Miller, D., G. Nadathur, F. Pfenning and A. Scedrov, Uniform proofs as a foundation for logic programming, Annals of Pure and Applied Logic 51 125–157. A proof-theoretic characterization of logical languages that form suitable bases for Prolog-like programming languages is provided. This characterization is based on the principle that the declarative meaning of a logic program, provided by provability in a logical system, should coincide with its operational meaning, provided by interpreting logical connectives as simple and fixed search instructions. The (...) operational semantics is formalized by the identification of a class of cut-free sequent proofs called uniform proofs. A uniform proof is one that can be found by a goal-directed search that respects the interpretation of the logical connectives as search instructions. The concept of a uniform proof is used to define the notion of an abstract logic programming language, and it is shown that first-order and higher-order Horn clauses with classical provability are examples of such a language. Horn clauses are then generalized to hereditary Harrop formulas and it is shown that first-order and higher-order versions of this new class of formulas are also abstract logic programming languages if the inference rules are those of either intuitionistic or minimal logic. The programming language significance of the various generalizations to first-order Horn clauses is briefly discussed. (shrink)

Rule consequentialism holds that an action's moral standing depends on its relation to the moral code whose general adoption would have the best consequences. Heretofore rule consequentialists have understood the notion of a code's being generally adopted in terms of its being generally obeyed or, more commonly, its being generally accepted. I argue that these ways of understanding general adoption lead to unacceptable formulations of the theory. For instance, Brad Hooker, Michael Ridge, and Holly Smith have recently offered different answers (...) to the question of what ‘acceptance rate’ we should build into our formulation of rule consequentialism, and all are unsatisfactory. I argue instead for a novel approach to formulating rule consequentialism, ‘uniform-moral-education’ rule consequentialism, on which what it means for a moral code to be generally adopted is not for it to be generally followed or generally accepted, but instead for it to be generally taught. (shrink)

The introduction (about 6,000 words) to _The Cambridge Companion to Utilitarianism_, in three sections: utilitarianism’s place in recent and contemporary moral philosophy (including the opinions of critics such as Rawls and Scanlon), a brief history of the view (again, including the opinions of critics, such as Marx and Nietzsche), and an overview of the chapters of the book.

What determines whether an action is right or wrong? Morality, Rules, and Consequences: A Critical Reader explores for students and researchers the relationship between consequentialist theory and moral rules. Most of the chapters focus on rule consequentialism or on the distinction between act and rule versions of consequentialism. Contributors, among them the leading philosophers in the discipline, suggest ways of assessing whether rule consequentialism could be a satisfactory moral theory. These essays, all of which are previously unpublished, provide students in (...) moral philosophy with essential material and ask key questions on just what the criteria for an adequate moral theory might be. (shrink)

Gentzen’s sequent calculi LK and LJ are landmark proof systems. They identify the structural rules of weakening and contraction as notable inference rules, and they allow for an elegant statement and proof of both cut elimination and consistency for classical and intuitionistic logics. Among the undesirable features of those sequent calculi is that their inferences rules are low-level and frequently permute over each other. As a result, large-scale structures within sequent calculus proofs are hard to identify. In this paper, we (...) present a different approach to designing a sequent calculus for classical logic. Starting with Gentzen’s LK proof system, we examine the proof search meaning of his inference rules and classify those rules as involving either don’t care nondeterminism or don’t know nondeterminism. Based on that classification, we design the focused proof system LKF in which inference rules belong to one of two phases of proof construction depending on which flavor of nondeterminism they involve. We then prove that the cut rule and the general form of the initial rule are admissible in LKF. Finally, by showing that the inference rules for LK are all admissible in LKF, we can give a relative completeness proof for LKF provability with respect to LK provability. We shall also apply these properties of the LKF proof system to establish other meta-theoretic properties of classical logic, including Herbrand’s theorem. (shrink)

I consider whether Mill intends for us to see the arguments that constitute his defense of the “Liberty of Thought and Discussion” in chapter 2 ofOn Libertyas a part of his larger case for the “harm” or “liberty” principle (LP). Several commentators depict this chapter as a digression that interrupts the flow between his introduction of this principle in the first chapter and his exposition and defense of it in the final three. I will argue instead for a reading ofOn (...) Libertyon which chapter 2 is well integrated with the rest of the essay and is in fact where Mill starts constructing his case for LP. (shrink)

