The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof theory of finite-valued first order (...) logics in a general way, and to present some of the more important results in this area. In Systems covered are the resolution calculus, sequent calculus, tableaux, and natural deduction. This report is actually a template, from which all results can be specialized to particular logics. (shrink)

Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as Hilbert developed systems of logic to formalize mathematics. These systems were meant to serve either as themselves foundational, or at least as formal analogs of mathematical reasoning amenable to mathematical study, e.g., in Hilbert’s consistency program. Similar efforts continue, but have been (...) expanded by the development of sophisticated methods to study the properties of such systems using proof and model theory. In parallel with this evolution of logical formalisms as tools for articulating mathematical theories (broadly speaking), much progress has been made in the quest for a mechanization of logical inference and the investigation of its theoretical limits, culminating recently in the development of new foundational frameworks for mathematics with sophisticated computer-assisted proof systems. In addition, logical formalisms developed by logicians in mathematical and philosophical contexts have proved immensely useful in describing theories and systems of interest to computer scientists, and to some degree, vice versa. Three examples of the influence of logic in computer science are automated reasoning, computer verification, and type systems for programming languages. (shrink)

Studies the politics of Heidegger in terms of "thrownness" or "existential contingency". Attempts to think through Heidegger's philosophy in a manner that parallels his own dialogue with other key western thinkers.

Methods available for the axiomatization of arbitrary finite-valued logics can be applied to obtain sound and complete intelim rules for all truth-functional connectives of classical logic including the Sheffer stroke and Peirce’s arrow. The restriction to a single conclusion in standard systems of natural deduction requires the introduction of additional rules to make the resulting systems complete; these rules are nevertheless still simple and correspond straightforwardly to the classical absurdity rule. Omitting these rules results in systems for intuitionistic versions of (...) the connectives in question. (shrink)

Textbook on Gödel’s incompleteness theorems and computability theory, based on the Open Logic Project. Covers recursive function theory, arithmetization of syntax, the first and second incompleteness theorem, models of arithmetic, second-order logic, and the lambda calculus.

This book is the complete story of the creation of the universe, as it was understood by the ancient Egyptians. It is a collection of harmonic and radical 'Black Thoughts' and the pursuit of equality for all of this planet's inhabitants"--P. vii.

Having visited Ireland regularly during the 1930s, Ludwig Wittgenstein resigned his Cambridge philosophy professorship in 1947 and moved there, living in a fishing village on the Atlantic coast and hotels in Dublin and the Wicklow Mountains. Although Wittgenstein spent some time out of the country, Ireland was effectively his base for three very productive years during which he worked on what would become one of his key books, the posthumously published Philosophical Investigations. Wittgenstein in Ireland represents the first sustained account (...) of Wittgenstein's time in Ireland, placing it in its historical context. Wall pays a good deal of attention to the representation of the Irish landscape in which the Austrian philosopher found himself able to work; a large part of his writings were produced in the bleak landscapes of Ireland and Norway. (shrink)

Written by a former student of Heidegger, this book examines the relationship between the philosophy and the politics of a celebrated teacher and the allure that Nazism held out for scholars committed to revolutionary nihilism.

The concepts of freedom and equality lie at the heart of much contemporary political debate. But how, exactly, are these concepts to be understood? And do they really represent desirable political values? Norman begins from the premise that freedom and equality are rooted in human experience, and thus have a real and objective content. He then argues that the attempt to clarify these concepts is therefore not just a matter of idle philosophical speculation, but also a matter of practical politics, (...) for the philosophical conclusions we reach also have important implications for the day-to-day world of political action. Touching on the work of such influential thinkers as Mill, Berlin, Hayek, Nozick, Rawls, and Williams, this book serves as a valuable introduction to the central issues in political philosophy. (shrink)

