The fundamental ideas concerning computation and recursion naturally find their place at the interface between logic and theoretical computer science. The contributions in this book, by leaders in the field, provide a picture of current ideas and methods in the ongoing investigations into the pure mathematical foundations of computability theory. The topics range over computable functions, enumerable sets, degree structures, complexity, subrecursiveness, domains and inductive inference. A number of the articles contain introductory and background material which it is hoped will (...) make this volume an invaluable resource for specialists and non-specialists alike. (shrink)

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.

The class of all recursive functions fails to possess a natural hierarchical structure, generated predicatively from "within". On the other hand, many (proof-theoretically significant) sub-recursive classes do. This paper attempts to measure the limit of predicative generation in this context, by classifying and characterizing those (predictably terminating) recursive functions which can be successively defined according to an autonomy condition of the form: allow recursions only over well-orderings which have already been "coded" at previous levels. The question is: how can a (...) recursion code a well-ordering? The answer lies in Girard's theory of dilators, but is reworked here in a quite different and simplified framework specific to our purpose. The "accessible" recursive functions thus generated turn out to be those provably recursive in $(\prod_{1}^{1}-CA)_{0}$. (shrink)

Girard’s maxim, that Peano Arithmetic is a theory of one inductive definition, is re-examined in the light of a weak theory EA formalising basic principles of Nelson’s predicative Arithmetic.

Wilfred Sieg and Stanley S. Wainer. Program Transformation and Proof Transformation.

There is a very simple way in which the safe/normal variable discipline of Bellantoni–Cook recursion [S. Bellantoni, S. Cook, A new recursion theoretic characterization of the polytime functions, Computational Complexity 2 97–110] can be imposed on arithmetical theories like PA: quantify over safes and induct on normals. This weakens the theory severely, so that the provably recursive functions become more realistically computable . Earlier results of D. Leivant [Intrinsic theories and computational complexity, in: D. Leivant , Logic and Computational Complexity, (...) Lecture Notes in Computer Science, vol. 960, Springer-Verlag, 1995, pp. 177–194] are re-worked and extended in this new context, giving proof-theoretic characterizations of complexity classes between Grzegorczyk’s E2 and E3. (shrink)

Following our [6], though with somewhat different methods here, further variants of Goodstein sequences are introduced in terms of parameterized Ackermann–Péter functions. Each of the sequences is shown to terminate, and the proof-theoretic strengths of these facts are calibrated by means of ordinal assignments, yielding independence results for a range of theories: PRA, PA,$\Sigma ^1_1$-DC$_0$, ATR$_0$, up to ID$_1$. The key is the so-called “Hardy hierarchy” of proof-theoretic bounding finctions, providing a uniform method for associating Goodstein-type sequences with parameterized normal (...) form representations of positive integers. (shrink)

Subrecursive hierarchy classifications are used to compare the complexities of recursive functions according to their derivations in a version of Kleene's equation calculus, and their computations by term-rewriting. In each case ordinal bounds are assigned, and it turns out that the respective complexity measures are given by a version of the Fast Growing Hierarchy, and the Slow Growing Hierarchy. Known comparisons between the two hierarchies then provide ordinal trade-offs between derivation and computation. Characteristics of some well-known subrecursive classes are also (...) read off. (shrink)

The emphasis on individual differences in evolutionary theories is important and has not received adequate attention. Strategic Pluralism makes a major contribution by addressing these issues, but like other evolutionary models (e.g., game theory) does not articulate the specific mechanisms underlying strategy selection. Specification of such mechanisms is an essential next step in the development of these models.