A structure which generalizes formulas by including substitution terms is used to represent proofs in classical logic. These structures, called expansion trees, can be most easily understood as describing a tautologous substitution instance of a theorem. They also provide a computationally useful representation of classical proofs as first-class values. As values they are compact and can easily be manipulated and transformed. For example, we present an explicit transformations between expansion tree proofs and cut-free sequential proofs. A theorem prover which represents (...) proofs using expansion trees can use this transformation to present its proofs in more human-readable form. Also a very simple computation on expansion trees can transform them into Craig-style linear reasoning and into interpolants when they exist. We have chosen a sublogic of the Simple Theory of Types for our classical logic because it elegantly represents substitutions at all finite types through the use of the typed -calculus. Since all the proof-theoretic results we shall study depend heavily on properties of substitutions, using this logic has allowed us to strengthen and extend prior results: we are able to prove a strengthen form of the firstorder interpolation theorem as well as provide a correct description of Skolem functions and the Herbrand Universe. The latter are not straightforward generalization of their first-order definitions. (shrink)

As a result of these restrictions, an implementation of L [subscript lambda] does not need to implement full higher-order unification. Instead, an extension to first-order unification that respects bound variable names and scopes is all that is required. Such unification problems are shown to be decidable and to possess most general unifiers when unifiers exist. A unification algorithm and logic programming interpreter are described and proved correct. Several examples of using L[subscript lambda] as a meta-programming language are presented.

After critiquing some earlier attempts (including those of Marcus Singer and Frances Howard–Snyder) to ground objections to actual–consequence act utilitarianism (ACAU) on human cognitive limitations, I present two new objections with this same foundation. Both start with the observation that, because human cognitive abilities are not up to the task of reliably recognizing utility–maximizing actions, any agents who are recognizably human – including the best possible humans, morally speaking – are certain to perform many actions every day that ACAU says (...) are immoral, and to perform some actions over the course of their lives that it says are highly immoral. The first objection is that, if Mill's analysis of what it means to call an action wrong is accurate, then ACAU entails a conclusion that no one will accept, viz., that the morally–best humans possible ought to undergo constant punishment. The second objection is that ACAU entails that even the morally–best humans possible are bad moral agents in some respect. This conclusion, while unpalatable, is not so obviously unacceptable as the first. However, I do briefly consider some ways in which it might be possible to demonstrate that it is false and thereby complete a reductio of ACAU. (shrink)

Insofar as John Stuart Mill can be accurately described as a socialist, his is a socialism that a classical liberal ought to be able to live with, if not to love. Mill's view is that capitalist economies should at some point undergo a `spontaneous' and incremental process of socialization, involving the formation of worker-controlled `socialistic' enterprises through either the transformation of `capitalistic' enterprises or creation de novo. This process would entail few violations of core libertarian principles. It would proceed by (...) way of a series of voluntary transactions. Capitalists' property rights would be respected throughout. The process would take place within a national system of laws that permits private ownership of productive property and competition, and would not result in that system's overthrow. And, if we accept some basic tenets of Mill's social philosophy, the outcome at which we should expect the process to arrive is a `patchwork' economy in which capitalistic and socialistic enterprises exist side by side. Key Words: Ludwig von Mises • John Stuart Mill • socialism • capitalism • worker control. (shrink)

We present a setting in which the search for a proof of B or a refutation of B can be carried out simultaneously: in contrast, the usual approach in automated deduction views proving B or proving ¬B as two, possibly unrelated, activities. Our approach to proof and refutation is described as a two-player game in which each player follows the same rules. A winning strategy translates to a proof of the formula and a counter-winning strategy translates to a refutation of (...) the formula. The game is described for multiplicative and additive linear logic . A game theoretic treatment of the multiplicative connectives is intricate and our approach to it involves two important ingredients. First, labeled graph structures are used to represent positions in a game and, second, the game playing must deal with the failure of a given player and with an appropriate resumption of play. This latter ingredient accounts for the fact that neither player might win. (shrink)

This paper explores the influence of social categories on the perceived trade-off between a relatively bad but equal distribution of resources between two parties and a profit maximizing yet unequal one. Studies 1 and 2 showed that people prefer to maximize profits when interacting within their social category, but chose not to maximize individual and joint profits when interacting across social categories. Study 3 demonstrated that outside observers, who were not members of the focal social categories, also were less likely (...) to maximize profits when resources were distributed across social category lines. Study 4 showed that the transaction utility of maximizing profits required greater compensation when resources were distributed across, in contrast to within social categories. We discuss the ethical implications of these decision making biases in the context of organizations. (shrink)