On the basis of careful textual exegesis and philosophical analysis, and contrary to the received view, Mark R. Wheeler demonstrates that Aristotle presents and systematically explicates his definition of the essence of the truth in the Metaphysics. Aristotle states the nominal definitions of the terms "truth" and "falsehood" as part of his arguments in defense of the logical axioms. These nominal definitions express conceptions of truth and falsehood his philosophical opponents would have recognized and accepted in the context of dialectical (...) argument. On the basis of these nominal definitions, Aristotle develops his definitions of the essences of truth and falsehood--his "real" definitions of truth and falsehood. Aristotle's methodical exposition of his essential definitions of truth and falsehood in the Metaphysics serves as a well-developed example of how his philosophical inquiry starts with nominal definitions and ends with real definitions. Wheeler also argues for the novel claim that Aristotle defines the most fundamental kind of truth in terms of accurate measurement. Aristotle's metrical conception of truth serves as the theoretical basis for specifying the truth conditions of various assertions, for identifying the sorts of beings implicated in these truth conditions, and for explaining the nature of approximate truth and falsehood. Far from offering us a minimal account of truth, Wheeler shows how Aristotle offers us a sophisticated and metrical theory of truth. (shrink)

. History of the concept of economic efficiency . INTRODUCTION James Buchanan won the Nobel Prize by proving that the process by which elected officials ...

The Curry-Howard isomorphism is a proof-theoretic result that establishes a connection between derivations in natural deduction and terms in typed lambda calculus. It is an important proof-theoretic result, but also underlies the development of type systems for programming languages. This fact suggests a potential importance of the result for a philosophy of code.

This paper explores two ways in which evaluations of an agent's character as virtuous or vicious are properly influenced by what the agent finds salient or attention-grabbing. First, we argue that ignoring salient needs reveals a greater deficit of benevolent motivation in the agent, and hence renders the agent more blameworthy. We use this fact to help explain our ordinary intuition that failing to give to famine relief is in some sense less bad than failing to help a child who (...) is drowning right before your eyes, in a way that's compatible with the contention that there's no principled reason to see the one life-saving act as any more or less choiceworthy than the other. Second, we argue that alleged ‘virtues of ignorance’ are better understood as ‘virtues of salience’. Rather than placing demands on what we believe, these virtues place demands on what we find salient. (shrink)

Drawing on a passage from Ramsey's Truth and Probability, we formulate a simple, plausible constraint on evaluating the accuracy of credences: the Calibration Test. We show that any additive, continuous accuracy measure that passes the Calibration Test will be strictly proper. Strictly proper accuracy measures are known to support the touchstone results of accuracy-first epistemology, for example vindications of probabilism and conditionalization. We show that our use of Calibration is an improvement on previous such appeals by showing how it answers (...) or sidesteps problems that have been raised for previous work in this area. (shrink)

This book gives a descriptive analysis of specific Madhyamika texts. It compares the ideology of Kumarajiva (a translator of the four Madhyamika treatises 400 A.D.) with the ideologies of the three Chinese contemporaries - HuiYuan, Seng-Jui and Seng-Chao. It envisages an intercultural transmission of religious and philosophical ideas from India to China.

ABSTRACT:Moral realism entails that there are metaphysically necessary moral principles of the form ‘all actions of nonmoral kind Z are morally good’; being discoverable a priori, these must be logically necessary. This article seeks to justify this apparently puzzling consequence. A sentence expresses a logically necessary proposition iff its negation entails a contradiction. The method of reflective equilibrium assumes that the simplest account of the apparently correct use of sentences of some type in paradigm examples is probably logically necessary. An (...) account is simple insofar as it uses few predicates designating properties easily recognizable in many different kinds of paradigm examples. I illustrate how reflective equilibrium uses these criteria to discover logically necessary nonmoral propositions such as ‘if S remembers doing X, S believes that he did X’ and ‘if it is scarlet, it is red’. I then illustrate how exactly the same procedures can lead us from paradigm examples of apparently true sentences asserting that actions of some kind are good to discovering moral principles. I advance the contingent hypothesis that most contemporary humans, although they initially disagree about moral issues, have derived from different paradigm examples the same concept of moral goodness, which will ensure that the use of reflective equilibrium will lead to eventual agreement about moral issues. That strongly suggests that the moral principles eventually reached by reflective equilibrium are logically necessary ones. (shrink)

The Intergovernmental Panel on Climate Change has developed a novel framework for assessing and communicating uncertainty in the findings published in their periodic assessment reports. But how should these uncertainty assessments inform decisions? We take a formal decision-making perspective to investigate how scientific input formulated in the IPCC’s novel framework might inform decisions in a principled way through a normative decision model.

