Ackermann’s function can be expressed using an iterative algorithm, which essentially takes the form of a term rewriting system. Although the termination of this algorithm is far from obvious, its equivalence to the traditional recursive formulation—and therefore its totality—has a simple proof in Isabelle/HOL. This is a small example of formalising mathematics using a proof assistant, with a focus on the treatment of difficult recursions.

Logic and Computation is concerned with techniques for formal theorem-proving, with particular reference to Cambridge LCF (Logic for Computable Functions). Cambridge LCF is a computer program for reasoning about computation. It combines methods of mathematical logic with domain theory, the basis of the denotational approach to specifying the meaning of statements in a programming language. This book consists of two parts. Part I outlines the mathematical preliminaries: elementary logic and domain theory. They are explained at an intuitive level, giving references (...) to more advanced reading. Part II provides enough detail to serve as a reference manual for Cambridge LCF. It will also be a useful guide for implementors of other programs based on the LCF approach. (shrink)

We present an embedding of quantified multimodal logics into simple type theory and prove its soundness and completeness. A correspondence between QKπ models for quantified multimodal logics and Henkin models is established and exploited. Our embedding supports the application of off-the-shelf higher-order theorem provers for reasoning within and about quantified multimodal logics. Moreover, it provides a starting point for further logic embeddings and their combinations in simple type theory.

We study straightforward embeddings of propositional normal multimodal logic and propositional intuitionistic logic in simple type theory. The correctness of these embeddings is easily shown. We give examples to demonstrate that these embeddings provide an effective framework for computational investigations of various non-classical logics. We report some experiments using the higher-order automated theorem prover LEO-II.

Examines the theories of Socrates, Kant, Dewey, Piaget, and others to explore the implications of Socrates' question "what is a virtuous man, and what is a virtuous school and society which educates virtuous men.".

Statistical mechanics is one of the crucial fundamental theories of physics, and in his new book Lawrence Sklar, one of the pre-eminent philosophers of physics, offers a comprehensive, non-technical introduction to that theory and to attempts to understand its foundational elements. Among the topics treated in detail are: probability and statistical explanation, the basic issues in both equilibrium and non-equilibrium statistical mechanics, the role of cosmology, the reduction of thermodynamics to statistical mechanics, and the alleged foundation of the very (...) notion of time asymmetry in the entropic asymmetry of systems in time. The book emphasises the interaction of scientific and philosophical modes of reasoning, and in this way will interest all philosophers of science as well as those in physics and chemistry concerned with philosophical questions. The book could also be read by an informed general reader interested in the foundations of modern science. (shrink)

The study of the physical world had its origins in philosophy, and, two-and-one-half millennia later, the scientific advances of the twentieth century are bringing the two fields closer together again. So argues Lawrence Sklar in this brilliant new text on the philosophy of physics.Aimed at students of both disciplines, Philosophy of Physics is a broad overview of the problems of contemporary philosophy of physics that readers of all levels of sophistication should find accessible and engaging. Professor Sklar’s talent for (...) clarity and accuracy is on display throughout as he guides students through the key problems: the nature of space and time, the problems of probability and irreversibility in statistical mechanics, and, of course, the many notorious problems raised by quantum mechanics.Integrated by the theme of the interconnectedness of philosophy and science, and linked by many references to the history of both disciplines, Philosophy of Physics is always clear, while remaining faithful to the complexity and integrity of the issues. It will take its place as a classic text in a field of fundamental intellectual importance. (shrink)

This book explores what anyone interested in ethics can draw from Heidegger's thinking. Heidegger argues for the radical finitude of being. But finitude is not only an ontological matter; it is also located in ethical life. Moral matters are responses to finite limit-conditions, and ethics itself is finite in its modes of disclosure, appropriation, and performance. With Heidegger's help, Lawrence Hatab argues that ethics should be understood as the contingent engagement of basic practical questions, such as how should human (...) beings live? (shrink)

In this paper, I want eventually to get around to proposing a criterion of identity for events which are changes in physical objects, where events are construed as comprising a distinct metaphysical category of thing. The proposal will be preceded by a discussion of what I take to be a mistaken suggestion for such a criterion; I will do that because I think that seeing what it takes to show why that suggestion fails helps to motivate a theory about what (...) it is to be an event; and that theory wi II supply the conceptual foundations for my proposal concerning the criterion of identity for events. Before that suggestion is discussed, however, I want to discuss briefly an aspect of the question, Why do we have to give a criterion of identity for events, or for objects of any sort whatsoever? I want to have a brief look at the connection between identity criteria and the idea of a kind of object. (shrink)

