It is generally believed that the uncertainty relation Δq Δp≥1/2ħ, where Δq and Δp are standard deviations, is the precise mathematical expression of the uncertainty principle for position and momentum in quantum mechanics. We show that actually it is not possible to derive from this relation two central claims of the uncertainty principle, namely, the impossibility of an arbitrarily sharp specification of both position and momentum (as in the single-slit diffraction experiment), and the impossibility of the determination of the path (...) of a particle in an interference experiment (such as the double-slit experiment). (shrink)

Girard and Reynolds independently invented System F to handle problems in logic and computer programming language design, respectively. Viewing F in the Curry style, which associates types with untyped lambda terms, raises the questions of typability and type checking. Typability asks for a term whether there exists some type it can be given. Type checking asks, for a particular term and type, whether the term can be given that type. The decidability of these problems has been settled for restrictions and (...) extensions of F and related systems and complexity lower-bounds have been determined for typability in F, but this report is the first to resolve whether these problems are decidable for System F. This report proves that type checking in F is undecidable, by a reduction from semi-unification, and that typability in F is undecidable, by a reduction from type checking. Because there is an easy reduction from typability to type checking, the two problems are equivalent. The reduction from type checking to typability uses a novel method of constructing lambda terms that simulate arbitrarily chosen type environments. All of the results also hold for the λI-calculus. (shrink)

A cutting-edge survey of contemporary thought at the intersection of science and Christianity. Provides a cutting-edge survey of the central ideas at play at the intersection of science and Christianity through 54 original articles by world-leading scholars and rising stars in the discipline Focuses on Christianity's interaction with Science to offer a fine-grained analysis of issues such as multiverse theories in cosmology, convergence in evolution, Intelligent Design, natural theology, human consciousness, artificial intelligence, free will, miracles, and the Trinity, amongst many (...) others Addresses major historical developments in the relationship between science and Christianity, including Christian patristics, the scientific revolution, the reception of Darwin, and twentieth century fundamentalism Divided into 9 Parts: Historical Episodes; Methodology; Natural Theology; Cosmology & Physics; Evolution; The Human Sciences; Christian Bioethics; Metaphysical Implications; The Mind; Theology; and Significant Figures of the 20th Century Includes diverse perspectives and broadens the conversation from the Anglocentric tradition. (shrink)

J. B. Schneewind's "The Invention of Autonomy" has been hailed as a major interpretation of modern moral thought. Schneewind's narrative, however, elides several serious interpretive issues, particularly in the transition from late medieval to early modern thought. This results in potentially distorted accounts of Thomas Aquinas, Hugo Grotius, and G. W. Leibniz. Since these thinkers play a crucial role in Schneewind's argument, uncertainty over their work calls into question at least some of Schneewind's larger agenda for the history of ethics.

Reasoning under uncertainty, that is, making judgements with only partial knowledge, is a major theme in artificial intelligence. Professor Paris provides here an introduction to the mathematical foundations of the subject. It is suited for readers with some knowledge of undergraduate mathematics but is otherwise self-contained, collecting together the key results on the subject, and formalising within a unified framework the main contemporary approaches and assumptions. The author has concentrated on giving clear mathematical formulations, analyses, justifications and consequences of the (...) main theories about uncertain reasoning, so the book can serve as a textbook for beginners or as a starting point for further basic research into the subject. It will be welcomed by graduate students and research workers in logic, philosophy, and computer science as a textbook for beginners, a starting point for further basic research into the subject, and not least, an account of how mathematics and artificial intelligence can complement and enrich each other. (shrink)

In the paper I offer a brief sketch of one of the sources of utilitarianism. Our biological ancestry is a matter of fact that is not altered by the way we describe ourselves. With philosophical theories it is otherwise. Utilitarianism can be described in ways that make it look as if it is as old as moral philosophy – as J. S. Mill thought it was. For my historical purposes, it is more useful to have an account that brings out (...) what is specific about Benthamism and its descendants. Let us try to make do with the following. First, utilitarianism asserts that the fundamental requirement of morality is that we are to maximize good, for everyone and not just for the agent. This basic principle presupposes that it makes sense to think of aggregating goods to make a total, and of comparing amounts of good thus aggregated. Second, the good to be brought about is located in feelings of pleasure, and the evil to be avoided in feelings of pain. These feelings have inherent value or disvalue regardless of how they are caused to exist and regardless of their own consequences. Third, all moral principles can be derived from the requirement that good be maximized. The principles involved in evaluating agents as well as in giving moral direction to action are nothing but applications of the basic principle. (shrink)

One usually identifies a particular collection of geometric objects with the models of general relativity. But within this standard collection lurk ‘physically unreasonable’ models of spacetime. If such models are ruled out, attention can be restricted to some sub-collection of ‘physically reasonable’ models which can be considered a variant theory of general relativity. Since we have yet to identify a privileged sub-collection of ‘physically reasonable’ models, it is helpful to think of ‘general relativity’ in a pluralistic way; we can study (...) a collection of such ‘physically reasonable’ collections of models. (shrink)

We give a complete characterization of Priest's Finite Inconsistent Arithmetics observing that his original putative characterization included arithmetics which cannot in fact be realized.

