The weak objectification of physical properties is shown to yield the same probabilistic implications as strong objectification and can therefore be refuted on the basis of suitable interference experiments. An alternative test of hypothetical objectification statements, as they occur in the EPR experiment, is based on joint probabilities and the ensuing Bell inequalities. Quantum mechanics turns out to be partially compatible with Bell's inequalities even in cases where weak objectification is excluded by interference.

In a quantum mechanical two-slit experiment one can observe a single photon simultaneously as particle (measuring the path) and as wave (measuring the interference pattern) if the path and the interference pattern are measured in the sense of unsharp observables. These theoretical predictions are confirmed experimentally by a photon split-beam experiment using a modified Mach—Zehnder interferometer.

The principle of excluded middle is the logical interpretation of the law V ≤ A v ヿA in an orthocomplemented lattice and, hence, in the lattice of the subspaces of a Hilbert space which correspond to quantum mechanical propositions. We use the dialogic approach to logic in order to show that, in addition to the already established laws of effective quantum logic, the principle of excluded middle can also be founded. The dialogic approach is based on the very conditions under (...) which propositions can be confirmed by measurements. From the fact that the principle of. excluded middle can be confirmed for elementary propositions which are proved by quantum mechanical measurements, we conclude that this principle is inherited by all finite compound propositions. For this proof it is essential that, in the dialog-game about a connective, a finite confirmation strategy for the mutual commensurability of the subpropositions is used. (shrink)

The logic of quantum mechanical propositions—called quantum logic—is constructed on the basis of the operational foundation of logic. Some obvious modifications of the operational method, which come from the incommensurability of the quantum mechanical propositions, lead to the effective quantum logic. It is shown in this paper that in the framework of a calculization of this effective quantum logic the negation of a proposition is uniquely defined (Theorem I), and that a weak form of the quasimodular law can be derived (...) (Theorem II). Taking account of the definiteness of truth values for quantum mechanical propositions, the calculus of full quantum logic can be derived (Theorem III). This calculus represents an orthocomplemented quasimodular lattice which has as a model the lattice of subspaces of Hilbert space. (shrink)

Compound propositions which can successfully be defended in a quantumdialogue independent of the elementary propositions contained in it, must have this property also independent of the mutual elementary commensur-abilities. On the other hand, formal commensurabilities must be taken into account. Therefore, for propositions which can be proved by P, irrespective of both the elementary propositions and of the elementary commensur-abilities, there exists a formal strategy of success. The totality of propositions with a formal strategy of success in a quantum dialogue (...) form the effective quantum logic. The propositions of the effective quantum logic can be derived from a calculus Q eff which is — on the other hand — equivalent to a lattice L qi.Propositions about measuring results are above all time dependent propositions A(S;t). In a dialogue, different partial propositions will have in general different time values. If one can (accidentally) win a material dialogue, this dialogue can be related to a single time value. For the propositions of the effective quantum logic there exist formal strategies of success, independent of the elementary propositions contained in it. All partial propositions appearing in the dialogue are formally commensurable. Therefore the propositions of effective quantum logic which can be proved by formal dialogues can always be related to a single time. They present a description of the system S considered in which all partial propositions can be related jointly to the state of S.Therefore in the effective quantum logic we have — in the limit of equal time values — a situation which corresponds conceptually to the description of the system (S; ψ) in Hilbert space. Consequently, one would expect that also the lattice L qi — except from the tertium non datur 8 — agrees with the lattice L q of subspaces of Hilbert space. It has been shown that these lattices are in fact isomorphic. (shrink)

Kant's theory of arithmetic is not only a central element in his theoretical philosophy but also an important contribution to the philosophy of arithmetic as such. However, modern mathematics, especially non-Euclidean geometry, has placed much pressure on Kant's theory of mathematics. But objections against his theory of geometry do not necessarily correspond to arguments against his theory of arithmetic and algebra. The goal of this article is to show that at least some important details in Kant's theory of arithmetic can (...) be picked up, improved by reconstruction and defended under a contemporary perspective: the theory of numbers as products of rule following construction presupposing successive synthesis in time and the theory of arithmetic equations, sentences or "formulas"—as Kant says—as synthetic a priori. In order to do so, two calculi in terms of modern mathematics are introduced which formalise Kant's theory of addition as a form of synthetic operation. (shrink)