Nietzsche announces his intentions to publish a “physiology of aesthetics”, namely a naturalistic explanation for how aesthetic judgements are grounded in the physiology of both the one experiencing the work, and the creator of it. But as well as the physiological reduction of aesthetic judgements, Nietzsche in many places across his oeuvre frames the apparatus of physiology, especially the prescriptive dimension of self-cultivation, in terms amenable to being treated as ‘aesthetic’. The first section will mount a (re-) defense of the (...) use of aestheticized language for discussing Nietzschean self-cultivation. The second section demonstrates an aesthetic evaluation of capacities that make possible the acquisition and removal of instinctual components, ultimately arguing for Nietzsche’s qualified indeterminism regarding the capacity for self-cultivation. The third section will assess the pres- ence of another aesthetic measure, this time in terms of envisaging one’s psycho-physiology by reference to an external spectacle. The final section discusses metaethical questions stemming from Nietzsche’s prescriptive language regarding the aestheticization of our physiology. (shrink)

In _Charles Peirce and Modern Science_, T.L. Short encourages us to read Peirce’s oeuvre in the spirit of philosophical experimentalism. The result is a rewarding and refreshing book that clarifies longstanding controversies and stakes out novel positions in the debates. In these comments, I subject Short’s statements regarding the validity of induction to critical scrutiny. I argue that while much of what he states is correct, he errs in holding that induction is invalid in the short run of an individual’s (...) life. (shrink)

Sociomaterial theories, including actor–network theory (ANT), materialist feminism and posthumanism, are sometimes argued to not be addressing or unable to address sufficiently the political and are therefore dismissed as irrelevant to educational research. Through an extended discussion of writers across the social sciences, this article seeks to counter such a view. Drawing specifically on the work of Latour on the nature of critique and on examples of political analysis from writers such as Barad, Bennett, Braidotti, Marres and Whatmore, we suggest (...) that sociomaterialist approaches to the more-than-human open up extended understandings and productive alternative practices of politics. While recognising that this is a work in progress and not without difficulties and challenges, we argue that there is much to be gained for educational researchers from engaging with such approaches. (shrink)

ABSTRACTThe modern view of economic conspiracies stands in stark contrast to the view in the eighteenth century. Such classical economists as Adam Smith took conspiracy to be the natural result of our tendency to associate with one another. It manifested itself in collusion among both laborers and manufacturers to raise their income. By the mid-twentieth century, however, economists had come around to an entirely different view, according to which voluntary collaboration, especially in large groups, was unnatural and irrational, such that (...) the only way to sustain cartels and trade unions was via compulsory, tyrannical measures. The notion of rationality that underlies such a view—as seen in the parallel notion that it is irrational to vote—threatens the understanding of agency that is essential to democracy. (shrink)

In terminally ill individuals who would otherwise end their own lives, active voluntary euthanasia (AVE) can be seen as life-extending rather than life-shortening. Accordingly, AVE supports key pro-euthanasia arguments (appeals to autonomy and beneficence) and meets certain sanctity of life objections. This paper examines the extent to which a terminally ill individual’s wish to donate organs after death contributes to those life-extension arguments. It finds that, in a terminally ill individual who wishes to avoid experiencing life he considers to be (...) not worth living, and who also wishes to donate organs after death, AVE maximizes the likelihood that such donations will occur. The paper finds that the wish to donate organs strengthens the appeals to autonomy and beneficence, and fortifies the meeting of certain sanctity of life objections, achieved by life-extension arguments, and also generates appeals to justice that form novel life-extension arguments in favour of AVE in this context. (shrink)

When making decisions, people naturally face uncertainty about the potential consequences of their actions due in part to limits in their capacity to represent, evaluate or deliberate. Nonetheless, they aim to make the best decisions possible. In Decision Theory with a Human Face, Richard Bradley develops new theories of agency and rational decision-making, offering guidance on how 'real' agents who are aware of their bounds should represent the uncertainty they face, how they should revise their opinions as a result (...) of experience and how they should make decisions when lacking full awareness of, or precise opinions on relevant contingencies. He engages with the strengths and flaws of Bayesian reasoning, and presents clear and comprehensive explorations of key issues in decision theory, from belief and desire to semantics and learning. His book draws on philosophy, economics, decision science and psychology, and will appeal to readers in all of these disciplines. (shrink)

