This work is derived from the SERC "Logic for IT" Summer School Conference on Proof Theory held at Leeds University. The contributions come from acknowledged experts and comprise expository and research articles which form an invaluable introduction to proof theory aimed at both mathematicians and computer scientists.

Mathematics is about proofs, that is the derivation of correct statements; and calculations, that is the production of results according to well-defined sets of rules. The two notions are intimately related. Proofs can involve calculations, and the algorithm underlying a calculation should be proved correct. The aim of the author is to explore this relationship. The book itself forms an introduction to simple type theory. Starting from the familiar propositional calculus the author develops the central idea of an applied lambda-calculus. (...) This is illustrated by an account of Gödel's T, a system which codifies number-theoretic function hierarchies. Each of the book's 52 sections ends with a set of exercises, some 200 in total. These are designed to help the reader get to grips with the subject, and develop a further understanding. An appendix contains complete solutions of these exercises. (shrink)

In Simmons (Arch Math Logic 43:65–83, 2004), I described a method of producing ordinal notations ‘from below’ (for countable ordinals up to the Howard ordinal) and compared that method with the current popular ‘from above’ method which uses a collapsing function from uncountable ordinals. This ‘from below’ method employs a slight generalization of the normal function—the fruitful functions—and what seems to be a new class of functions—the helpful functions—which exist at all levels of the function space hierarchy over ordinals. (...) Unfortunately, I was rather sparing in my description of these classes of functions. In this paper I am much more generous. I describe the properties of the helpful functions on all finite levels and, in the final section, indicate how they can be used to simplify the generation of ordinal notations. The main aim of this paper is to fill in the details missing from [7]. The secondary aim is to indicate what can be done with helpful functions. Fuller details of this development will appear elsewhere. (shrink)

I modify the standard coverage construction of the reals to obtain the irrationals. However, this causes a jump in ordinal complexity from ω+1 to Ω.

The standard method of generating countable ordinals from uncountable ordinals can be replaced by a use of fixed point extractors available in the term calculus of Howard’s system. This gives a notion of the intrinsic complexity of an ordinal analogous to the intrinsic complexity of a function described in Gödel’s T.

I survey the syntactic technique of tiering which can be used to restrict the power of a recursion scheme. I show how various results can be obtained entirely proof theoretically without the use of a model of computation.

Providing a model for the transformative work that is required going forward, The Crisis of US Hospice Care illustrates the potential of hospice for facilitating a new way of living our last days and for having the best death possible.

Optimism and pessimism are two diametrically opposed views about the value of existence. Optimists maintain that existence is better than non-existence, while pessimists hold that it is worse. Arthur Schopenhauer put forward a variety of arguments against optimism and for pessimism. I will offer a synoptic reading of these arguments, which aims to show that while Schopenhauer’s case against optimism primarily focuses on the value or disvalue of life’s contents, his case for pessimism focuses on the ways in which life (...) as a whole is structurally defective. (shrink)

This paper presents a model-theoretic semantics for discourse "about" natural numbers, one that captures what I call "the mathematical-object picture", but avoids what I can "the mathematical-object theory".

Joyful Human Rights espouses a joy-centered approach that provides new insights into foundational human rights issues. William Paul Simmons offers a framework -- surveying a more comprehensive understanding of human experiences -- for theorizing and practicing a more affirmative and robust notion of human rights.

Aesthetic internalism claims a link between judgement and motivation: aesthetic judgements bring with them motivations to act in characteristic ways. Critics object that there is a difference between merely liking something and judging it to be aesthetically good, and that it is our likings, not our aesthetic judgements, that motivate us. This paper develops a version of aesthetic internalism that can respond to this criticism. Wholehearted aesthetic judgements are characterized by stability, attention, and motivation. Making such judgements is an important (...) part of a good life, and so at least some aesthetic judgements are motivating. So we have reason to think that this version of aesthetic internalism is true. This paper defends wholehearted aesthetic internalism against objections, and assesses an argument from aesthetic internalism to aesthetic non-cognitivism. While wholehearted aesthetic internalism can only offer qualified support to non-cognitivism, it nonetheless offers a number of fruitful avenues for further work. (shrink)

In The Case for Animal Rights, Tom Regan defends the view that all animals who are “subjects of a life” have an equal moral right to life. In this chapter, I consider whether it makes sense to think that animals have an equal right to life in light of the challenge that life has less value for animals than humans. This challenge raises two central questions: (1) does life have less value for animals than humans and (2) if it does, (...) does this fact justify the view that animals do not have an equal right to life. I argue, first, that life has greater value for most humans than animals because most humans are capable of experiencing higher qualities of enjoyment in life, in the form of creative, intellectual pleasures. However, this does not justify denying that animals have an equal right to life. Whether beings’ lives deserve strong respect depends on whether the value of life for those beings meets a certain threshold. I argue that the value of life for many animals meets this threshold because it is compatible with the virtue of compassion. (shrink)