Dealing with the continuously increasing rates of families wanting to either significantly delay or completely postpone their infant's vaccines has created an alarmingly untenable dilemma for the general pediatricians dealing with these families on a daily basis. Pediatricians must decide whether to continue to provide substandard care by foregoing many or most of the infant's highly recommended protective vaccines, or whether to dismiss from the practice the family who refuses vaccines. Much has been written about why they should retain these (...) families, but this paper will discuss some reasonable rationales as to why nearly 40% of pediatricians choose dismissal of these families. (shrink)

Featuring an exceptionally clear writing style and a wealth of real-world examples and exercises, Logic, Second Edition, shows how logic relates to everyday life, demonstrating its applications in such areas as the workplace, media and entertainment, politics, science and technology, student life, and elsewhere.Thoroughly revised and expanded in this second edition, the text now features 2600 exercises, more than 1000 of them new; three new chapters on legal arguments, moral arguments, and analyzing a long essay; enhanced pedagogy; and much more.FEATURES* (...) 2600 exercises--more than 1000 of them new--breathe new life into logic* Real-world examples help bring logic down to earth for students* A unique, extended explanation or model of the answer to the first question of each "Check Your Understanding" section shows students what is expected of their answers* An additional 25% of the exercises are answered at the back of the book* "Profiles in Logic" provide short sketches of logicians, philosophers, mathematicians, and others associated with logic* "Logic Challenge" problems present puzzles and paradoxes that end each chapter on a fun note* Additional pedagogical elements--marginal definitions, key terms, a glossary, reference boxes, and bulleted chapter summaries--make the material even more accessible* Detailed guides help students learn to create "truth tables" and Venn diagramsSUPPORT PACKAGEAn Instructor's Manual with Computerized Test Bank on CD includes: Solutions to all exercises in the book, enhanced by explanations and answers that elucidate the details of the correct answersKey Terms and a summary for each chapterA customizable Computerized Test Bank--with multiple-choice, true/false, and fill-in-the-blank questions--that allows instructors to give exams or homework problems that can be auto-gradedA traditional "pencil-and-paper" Test Bank and answer key containing the same questions as the Computerized Test BankPowerPoint-based lecture outlinesThe Instructor's Manual with Computerized Test Bank and the traditional Test Bank are also available in printed format.A Companion Website offers:Instructor Resources :A downloadable version of the Instructor's Manual PowerPoint-based lecture outlinesStudent Resources:Brief chapter summariesInteractive Flash Cards with key terms and definitionsWeb links and other media resourcesPractice quizzes with answers and explanations The Learning Management System Cartridges include, in a fully downloadable format:Instructor's Manual and Computerized Test Bank Student material from the companion websiteThe Perfect Text for Your Course... No Matter How You Teach ItYour course is unique; you have your own teaching philosophy and style. Whether you teach traditional Introduction to Logic, Critical Thinking/Informal Logic, or Formal Logic, Baronett: Logic, Second Edition, can be tailored to fulfill your course needs.We'll make it easy for you; choose one of our Alternate Editions or build the book you want, chapter by chapter.Option 1. Author Stan Baronett has suggested four Alternate Editions that may work for you. Each Alternate Edition comes in full color, with answers to problems, a full glossary, and an index. The books are in stock and available for ordering. Please see the ISBN information below.Logic: Concise EditionChapters 1, 3, 4, 5, 6, 7, 8Order using ISBN: 978-0-19-994129-2Logic: An Emphasis on Critical Thinking and Informal LogicChapters 1, 2, 3, 4, 10, 11, 12, 13 A-E, 14, 15Order using ISBN: 978-0-19-994128-5Logic: An Emphasis on Formal LogicChapters 1, 5, 6, 7, 8, 9Order using ISBN: 978-0-19-994126-1Logic: With Diagramming used in Chapter 4. Informal FallaciesFull textOrder using ISBN: 978-0-19-997081-0Option 2. Create your own customized textbook by choosing the specific chapters that you need for your course. Please contact your Oxford University Press Sales Representative or call 800.280.0280 for details. (shrink)