In the recent philosophical literature on inquiry, epistemologists point out that their subject has often begun at the point at which you already have your evidence and then focussed on identifying the beliefs for which that evidence provides justification. But we are not mere passive recipients of evidence. While some comes to us unbidden, we often actively collect it. This has long been recognised, but typically epistemologists have taken the norms that govern inquiry to be practical, not epistemic. The recent (...) literature challenges this assumption and uncovers a rich range of questions about the epistemic normativity of inquiry. In this paper, I approach these questions from the formal side of epistemology. Developing out of the philosophy of science, as it did, this branch of epistemology has long discussed inquiry. And, building on the insights of Janina Hosiasson (1931), David Blackwell (1951), and I. J. Good (1967), it has produced a reasonably well-developed framework in which to understand norms of inquiry, both epistemic and practical. In the first half of the paper, I will present the pragmatic versions of this framework due to Hosiasson, Blackwell, and Good, and the epistemic version due to Graham Oddie (1997); in the second half of the paper, I put this framework to work, turning to some of the questions from the recent debate about inquiry and asking how the framework can help us answer them. Questions will include: When should we initiate an inquiry, when should we continue it, when should we conclude it, and when should we reopen it? How should we understand Julia Staffel's distinction between transitional attitudes and terminal attitudes (Staffel 2021a,b)? How do epistemic norms of inquiry relate to epistemic norms of belief or credence, and can they conflict (Friedman 2020)? And how should we understand the epistemic error that occurs when someone is resistant to evidence (Simion 2023)? (shrink)

Conscientious refusal involves decisions by healthcare workers, on grounds of their conscience, to refuse to provide legal, professionally permissible and safe health interventions to patients. Conscientious provision involves decisions by healthcare workers, also on grounds of conscience, to provide safe and beneficial healthcare to patients that is prohibited by law or policy. Some bioethicists believe that the moral issues governing both are identical, and that if one permits conscientious refusals, one should also permit conscientious provisions. This article argues that this (...) assumption of symmetry is incorrect. To demonstrate this, it does the following: first, it establishes why it matters that we understand the difference between them; second, it describes three recent cases of conscientious provision in Canadian healthcare to help characterize its nature and scope; third, it situates these cases in a socio-economically nuanced analysis of the role of the conscientious provider under conditions or privilege and oppression; finally, it applies insights from the cases and the intersectional analysis to common criticisms of conscientious refusal to reinforce the fundamental asymmetries between conscientious refusal and conscientious provision. (shrink)

Theology Without Walls is a project that seeks to understand the nature of divine reality through an exploration of all the world's religious traditions, without confining itself to any one in particular. In this essay, I discuss why theology has traditionally been done within the boundaries of specific traditions and suggest that, in our time, we are called to a new, more comprehensive, approach to theology.

Effective altruism sounds so innocuous—who could possibly be opposed to doing good more effectively? Yet it has inspired significant backlash in recent years. This paper addresses some common misconceptions and argues that the core “beneficentric” ideas of effective altruism are both excellent and widely neglected. Reasonable people may disagree on details of implementation, but all should share the basic goals or values underlying effective altruism.

Few philosophers have left a legacy like that of Gottfried Wilhelm Leibniz. He has been credited not only with inventing the differential calculus, but also with anticipating the basic ideas of modern logic, information science, and fractal geometry. He made important contributions to such diverse fields as jurisprudence, geology and etymology, while sketching designs for calculating machines, wind pumps, and submarines. But the common presentation of his philosophy as a kind of unworldly idealism is at odds with all this bustling (...) practical activity. In this book Richard. T. W. Arthur offers a fresh reading of Leibniz’s philosophy, clearly situating it in its scientific, political and theological contexts. He argues that Leibniz aimed to provide an improved foundation for the mechanical philosophy based on a new kind of universal language. His contributions to natural philosophy are an integral part of this programme, which his metaphysics, dynamics and organic philosophy were designed to support. Rather than denying that substances really exist in space and time, as the idealist reading proposes, Leibniz sought to provide a deeper understanding of substance and body, and a correct understanding of space as an order of situations and time as an order of successive things. This lively and approachable book will appeal to students of philosophy, as well as anyone seeking a stimulating introduction to Leibniz's thought and its continuing relevance. (shrink)

