We show, relative to the base theory RCA₀: A nontrivial tree satisfies Ramsey's Theorem only if it is biembeddable with the complete binary tree. There is a class of partial orderings for which Ramsey's Theorem for pairs is equivalent to ACA₀. Ramsey's Theorem for singletons for the complete binary tree is stronger than $B\sum_{2}^{0}$ , hence stronger than Ramsey's Theorem for singletons for ω. These results lead to extensions of results, or answers to questions, of Chubb, Hirst, and McNicholl (...) [3]. (shrink)

In seeking an answer to the question of what it means for a theory to be fundamental, it is enlightening to ask why the current best theories of physics are not generally believed to be fundamental. This reveals a set of conditions that a theory of physics must satisfy in order to be considered fundamental. Physics aspires to describe ever deeper levels of reality, which may be without end. Ultimately, at any stage we may not be able to tell whether (...) we've reached rock bottom, or even if there is a base level – nevertheless, I draft a checklist to help us identify when to stop digging, in the case where we may have reached a candidate for a final theory. Given that the list is – according to (current) mainstream belief in high-energy physics – complete, and each criterion well-motivated, I argue that a physical theory that satisfies all the criteria can be assumed to be fundamental in the absence of evidence to the contrary (i.e., I argue that the necessary conditions are jointly sufficient for a claim of fundamentality in physics). (shrink)

In his Critical Aesthetics and Postmodernism, Paul Crowther argued that art and aesthetic experiences have the capacity to humanize. In Art and Embodiment he develops this theme in much greater depth, arguing that art can bridge the gap between philosophy's traditional striving for generality and completeness, and the concreteness and contingency of humanity's basic relation to the world. As the key element in his theory, he proposes an ecological definition of art. His strategy involves first mapping out and analyzing (...) the logical boundaries and ontological structures of the aesthetic domain. He then considers key concepts from this analysis in the light of a tradition in Continental philosophy (notably the work of Kant, Heidegger, Merleau-Ponty, and Hegel) which--by virtue of the philosophical significance that it assigns to art--significantly anticipates the ecological conception. On this basis, Crowther is able to give a full formulation of his ecological definition. Art, in making sensible or imaginative material into symbolic form, harmonizes and conserves what is unique and what is general in human experience. The aesthetic domain answers basic needs intrinsic to self-consciousness itself, and art is the highest realization of such needs. In the creation and reception of art the embodied subject is fully at home with his or her environment. (shrink)

Theories of discourse bring to realism new ideas about how knowledge develops and how representations of reality are influenced. We gain an understanding of the conceptual aspect of social life and the processes by which meaning is produced. This collection reflects the growing interest realist critics have shown towards forms of discourse theory and deconstruction. The diverse range of contributions address such issues as the work of Derrida and deconstruction, discourse theory, Eurocentrism and poststructuralism. What unites all of the contributions (...) is a sense that it is essential to provide a realist alternative to the hitherto dominance of social constructionism, hermeneutics and postmodernism, over many of the issues discussed. By developing a realist perspective the different authors attempt to embed discourse within the structured nature of the reality of the world. Realism can situate language, discourse and ideology within context specific, or 'causally efficacious' circumstances. Realism can help to uncover issues of power, representation, and subjectivity and how discursive and other social practices produce real effects. This can help us understand the manner in which social structures are reproduced through various forms of ideology and discourse. And by knowing this, we can start to address questions concerning human emancipation and how the world is to be transformed. (shrink)

The first sustained phenomenological approach to modern art, taking a new approach and drawing upon an unsual selection of thinkers.

This is done by exploring some of his other ideas concerning how critical comparisons inform our cultivation of taste, and art's relation to genius.

Topics covered in Discrete Mathematics have become essential tools in many areas of studies in recent years. This is primarily due to the revolution in technology, communications, and cyber security. The book treats major themes in a typical introductory modern Discrete Mathematics course: Propositional and predicate logic, proof techniques, set theory (including Boolean algebra, functions and relations), introduction to number theory, combinatorics and graph theory. An accessible, precise, and comprehensive approach is adopted in the treatment of each topic. The ability (...) of abstract thinking and the art of writing valid arguments are emphasized through detailed proof of (almost) every result. Developing the ability to think abstractly and roguishly is key in any areas of science, information technology and engineering. Every result presented in the book is followed by examples and applications to consolidate its comprehension. The hope is that the reader ends up developing both the abstract reasoning as well as acquiring practical skills. All efforts are made to write the book at a level accessible to first-year students and to present each topic in a way that facilitates self-directed learning. Each chapter starts with basic concepts of the subject at hand and progresses gradually to cover more ground on the subject. Chapters are divided into sections and subsections to facilitate readings. Each section ends with its own carefully chosen set of practice exercises to reenforce comprehension and to challenge and stimulate readers. As an introduction to Discrete Mathematics, the book is written with the smallest set of prerequisites possible. Familiarity with basic mathematical concepts (usually acquired in high school) is sufficient for most chapters. However, some mathematical maturity comes in handy to grasp some harder concepts presented in the book. (shrink)

We show that a statement HIL, which is motivated by a lemma of Hilbert and close in formulation to Hindman’s theorem, is actually much weaker than Hindman’s theorem. In particular, HIL is finitistically reducible in the sense of Hilbert’s program, while Hindman’s theorem is not.

