This chapter explores some fundamental consequences of the correspondence between physical process and computations. Most physical questions may be answerable only through irreducible amounts of computation. Those that concern idealized limits of infinite time, volume, or numerical precision can require arbitrarily long computations, and so be considered formally undecidable. The behavior of a physical system may always be calculated by simulating explicitly each step in its evolution. Much of theoretical physics has, however, been concerned with devising shorter methods of calculation (...) that reproduce the outcome without tracing each step. Computational irreducibility is common among the systems investigated in mathematics and computation theory, but it may well be the exception rather than the rule, since most physical questions may be answerable only through irreducible amounts of computation. (shrink)

"What is mathematics?" is a question that has been debated since antiquity. This book presents a groundbreaking and surprising answer to the question-showing through the concept of the physicalization of metamathematics how both mathematics and physics as experienced by humans can be seen to emerge from the unique underlying computational structure of the recently formulated ruliad. Written with Stephen Wolfram's characteristic expositional flair and richly illustrated with remarkable algorithmic diagrams, the book takes the reader on a unprecedented intellectual (...) journey to the center of some of the deepest questions about mathematics and its nature-and points the way to a new understanding of the foundations and future of mathematics, taking a major step beyond ideas from Plato, Kant, Hilbert, Gödel and others. (shrink)

The most elementary way to think about Mathctrtati ca is as an enhance calculator — a calculator that does not only numerical computation but also algebraic computation and graphics. Matltcmatica can function much like a standard calt".1a- tor. you type in a question, you get back an answer. But Mat/tctttadca ga's turthcr I ue an ordinary calculator. You can type in questions that require answers that arc longer than a calculator can handle. For example, Matltcmatictt can giv; you thc numerical (...) value of tr to a hundred decimal places, or the exact result for a numerical calculation as complicated as the result of 3)tI0, (m Fig. 1). (shrink)

Aboutness has been studied from any number of angles. Brentano made it the defining feature of the mental. Phenomenologists try to pin down the aboutness-features of particular mental states. Materialists sometimes claim to have grounded aboutness in natural regularities. Attempts have even been made, in library science and information theory, to operationalize the notion. But it has played no real role in philosophical semantics. This is surprising; sentences have aboutness-properties if anything does. Aboutness is the first book to examine through (...) a philosophical lens the role of subject matter in meaning. A long-standing tradition sees meaning as truth-conditions, to be specified by listing the scenarios in which a sentence is true. Nothing is said about the principle of selection--about what in a scenario gets it onto the list. Subject matter is the missing link here. A sentence is true because of how matters stand where its subject matter is concerned. Stephen Yablo maintains that this is not just a feature of subject matter, but its essence. One indicates what a sentence is about by mapping out logical space according to its changing ways of being true or false. The notion of content that results--directed content--is brought to bear on a range of philosophical topics, including ontology, verisimilitude, knowledge, loose talk, assertive content, and philosophical methodology. Written by one of today's leading philosophers, Aboutness represents a major advance in semantics and the philosophy of language. (shrink)

Sir Roger Penrose, retired professor of mathematics at the University of Oxford and collaborator with Stephen Hawking on black hole theory, has written 'a complete guide to the laws of the universe' called The Road to Reality. His publisher calls it the most important and ambitious work of science for a generation. Penrose caused a furore in the world of consciousness studies with his 1989 book The Emperor's New Mind, which conjectured a new mechanism for consciousness and kept a (...) faithful band of researchers busy for a decade with models based on microtubules and the like. Sadly, the idea fizzled out. The title of the 2002 Tucson 'Toward a Science of Consciousness' conference poetry slam winner was: Microtubules - my ass! (shrink)

Doing epistemology -- Kinds of knowledge? -- A first theory of knowledge -- Refining our theory of knowledge -- Is it even possible to have knowledge? -- Applying epistemology.

The Hedgehog, the Fox, and the Magister's Pox is a controversial discourse, rich with facts and observations gathered by one of the most erudite minds of our ...

In Return to Reason, Stephen Toulmin argues that the potential for reason to improve our lives has been hampered by a serious imbalance in our pursuit of ...

