This book presents modern logic as the formalization of reasoning that needs and deserves a semantic foundation. Chapters on propositional logic; parsing propositions; and meaning, truth and reference give the reader a basis for establishing criteria that can be used to judge formalizations of ordinary language arguments. Over 120 worked examples illustrate the scope and limitations of modern logic, as analyzed in chapters on identity, quantifiers, descriptive names, and functions. The chapter on second-order logic shows how different conceptions of predicates (...) and propositions do not lead to a common basis for quantification over predicates, as they do for quantification over things. Notable for its clarity of presentation and supplemented by many exercises, this volume will be invaluable for philosophers, linguists, mathematicians, and computer scientists who wish to better understand the tools they use in formal reasoning. (shrink)

This book is dedicated to a classic presentation of the theory of computable functions in the context of the foundations of mathematics. Part I motivates the study of computability with discussions and readings about the crisis in the foundations of mathematics in the early 20th century, while presenting the basic ideas of whole number, function, proof, and real number. Part II starts with readings from Turing and Post leading to the formal theory of recursive functions. Part III presents sufficient formal (...) logic to give a full development of Gödel's incompleteness theorems. Part IV considers the significance of the technical work with a discussion of Church's Thesis and readings on the foundations of mathematics. This new edition contains the timeline "Computability and Undecidability" as well as the essay "On mathematics". (shrink)

The contributions in the book examine the historical and contemporary manifestations of organized crime, the symbiotic relationship between legitimate and ...

The most popular method of incorporating time into a formal logic is based on the work of Arthur Prior. It treats tenses as operators on sentences. In this essay I show a serious problem with that approach, a confusion of scheme versus proposition, which makes any system built in that way incoherent. I will compare how other formal logics deal with the scheme versus proposition distinction and find that only for formal modal logics does the same problem arise. I then (...) compare Prior’s approach to other ways of taking time into account in formal logics. (shrink)

This book grew out of my confusion. If logic is objective how can there be so many logics? Is there one right logic, or many right ones? Is there some underlying unity that connects them? What is the significance of the mathematical theorems about logic which I've learned if they have no connection to our everyday reasoning? The answers I propose revolve around the perception that what one pays attention to in reasoning determines which logic is appropriate. The act of (...) abstracting from our reasoning in our usual language is the stepping stone from reasoned argument to logic. We cannot take this step alone, for we reason together: logic is reasoning which has some objective value. For you to understand my answers, or perhaps better, conjectures, I have retraced my steps: from the concrete to the abstract, from examples, to general theory, to further confirming examples, to reflections on the significance of the work. (shrink)

What do we mean by ‘countable’?Export citation.

MOTIVATION The constructivization of ; => D(_£^') poses several problems. For some of these the tools of MD can be modified; for others new methods will need to be established. What must we do to make a full approximation to ; * D? We ...

For the purposes of this monograph, "by a degree" is meant a degree of recursive unsolvability. A degree [script bold]m is said to be minimal if 0 is the unique degree less than [script bold]m. Each of the six chapters of this self-contained monograph is devoted to the proof of an existence theorem for minimal degrees.

Richard Tieszen presents an analysis, development, and defense of a number of central ideas in Kurt Gödel's writings on the philosophy and foundations of mathematics and logic. Tieszen structures the argument around Gödel's three philosophical heroes - Plato, Leibniz, and Husserl - and his engagement with Kant, and supplements close readings of Gödel's texts on foundations with materials from Gödel's Nachlass and from Hao Wang's discussions with Gödel. He provides discussions of Gödel's views, and develops a new type of (...) platonic rationalism that requires rational intuition, called 'constituted platonism'. (shrink)

Gödel's relation to the work of Plato, Leibniz, Kant, and Husserl is examined, and a new type of platonic rationalism that requires rational intuition, called ...

We can't understand ourselves or our world without knowing God. Designed for formal or informal study, this book explores God's plan, works, and attributes and answers key questions about him.