Although now replaced by more modern theories, classical mechanics remains a core foundational element of physical theory. From its inception, the theory of dynamics has been riddled with conceptual issues and differing philosophical interpretations and throughout its long historical development, it has shown subtle conceptual refinement. The interpretive program for the theory has also shown deep evolutionary change over time. Lawrence Sklar discusses crucial issues in the central theory from which contemporary foundational theories are derived and shows how some (...) core issues have nevertheless remained deep puzzles despite the increasingly sophisticated understanding of the theory which has been acquired over time. His book will be of great interest to philosophers of science, philosophers in general and physicists concerned with foundational interpretive issues in their field. (shrink)

Manuel Velasquez and F. Neil Brady apply the doctrine of double effect to business ethics and conclude that the doctrine allows a pharmaceutical company to sell a drug with potentially fatal side effects only if it also has the good effect of saving lives. This forbidsthe sale of many common products, such as automobiles and alcohol. My account preserves the virtues of the doctrine of double effectwithout making it too restrictive. I apply the doctrine to a pharmaceutical company’s decision to (...) market a drug with dangerous side effects and argue that free markets often offer the best way to compare the good and bad effects of business decisions. I conclude that the doctrine does allow a business to sell a potentially fatal product that does not save lives, provided that it warns consumers about the danger. (shrink)

Search engines play an increasingly pivotal role in the distribution and eventual construction of knowledge, yet they are largely unnoticed, their procedures are opaque, and they are almost completely devoid of independent oversight. In this paper the author examines three areas in which we encounter difficult and persistent ethical issues in search engine technology: The problem of algorithm and the lack of transparency of the search process, the problem of privacy with regards of the possibility to monitor search histories, and (...) the problem of local censorship. The given findings lead to the conclusion that the development of structures of accountability for search engines is an important task for the near future. (shrink)

In _Civil Society_, Lawrence Cahoone stages a critical engagement between the social-political viewpoints of liberalism, communitarianism, and conservatism in order to effect a balanced relation that will bypass or overcome the inadequacies of each position.

Cloning and reproductive technologies -- Abortion -- Euthanasia -- Punishment and the death penalty -- War, terrorism, and counterterrorism -- Race and ethnicity -- Gender -- Sexual orientation -- World hunger and poverty -- Living together with animals -- Environmental ethics -- Cyberethics.

The topic of this conference, directed toward exploring the relationships between Hegel’s Naturphilosophie and his conception of spirit, drew a total of about 300 registrants, with about 140 papers being presented. Although sixteen countries were represented, well over half of the participants came from German universities. Next in the number of participants were those from Yugoslavia and Poland. There were five North Americans listed on the printed program, but only three attended: H.S. Harris, Leo Rauch, and this writer. Among the (...) welcome and familar faces in the audience were those of Howard P. Kainz, James Wilkinson, and Shlomo Avineri. Those of us who recalled the fine paper which Professor Avineri had presented at the 1986 Zürich conference were unhappy to learn that he had chosen not to present one at this time. (shrink)

The course of Western philosophy has been profoundly altered by the philosophy of Hegel. The first of those who set about the transforming and revisioning of the world according to Hegel's dialectical theory were called "The Young Hegelians." Today, the most recognized names among them are Karl Marx and Friedrich Engels, but in their own age each of the Young Hegelians shared an equal notoriety. Each in turn, from Strauss with his reduction of the historical jesus into a Messianic myth, (...) to Stirner with his uncompromising egoism, shocked every cultural convention of their age. The aftershocks of their unrestrained criticism have forever altered the topography of our own. The Young Hegelians retrieves some of the central writings of that troubling generation. (shrink)

Commençant par une revue sommaire des types de questions qu’une fondation des mathématiques devrait poser, cet article présente premièrement une critique des fondements basés sur la théorie des ensembles, puis propose l’idée que plusieurs fondements catégoriques, reliés les uns aux autres, seraient plus avantageux, et finalement indique une méthode pour retrouver la théorie des ensembles à travers une approche catégorique.

It is obvious that identical events must occur at the same time. This follows simply from the principle of the indiscernibility of identicals and from the fact that events have temporal features among which are those which attribute to events times of occurrence. Thus, )).But from the fact that is true, and is, indeed, true necessarily, it does not follow that events necessarily occur at the times at which they in fact occur. This latter claim about events is expressed as (...) follows: ). (shrink)