Members of the Student Clinical Ethics Committee discussed whether tube feeding should be instigated for a man who had indicated through his actions that he may be refusing it, although his family stated that he would have wanted to be kept alive in such a situation. The Committee considered the key issues of capacity and best interests, which in this case were confounded by lack of clarity about whether the patient’s actions amounted to a valid refusal of life sustaining treatment, (...) and if his previous views still pertained to his current, yet unforeseen, circumstances. As the discussion progressed, it became apparent that some members were reluctant to accept that non-insertion of clinically assisted feeding could ever be in a patient’s best interests. (shrink)

A good argument is one whose conclusions follow from its premises; its conclusions are consequences of its premises. But in what sense do conclusions follow from premises? What is it for a conclusion to be a consequence of premises? Those questions, in many respects, are at the heart of logic (as a philosophical discipline). Consider the following argument: 1. If we charge high fees for university, only the rich will enroll. We charge high fees for university. Therefore, only the rich (...) will enroll. There are many different things one can say about this argument, but many agree that if we do not equivocate (if the terms mean the same thing in the premises and the conclusion) then the argument is valid, that is, the conclusion follows deductively from the premises. This does not mean that the conclusion is true. Perhaps the premises are not true. However, if the premises are true, then the conclusion is also true, as a matter of logic. This entry is about the relation between premises and conclusions in valid arguments. (shrink)

In this paper we introduce a distinct metaethical position, fictionalism about morality. We clarify and defend the position, showing that it is a way to save the 'moral phenomena' while agreeing that there is no genuine objective prescriptivity to be described by moral terms. In particular, we distinguish moral fictionalism from moral quasi-realism, and we show that fictionalism possesses the virtues of quasi-realism about morality, but avoids its vices.

In this paper we offer a new argument for the existence of God. We contend that the laws of logic are metaphysically dependent on the existence of God, understood as a necessarily existent, personal, spiritual being; thus anyone who grants that there are laws of logic should also accept that there is a God. We argue that if our most natural intuitions about them are correct, and if they are to play the role in our intellectual activities that we take (...) them to play, then the laws of logic are best construed as necessarily existent thoughts -- more specifically, as divine thoughts about divine thoughts. We conclude by highlighting some implications for both theistic arguments and antitheistic arguments. (shrink)

Scientific anti-realists who appeal to the pessimistic induction (PI) claim that the theoretical terms of past scientific theories often fail to refer to anything. But on standard views in philosophy of language, such reference failures prima facie lead to certain sentences being neither true nor false. Thus, if these standard views are correct, then the conclusion of the PI should be that significant chunks of current theories are truth-valueless. But that is semantic anti-realism about scientific discourse—a position most philosophers of (...) science, anti-realists included, consider anathema today. Therefore, proponents of the PI confront a dilemma: either accept semantic anti-realism or reject common semantic views. I examine strategies (with particular emphasis on supervaluations) for the PI proponent to either lessen the sting of this argument, or learn to live with it. 1 Introduction2 Designation Failure 2.1 Designation failure leads to truth-valueless sentences2.1.1 Direct reference theory2.1.2 Fregeanism2.1.3 Accounts of reference-fixing: why ‘phlogiston’ fails to designate 2.2 Objection: sentences exhibiting designation failure are false not truth-valueless 2.3 Avoiding truth-valuelessness via controversial semantic positions3 What to do? Closing the Gaps4 Conclusion. (shrink)

Assuming AD + DC, we characterize the self-dual boldface pointclasses which are strictly larger than the pointclasses contained in them: these are exactly the clopen sets, the collections of all sets of Wadge rank [Formula: see text], and those of Wadge rank [Formula: see text] when ξ is limit.

SummaryThis article offers a novel and comprehensive account of Walter Bagehot's political thought. It ties together an interpretation of Bagehot's liberal commitment to norms of discussion and deliberation, with an analysis of Bagehot's extensive arguments about the institutions of representative government. We show how Bagehot's opposition to American-style presidentialism, to parliamentary democracy, and to proportional representation were profoundly shaped by his conceptions of government by discussion, and the rule of public opinion. Bagehot's criticisms of English parliamentarianism, both of its pre-1832 (...) and post-1832 varieties were also motivated by those principles, as was his own proposal for parliamentary reform. By examining the whole range of Bagehot's writings on representative government and by connecting his institutional recommendations to his liberal principles, we are also able to better clarify Bagehot's position in Victorian political thought. The article concludes with a discussion of the debate leading up to the Second Reform Act, in which we elucidate Bagehot's disagreements with other prominent exponents of liberalism including John Stuart Mill, the “university liberals,” and Robert Lowe. (shrink)