In this era of increased polarization of opinion and contentious disagreement, CRITICAL REASONING presents a cooperative approach to critical thinking and formation of beliefs. CRITICAL REASONING emphasizes the importance of developing and applying analytical skills in real life contexts. This book is unique in providing multiple, diverse examples of everyday arguments, both textual and visual, including hard to find long argument passages from real-life sources. The book provides clear, step-by-step procedures to help you decide for yourself what to believe--to be (...) a consumer of information in our contemporary "world of experts.". (shrink)

I analyze a number of the quantum no-signalling proofs (Ghirardi et al. 1980, Bussey 1982, Jordan 1983, Shimony 1985, Redhead 1987, Eberhard and Ross 1989, Sherer and Busch 1993). These purport to show that the EPR correlations cannot be exploited for transmitting signals, i.e., are not causal. First, I show that these proofs can be mathematically unified; they are disguised versions of a single theorem. Second, I argue that these proofs are circular. The essential theorem relies upon the tensor product (...) representation for combined systems, which has no physical basis in the von Neumann axioms. Historically, the construction of this representation scheme by von Neumann and Weyl built no-signalling assumptions into the quantum theory. Signalling between the wings of the EPR-Bell experiments is unlikely but is not ruled out empirically by the class of proofs considered. (shrink)

Philosophy and the scientific revolution / Daniel Garber -- Old history and introductory teaching in early modern philosophy : a response to Daniel Garber / Lisa Downing -- Meaning and metaphysics / Susan Neiman -- Evil and wonder in early modern philosophy : a response to Susan Neiman / Mark Larrimore -- The forgetting of gender / Nancy Tuana -- The forgetting of gender and the new histories of philosophy : a response to Nancy Tuana / Eileen O’Neill -- The (...) idea of early modern philosophy / Knud Haakonssen -- Response to Knud Haakonssen / Jeffrey Edwards -- Arguments over obligation : teaching time and place in moral philosophy / Ian Hunter -- Response to Ian Hunter / T.J. Hochstrasser -- Teaching the history of moral philosophy / J.B. Schneewind -- Historicism, moral judgment, and the good life : a response to J.B. Schneewind / Jennifer A. Herdt -- Integrating history of philosophy with history of science after Kant / Michael Friedman -- Response to Michael Friedman / Juliet Floyd -- Thought versus history : reflections on a French problem / Denis Kambouchner -- Response to Denis Kambouchner / Bé́atrice Longuenesse -- Teaching the history of philosophy in 19th-century Germany / Ulrich Johannes Schneider -- Response to Ulrich Johannes Schneider / Karl Ameriks -- Comment : philosophy in practice / Lorraine Daston -- A note from inside the teapot / Anthony Grafton -- Philosophy, history of philosophy, and L’histoire de l’esprit humain : a historiographical question and problem for philosophers / Jonathan Israel -- History and/or philosophy / Donald R. Kelly -- Historians look at the new histories of philosophy : roundtable discussion. (shrink)

This book has been considered by academicians and scholars of great significance and value to literature. This forms a part of the knowledge base for future generations. So that the book is never forgotten we have represented this book in a print format as the same form as it was originally first published. Hence any marks or annotations seen are left intentionally to preserve its true nature.

We give an account of some relationships between the principles of Constant and Atom Exchangeability and various generalizations of the Principle of Instantial Relevance within the framework of Inductive Logic. In particular we demonstrate some surprising and somewhat counterintuitive dependencies of these relationships on ostensibly unimportant parameters, such as the number of predicates in the overlying language.

This anthology contains excerpts from some thirty-two important seventeenth- and eighteenth-century moral philosophers. Including a substantial introduction and extensive bibliographies, the anthology facilitates the study and teaching of early modern moral philosophy in its crucial formative period. As well as well-known thinkers such as Hobbes, Hume, and Kant, there are excerpts from a wide range of philosophers never previously assembled in one text, such as Grotius, Pufendorf, Nicole, Clarke, Leibniz, Malebranche, Holbach and Paley. Originally issued as a two-volume edition in (...) 1990, the anthology is now re-issued with a new foreword by Professor Schneewind, as a one-volume anthology to serve as a companion to his highly successful history of modern ethics, The Invention of Autonomy. The anthology provides many of the sources discussed in The Invention of Autonomy and taken together the two volumes will be an invaluable resource for the teaching of the history of modern moral philosophy. (shrink)