Now in a third edition, Introduction to Philosophy: Classical and Contemporary Readings is a highly acclaimed, topically organized collection that covers five major areas of philosophy--theory of knowledge, philosophy of religion, philosophy of mind, freedom and determinism, and moral philosophy. Editor Louis P. Pojman enhances the text's topical organization by arranging the selections into a pro/con format to help students better understand opposing arguments. He also includes accessible introductions to each chapter, subsection, and individual reading, a unique feature for an (...) anthology of this depth. While the book focuses on a compelling sampling of classical material--including selections from Plato, Aristotle, Descartes, Locke, Berkeley, Hume, and Kant--it also incorporates some of philosophy's best twentieth-century and contemporary work, featuring articles by Bertrand Russell, Richard Taylor, John Searle, Thomas Nagel, and others. This third edition contains an expanded glossary, more extensive section introductions, and twelve new selections: Karl Popper: "Epistemology without a Knowing Subject" Richard Rorty: "Dismantling Truth: Solidarity Versus Objectivity" Daniel Dennett: "Postmodernism and Truth" Bruce Russell: "The Problem of Evil: Too Much Suffering" David Chalmers: "Against Materialism: Can Consciousness Be Reductively Explained?" Baron Paul Henri d'Holbach: "A Defense of Determinism" Michael Levin: "A Compatibilist Defense of Moral Responsibility" Plato: Socratic Morality: "Crito" Herodotus: "Custom Is King" J. L. Mackie: "The Subjectivity of Values" Louis P. Pojman: "A Critique of Mackie's Theory of Moral Subjectivism" Thomas Nagel: "Moral Luck". (shrink)

The hypotheses of weak and strong objectification of quantum mechanical observables, as well as theoretical arguments and experimental evidence against these hypotheses, are systematically reviewed.

In 1936, G. Birkhoff and J. v. Neumann published an article with the title The logic of quantum mechanics'. In this paper, the authors demonstrated that in quantum mechanics the most simple observables which correspond to yes-no propositions about a quantum physical system constitute an algebraic structure, the most important proper ties of which are given by an orthocomplemented and quasimodular lattice Lq. Furthermore, this lattice of quantum mechanical proposi tions has, from a formal point of view, many similarities with (...) a Boolean lattice L8 which is known to be the lattice of classical propositional logic. Therefore, one could conjecture that due to the algebraic structure of quantum mechanical observables a logical calculus Q of quantum mechanical propositions is established, which is slightly different from the calculus L of classical propositional logic but which is applicable to all quantum mechanical propositions. This calculus has sometimes been called 'quan tum logic'. However, the statement that propositions about quantum physical systems are governed by the laws of quantum logic, which differ from ordinary classical logic and which are based on the empirically well-established quantum theory, is exposed to two serious objec tions: Logic is a theory which deals with those relationships between various propositions that are valid independent of the content of the respective propositions. Thus, the validity of logical relationships is not restricted to a special type of proposition, e. g. to propositions about classical physical systems. (shrink)

This paper is concerned with the problem of the validity of Leibniz's principle of the identity of indiscernibles in physics. After briefly surveying how the question is currently discussed in recent literature and which is the actual meaning of the principle for what concerns physics, we address the question of the physical validity of Leibniz's principle in terms of the existence of a sufficient number of naming predicates in the formal language of physics. This approach allows us to obtain in (...) a formal way the result that a principle of the identity of indiscernibles can be justified in the domain of classical physics, while this is not the case in the domain of quantum physics. (shrink)

In ”Skepticism,” Peter Klein distinguishes between the “Academic Skeptic” who proposes that we cannot have knowledge of a certain set of propositions and the “Pyrrhonian Skeptic” who refrains from opining about whether we can have knowledge. Klein argues that Academic Skepticism is plausibly supported by a “Closure Principle‐style” argument based on the claim that if x entails y and S has justification for x, then S has justification for y. He turns to contextualism to see if it can contribute to (...) the discussion between one who claims that we can have knowledge about some epistemically interesting class of propositions and the Academic Skeptic. He outlines the background of Pyrrhonian Skepticism, pointing out that the Pyrrhonist withholds assent concerning our knowledge‐bearing status because reason cannot provide an adequate basis for assent. He assesses three possible patterns of reasoning, and concludes that the Pyrrhonist view, that reason cannot resolve matters concerning the nonevident, is vindicated. (shrink)

Bioethics needs an expanded moral vision. It is now time for bioethics to take full account of the problems of health disparities and structural injustice that are made newly urgent by the COVID-19 pandemic and the effects of climate change. Nancy M. P. King, Gail E. Henderson, and Larry R. Churchill make the case for a more social understanding and application of justice, a deeper humility in assessing expertise in bioethics consulting, a broader and more relevant research agenda, and greater (...) appreciation of the profound health implications of global warming. (shrink)

First published in 1987. Routledge is an imprint of Taylor & Francis, an informa company.