This paper applies concepts Deleuze developed in his ‘Postscript on the Societies of Control’, especially those relating to modulatory power, dividuation and control, to aspects of Australian schooling to explore how this transition is manifesting itself. Two modulatory machines of assessment, NAPLAN and My Schools, are examined as a means to better understand how the disciplinary institution is changing as a result of modulation. This transition from discipline to modulation is visible in the declining importance of the disciplinary teacher–student relationship (...) as a measure of the success of the educative process. The transition occurs through seduction because that which purports to measure classroom quality is in fact a serpent of modulation that produces simulacra of the disciplinary classroom. The effect is to sever what happens in the disciplinary space from its representations in a luminiferous ether that overlays the classroom. (shrink)

This article investigates infrastructure spending from a biopolitical perspective and rethinks its connections to emerging regimes of securitization. Starting with a study of the organization and contestation of the G8/G20 summits in Toronto in June 2010, the analysis moves through the shifty territory of a governmental logic that is reconfiguring the body politics of civic participation, as well as the ways in which discourses on economic growth, property and public safety intertwine in the aftermath of the 2008 global financial crisis. (...) The case of Toronto shows significant changes to recent security practices, control techniques and funding arrangements. Rather than ‘war on terror’, ‘austerity and crisis’ are the new keywords sustaining current governmental rationality and the criminalization of dissent, which are no longer funded by defence budgets but by economic stimuli packages. This new rationality, while still relying on fear as an affective mode to mobilize masses, has exchanged a set of discourses on the clash of cultures or civilization for one on sacrifice. Following Foucault’s work on the government of populations and security, it is now possible to talk about ‘a sacrifice series’ to describe the series of elements that connect military or economic logics of securitization. (shrink)

Food Problems and Economic Problems in America, Africa, the Middle East and Asia : Struggles and Resignation What are the various dynamics of crisis, revolt, and resignation currently operating on the American and African continents, in the Middle East and in Asia. What effects do they have on the policies adopted to “get out of the crisis”? These are the issues which Greg Albo, Kako Nubukpo, Rhina Roux, Marie Noëlle Abiyaghi and Son Youg Woo address in this article. They (...) examine the consequences of neo-liberal capitalism and the succession of crises in food, oil, finance, and in the economy, before going on to explain how they emerge in their regional contexts where they take on their specific guises. (shrink)

The objective of this paper is to examine the ‘Code of Ethics Quality’ (CEQ) in the largest companies of Australia, Canada and the United States. For this purpose, a proposed CEQ construct has been applied. It appears from the empirical findings that while Australia, Canada and the United States are extremely similar in their economic and social development, there may well be distinct cultural mores and issues that are forming their business ethics practices. A research implication derived from the performed (...) research is that the construct provides a selection of observable and measurable elements in the context of CEQ. The construct of CEQ consists of nine measures divided into two dimensions (i.e. staff support and regulation). They should not be seen as a complete list. On the contrary, it is encouraged that others propose and elaborate revisions and extensions. A practical implication of this paper is a structure of what and how to examine the CEQ in a managerial setting. It may assist companies in their efforts to establish, maintain and improve their ethical culture, norms and beliefs within the organization and supporting them in their ethical business practices with different stakeholders in the marketplace and society. The dimensions and measures of the construct may be used as a frame of reference for further research. They may be useful and applicable across contexts and over time using similar samples when it comes to large companies, as small‐ or medium‐sized ones may not have considered all areas nor have the elements in place. This is a research limitation, but it provides an opportunity for further research. (shrink)

A number of Christian philosophers, most recently Gary R. Habermas and William Lane Craig, have claimed that there is sufficient historical evidence to establish the resurrection of Jesus conceived as the transformation of Jesus’ corpse into a living supernatural body that possesses such extraordinary dispositional properties as the inability to ever die again. I argue that, given this conception of resurrection, our only source of potential evidence, the New Testament Easter traditions, cannot provide adequate information to enable us to establish (...) the historicity of the resurrection---even on the assumption that these traditions are completely historically reliable. (shrink)