This book offers a clear and highly readable introduction to the ethical and social-political philosophy of John Stuart Mill. Dale E. Miller argues for a "utopian" reading of Mill's utilitarianism. He analyses Mill's views on happiness and goes on to show the practical, social and political implications that can be drawn from his utilitarianism, especially in relation to the construction of morality, individual freedom, democratic reform, and economic organization. By highlighting the utopian thinking which lies at the heart of Mill's (...) theories, Miller shows that rather than allowing for well-being for the few, Mill believed that a society must do everything in its power to see to it that each individual can enjoy a genuinely happy life if the happiness of its members is to be maximized. Miller provides a cogent and careful account of the main arguments offered by Mill, considers the critical responses to his work, and assesses its legacy for contemporary philosophy. Lucidly and persuasively written, this book will be a valuable resource for students and scholars seeking to understand the continued importance of Mill's thinking. (shrink)

, from Stanford Encyclopaedia of Philosophy.

We present a compact sequent calculus LKU for classical logic organized around the concept of polarization. Focused sequent calculi for classical, intuitionistic, and multiplicative–additive linear logics are derived as fragments of the host system by varying the sensitivity of specialized structural rules to polarity information. We identify a general set of criteria under which cut-elimination holds in such fragments. From cut-elimination we derive a unified proof of the completeness of focusing. Furthermore, each sublogic can interact with other fragments through cut. (...) We examine certain circumstances, for example, in which a classical lemma can be used in an intuitionistic proof while preserving intuitionistic provability. We also examine the possibility of defining classical–linear hybrid logics. (shrink)

This paper explores the influence of social categories on the perceived trade-off between a relatively bad but equal distribution of resources between two parties and a profit maximizing yet unequal one. Studies 1 and 2 showed that people prefer to maximize profits when interacting within their social category, but chose not to maximize individual and joint profits when interacting across social categories. Study 3 demonstrated that outside observers, who were not members of the focal social categories, also were less likely (...) to maximize profits when resources were distributed across social category lines. Study 4 showed that the transaction utility of maximizing profits required greater compensation when resources were distributed across, in contrast to within social categories. We discuss the ethical implications of these decision making biases in the context of organizations. (shrink)

In The Second-Person Standpoint, Stephen Darwall offers an interpretation of P. F. Strawson’s “Freedom and Resentment” according to which the essay advances the thesis that good consequences are the “wrong kind of reason” to justify “practices of punishment and moral responsibility.” Darwall names this thesis “Strawson’s Point.” I argue for a different reading of Strawson, one according to which he holds this thesis only in a qualified way and, more generally, is not the unequivocal critic of consequentialism that Darwall makes (...) him out to be. In fact, I contend, Strawson’s account of the reactive attitudes can potentially be a useful resource for consequentialists. (shrink)

The 'Art of Life' is John Stuart Mill's name for his account of practical reason. In this volume, eleven leading scholars elucidate this fundamental, but widely neglected, element of Mill's thought. Mill divides the Art of Life into three 'departments': 'Morality, Prudence or Policy, and Æsthetics'. In the volume's first section, Rex Martin, David Weinstein, Ben Eggleston, and Dale E. Miller investigate the relation between the departments of morality and prudence. Their papers ask whether Mill is a rule utilitarian and, (...) if so, whether his practical philosophy must be incoherent. The second section contains papers by Jonathan Riley and Wendy Donner, who explore the relation between the departments of morality and aesthetics. They discuss issues ranging from supererogation to aesthetic pleasure and humanity's relationship with nature. -/- The papers in the third section consider the Art of Life's axiological first principle, the principle of utility. Elijah Millgram contends that Mill's own life refutes his claim that the Art of Life has a single axiological first principle. Philip Kitcher maintains that Mill has a dynamic axiology requiring us to continually refine our conception of the good. In the final section, three papers address what it means to put the Art of Life into practice. Robert Haraldsson locates an 'Art of Ethics' in On Liberty that is in tension with the Art of Life. Nadia Urbinati plumbs the classical roots of Mill's view of the good life. Finally, Colin Heydt develops Mill's suggestion that we regard our own lives as works of art. (shrink)