[Stephen Yablo] The usual charge against Carnap's internal/external distinction is one of 'guilt by association with analytic/synthetic'. But it can be freed of this association, to become the distinction between statements made within make-believe games and those made outside them-or, rather, a special case of it with some claim to be called the metaphorical/literal distinction. Not even Quine considers figurative speech committal, so this turns the tables somewhat. To determine our ontological commitments, we have to ferret out all traces (...) of nonliterality in our assertions; if there is no sensible project of doing that, there is no sensible project of Quinean ontology. /// [Andre Gallois] I discuss Steve Yablo's defence of Carnap's distinction between internal and external questions. In the first section I set out what I take that distinction, as Carnap draws it, to be, and spell out a central motivation Carnap has for invoking it. In the second section I endorse, and augment, Yablo's response to Quine's arguments against Carnap. In the third section I say why Carnap's application of the distinction between internal and external questions runs into trouble. In the fourth section I spell out what I take to be Yablo's version of Carnap. In the last I say why that version is especially vulnerable to the objection raised in the second. (shrink)

Stephen Toulmin argues that the potential for reason to improve our lives has been hampered by a serious imbalance in our pursuit of knowledge. The centuries-old dominance of rationality has diminished the value of reasonableness. Toulmin issues a powerful call to redress the balance between rationality and reasonableness.

"Biophilia" is the term coined by Edward O. Wilson to describe what he believes is humanity's innate affinity for the natural world. In his landmark book Biophilia, he examined how our tendency to focus on life and lifelike processes might be a biologically based need, integral to our development as individuals and as a species. That idea has caught the imagination of diverse thinkers. The Biophilia Hypothesis brings together the views of some of the most creative scientists of our time, (...) each attempting to amplify and refine the concept of biophilia. The variety of perspectives -- psychological, biological, cultural, symbolic, and aesthetic -- frame the theoretical issues by presenting empirical evidence that supports or refutes the hypothesis. Numerous examples illustrate the idea that biophilia and its converse, biophobia, have a genetic component: fear, and even full-blown phobias of snakes and spiders are quick to develop with very little negative reinforcement, while more threatening modern artifacts -- knives, guns, automobiles -- rarely elicit such a response people find trees that are climbable and have a broad, umbrella-like canopy more attractive than trees without these characteristics people would rather look at water, green vegetation, or flowers than built structures of glass and concrete The biophilia hypothesis, if substantiated, provides a powerful argument for the conservation of biological diversity. More important, it implies serious consequences for our well-being as society becomes further estranged from the natural world. Relentless environmental destruction could have a significant impact on our quality of life, not just materially but psychologically and even spiritually. (shrink)

Gayatri Chakravorty Spivaks seminal contribution to contemporary thought defies disciplinary boundaries. From her early translations of Derrida to her subsequent engagement with Marxism, feminism and postcolonial studies and her recent work on human rights, the war on terror and globalization, she has proved to be one of the most vital of present-day thinkers. In this book Stephen Morton offers a wide-ranging introduction to and critique of Spivaks work. He examines her engagements with philosophers and other thinkers from Kant to (...) Paul de Man, feminists from Cixous to Helie-Lucas and literary texts by Charlotte Bronte, J. M. Coetzee, Mahasweta Devi and Jean Rhys. Spivaks thought is also situated in relation to subaltern studies. Throughout the book, Morton interrogates the materialist basis of Spivaks thought and demonstrates the ethical and political commitment which lies at the heart of her work. Stephen Morton provides an ideal introduction to the work of this complex and increasingly important thinker. (shrink)

A scholarly synthesis of biblical studies and Christian social ethics, designed to provide a biblical argument for intentional institutional change on behalf of social justice.

Life's Solution builds a persuasive case for the predictability of evolutionary outcomes. The case rests on a remarkable compilation of examples of convergent evolution, in which two or more lineages have independently evolved similar structures and functions. The examples range from the aerodynamics of hovering moths and hummingbirds to the use of silk by spiders and some insects to capture prey. Going against the grain of Darwinian orthodoxy, this book is a must read for anyone grappling with the meaning of (...) evolution and our place in the Universe. Simon Conway Morris is the Ad Hominen Professor in the Earth Science Department at the University of Cambridge and a Fellow of St. John's College and the Royal Society. His research focuses on the study of constraints on evolution, and the historical processes that lead to the emergence of complexity, especially with respect to the construction of the major animal body parts in the Cambrian explosion. Previous books include The Crucible of Creation (Getty Center for Education in the Arts, 1999) and co-author of Solnhofen (Cambridge, 1990). Hb ISBN (2003) 0-521-82704-3. (shrink)

In punishment, proportionality is the systematic mathematical relationship between the significance of the wrongdoing and the amount of punishment that may be imposed on the wrongdoer. In this chapter, Kershnar argues that there is no adequate equation for proportionality. The lack of an adequate equation rests on intuitions and the absence of a shared metric. If there is no equation for proportionality, then there is no proportionality. This is because if there is no equation for proportionality, then there is no (...) general justification for proportionality. Purported justifications of punishment that lack proportionality—specifically, consequentialism and consent theory—are implausible. The lack of proportionality, then, is a threat to the notion that some punishment is justified and, more generally, non-consequentialism. (shrink)