Something has been going wrong on many college campuses in the last few years. Speakers are shouted down. Students and professors say they are walking on eggshells and are afraid to speak honestly. Rates of anxiety, depression, and suicide are rising--on campus as well as nationally. How did this happen? First Amendment expert Greg Lukianoff and social psychologist Jonathan Haidt show how the new problems on campus have their origins in three terrible ideas that have become increasingly woven into (...) American childhood and education: What doesn't kill you makes you weaker; always trust your feelings; and life is a battle between good people and evil people. These three Great Untruths contradict basic psychological principles about well-being and ancient wisdom from many cultures. Embracing these untruths--and the resulting culture of safetyism--interferes with young people's social, emotional, and intellectual development. It makes it harder for them to become autonomous adults who are able to navigate the bumpy road of life. Lukianoff and Haidt investigate the many social trends that have intersected to promote the spread of these untruths. They explore changes in childhood such as the rise of fearful parenting, the decline of unsupervised, child-directed play, and the new world of social media that has engulfed teenagers in the last decade. They examine changes on campus, including the corporatization of universities and the emergence of new ideas about identity and justice. They situate the conflicts on campus within the context of America's rapidly rising political polarization and dysfunction. This is a book for anyone who is confused by what is happening on college campuses today, or has children, or is concerned about the growing inability of Americans to live, work, and cooperate across party lines. (shrink)

Our topic is the notion of logical consequence: the link between premises and conclusions, the glue that holds together deductively valid argument. How can we understand this relation between premises and conclusions? It seems that any account begs questions. Painting with very broad brushtrokes, we can sketch the landscape of disagreement like this: “Realists” prefer an analysis of logical consequence in terms of the preservation of truth [29]. “Anti-realists” take this to be unhelpful and o:er alternative analyses. Some, like Dummett, (...) look to preservation of warrant to assert [9, 36]. Others, like Brandom [5], take inference as primitive, and analyse other notions in terms of it. There is plenty of disagreement on the “realist” side of the fence too. It is one thing to argue that logical consequence involves preservation of truth. It is another to explain how far truth must be preserved. Is the preservation essentially modal (in all circumstances [25]) or analytic (vouchsafed by.. (shrink)

Technological progress may eventually produce sophisticated robots with human-like traits that result in humans forming meaningful relationships with them. Such relationships would likely lead to a demand for human–artificial intelligence matrimony. U.S. Supreme Court decisions that expanded the definition of marriage to include interracial and same-sex couples, as well as those that have not extended marriage to polygamous relationships, provide guidance regarding the criteria that human–AI would have to meet to successfully assert a right to marry. Ultimately, robots will have (...) to possess certain characteristics of personhood to marry, including the capacity to contract and to engage in an intimate relationship. Alternatively, if AIs can simulate these abilities sufficiently, we may believe that they have these capacities. Even if AIs genuinely possess the capabilities necessary to enter into a marriage, it is social acceptance of intelligent non-humans as life partners that will likely influence legal development is this realm rather than personhood criteria. However, AIs are likely to face bias due to their “artificial” rather than biological nature. Yet, Peter Singer’s influential argument regarding speciesism in the context of animal rights implies that AIs with specific human-like qualities cannot be justifiably denied certain rights. (shrink)

This book introduces an important group of logics that have come to be known under the umbrella term 'susbstructural'. Substructural logics have independently led to significant developments in philosophy, computing and linguistics. _An Introduction to Substrucural Logics_ is the first book to systematically survey the new results and the significant impact that this class of logics has had on a wide range of fields.The following topics are covered: * Proof Theory * Propositional Structures * Frames * Decidability * Coda Both (...) students and professors of philosophy, computing, linguistics, and mathematics will find this to be an important addition to their reading. (shrink)

In an attempt to address the theoretical gap between linguistics and philosophy, a group of semanticists, calling itself the Generic Group, has worked to develop a common view of genericity. Their research has resulted in this book, which consists of a substantive introduction and eleven original articles on important aspects of the interpretation of generic expressions. The introduction provides a clear overview of the issues and synthesizes the major analytical approaches to them. Taken together, the papers that follow reflect the (...) current state of the art in the semantics of generics, and afford insight into various generic phenomena. (shrink)

Carruthers offers a refreshing piece of “substantive philosophy.” Going beyond the limitations of pure analysis, he adopts a methodology which is one part analysis, one part empirical data, and a heavy dose of inference to the best explanation. The overarching goal is to advance the commonsense—yet unfashionable—thesis that natural language is the primary medium of thought, and to defend the related cognitive conception of NL. In particular, Carruthers argues that imaginative phonological representations of “inner speech” are constitutive of conscious thoughts, (...) and that thinking involves operations on such symbols. While there is still a role for mentalese cognition, such thinking is always unconscious, and probably of limited innate conceptual resources. The weak thesis is that, of natural necessity, all conscious propositional thought requires NL. The strong thesis is that, of natural necessity, distinctively human thoughts can only be tokened in natural language—hence even much of our unconscious thinking occurs in English. (shrink)