In the course of making nearly 400 films over the past 50 years, "Stan Brakhage" became synonymous with independent American filmmaking, particularly its avant-garde component. This major collection of writings draws primarily upon two long out-of-print books--Metaphors on Vision and Brakhage Scrapbook. Brakhage examines filmmaking in relation to social and professional contexts, the nature of influence and collaboration, the aesthetics of personal experience, and the conditions under which various films were made. Brakhage discusses his predecessors and contemporaries, relates film (...) to dance and poetry, and in "A Moving Picture Giving and Taking Book" provides a manual for the novice filmmaker. Lectures, interviews, essays, and manifestos document Brakhage's personal vision and public persona. (shrink)

Faith in the universal moral equality of people enjoys close to unanimous consensus in present moral and political philosophy. Yet its philosophical justification remains precarious. The search for the basis of equality encounters insurmountable difficulties. Nothing short of a miracle seems required to stabilize universal equality in moral status amidst a vast space of distinctions sprawling between people. The difficulties of stabilizing equality against differentiation are not specific to any particular choice regarding the basis of equality. To show this, I (...) will provide a general diagnosis of the difficulty together with its application to the arguably best attempt at a solution, namely to ground moral equality in a form of subjectivity. In his recent book Equality for Nonegalitarians, George Sher advances the view that “we are moral equals because we are equally centers of consciousness. …The fact that we are equals in this respect—that each is a world unto himself—…explains why each person’s interests are of equal moral importance”. Yet the worlds we are unto ourselves can no more withstand the force of differentiation than previous candidates suggested in the literature, and the reasons why run deeper than even some critics have recognized. The prospects for vindicating universal moral equality remain bleak. (shrink)

Faith in the universal moral equality of people enjoys close to unanimous consensus in present moral and political philosophy. Yet its philosophical justification remains precarious. The search for the basis of equality encounters insurmountable difficulties. Nothing short of a miracle seems required to stabilize universal equality in moral status amidst a vast space of distinctions sprawling between people. The difficulties of stabilizing equality against differentiation are not specific to any particular choice regarding the basis of equality. To show this, I (...) will provide a general diagnosis of the difficulty together with its application to the arguably best attempt at a solution, namely to ground moral equality in a form of subjectivity. In his recent book Equality for Nonegalitarians, George Sher advances the view that “we are moral equals because we are equally centers of consciousness. …The fact that we are equals in this respect—that each is a world unto himself—…explains why each person’s interests are of equal moral importance”. Yet the worlds we are unto ourselves can no more withstand the force of differentiation than previous candidates suggested in the literature, and the reasons why run deeper than even some critics have recognized. The prospects for vindicating universal moral equality remain bleak. (shrink)

Does not contain all chapters present in the main book--from publisher's comments.

Implicit Rhetoric examines the implications of Kenneth Burke's concept of entelechy, the most transcendent term in Burke's philosophical system. The author discusses Burke's ideas on the existence of 'implicit' rhetoric which goes against Aristotle's view that rhetoric includes an essentially 'explicit' view of criticism.

I argue that our current practice of ascribing the term “ memory ” to mental states and processes lacks epistemic warrant. Memory, according to the “received view”, is any state or process that results from the sequential stages of encoding, storage and retrieval. By these criteria, memory, or its footprint, can be seen in virtually every mental state we are capable of having. This, I argue, stretches the term to the breaking point. I draw on phenomenological, historical and conceptual considerations (...) to make the case that an act of memory entails a direct, non-inferential feeling of re-acquaintance with one’s past. It does so by linking content retrieved from storage with autonoetic awareness during retrieval. On this view, memory is not the content of experience, but the manner in which that content is experienced. I discuss some theoretical and practical implications and advantages of adopting this more nuanced view of memory. -/-. (shrink)