Collected critical essays analyzing Kierkegaard’s work in regards to theology and social-moral thought. Kierkegaard’s God and the Good Life focuses on faith and love, two central topics in Kierkegaard’s writings, to grapple with complex questions at the intersection of religion and ethics. Here, leading scholars reflect on Kierkegaard’s understanding of God, the religious life, and what it means to exist ethically. The contributors then shift to psychology, hope, knowledge, and the emotions as they offer critical and constructive readings for contemporary (...) philosophical debates in the philosophy of religion, moral philosophy, and epistemology. Together, they show how Kierkegaard continues to be an important resource for understandings of religious existence, public discourse, social life, and how to live virtuously. “All in all, the editors of this volume have put together a thoughtful and sometimes provocative collection of essays by a number of Kierkegaard scholars and philosophers for the reader’s consideration.... The volume undoubtedly makes a contribution to contemporary philosophical debates in the philosophy of religion, moral philosophy, and epistemology, especially with regard to the importance of faith and love for leading a good and meaningful human life.” —International Journal for Philosophy of Religion “Invites the reader to think anew about what Kierkegaard was saying and what we can learn from him in the context of our time, particularly what it means to become a Christian in terms of the moral task of love and living a life worthy of a human being.” —Sylvia Walsh, translator of Kierkegaard’s Discourses at the Communion on Fridays. (shrink)

Restless Ideas is a lively new textbook of contemporary social theory that speaks directly to the anxious age in which we live today. In addition to providing a highly readable guided tour of major social theories from the mid-20th to the early 21st century, this book is full of dynamic examples that show how these theories may be used to deepen our understanding of current events and of our own life experiences. The emergence of demagogic political leaders like Donald Trump (...) in the USA, Rodrigo Duterte in the Philippines, and Recep Tayyip Erdoğan in Turkey; the rise of religious fundamentalism, terrorism, and political populism; the digital echo-chamber of social media; and the underlying causes of Brexit are only some of the many current social issues that can be framed through contemporary social theories. Similarly, the politics of sexual, racial and ethnic minorities can be analyzed through the prism of theoretical perspectives such as queer theory, standpoint and intersectional theory, postcolonial theory and critical race theory, while the ongoing struggles for gender equality and gender justice can usefully be examined through the generational perspectives of feminist theories. This book sets the stage with a critical discussion of the loaded history of the social theory canon and makes the argument that there has never been a better time than the present to broaden our understanding of our shared global heritage of social theory, to include some of the formerly excluded classics of past social thinkers, and to open the doors to current social thinkers theorizing from the margins. The book traces the modern roots of contemporary social theory back to the works of the early structural functionalists, systems theorists, conflict theorists, symbolic interactionists, ethnomethodologists and sociobiologists, building on and at times inverting the canon with the critical advancements to social theory. Later chapters focus on the current influence of structuration theory, third wave critical theory, postmodernism and poststructuralism, critical race theory, postcolonialism, liquid and late modernity theories, and globalization theories. These perspectives include the works of contemporary social theorists such as Anthony Giddens, Pierre Bourdieu, Juliet Mitchell, Dorothy Smith, Judith Butler, Jean-Francois Lyotard, Jacques Derrida, Jean Baudrillard, Gayatri Spivak, Homi K. Bhabha, Zygmunt Bauman, Slavoj Zizek, Alain Badiou, Jürgen Habermas, Axel Honneth, Nancy Fraser, Manuel Castells and Ulrich Beck. The underlying premise - and the promise - of this book is that social theory has the power to provide us with the skills for more informed observation, analysis, and empathic understanding of social behavior and social interaction. In a word: the value of social theory may be seen in how it can enhance social literacy - by deepening our understanding of the world around us, and by empowering us to become practical theorists in our own lives. (shrink)

Welcome to the family -- The sources of new phenomenology in Husserl and Heidegger -- How to be a phenomenological heretic: the origins and development of new phenomenology -- Phenomenology and onto-theology -- Phenomenology and theology reconsidered -- New phenomenology on the existence and nature of God -- The call, prayer, and Christian philosophy -- Proposals for new phenomenology and analytic philosophy of religion -- Normativity: ethics, politics, and society -- Possible futures for new phenomenology.