This paper concerns a key point of decision in Donald Davidson's early work in philosophy of language — a fateful decision that set him and the discourse in the area on the path of truth-theoretic semantics. The decision of moment is the one Davidson makes when, in the face of a certain barrier, he gives up on the idea of constructing an explicit meaning theory that would parallel Tarski's recursive way with truth theory. For Davidson there was little choice: he (...) tells us he does not see how to deal with the difficulty except in the radical way he proposes. But there is a way to give such a meaning theory — a meaning theory proper which, using classical logic only, meets a meaning-theoretic analogue of Convention T, satisfies Davidson’s three key desiderata for a theory of meaning, reflects linguistic competence, and avoids quantifying over meanings. The meaning theory sketched here uses Tarskian strategies, as Davidson proposed, but differs from Davidson's approach in not going by way of a truth theory for the target language. (shrink)

In barely the space of one generation, Athens was transformed from a conventional city-state into something completely new--a region-state on a scale previously unthinkable. This book sets out to answer a seemingly simple question: How and when did the Athenian state attain the anomalous size that gave it such influence in Greek politics and culture in the classical period? Many scholars argue that Athens's incorporation of Attica was a gradual development, largely completed some two hundred years before the classical era. (...) Anderson, however, suggests that it is not until the late sixth century that we see the first systematic attempts by the Athenian polis to integrate all of Attica. Anderson first takes issue with the prevailing view of Cleisthenes' landmark political reforms of 508-7 b.c., arguing that they were animated by a more comprehensive vision of regional political community in Attica. The Athenians' strengthened the state by establishing institutional mechanisms that would allow inhabitants of the Attic periphery to participate as never before in the life of the center. The creation of a suitable physical setting for the new order was accompanied by religious, military, and symbolic innovations. Regional participation in Athenian affairs was stimulated by encouraging the Attic populace to imagine themselves, for the first time ever, as members of a single, like-minded, self-governing political community. Greg Anderson is Assistant Professor of Classics and History, University of Illinois at Chicago. (shrink)

It is argued that the English bare plural (an NP with plural head that lacks a determiner), in spite of its apparently diverse possibilities of interpretation, is optimally represented in the grammar as a unified phenomenon. The chief distinction to be dealt with is that between the generic use of the bare plural (as in Dogs bark) and its existential or indefinite plural use (as in He threw oranges at Alice). The difference between these uses is not to be accounted (...) for by an ambiguity in the NP itself, but rather by explicating how the context of the sentence acts on the bare plural to give rise to this distinction. A brief analysis is sketched in which bare plurals are treated in all instances as proper names of kinds of things. A subsidiary argument is that the null determiner is not to be regarded as the plural of the indefinite article a. (shrink)

This paper continues the work of Priest and Sylvan in Simplified Semantics for Basic Relevant Logics, a paper on the simplified semantics of relevant logics, such as B⁺ and B. We show that the simplified semantics can also be used for a large number of extensions of the positive base logic B⁺, and then add the dualising '*' operator to model negation. This semantics is then used to give conservative extension results for Boolean negation.

Many people have claimed that integrity requires sticking to one's convictions come what may. Greg Scherkoske challenges this claim, arguing that it creates problems in distinguishing integrity from fanaticism, close-mindedness or mere inertia. Rather, integrity requires sticking to one's convictions to the extent that they are justifiable and likely to be correct. In contrast to traditional views of integrity, Scherkoske contends that it is an epistemic virtue intimately connected to what we know and have reason to believe, rather than (...) an essentially moral virtue connected to our values. He situates integrity in the context of shared cognitive and practical agency and shows that the relationship between integrity and impartial morality is not as antagonistic as many have thought - which has important implications for the 'integrity objection' to impartial moral theories. This original and provocative study will be of great interest to advanced students and scholars of ethics. (shrink)

introduction Rhetoric/Memory/Place Carole Blair, Greg Dickinson, and Brian L. Ott The story is told of the poet Simonides of Ceos who, after chanting a poem ...