The philosophical interest in experimental practice in neuroscience has brought renewed attention to the study of the development and use of techniques and tools for data production. John Bickle has argued that the construction and progression of theories in neuroscience are entirely dependent on the development and ingenious use of research tools. In Bickle's account, theory plays a tertiary role, as it depends on what the tools allow researchers to manipulate, and the tools, in turn, are developed not in order (...) to test theories but as solutions to engineering problems. However, Bickle's account is not entirely precise in explaining what informs researchers' decision-making in their atheoretical laboratory tinkering. Identifying the sources that guide researchers in tool development and use is crucial if one wishes to contribute to the philosophical or meta-scientific understanding of experimental practice in neuroscience. In the following paper, I claim that decision-making in tools' development and use in neuroscience is doubly guided. Pre-existing theory and concepts determine information's relevance, whereas tools' functioning in controlled situations determines information's reliability. Accordingly, experimenters' decision-making is situated both in the context of analysing, modelling or interpreting information and in the context of producing information. I study the case of the tungsten microelectrode developed by David Hubel during the 1950s. First, I show that pre-existing theory and concepts determine in advance what information would be relevant to obtain from the microelectrode. Second, I show that Hubel's tinkering follows the guidelines derived from the very structure of what we recognise as reliable experimentally produced information. Finally, I suggest that data-production processes allow experimenters to assess what to expect from an experimental system in terms of concept- and theory-generation and confirmation, thereby endorsing Bickle's tenet on the tertiary role of theory in neuroscience. (shrink)

I argue that the feeling that one is the owner of his or her mental states is not an intrinsic property of those states. Rather, it consists in a contingent relation between consciousness and its intentional objects. As such, there are (a variety of) circumstances, varying in their interpretive clarity, in which this relation can come undone. When this happens, the content of consciousness still is apprehended, but the feeling that the content “belongs to me” no longer is secured. I (...) discuss the implications of a mechanism enabling personal ownership for understanding a variety of clinical syndromes as well normal mental function. (shrink)

Common wisdom, philosophical analysis and psychological research share the view that memory is subjectively positioned toward the past: Specifically, memory enables one to become re-acquainted with the objects and events of his or her past. In this paper I call this assumption into question. As I hope to show, memory has been designed by natural selection not to relive the past, but rather to anticipate and plan for future contingencies -- a decidedly future-oriented mode of subjective temporality. This is not (...) to say memory makes no reference to the past. But, I argue, past-oriented subjectivity is a by-product of a system designed by natural selection to help us face and respond to the "now and the next". I discuss the implications of the proposed temporal realignment for research agendas as well as the potential limitations of measures designed to explore memory by focusing on its retentive capabilities. (shrink)

Following the seminal work of Ingvar (1985. “Memory for the future”: An essay on the temporal organization of conscious awareness. Human Neurobiology, 4, 127–136), Suddendorf (1994. The discovery of the fourth dimension: Mental time travel and human evolution. Master’s thesis. University of Waikato, Hamilton, New Zealand), and Tulving (1985. Memory and consciousness. Canadian Psychology/Psychologie Canadienne, 26, 1–12), exploration of the ability to anticipate and prepare for future contingencies that cannot be known with certainty has grown into a thriving research enterprise. (...) A fundamental tenet of this line of inquiry is that future-oriented mental time travel, in most of its presentations, is underwritten by a property or an extension of episodic recollection. However, a careful conceptual analysis of exactly how episodic memory functions in this capacity has yet to be undertaken. In this paper I conduct such an analysis. Based on conceptual, phenomenological, and empirical considerations,I conclude that the autonoetic component of episodic memory, not episodic memory per se, is the causally determinative factor enabling an individual to project him or herself into a personal future. (shrink)

This paper examines the issue of what the self is by reviewing neuropsychological research,which converges on the idea that the self may be more complex and differentiated than previous treatments of the topic have suggested. Although some aspects of self-knowledge such as episodic recollection may be compromised in individuals, other aspects—for instance, semantic trait summaries—appear largely intact. Taken together, these findings support the idea that the self is not a single, unified entity. Rather, it is a set of interrelated, functionally (...) independent systems. Implications for understanding the self in various areas of psychological research—e.g., neuroimaging, autism, amnesia, Alzheimer’s disease, and mirror self-recognition—are discussed in brief. (shrink)