In this paper, I examine a solution to the Liar paradox found in the work of Ockham, Burley, and Pseudo-Sherwood. I reject the accounts of this solution offered by modern commentators. I argue that this medieval line suggests a non-hierarchical solution to the Liar, according to which ?true? is analysed as an indexical term, and paradox is avoided by minimal restrictions on tokens of ?true?. In certain respects, this solution resembles the recent approaches of Charles Parsons and Tyler Burge; in (...) other respects, it is related to a suggestion of Gödel. But, as a whole, it suggests an original solution to the Liar paradox, quite unlike any current proposals. (shrink)

Contrary to economics or history, for example, there does not exist an organized field dedicated to the philosophy of political science. Given that the philosophical issues raised by political science research are just as pressing and vibrant as those raised in these more organized fields, fostering a field that labels itself Philosophy of Political Science (PoPS) is important. PoPS is advanced here as a fruitful meeting place where both philosophers and practicing political scientists contribute and discuss—with philosophical discussions that are (...) close to and informed by actual developments in political science, making philosophy of science continuous with the sciences in line with contemporary naturalist philosophy of science. The topics scrutinized in the different chapters of the Handbook will figure prominently in PoPS, as we lay out in this chapter. (shrink)

In 1905, Richard discovered his paradox of definability, and in a letter written that year he presented both the paradox and a solution to it.Soon afterwards, Poincaré endorsed a variant of Richard?s solution.In this paper, I critically examine Richard?s and Poincaré?s ways out.I draw on an objection of Peano?s, and argue that their stated solutions do not work.But I also claim that their writings suggest another way out, different from their stated solutions, and different from the orthodox Tarskian approach.I argue (...) that this second solution does not prevent the return of the paradox. (shrink)

Philosophy of science is still, in the minds of many, identified with positivism. This is understandable since twentieth century philosophy of science originates with the work of the Vienna Circle. Positivism is most famous for the verification theory of meaning, the doctrine that the meaning of any proposition is the method by which it is verified, and that any nonanalytic locution which cannot be proven or disproven by some empirical test has no cognitive significance. Positivism is an attempt to construct (...) a “scientific philosophy” in the worst sense: it is maintained that (with the exception of propositions which are analytic and thus vacuous) only those propositions which occur in the sciences are meaningful, all other discourse having at best some emotive value, but no cognitive content, and all of this is maintained within the confines of an exceedingly narrow notion of scientific knowledge. This notion is so narrow that its advocates found themselves in danger of having to relegate most of physics to the realm of nonsense since physics contains many statements which are strictly universal and thus cannot be conclusively verified. (shrink)

The novel has always provided a vehicle for commenting on various aspects of human existence. We are familiar with the political novel, the historical novel, or the metaphysical novel, and in this sense Sorrentino's Mulligan Stew, with its running commentary on novels, novelists, critics and publishers, may be viewed as a critical novel. A critical novel, however, has a striking feature which it does not share with the other sorts of novels mentioned above in that a critical novel is itself (...) a novel, and a member of the class of objects on which it is commenting. This is a structure that logicians call “self-reference” and the phenomenon of self-reference has provided a central theme in twentieth century logic and philosophy. (shrink)

“There is, in addition, a second reason for doubting that scientists reject paradigms because confronted with anomalies or counterinstances. In developing it my argument will itself foreshadow another of this essay's main theses. The reasons for doubt sketched above were purely factual; they were, that is, themselves counterinstances to a prevalent epistemological theory. As such, if my present point is correct, they can at best help to create a crisis or, more accurately, to reinforce one that is already very much (...) in existence. By themselves they cannot and will not falsify that philosophical theory, for its defenders will do what we have already seen scientists doing when confronted by anomaly. They will devise numerous articulations and ad hoc modifications of their theory in order to eliminate any apparent conflict. Many of the relevant modifications and qualifications are, in fact, already in the literature. If, therefore, these epistemological counterinstances are to constitute more than a minor irritant, that will be because they help to permit the emergence of a new and different analysis of science within which they are no longer a source of trouble. Furthermore, if a typical pattern, which we shall later observe in scientific revolutions, is applicable here, these anomalies will then no longer seem to be simply facts. From within a new theory of scientific knowledge, they may instead seem very much like tautologies, statements of situations that could not conceivably have been otherwise.”. (shrink)

For many Christians, personal experiences of God provide an important ground or justification for accepting the truth of the gospel. But we are sometimes mistaken about our experiences, and followers of other religions also provide impressive testimonies to support their religious beliefs. This book explores from a philosophical and theological perspective the viability of divine encounters as support for belief in God, arguing that some religious experiences can be accepted as genuine experiences of God and can provide evidence for Christian (...) beliefs. (shrink)