Should organ transplants be given to patients who have waited the longest, or need it most urgently, or those whose survival prospects are the best? The rationing of health care is universal and inevitable, taking place in poor and affluent countries, in publicly funded and private health care systems. Someone must budget for as well as dispense health care whilst aging populations severely stretch the availability of resources. The Ethics of Health Care Rationing is a clear and much-needed introduction to (...) this increasingly important topic, considering and assessing the major ethical problems and dilemmas about the allocation, scarcity and rationing of health care. Beginning with a helpful overview of why rationing is an ethical problem, the authors examine the following key topics: What is the value of health? How can it be measured? What does it mean that a treatment is "good value for money"? What sort of distributive principles - utilitarian, egalitarian or prioritarian - should we rely on when thinking about health care rationing? Does rationing health care unfairly discriminate against the elderly and people with disabilities? Should patients be held responsible for their health? Why does the debate on responsibility for health lead to issues about socioeconomic status and social inequality? Throughout the book, examples from the US, UK and other countries are used to illustrate the ethical issues at stake. Additional features such as chapter summaries, annotated further reading and discussion questions make this an ideal starting point for students new to the subject, not only in philosophy but also in closely related fields such as politics, health economics, public health, medicine, nursing and social work. (shrink)

An advanced-level logic textbook that presents proof construction on equal footing with model building. Potentially relevant to students of mathematics and computer science as well.

This article underlines and draws attention to critical insights Esposito makes regarding the prospects of rethinking community in a globalized world. Alongside Agamben and Nancy, Esposito challenges the property prejudice found in mainstream models of community. In identity politics, collective identity is converted into a form of communal property. Borders, sovereign territories, and exclusive rights are fiercely defended in the name of communal property. Esposito responds to this problem by developing what I call a “deontological communal contract” where being and (...) ethics are prioritized over having and economics. I examine this new perspective on community in relation to mainstream models found in contemporary and classical social theory. (shrink)

I am grateful to Catharine Abell and Jonathan Gilmore for their comments and for the opportunity to think again about some important questions. Before I respond.

Three decades ago, James Bogen and James Woodward argued against the possibility and usefulness of scientific explanations of data. They developed a picture of scientific reasoning where stable phenomena were identified via data without much input from theory. Rather than explain data, theories ‘save the phenomena’. In contrast, I argue that there are good reasons to explain data, and the practice of science reveals attempts to do so. I demonstrate that algorithms employed to address inverse problems in remote-sensing applications should (...) be understood as attempts to identify phenomena by explaining the data. Thus, this paper furthers understanding of data-to-phenomena reasoning in science, and demonstrates theory may play a more central role in phenomena identification than previously recognized. (shrink)

Some empirical findings seem to show that people value health benefits differently depending on the age of the beneficiary. Health economists and philosophers have offered justifications for these preferences on grounds of both efficiency and equity. In this paper, I examine the most prominent examples of both sorts of justification: the defence of age-weighting in the WHO's global burden of disease studies and the fair innings argument. I argue that neither sort of justification has been worked out in satisfactory form: (...) age should not be taken into account in the framework of the burden of disease measure, and on the most promising formulations of the fair innings argument, it turns out to be merely an indicator of some other factor. I conclude by describing the role of age in theories of justice of healthcare resource allocation. (shrink)

Stanley and Williamson reject Ryle's knowing‐how/knowing‐that distinction charging that it obstructs our understanding of human action. Incorrectly interpreting the distinction to imply that knowledge‐how is non‐propositional, they object that Ryle's argument for it is unsound and linguistic theory contradicts it. I show that they (and their interlocutors) misconstrue the distinction and Ryle's argument. Consequently, their objections fail. On my reading, Ryle's distinction pertains to, not knowledge, but an explanatory gap between explicit and implicit content, and his argument for it is (...) sound. I defend the distinction's necessity in explaining human action and show that it propels a fruitful explanatory program. (shrink)

This Element is an introduction to recent work proofs and models in philosophical logic, with a focus on the semantic paradoxes the sorites paradox. It introduces and motivates different proof systems and different kinds of models for a range of logics, including classical logic, intuitionistic logic, a range of three-valued and four-valued logics, and substructural logics. It also compares and contrasts the different approaches to substructural treatments of the paradox, showing how the structural rules of contraction, cut and identity feature (...) in paradoxical derivations. It then introduces model theoretic treatments of the paradoxes, including a simple fixed-point model construction which generates three-valued models for theories of truth, which can provide models for a range of different non-classical logics. The Element closes with a discussion of the relationship between proofs and models, arguing that both have their place in the philosophers' and logicians' toolkits. (shrink)