Episodic memory often is conceptualized as a uniquely human system of long-term memory that makes available knowledge accompanied by the temporal and spatial context in which that knowledge was acquired. Retrieval from episodic memory entails a form of first–person subjectivity called autonoetic consciousness that provides a sense that a recollection was something that took place in the experiencer’s personal past. In this paper I expand on this definition of episodic memory. Specifically, I suggest that (a) the core features assumed unique (...) to episodic memory are shared by semantic memory, (b) episodic memory cannot be fully understood unless one appreciates that episodic recollection requires the coordinated function of a number of distinct, yet interacting, “enabling” systems. Although these systems – ownership, self, subjective temporality, and agency – are not traditionally viewed as memorial in nature, each is necessary for episodic recollection and jointly they may be sufficient, and (c) the type of subjective awareness provided by episodic recollection (autonoetic) is relational rather than intrinsic – i.e., it can be lost in certain patient populations, thus rendering episodic memory content indistinguishable from the content of semantic long-term memory. (shrink)

Memory evolved to supply useful, timely information to the organism’s decision-making systems. Therefore, decision rules, multiple memory systems, and the search engines that link them should have coevolved to mesh in a coadapted, functionally interlocking way. This adaptationist perspective suggested the scope hypothesis: When a generalization is retrieved from semantic memory, episodic memories that are inconsistent with it should be retrieved in tandem to place boundary conditions on the scope of the generalization. Using a priming paradigm and a decision task (...) involving person memory, the authors tested and confirmed this hypothesis. The results support the view that priming is an evolved adaptation. They further show that dissociations between memory systems are not—and should not be—absolute: Independence exists for some tasks but not others. (shrink)

Throughout a career spanning half a century, Stan Brakhage--the foremost experimental filmmaker in America, and perhaps the world--wrote controversial essays on the art of film and its intersections with poetry, music, dance, and painting. Published in small circulation literary and arts journals, they were gathered later into such books as Metaphors on Vision and Film at Wit's End. Beginning in 1989, and for a decade thereafter, Brakhage wrote the essays in Telling Time as an occasional column for Musicworks, a (...) Toronto quarterly. Ostensibly about the relation of film to music, they soon enlarged to explore primary concerns beyond film, including Brakhage's aesthetic theories based on the phenomenology of human cognition. In these essays he is as brilliant discussing Gertrude Stein or romantic love as he is on child psychology, astronomy, and physiology, all the while teasing out vital correspondences between the arts, and upending conventional ideas of how we perceive. His investigations of other artists are models of sympathetic intuition and generosity. Above all, he shares his theories, discoveries and understandings in the spirit of establishing a groundwork for many varieties of human liberation. His prose is filled with flashes of insight, elaborated metaphors, playful elisions, shorthand puns and neologisms, personal digressions, surprising epiphanies, leaps of faith, affronts to authority. He appeals to the imagination, and invites us to a more profound and personal experience of art. (shrink)

Over the last dozen years, the writings of Richard Taruskin have transformed the debate about "early music" and "authenticity." Text and Act collects for the first time the most important of Taruskin's essays and reviews from this period, many of which now classics in the field. Taking a wide-ranging cultural view of the phenomenon, he shows that the movement, far from reviving ancient traditions, in fact represents the only truly modern style of performance being offered today. He goes on to (...) contend that the movement is therefore far more valuable and even authentic than the historical verisimilitude for which it ostensibly strives could ever be. These essays cast fresh light on many aspects of contemporary music-making and music-thinking, mixing lighthearted debunking with impassioned argumentation. Taruskin ranges from theoretical speculation to practical criticism, and covers a repertory spanning from Bach to Stravinsky. Including a newly written introduction, Text and Act collects the very best of one of our most incisive musical thinkers. (shrink)

Does not include all chapters from the main book--publisher's comments.

In his article on The Liabilities of Mobility, Merker asserts that “Consciousness presents us with a stable arena for our actions—the world …” and argues for this property as providing evolutionary pressure for the evolution of consciousness. In this commentary, I will explore the implications of Merker’s ideas for consciousness in artificial agents as well as animals, and also meet some possible objections to his evolutionary pressure claim.