Why are visual artworks experienced as having intrinsic significance or normative depth? Why are some works of art better able to manifest this significance than others? In his latest book Paul Crowther argues that we can answer these questions only if we have a full analytic definition of visual art. Crowther's approach focuses on the pictorial image, broadly construed to include abstract work and recent conceptually-based idioms. The significance of art depends, however, essentially on the transhistorical nature of (...) the pictorial image, the way in which its illuminative power is extended through historical transformation of the relevant artistic medium. Crowther argues against fashionable forms of cultural relativism, while at the same time showing why it is important that an appreciation of the history of art is integral to aesthetic judgment. (shrink)

Renowned as the chief challenger of traditional views of morality, man's freedom, and religion from 1650-1750, Benedict de Spinoza (1632-77) spread alarm and ...

Ranging over central issues of morals and politics and the nature of freedom and authority, this study examines the role of value-neutrality, rights, equality, ...

One of the earliest applications of Cantor's Normal Form Theorem is Jacobstahl's proof of the existence of prime factorizations of ordinals. Applying the techniques of reverse mathematics, we show that the full strength of the Normal Form Theorem is used in this proof.

Watching, looking at, and listening to, are all things that perceiving agents actively do. Though the occurrence of these activities appears to entail perception of elements of the agent's environment, perception is not something that can be actively done by agents. This raises the question how perceptual activity and perception are related to one another. This chapter, through reflecting on a discussion of listening offered by Brian O'Shaughnessy, argues that listening to material particulars ought to be understood as the agential (...) maintenance of aural awareness of those particulars, with the aim of knowing what sounds they are making. He goes on to explore some of the consequences of these claims about listening for exercises of perceptual agency involving the other sensory modalities. (shrink)

Samkara (c. 700 CE), the great Indian Advaitin thinker, was a commentator on sacred text and an Advaitin teacher. This book provides an introduction to the thought of Samkara, who is the most well-known and most perhaps the most authoritative Hindu thinker of all time. The author develops an innovative approach using Samkara's method of interpreting sacred texts and creatively examines the profound interrelationship between sacred text, content and method in Samkara's thought. In particular Samkara's teaching method is the main (...) focus of this book; it is a method that is based on Upanisadic truth and expects teachers to skillfully draw pupils towards it. This book will be of interest to students and scholars of Indian philosophy. (shrink)

Jennifer Hornsby has defended the Reasons-Knowledge Thesis : the claim that \-ing because p requires knowing that p, where the ‘because’ at issue is a rationalising ‘because’. She defends by appeal to the thought that it provides the best explanation of why the subject in a certain sort of Gettier case fails to be in a position to \ because p. Dustin Locke and, separately, Nick Hughes, present some modified barn-façade cases which seem to constitute counterexamples to and undermine Hornsby’s (...) way of motivating it by rendering their alternative Reasons-Explanation Thesis a better explanation of Hornsby’s datum. This paper defends and Hornsby’s argument for it against those objections. First, I point out that their supposedly intuitive verdict about the relevant barn-façade cases is not as intuitive as they think. Second, I point out that even if we share the intuition: we have strong reason to doubt the verdict anyway. And finally, I point out that since is independently implausible, the two problems can be tackled anyway. (shrink)

According to standard comparativist views, death is bad insofar as it deprives someone of goods she would otherwise have had. In The Ethics of Killing, Jeff McMahan argues against such views and in favor of a gradualist account according to which how bad it is to die is a function of both the future goods of which the decedent is deprived and her cognitive development when she dies. Comparativists and gradualists therefore disagree about how bad it is to die at (...) different ages. In this paper I examine two prominent criticisms of gradualism and show that both misconstrue McMahan. I develop a related criticism that seems to show that a gradualist cannot coherently relate morbidity and mortality. This criticism also fails, but has an instructive implication for how policy-makers setting priorities for health care investments should regard choices between life-saving interventions and interventions against non-fatal diseases in the very young. (shrink)

Over the last few decades, multiple studies have examined the understanding of participants in clinical research. They show variable and often poor understanding of key elements of disclosure, such as expected risks and the experimental nature of treatments. Did the participants in these studies give valid consent? According to the standard view of informed consent they did not. The standard view holds that the recipient of consent has a duty to disclose certain information to the profferer of consent because valid (...) consent requires that information to be understood. The contents of the understanding and disclosure requirements are therefore conceptually linked. In this paper, we argue that the standard view is mistaken. The disclosure and understanding requirements have distinct grounds tied to two different ways in which a token of consent can be rendered invalid. Analysis of these grounds allows us to derive the contents of the two requirements. It also implies that it is sometimes permissible to enroll willing participants who have not understood everything that they ought to be told about their clinical trials. (shrink)

Painting as an art: Wollheim and the subjective dimension -- Abstract art and transperceptual space: Wolheim, and beyond -- Truth in art: Heidegger against contextualism -- Space, place, and sculpture: Heidegger's pathways -- Vision in being: Merleau-Ponty and the depths of painting -- Subjectivity, the gaze, and the picture: developing Lacan -- Dimensions in time: Dufrenne's phenomenology of pictorial art -- Conclusion: a preface to post-analytic phenomenology.