Philosophie ist wissentlicher Einhegungsversuch des Nichtwissens. Wo immer sie daher die Bedeutung und Wirksamkeit des Nichtwissens nicht präsent hält, verfehlt sie ihre Mitte. Das hat sich seit der Antike bis heute nicht geändert. Allerdings blieb es den Interessen der Zeiten und Denker vorbehalten, die Mischformen von Wissen und Nichtwissen in ihrer Eigenart mehr oder weniger eingehend zu analysieren. Selbst wenn die sokratische Formel vom Wissen des Nichtwissens durchgängig gerne zitiert wurde: Wie die Formen des Wissens in ihren schwachen, aber unentbehrlichen (...) Variationen näherhin zu charakterisieren sind, hat über die Zeiten die Philosophen eher selten interessiert. Aber diese schwachen Formen des Wissens wie Ahnung, Mutmaßung und das Gefühl als Grundlage von Situationseinschätzungen sind für unseren Alltag von erheblicher Bedeutung. Wolfram Hogrebe diskutiert in seinem Buch Formen des Wissens in ihrer szenischen Relevanz, ja das Szenische als Wissensform selbst. Ein von der Philosophie bislang völlig ignoriertes Thema. Aber die Philosophie kann gar nicht ignorieren, ohne dennoch auch in ihrem Absehen noch etwas Mitgesehenes hervortreten zu lassen. (shrink)

This chapter addresses the potential contributions of neuroscience to criminal justice decision-making and policy, with special emphasis on criminal responsibility. The central question is whether neuroscience is relevant to criminal justice. The general conclusion is that it is scarcely useful at present but may become more relevant as the science progresses. After explaining the meaning of criminal responsibility in use, the chapter speculates about the source of claims for the positive influence of neuroscience. The scientific status of behavioral neuroscience and (...) two radical challenges to responsibility neuroscience allegedly raises, determinism and the death of agency, are discussed next. Then, the specific relevance of neuroscience to criminal law and the use of neuroscience in criminal cases in the United States and abroad are addressed. The penultimate section points to some areas warranting modest optimism for the use of neuroscience in criminal justice. A brief conclusion follows. (shrink)

An examination of verbal hallucinations and thought insertion as examples of "alienated self-consciousness.".

Transnational corporations have become actors with significant political power and authority which should entail responsibility and liability, specifically direct liability for complicity in human rights violations. Holding TNCs liable for human rights violations is complicated by the discontinuity between the fragmented legal/political structure of the TNC and its integrated strategic reality and the international state system which privileges sovereignty and non-intervention over the protection of individual rights. However, the post-Westphalian transition—the emergence of multiple authorities, increasing ambiguity of borders and jurisdiction (...) and blurring of the line between the public and private spheres—should facilitate imposing direct responsibility on transnational firms. Mechanisms for imposing direct responsibility on TNCs are considered including voluntary agreements and international law. However, I conclude that a hybrid public-private regime which relies on non-hierarchical compliance mechanisms is likely to be both more effective and consistent with the structure of the emerging transnational order. (shrink)

Undergraduate students with no prior classroom instruction in mathematical logic will benefit from this evenhanded multipart text by one of the centuries greatest authorities on the subject. Part I offers an elementary but thorough overview of mathematical logic of first order. The treatment does not stop with a single method of formulating logic; students receive instruction in a variety of techniques, first learning model theory (truth tables), then Hilbert-type proof theory, and proof theory handled through derived rules. Part II supplements (...) the material covered in Part I and introduces some of the newer ideas and the more profound results of logical research in the twentieth century. Subsequent chapters introduce the study of formal number theory, with surveys of the famous incompleteness and undecidability results of Godel, Church, Turing, and others. The emphasis in the final chapter reverts to logic, with examinations of Godel's completeness theorem, Gentzen's theorem, Skolem's paradox and nonstandard models of arithmetic, and other theorems. Unabridged republication of the edition published by John Wiley & Sons, Inc. New York, 1967. Preface. Bibliography. Theorem and Lemma Numbers: Pages. List of Postulates. Symbols and Notations. Index. (shrink)

In his second book, Tierney argues that the purpose of education must move to the heart of the educational debate. Purpose will significantly influence what schools and the education system as a whole will do next.

Introduction: discursive conditions -- Language, philosophy, and sophistry -- Contributions to a conversation about the conversation of humanity: Heidegger and Gadamer, Oakeshott and Rorty -- Lectures and letters as conversation: Cavell as educator in Cities of words -- Conclusion: redeeming words.