral principles, but rather in the development of moral sensitivity. Moral Vision is a clear and engaged introduction to an important, and often troubling, debate. (shrink)

Forgiveness usually gets a very good press in our culture: we are deluged with self-help books and television shows all delivering the same message, that forgiveness is good for everyone, and is always the right thing to do. But those who have suffered seriously at the hands of others often and rightly feel that this boosterism about forgiveness is glib and facile. Perhaps forgiveness is not always desirable, especially where the wrongdoing is terrible or the wrongdoer unrepentant. In this book, (...) Garrard and McNaughton suggest that the whole debate suffers from a crippling lack of clarity about what forgiveness really amounts to. They argue that it is more difficult, complex and troubling than many of its advocates suppose. Nevertheless, they conclude, a proper understanding of forgiveness allows us to avoid cheap and shallow forms of it, and enables us to see why it is right and admirable to forgive even unrepentant wrongdoers. (shrink)

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)

Stephen Kearns and Daniel Star have made the following interesting proposal concerning the relation between practical reasons and evidence : Necessarily: A fact F is a reason for you to φ iff F is evidence that you ought to φ We're not sure about this. Although moving from left to right might be OK, the converse is problematic. For example, the fact that your reliable friend told you that you have overriding moral reason to φ is ….

This paper comprises three sections. First, we offer a traditional defence of deontology, in the manner of, for example, W.D. Ross (1965). The leading idea of such a defence is that the right is independent of the good. Second, we modify the now standard account of the distinction, in terms of the agent-relative/agentneutral divide, between deontology and consequentialism. (This modification is necessary if indirect consequentialism is to count as a form of consequentialism.) Third, we challenge a value-based defence of deontology (...) proposed by Quinn (1993), Kamm (1989, 1992), and Nagel (1995). (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)

Prostate cancer has become a major health concern of male Americans. It is now the most common nondermatologic cancer and the second leading cause of cancer death among men. The incidence of detected prostate cancer rose rapidly in recent years, partly because of prostate-specific antigen testing; it is only now tapering off. Screening for prostate cancer with PSA is widespread in the United States, yet controversial: the American Urological Association recommends PSA screening and the American Cancer Society recommends offering screening; (...) however, the United States Preventive Services Task Force and the American College of Physicians recommend against routine screening; and the American Academy of Family Physicians believes that the decision to screen should be left to the patient. (shrink)

Prostate cancer has become a major health concern of male Americans. It is now the most common nondermatologic cancer and the second leading cause of cancer death among men. The incidence of detected prostate cancer rose rapidly in recent years, partly because of prostate-specific antigen testing; it is only now tapering off. Screening for prostate cancer with PSA is widespread in the United States, yet controversial: the American Urological Association recommends PSA screening and the American Cancer Society recommends offering screening; (...) however, the United States Preventive Services Task Force and the American College of Physicians recommend against routine screening; and the American Academy of Family Physicians believes that the decision to screen should be left to the patient. (shrink)

Some of the virtues have a very stable place in our understanding of goodness – beneficence and courage are unlikely ever to lose their high standing. But other virtues have something like a life cycle: they move from a marginal status to to a central one, and sometimes they move back again to the margins, or even beyond the domain of virtue altogether. Chastity is one example of this; humility is another. There was a period in which humility wasn’t a (...) virtue at all (see Aristotle on the great-souled man); with the rise of Christianity (blessed are the meek) it became, not a cardinal, but still a central, virtue, though possibly more honoured in the breach than in the observance; now in the post-Christian world it seems, if a virtue at all, a somewhat creepy one. Why is this – what is it about humility that made it so important during the Christian period, and now makes us so ambivalent about it? And is there any way of rescuing it for a secular context, so that we can once again wholeheartedly endorse and admire it as one of the virtues? (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?