To attribute confusion to someone is to take up a paternalistic stance in evaluating his reasoning.

This book discusses the notion that quantum gravity may represent the "breakdown" of spacetime at extremely high energy scales. If spacetime does not exist at the fundamental level, then it has to be considered "emergent", in other words an effective structure, valid at low energy scales. The author develops a conception of emergence appropriate to effective theories in physics, and shows how it applies (or could apply) in various approaches to quantum gravity, including condensed matter approaches, discrete approaches, and loop (...) quantum gravity. (shrink)

Introduction -- Instrumental rationality -- Social order -- Deontic constraint -- Intentional states -- Preference noncognitivism -- A naturalistic perspective -- Transcendental necessity -- Weakness of will -- Normative ethics.

Is the assimilation of these two formulations of the moral principle by Kant and some of his expositors justified? In the Analytic of Pure Practical Reason Kant claims that his view of morality agrees with the ancient command that man should love his neighbour as himself. Also in the Fundamental Principles of the Metaphysic of Morals he regards the Golden Rule as a deduction, though with several limitations, from the second version of the Categorical Imperative.

Recently, several authors have explored the connections between NP-complete problems for finite objects and the complexity of their analogs for infinite objects. In this paper, we will categorize infinite versions of several problems arising from finite complexity theory in terms of their recursion theoretic complexity and proof theoretic strength. These infinite analogs can behave in a variety of unexpected ways.

Principles are central to physical reasoning, particularly in the search for a theory of quantum gravity (QG), where novel empirical data is lacking. One principle widely adopted in the search for QG is UV completion: the idea that a theory should (formally) hold up to all possible high energies. We argue---/contra/ standard scientific practice---that UV-completion is poorly-motivated as a guiding principle in theory-construction, and cannot be used as a criterion of theory-justification in the search for QG. For this, we explore (...) the reasons for expecting, or desiring, a UV-complete theory, as well as analyse how UV completion is used, and how it should be used, in various specific approaches to QG. (shrink)

Relationships between current theories, and relationships between current theories and the sought theory of quantum gravity (QG), play an essential role in motivating the need for QG, aiding the search for QG, and defining what would count as QG. Correspondence is the broad class of inter-theory relationships intended to demonstrate the necessary compatibility of two theories whose domains of validity overlap, in the overlap regions. The variety of roles that correspondence plays in the search for QG are illustrated, using examples (...) from specific QG approaches. Reduction is argued to be a special case of correspondence, and to form part of the definition of QG. Finally, the appropriate account of emergence in the context of QG is presented, and compared to conceptions of emergence in the broader philosophy literature. It is argued that, while emergence is likely to hold between QG and general relativity, emergence is not part of the definition of QG, and nor can it serve usefully in the development and justification of the new theory. (shrink)

We argue that there is a conflict among classical theism's commitments to divine simplicity, divine creative freedom, and omniscience. We start by defining key terms for the debate related to classical theism. Then we articulate a new argument, the Aloneness Argument, aiming to establish a conflict among these attributes. In broad outline, the argument proceeds as follows. Under classical theism, it's possible that God exists without anything apart from Him. Any knowledge God has in such a world would be wholly (...) intrinsic. But there are contingent truths in every world, including the world in which God exists alone. So, it's possible that God contingently has wholly intrinsic knowledge. But whatever is contingent and wholly intrinsic is an accident. So, God possibly has an accident. This is incompatible with classical theism. Finally, we consider and rebut several objections. (shrink)

A distinction has often been drawn between processes and accomplishments; between, say, *walking* and *walking to the shops*. But it has proved difficult to explain the nature of this distinction in a satisfying way. This paper offers an explanation of the nature of this distinction that is suggested by the idea that there is an ontologically significant correspondence between temporal and spatial notions. A number of writers, such as Alexander Mourelatos (1978) and Barry Taylor (1985), have argued that the spatial (...) notions of space-occupying stuff and space-occupying particular have temporal analogues. This paper builds on these discussions in offering the fuller development of a temporal ontology at the core of which are the notions of time-occupying stuff and of a time-occupying particular. It is then argued that when this analogy is properly understood it is possible to advance a distinctive explanation of the nature of the distinction between processes and accomplishments. The paper then goes on to develop some suggestions about how a temporal ontology involving the notions of temporal mass and of a temporal particular can help to provide explanations of a range of further puzzling temporal notions. In the final section of the paper, this temporal ontology is defended in the face of some possible sources of criticism. (shrink)

This is a new edition of Joseph Fletcher's 1966 work that ignited a firestorm of controversy at the time of its publication.