In recent years empiricism has been under persistent attack, and serious questions have been raised about the ability of empiricism to provide the basis for a viable philosophy of science. The attack has been sufficiently vigorous, and in some quarters sufficiently successful, that many now maintain that empiricism is dead. My aim in this paper is to argue that, rather than being ready for embalmment and emplacement in the museum of philosophic oddities, empiricism is very much alive, and the central (...) thesis of empiricism remains the cornerstone for any viable philosophy of science. This is not to say that the recent attacks on empiricism have been without a point, rather, they have put anyone who would defend empiricism in the position of having to rethink many datails of the empiricist viewpoint. But it is the details, the way in which empiricism has been elaborated by its proponents, not the central empiricist insight, that must be reconsidered. (shrink)

Psychology, philosophy and common sense -- Psychological empiricism (part A): do non-empirical psychological phenomena exist? -- Psychological empiricism (part B): a critique -- The subject matter of psychology (part A): the conscious personal self -- The subject matter of psychology (part B): differing kinds of psychic phenomena -- Locating the empirical in psychology -- Human nature and rational psychology -- Psychology, truth and personalism -- The reality and psychological significance of freedom.

Brian Calvert has offered us a clear and careful analysis of Locke′s views on punishment and capital punishment. 1 The primary goal of his paper–that of correcting the misperception of Locke as a wholehearted proponent of capital punishment for a wide range of offences–must be allowed to be both laudable and largely achieved in his discussion. But Calvert′s analysis also encourages, I think, a number of serious misunderstandings of Locke′s true position.

Creative Intelligence: Essays in the Pragmatic Attitude represents an attempt at intellectual cooperation. No effort has been made, however, to attain unanimity of belief nor to proffer a platform of "planks" on which there is agreement. The consensus represented lies primarily in outlook, in conviction of what is most likely to be fruitful in method of approach. As the title page suggests, the volume presents a unity in attitude rather than a uniformity in results. Consequently each writer is definitively responsible (...) only for his own essay. The reader will note that the Essays endeavor to embody the common attitude in application to specific fields of inquiry which have been historically associated with philosophy rather than as a thing by itself. Beginning with philosophy itself, subsequent contributions discuss its application to logic, to mathematics, to physical science, to psychology, to ethics, to economics, and then again to philosophy itself in conjunction with esthetics and religion. The reader will probably find that the significant points of agreement have to do with the ideas of the genuineness of the future, of intelligence as the organ for determining the quality of that future so far as it can come within human control, and of a courageously inventive individual as the bearer of a creatively employed mind. (shrink)

In this paper, I criticize Michael Huemer's phenomenal conservatism, the theory of justification according to which if it seems to S that p, then in the absence of defeaters, S thereby has at least some degree of justification for believing that p. Specifically, I argue that beliefs and hunches provide counterexamples to phenomenal conservatism. I then defend a version of restricted phenomenal conservatism, the view that some but not all appearances confer prima facie justification on their propositional contents. Specifically, I (...) defend the view that S has defeasible justification for believing that p if and only if it seems to S that p and it seems to S that she is acquainted with the fact that makes p true. Finally, I criticize Huemer's self-defeat argument for phenomenal conservatism. (shrink)

This book is an in-depth exploration of the nature of sensations and how they are affected by different types of stimuli. The author, Harold Griffing, presents a detailed analysis of the ways in which pressure and impact can influence sensations, and offers insights into how these findings can be applied in a variety of contexts. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This (...) work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

In The Contemplative Foundations of Classical Daoism, Harold D. Roth explores the origins and nature of the Daoist tradition, arguing that its creators and innovators were not abstract philosophers but, rather, mystics engaged in self-exploration and self-cultivation, which in turn provided the insights embodied in such famed works as the Daodejing and Zhuangzi. In this compilation of essays and chapters representing nearly thirty years of scholarship, Roth examines the historical and intellectual origins of Daoism and demonstrates how this distinctive (...) philosophy emerged directly from practices that were essentially contemplative in nature. In the first part of the book, Roth applies text-critical methods to derive the hidden contemplative dimensions of classical Daoism. In the second part, he applies a "contemplative hermeneutic" to explore the relationship between contemplative practices and classical Daoist philosophy and, in so doing, brings early Daoist writings into conversation with contemporary contemplative studies. To this he adds an introduction in which he reflects on the arc and influence on the field of early Chinese thought of this rich vein of scholarship and an afterword in which he applies both interpretive methods to the vexing question of the authorship of the Inner Chapters of the Zhuangzi. The Contemplative Foundations of Classical Daoism brings to fruition the cumulative investigations and observations of a leading figure in the emerging field of contemplative studies as they pertain to a core component of early Chinese thought. (shrink)