In my book J. S. Mill: Moral, Social and Political Thought I explained the absence of a standalone chapter on women's rights by explaining that for Mill no special explanation of why women should have the right to vote, work in the careers of their choice, etc., was needed; they should have these rights for the same reasons as men. The real lacuna, I admitted, was the absence of a chapter on Mill's views on marriage and the family. This chapter (...) remedies that deficiency. (shrink)

In “’But It Would Be Wrong,’” Stephen Darwall advances a mixed view regarding “deontic buck-passing.” He holds that a wrong action’s “wrong-making features” are our reasons for reactive attitudes like blame; with respect to these reasons, the action’s wrongness “passes the buck” to these features. Yet the action’s being wrong is itself an additional reason for the agent not to do the action, Darwall contends, a “second-personal” moral reason. So with respect to reasons for action, the buck doesn’t get passed. (...) But once we remember that compunction is one of the moral reactive attitudes, we can see that Darwall’s rationale for treating these two sorts of reasons differently is insufficient. While giving up on deontic buck-passing altogether would require significant revisions to his second-personal account of morality, Darwall can easily adopt a thoroughgoing buck-passing, since a wrong action’s wrong-making features can be second-personal reasons not to do it. (shrink)

We combine intuitionistic logic and classical logic into a new, first-order logic called polarized intuitionistic logic. This logic is based on a distinction between two dual polarities which we call red and green to distinguish them from other forms of polarization. The meaning of these polarities is defined model-theoretically by a Kripke-style semantics for the logic. Two proof systems are also formulated. The first system extends Gentzenʼs intuitionistic sequent calculus LJ. In addition, this system also bears essential similarities to Girardʼs (...) LC proof system for classical logic. The second proof system is based on a semantic tableau and extends Dragalinʼs multiple-conclusion version of intuitionistic sequent calculus. We show that soundness and completeness hold for these notions of semantics and proofs, from which it follows that cut is admissible in the proof systems and that the propositional fragment of the logic is decidable. (shrink)

Utilitarianism, the approach to ethics based on the maximization of overall well-being, continues to have great traction in moral philosophy and political thought. This Companion offers a systematic exploration of its history, themes, and applications. First, it traces the origins and development of utilitarianism via the work of Jeremy Bentham, John Stuart Mill, Henry Sidgwick, and others. The volume then explores issues in the formulation of utilitarianism, including act versus rule utilitarianism, actual versus expected consequences, and objective versus subjective theories (...) of well-being. Next, utilitarianism is positioned in relation to Kantianism and virtue ethics, and the possibility of conflict between utilitarianism and fairness is considered. Finally, the volume explores the modern relevance of utilitarianism by considering its practical implications for contemporary controversies such as military conflict and global warming. The volume will be an important resource for all those studying moral philosophy, political philosophy, political theory, and history of ideas. (shrink)

The civic republican tradition in political thought includes Niccolo Machiavelli, Jean-Jacques Rousseau, and Alexis de Tocqueville. The belief that it is imperative that citizens participate actively and disinterestedly in public affairs, i.e., that they possess "civic virtue" or "public spirit" is a prominent family resemblance between its members. Civic republican thought has undergone a recent resurgence, and one consequence is that political philosophers and other theorists have begun to ask whether liberals can take civic virtue seriously. Certain critics of liberalism, (...) including Michael Sandel and Charles Taylor, have answered this question in the negative. They give a variety of reasons for this answer, ranging from the inability of the atomistic ontologies underlying many liberal theories to make sense of the existence of a common good to the inability of the liberal state to concern itself with the character of its citizens. ;For the most part, unsurprisingly, these antiliberals direct their arguments at the work of twentieth-century "deontological" liberals such as John Rawls and Ronald Dworkin. While Rawls and Dworkin say relatively little about civic virtue, many earlier liberals believed firmly in its importance. John Stuart Mill's centrality to the liberal tradition and the thoroughgoing nature of his liberalism make him an especially interesting "civic liberal." My central thesis is that the civic and liberal components of his political philosophy combine to form a coherent whole. In my early exegetical chapters I provide the first systematic exposition of the frequently ignored civic component. I then address the work of several of Mill's interpreters who either explicitly or implicitly point to possible problems with his attempt to weave together the civic and liberal strands in his thought, and conclude that these problems are either not real or not insoluble. Finally, I consider whether the arguments which Sandel and Taylor, et. al., have given to show that contemporary liberal theories cannot consistently incorporate the civic republican belief in the importance of active and disinterested civic participation might have force against Mill. I show that they do not, and not simply because On Liberty is not A Theory of Justice but because the many of the objections are poorly reasoned. (shrink)