Die Reihe Monographien und Texte zur Nietzsche-Forschung (MTNF) setzt seit mehreren Jahrzehnten die Agenda in der sich stetig verändernden Nietzsche-Forschung. Die Bände sind interdisziplinär und international ausgerichtet und spiegeln das gesamte Spektrum der Nietzsche-Forschung wider, von der Philosophie über die Literaturwissenschaft bis zur politischen Theorie. Die Reihe veröffentlicht Monographien und Sammelbände, die einem strengen Peer-Review-Verfahren unterliegen. Die Buchreihe wird von einem internationalen Redaktionsteam geleitet.

This important new study is an intellectual history exploring the reception of Darwinism by prominent German socialist theoriests: Karl Marx, Friedrich Engles, Friedrich Albert Lange, Ludwig B chner, August Bebel, Karl Katusky, and Eduard Bernstein. It relies not only on published books, articles, and speeches by these men, but also on some unpublished correspondence. In addition, one chapter covers the anti-socialist stance of prominent Darwinian biologists, including Charles Darwin and the foremost champion of Darwinism in Germany, Ernst Haeckel. Darwinism's effect (...) on German socialism's view of eugenics, race and religion are also discussed. (shrink)

In this paper I will address a few of the many questions that fall under the general heading of “the ethics of belief.” In section I I will discuss the adequacy of what has come to be known as the “deontological conception of epistemic justification” in the light of our apparent lack of voluntary control over what we believe. In section II I’ll defend an evidentialist view about what we ought to believe. And in section III I will briefly discuss (...) apparent conflicts between epistemic considerations and moral or other considerations. (shrink)

This article examines the post-Ryle developments in philosophy of mind and psychology, in particular tracing the emergence of the concept of a mental state. The climate immediately following the large-scale rejection of Descartes seems rather hostile to the idea of mental properties as internal states that cause behaviour. In this context, the emergence of the reificatory view of mental states is quite surprising, and it appears to stem from Putnam's adoption of the Turing machine as a model for human psychology. (...) I conclude that the success of the “mental state” is down to the fact that it neatly conforms to the picture painted by the metaphorical expressions we use when talking about minds and mental things, and that its success is more accidental than inevitable. (shrink)

Very few scholars discuss the moral basis of the right of persons accused of crimes to be supplied with attorneys if they cannot afford them. More discussion of the topic is needed, in particular because political theorists who prefer a minimal state deny that indigent persons have such a moral right. This article addresses their contentions by developing three arguments for supplying poor persons accused of crimes with defense attorneys. First, doing so will prevent state officials from becoming emboldened in (...) their dealings with the poor, such that they might come to pose a threat to the non-poor. Second, poor persons who believe that the state does not treat them fairly will have reduced incentives to abide by the law, which will, in turn, increase the cost of the minimal state. Third, the better off should show solidarity with the poor in demanding that the minimal state honor all citizens’ rights to life, liberty, and property. Crucial to these arguments is the claim that a right of indigent defense is unlike other welfare rights in that securing it protects other basic moral rights that minimal statists acknowledge. (shrink)

I argue that uniquely human forms of ‘Theory of Mind’ (or ‘ToM’) are a product of cultural evolution. Specifically, propositional attitude psychology is a linguistically constructed folk model of the human mind, invented by our ancestors for a range of tasks and refined over successive generations of users. The construction of these folk models gave humans new tools for thinking and reasoning about mental states—and so imbued us with abilities not shared by non-linguistic species. I also argue that uniquely human (...) forms of ToM are not required for language development, such that an account of the cultural origins of ToM does not jeopardise the explanation of language development. Finally, I sketch a historical model of the cultural evolution of mental state talk. (shrink)