Concepts, Experiments, History and Philosophy Daniel Greenberger, Klaus Hentschel, Friedel Weinert. 5. W. Hittorf, Ueber die Elektricit ̈atsleitung der Gase , Annalen der Physik 136, 1–31, 197–234 (1869); Engl. transl. On the Conduction of ...

We describe punctual categoricity in several natural classes, including binary relational structures and mono-unary functional structures. We prove that every punctually categorical structure in a finite unary language is${\text {PA}}(0')$-categorical, and we show that this upper bound is tight. We also construct an example of a punctually categorical structure whose degree of categoricity is$0''$. We also prove that, with a bit of work, the latter result can be pushed beyond$\Delta ^1_1$, thus showing that punctually categorical structures can possess arbitrarily complex (...) automorphism orbits.As a consequence, it follows that binary relational structures and unary structures are not universal with respect to primitive recursive interpretations; equivalently, in these classes every rich enough interpretation technique must necessarily involve unbounded existential quantification or infinite disjunction. In contrast, it is well-known that both classes are universal for Turing computability. (shrink)

Sometimes it is possible in quantum theory for a system to interact with another system in such a way that the information contained in the wave function becomes very scrambled and apparently incoherent. We produce an example which is exactly calculable, in which a macroscopic change is induced in the environment, and all phase information for the system is apparently lost, so that a measurement has seemingly been made. But actually, although the wave function has been badly scrambled, all the (...) original information is still present. We call this situation one of “latent order.”Subsequently, the system interacts again with the environment, wiping out the macroscopic change, and the wave function once again becomes manifestly coherent. Thus the apparent measurement has been undone, and leaves no aftereffect. Thus, our “measurement” has disappeared without a trace. We call such a measurement a “haunted measurement,” and we believe that until the measurement process is rigorously understood, the concept of measurement is ambiguous. It is just not good enough to say that an amplification stage occurs “somewhere” in the process.We also point out the connection between the haunted measurement and delayed-choice experiments and discuss a haunted version of the “Schrödinger's Cat” experiment and of the Einstein-Podolsky-Rosen experiment. (shrink)

Ed. Daniel Greenberger, 750pp May 1995 164.95.

We show that the fact that the first player wins every instance of Galvin’s “racing pawns” game is equivalent to arithmetic transfinite recursion. Along the way we analyze the satisfaction relation for infinitary formulas, of “internal” hyperarithmetic comprehension, and of the law of excluded middle for such formulas.

We give two new characterizations of K-triviality. We show that if for all Y such that Ω is Y-random, Ω is -random, then A is K-trivial. The other direction was proved by Stephan and Yu, giving us the first titular characterization of K-triviality and answering a question of Yu. We also prove that if A is K-trivial, then for all Y such that Ω is Y-random, ≡LRY. This answers a question of Merkle and Yu. The other direction is immediate, so (...) we have the second characterization of K-triviality.The proof of the first characterization uses a new cupping result. We prove that if A≰LRB, then for every set X there is a B-random set Y such that X is computable from Y⊕A. (shrink)

We point out that the Aharonov-Bohm effect is a 4-dimensional nonlocal geometric phenomenon. We give two examples which in 3 dimensions appear rather mysterious, but which are easily understood in 4 dimensions. We also discuss why it is integrated effects over fields (potentials) rather than the fields themselves that are important.

A model theory is constructed that exhibits quantization on a cosmic scale. A holistic rationale for the theory is discussed. The theory incorporates a fundamental length, of cosmic size, and preserves the weak, geometrical equivalence principle. The momentum operator is an integral, nonlocal, naturally contravariant operator, in contrast to the usual quantum case. In the limit of high quantum numbers the theory reduces to classical physics, giving rise to a world which is quantized both on the microscopic and cosmic scale, (...) each of which passes over to the usual macroscopic, continuous, classical, world in the highn limit.The theory is applied to two experimental situations, absorption lines in high-z quasars and elliptical rings around normal galaxies, with suggestive but not definitive results. (shrink)

Bering's analysis is inadequate because it fails to consider past and present adult soul beliefs and the psychological functions they serve. We suggest that a valid folk psychology of souls must consider features of adult soul beliefs, the unique problem engendered by awareness of death, and terror management findings, in addition to cognitive inclinations toward dualistic and teleological thinking.

Review of Peter Mittelstaedt, The Interpretation of Quantum Mechanics and the Measurement Process (Cambridge: Cambridge University Press, 1998), 140pp., ISBN 0-521-55445-4, hardback US$44.95, £30.00.