Theories of Truth provides a clear, critical introduction to one of the most difficult areas of philosophy. It surveys all of the major philosophical theories of truth, presenting the crux of the issues involved at a level accessible to nonexperts yet in a manner sufficiently detailed and original to be of value to professional scholars. Kirkham's systematic treatment and meticulous explanations of terminology ensure that readers will come away from this book with a comprehensive general understanding of one of philosophy's (...) thorniest set of topics. -/- Included are discussions of the correspondence, coherence, pragmatic, semantic, performative, redundancy, appraisal, and truth-as-justification theories. There are also chapters or sections of chapters on the liar paradox, three-valued logic, Field's critique of Tarski, Davidson's program, Dummett's theory of linguistic competence, satisfaction, recursion, the extension/intension distinction, and an explanation of how theories of justification, properly understood, differ from theories of truth. -/- A persistent theme is that philosophers have too often failed to recognize that not all theories of truth are intended to answer the same question. When the various questions are made distinct, it is apparent that many of the "debates" in this field are really cases of philosophers talking past one another. There is much less disagreement within the field than has commonly been thought. (shrink)

"This book explores the religious underpinnings of psychoanalysis and examines how the tenets of Judaism and Christianity specifically influenced the theories and practices of Freud and Jung, respectively. It demonstrates that secular psychoanalysis is in large measure a revision of religious principles contained within the Judeo-Christian ethic and questions whether Freud's and Jung's approaches may best be suited to the psychological configurations of their fellow religionists." -- Back cover.

We propose a framework for including information‐processing bounds in rational analyses. It is an application of bounded optimality (Russell & Subramanian, 1995) to the challenges of developing theories of mechanism and behavior. The framework is based on the idea that behaviors are generated by cognitive mechanisms that are adapted to the structure of not only the environment but also the mind and brain itself. We call the framework computational rationality to emphasize the incorporation of computational mechanism into the definition of (...) rational action. Theories are specified as optimal program problems, defined by an adaptation environment, a bounded machine, and a utility function. Such theories yield different classes of explanation, depending on the extent to which they emphasize adaptation to bounds, and adaptation to some ecology that differs from the immediate local environment. We illustrate this variation with examples from three domains: visual attention in a linguistic task, manual response ordering, and reasoning. We explore the relation of this framework to existing “levels” approaches to explanation, and to other optimality‐based modeling approaches. (shrink)

Offering a collection of fifteen essays that deal with issues at the intersection of phenomenology, logic, and the philosophy of mathematics, this 2005 book is divided into three parts. Part I contains a general essay on Husserl's conception of science and logic, an essay of mathematics and transcendental phenomenology, and an essay on phenomenology and modern pure geometry. Part II is focused on Kurt Godel's interest in phenomenology. It explores Godel's ideas and also some work of Quine, Penelope Maddy and (...) Roger Penrose. Part III deals with elementary, constructive areas of mathematics. These are areas of mathematics that are closer to their origins in simple cognitive activities and in everyday experience. This part of the book contains essays on intuitionism, Hermann Weyl, the notion of constructive proof, Poincaré and Frege. (shrink)

The purpose of this paper is to examine the distinction between "negative" and "positive" duties. Special attention will be given to certain criticism raised against this distinction by Michael Tooley.

The claim that visually masked, unidentifiable words are analyzed at the level of whole word meaning has been challenged by recent findings indicating that instead, analysis occurs mainly at the subword level. The present experiments examined possible limits on subword analysis. Experiment 1 obtained semantic priming from pleasant- and unpleasant-meaning subliminal words in which no individual letter contained diagnostic information about a word’s evaluative valence; thus analysis must operate on information more complex than that contained in individual letters. Experiments 2 (...) and 3 showed that analysis must operate on information more complex than that represented by individual bigrams or trigrams . These findings suggest that while subliminal priming is driven by subword analysis, the effective units of analysis are distributed widely across at least short words. (shrink)