This article underlines and draws attention to critical insights that Esposito makes regarding the prospects of rethinking community in a globalized world. Alongside Agamben and Nancy, Esposito challenges the property prejudice found in mainstream models of community. In identity politics, collective identity is converted into a form of communal property. Borders, sovereign territories, and exclusive rights are fiercely defended in the name of communal property. Esposito responds to this problem by developing what I call a “deontological communal contract” where being (...) and ethics are prioritized over having and economics. I examine this new perspective on community in relation to mainstream models found in contemporary and classical social theory. (shrink)

The precise relationship between the autonomic nervous system and emotion has been a topic of intense debate and research throughout the history of modern psychology. The present article considers some of the more influential theoretical frameworks that continue to drive contemporary research on the relationship between emotion and physiological processes. In particular, we highlight the multiple routes through which somatovisceral afference influences emotion and how this relates to the topic of emotion-specific patterns of autonomic nervous system activity.

The stock market crash of 1987 had a profound effect on corporate Australia and the Australian community in general. The fall-out revealed that some of our most respected business figures had not been as ethical, or even as lawful, as we would have hoped. This impropriety produced in Australia an awakening to business ethics. Whilst many companies endeavoured to introduce ethical practices into their corporations, they perceived ethics as a way of minimising damage to the corporation and in some cases (...) as a means of competitive advantage. What was lost was the reason that one should embark on business ethics; and that is to make the society and corporate Australia a more ethical place in which to exist.This paper proposes a model based on 2 factors: commitment and partnerships, as a means of enabling corporate Australia to refocus attention on the main purpose of being inherently ethical in all that we do. This ethical model requires a commitment to partnerships with all stakeholders both internal and external in an attempt to enhance the level of ethical business practices that are contemplated and pursued within corporate Australia. Whilst the research agenda and the information collected is Australian-based, it is hoped that the ideas contained within this paper will have a wider appeal to corporations in similar cultural settings. (shrink)

In a recent paper, Michael Otsuka and Alex Voorhoeve present a novel argument against prioritarianism. The argument takes its starting point from empirical surveys on people's preferences in health care resource allocation problems. In this article, I first question whether the empirical findings support their argument, and then I make some general points about the use of ‘empirical ethics’ in ethical theory.

In the near future developments in non-invasive prenatal testing may soon provide couples with the opportunity to test for and diagnose a much broader range of heritable and congenital conditions than has previously been possible. Inevitably, this has prompted much ethical debate on the possible implications of NIPT for providing couples with opportunities for reproductive choice by way of routine prenatal screening. In view of the possibility to test for a significantly broader range of genetic conditions with NIPT, the European (...) Society of Human Genetics and American Society of Human Genetics recommend that, pending further debate, prenatal screening for reproductive choice should only be offered where concerning serious congenital conditions and childhood disorders. In support of this recommendation, the ESHG and ASHG discuss a number of ethical issues on which they prompt further debate: the informational privacy of the future child, the trivialization of abortion, the risk of information overload, and issues of distributive justice. This paper responds to this call with further reflection on each ethical issue and how it relates to the moral justification of providing couples with opportunities for meaningful reproductive choice. The paper concludes that whilst there may be good reasons for qualifying the scope of any unsolicited prenatal screening offer to serious congenital conditions and childhood disorders, if prenatal screening is justified for providing couples with opportunities for meaningful reproductive choice, then health services may have obligations to empower couples with the same opportunity where concerning other conditions. (shrink)

Natural deduction with alternatives extends Gentzen–Prawitz-style natural deduction with a single structural addition: negatively signed assumptions, called alternatives. It is a mildly bilateralist, single-conclusion natural deduction proof system in which the connective rules are unmodi_ed from the usual Prawitz introduction and elimination rules — the extension is purely structural. This framework is general: it can be used for (1) classical logic, (2) relevant logic without distribution, (3) affine logic, and (4) linear logic, keeping the connective rules fixed, and varying purely (...) structural rules. The key result of this paper is that the two principles that introduce kinds of irrelevance to natural deduction proofs: (a) the rule of explosion (from a contradiction, anything follows); and (b) the structural rule of vacuous discharge; are shown to be two sides of a single coin, in the same way that they correspond to the structural rule of weakening in the sequent calculus. The paper also includes a discussion of assumption classes, and how they can play a role in treating additive connectives in substructural natural deduction. (shrink)