Es werden die Veränderungen der Wissenschaftssprache der Physik untersucht, die durch den Übergang von der klassich-relativistichen Physik zur Quantenphysik erfolgt sind. Die neuen und prinzipiellen Beschränkungen der Möglichkeiten der Überprüfung wissenschaftlicher Aussagen führen zu Reduktionen der hypothetischen Annahmen, die der Sprache der klassischen Physik zu Grunde liegen. Diese Reduktionen haben ihrerseits Abschwächungen der syntaktischen Strukturen zur Folge, die besonders in der formalen Logik und der Modallogik deutlich werden. Diese auf schwächeren Prämissen basierenden Strukturen sind die Quanten-Logik und die Quanten-Modallogik, die (...) damit auch einen weiteren Geltungsbereich besitzen als die entsprechenden klassischen formalen Systeme. (shrink)

First published in 1987. Routledge is an imprint of Taylor & Francis, an informa company.

Reichenbach, Grünbaum, and others have argued that special relativity is based on arbitrary conventions concerning clock synchronizations. Here we present a mathematical framework which shows that this conventionality is almost equivalent to the arbitrariness in the choice of coordinates in an inertial system. Since preferred systems of coordinates can uniquely be defined by means of the Lorentz invariance of physical laws irrespective of the properties of light signals, a special clock synchronization—Einstein's standard synchrony—is selected by this principle. No further restrictions (...) conerning light signal synchronization, as proposed, e.g., by Ellis and Bowman, are required in order to refute conventionalism in special relativity. (shrink)

Engineering is 'the people-serving profession'. The work of engineers involves interaction with clients, other engineers, and the public at large. More than any other profession, their work also directly involves and affects the environment. This book makes the case that engineers have special professional obligations to protect and enhance the environment, and the authors - one, an engineer and the other, a philosopher - seek to provide an ethical basis for these obligations. In exploring these ethical issues, the authors aim (...) to show that engineers make a difference. The text opens with a series of case studies in which engineers face complex and challenging decisions about the environment. Succeeding chapters examine different ideas about environmental ethics for engineers, including professional codes and both modern and historical discussions of environmental responsibility. The book concludes with a collection of readings that complement the text. Students, as well as practising engineers, will find much of interest in this well-argued and thought-provoking book. (shrink)

Gordon Baker and I had been colleagues at St John’s for almost ten years when we resolved, in 1976, to undertake the task of writing a commentary on Wittgenstein’s Philosophical Investigations. We had been talking about Wittgenstein since 1969, and when we cooperated in writing a long critical notice on the Philosophical Grammar in 1975, we found that working together was mutually instructive, intellectually stimulating and great fun. We thought that we still had much to say about Wittgenstein’s philosophy, and (...) it seemed to us that misinterpretations of passages in the Investigations were so extensive that it would be worth trying to write a detailed analytical commentary. It is difficult to recapture the excitement of those early days in being among the first to work on the microfilms and, subsequently, on the photocopies of Wittgenstein’s Nachlass. We spent many hundreds of hours poring over the typescripts and the often only semi-legible manuscripts, fascinated and privileged to be able to try to follow the development of the thoughts of a great philosophical genius. We talked endlessly about what we had found in Wittgenstein’s manuscripts and typescripts, and debated how it should be understood. The first fruit of our labours was Wittgenstein – Understanding and Meaning. Its guiding idea was to draw attention to the manner in which Wittgenstein linked the concepts of meaning, understanding and explanation, and so to bypass the connections between meaning, truth and truth-conditions that so fascinated philosophers of the 1970s, and to abandon the red-herring of assertion-conditions and anti-realism. After a hiatus of four years, during which time we wrote a controversial book entitled Frege – Logical Excavations and a polemical book on contemporary philosophy of language – Language, Sense. (shrink)