One of Hume's most well-known works and a masterpiece of philosophy, A Treatise of Human Nature is indubitably worth taking the time to read.

A Treatise of Human Nature, David Hume's comprehensive attempt to base philosophy on a new, observationally grounded study of human nature, is one of the most important texts in Western philosophy. It is also the focal point of current attempts to understand 18th-century western philosophy. The Treatise addresses many of the most fundamental philosophical issues: causation, existence, freedom and necessity, and morality. The volume also includes Humes own abstract of the Treatise, a substantial introduction, extensive annotations, a glossary, a comprehensive (...) index, and suggestions for further reading. (shrink)

Stephen Cole Kleene was one of the greatest logicians of the twentieth century and this book is the influential textbook he wrote to teach the subject to the next generation. It was first published in 1952, some twenty years after the publication of Godel's paper on the incompleteness of arithmetic, which marked, if not the beginning of modern logic. The 1930s was a time of creativity and ferment in the subject, when the notion of computable moved from the realm of (...) philosophical speculation to the realm of science. This was accomplished by the work of Kurt Gode1, Alan Turing, and Alonzo Church, who gave three apparently different precise definitions of computable. When they all turned out to be equivalent, there was a collective realization that this was indeed the right notion. Kleene played a key role in this process. One could say that he was there at the beginning of modern logic. He showed the equivalence of lambda calculus with Turing machines and with Godel's recursion equations, and developed the modern machinery of partial recursive functions. This textbook played an invaluable part in educating the logicians of the present. It played an important role in their own logical education.". (shrink)

A comprehensive one-year graduate (or advanced undergraduate) course in mathematical logic and foundations of mathematics. No previous knowledge of logic is required; the book is suitable for self-study. Many exercises (with hints) are included.

Normal propositional modal systems This first chapter has two main aims. One is to give a general account of the propositional modal systems that we shall ...

"Necessity is the mother of invention. " Part I: What is in this book - details. There are several different types of formal proof procedures that logicians have invented. The ones we consider are: 1) tableau systems, 2) Gentzen sequent calculi, 3) natural deduction systems, and 4) axiom systems. We present proof procedures of each of these types for the most common normal modal logics: S5, S4, B, T, D, K, K4, D4, KB, DB, and also G, the logic that (...) has become important in applications of modal logic to the proof theory of Peano arithmetic. Further, we present a similar variety of proof procedures for an even larger number of regular, non-normal modal logics. We also consider some quasi-regular logics, including S2 and S3. Virtually all of these proof procedures are studied in both propositional and first-order versions. Finally, we present the full variety of proof methods for Intuitionistic logic. We actually give two quite different kinds of tableau systems for the logics we consider, two kinds of Gentzen sequent calculi, and two kinds of natural deduction systems. Each of the two tableau systems has its own uses; each provides us with different information about the logics involved. They complement each other more than they overlap. Of the two Gentzen systems, one is of the conventional sort, common in the literature. (shrink)

A key to modern studies of 18th century Western philosophy, the Treatise considers numerous classic philosophical issues, including causation, existence, freedom and necessity and morality. This abridged edition has an introduction which explain's Hume's thought and places it in the context of its times.

In der Diskussion metaethischer Fragen spielt das Humesche Gesetz eine wichtige Rolle, nach dem normative Aussagen, d.h. Aussagen über Gebote oder Werte, sich nicht aus deskriptiven Aussagen ableiten lassen. In dieser Arbeit wird das Gesetz präzise formuliert und bewiesen, und es wird seine Relevanz für eine Kritik naturalistischer ethischer Theorien erörtert.

Eine Deduktion resp. eine logisch gültige Implikation ist Stephan Körner zufolge relevant gdw keine Formelkomponente salva validitate, d.h. unter Bewahrung der Gültigkeit, durch ihre Negation ersetzt werden kann. In der folgenden Arbeit wird 1. dieses Kriterium philosophisch-grundlagentheoretisch diskutiert, 2. in eine präzise Formulierung übergeführt; 3. wird gezeigt, wie eine Reihe unterschiedlicher Relevanzkriterien sich einheitlich auf das Körner-Kriterium zurückführen lassen, und 4. werden wissenschaftstheoretische Anwendungen des Körner-Kriteriums am Beispiel des D-N-Systematisierungsbegriffs, des Begriffs der Theorienbewährung, des Mackieschen Ursachebegriffs als Inus-Bedingung und des (...) probabilistischen Systematisierungsbegriffs demonstriert. (shrink)

Eine Deduktion resp. eine logisch gültige Implikation ist Stephan Körner zufolge relevant gdw keine Formelkomponente salva validitate, d.h. unter Bewahrung der Gültigkeit, durch ihre Negation ersetzt werden kann. In der folgenden Arbeit wird 1. dieses Kriterium philosophisch-grundlagentheoretisch diskutiert, 2. in eine präzise Formulierung übergeführt; 3. wird gezeigt, wie eine Reihe unterschiedlicher Relevanzkriterien sich einheitlich auf das Körner-Kriterium zurückführen lassen, und 4. werden wissenschaftstheoretische Anwendungen des Körner-Kriteriums am Beispiel des D-N-Systematisierungsbegriffs, des Begriffs der Theorienbewährung, des Mackieschen Ursachebegriffs als Inus-Bedingung und des (...) probabilistischen Systematisierungsbegriffs demonstriert. (shrink)

The papers collected in this volume were written over a period of some eight or nine years, with some still earlier material incorporated in one of them. Publishing them under the same cover does not make a con tinuous book of them. The papers are thematically connected with each other, however, in a way which has led me to think that they can naturally be grouped together. In any list of philosophically important concepts, those falling within the range of application (...) of modal logic will rank high in interest. They include necessity, possibility, obligation, permission, knowledge, belief, perception, memory, hoping, and striving, to mention just a few of the more obvious ones. When a satisfactory semantics (in the sense of Tarski and Carnap) was first developed for modal logic, a fascinating new set of methods and ideas was thus made available for philosophical studies. The pioneers of this model theory of modality include prominently Stig Kanger and Saul Kripke. Several others were working in the same area independently and more or less concurrently. Some of the older papers in this collection, especially 'Quantification and Modality' and 'Modes of Modality', serve to clarify some of the main possibilities in the semantics of modal logics in general. (shrink)