This book contains new essays in honor of Melvin J. Lerner, a pioneer in the psychological study of justice. The contributors to this volume are internationally renowned scholars from psychology, business, and law. They examine the role of justice motivation in a wide variety of contexts, including workplace violence, affirmative action programs, helping or harming innocent victims and how people react to their own fate. Contributors explore fundamental issues such as whether people's interest in justice is motivated by self-interest or (...) a genuine concern for the welfare of others, when and why people feel a need to punish transgressors, how a concern for justice emerges during the development of societies and individuals, and the relation of justice motivation to moral motivation. How an understanding of justice motivation can contribute to the amelioration of major social problems is also examined. (shrink)

In a recent article in Ethics, Elijah Millgram presents a novel reconstruction of J. S. Mill's ‘proof’ of the principle of utility. Millgram's larger purpose is to critique instrumentalist approaches to practical reasoning. His reading of the proof makes Mill out to be an instrumentalist, and Millgram thinks that the ultimate failure of Mill's argument usefully illustrates an inconsistency inherent in instrumentalism. Yet Millgram's interpretation of the proof does not succeed. Mill is not an instrumentalist. Millgram may be right that (...) instrumentalism is incoherent, but he has chosen the wrong figure to illustrate the point. (shrink)

In Ideal Code, Real World, Brad Hooker proposes an account of the relation between his rule-consequentialism and virtue according to which the virtues (1) have intrinsic value and (2) are identical with the dispositions that are of the ideal code. While it is not clear whether Hooker actually intends to endorse this account or only intends to moot it for discussion, I argue that for him to adopt it would be a mistake. Not only would this mean that his moral (...) theory was no longer properly a consequentialist view at all, but it would commit him to inconsistent views about how normative theories are justified. (shrink)

Climate change has become the most pressing moral and political problem of our time. Ethical theories help us think clearly and more fully about important moral and political issues. And yet, to date, there have been no books that have brought together a broad range of ethical theories to apply them systematically to the problems of climate change. This volume fills that deep need. Two preliminary chapters--an up-to-date synopsis of climate science and an overview of the ethical issues raised by (...) climate change--set the stage. After this, ten leading ethicists in ten separate chapters each present a major ethical theory and discuss the implications of that view for how we decide to respond to a rapidly warming planet. Each chapter first provides a brief exposition of the view before working out what that theory "has to say" about climate change and our response to the problems it poses. Key features: - Up-to-date synopsis of climate science - Clear overviews of a wide range of ethical theories and perspectives by leading experts - Insightful discussions of the implications of these theories and perspectives for our response to climate change - A unique opportunity to assess the relative strengths and weaknesses of various ethical viewpoints. (shrink)

In 'Axiological Actualism' Josh Parsons argues that 'axiological actualism', which is 'the doctrine that ethical theory should refrain from assigning levels of welfare, or preference orderings, or anything of the sort to merely possible people', lends plausibility to 'the converse intuition'. This is the proposition that 'the welfare a person would have, were they actual, can give us a reason not to bring that person into existence'. I show that Parsons's argument delivers less than he promises. It could be convincing (...) only to actualists who hold certain views about normative ethics, and could at most convince them to heed the converse intuition only under certain circumstances. (shrink)

In 'Axiological Actualism' Josh Parsons argues that 'axiological actualism', which is 'the doctrine that ethical theory should refrain from assigning levels of welfare, or preference orderings, or anything of the sort to merely possible people', lends plausibility to 'the converse intuition'. This is the proposition that 'the welfare a person would have, were they actual, can give us a reason not to bring that person into existence'. I show that Parsons's argument delivers less than he promises. It could be convincing (...) only to actualists who hold certain views about normative ethics, and could at most convince them to heed the converse intuition only under certain circumstances. (shrink)

In this article, I argue that the reading of Mill that D.G. Brown presents in ‘Mill’s Moral Theory: Ongoing Revisionism’ is inconsistent with several key passages in Mill’s writings. I also show that a rule-utilitarian interpretation that is very close to the one developed by David Lyons is able to account for these passages without difficulty.