The Tic-Tac-Toe theory is a qualitative, phenomenological theory that automatically explains many of the features of the universe that we see, such as dark matter and dark energy. In that sense it is a Copernican theory that gives an alternate approach, which immediately and intuitively explains phenomena,independently of any detailed dynamics, for which the explanations in accepted standard theories are usually somewhat ad-hoc.The basic concept is to take the possibility of negative masses seriously, and generalize this to counter the unconvincing (...) treatment of negative masses by the equivalence principle. Surprisingly, this automatically solves all sorts of other problems at the same time. Since the theory comes without a detailed dynamics, one can hardly expect people to embrace it with open arms, but it is presented to help convince students that there are many plausible new ideas available to them, and they should not let themselves be intimidated into believing that we are close to understanding nature. (shrink)

Music can reduce stress and anxiety, enhance positive mood, and facilitate social bonding. However, little is known about the role of music and related personal or cultural variables in maintaining wellbeing during times of stress and social isolation as imposed by the COVID-19 crisis. In an online questionnaire, administered in 11 countries, participants rated the relevance of wellbeing goals during the pandemic, and the effectiveness of different activities in obtaining these goals. Music was found to be the most effective activity (...) for three out of five wellbeing goals: enjoyment, venting negative emotions, and self-connection. For diversion, music was equally good as entertainment, while it was second best to create a sense of togetherness, after socialization. This result was evident across different countries and gender, with minor effects of age on specific goals, and a clear effect of the importance of music in people's lives. Cultural effects were generally small and surfaced mainly in the use of music to obtain a sense of togetherness. Interestingly, culture moderated the use of negatively valenced and nostalgic music for those higher in distress. (shrink)

Orthodox Judaism is one of the fastest-growing religious communities in contemporary American life. According to the 2013 Pew Center Survey on American religious life, Orthodox Judaism is poised to surpass all other denominations of Judaism in the United States by 2050. Anyone who wishes to understand more about Judaism in America will need to consider the tenets and practices of Orthodox Judaism: who its adherents are, what they believe in, what motivates them, and to whom they turn for moral, intellectual, (...) and spiritual guidance. Among those spiritual leaders none looms larger than Rabbi Joseph B. Soloveitchik, heir to the legendary Talmudic dynasty of Brisk and a teacher and ordainer of thousands of rabbis during his time as a Talmud teacher at Yeshiva University from the Second World War until the 1980s. Soloveitchik was not only a Talmudic authority but a scholar of Western philosophy. While many books and articles have been written about Soloveitchik's legacy and his influence on American Orthodoxy, few have looked carefully at his disciples in Torah and Talmud study, and even fewer at his Jewish thought and philosophy. "Soloveitchik's Children: Irving Greenberg, David Hartman, Jonathan Sacks, and the Future of Jewish Theology in America" is the first book to study closely three of Soloveitchik's major disciples in Jewish thought and philosophy: Rabbis Irving ("Yitz") Greenberg, David Hartman, and Jonathan Sacks. These three figures hold unique places in modern and contemporary American Jewish life. Each has been highly influential not only within American Orthodoxy but within American Judaism more broadly; each has contributed significantly in the development of Jewish philosophy and theology in the postwar era; each has founded and presided over institutions of their own. David Ross Goodman narrates how each of these three major modern Jewish thinkers learned from and adapted Soloveitchik's teachings in their own ways, even while advancing his philosophical and theological legacy. Goodman highlights the approaches taken by Greenberg, Hartman, and Sacks to some of the most critical religious and philosophical issues of our time: Jewish-Christian relations and interfaith theology; the proper religious response to the Holocaust; the place of creativity in religious life; and the primacy of life in the Jewish tradition. The story of religious life and Judaism in contemporary America is incomplete without an understanding of how three of the most consequential Jewish thinkers of this generation adapted the teachings of one of the most consequential Jewish thinkers of the previous generation. "Soloveitchik's Children" tells this gripping intellectual and religious story in a learned, and engaging manner, shining a light on where Jewish religious thought in the United States currently stands-and where it may be heading in the coming generations. (shrink)

It is shown that completely entangled two-particle quantum states are simultaneous eigenstates of a large set of commuting, nonlocal observables, a characterization that generalizes to multiparticle systems. This leads to a nonstatistical proof of the Bell-EPR no-hidden-variable theorem for two-particle systems and to a family of multiparticle generalizations of the three-particle system of Greenberger, Horne, and Zeilinger.

We review an argument that bipartite "PR-box" correlations, though designed to respect relativistic causality, in fact violate relativistic causality in the classical limit. As a test of this argument, we consider Greenberger-Horne-Zeilinger (GHZ) correlations as a tripartite version of PR-box correlations, and ask whether the argument extends to GHZ correlations. If it does-i.e., if it shows that GHZ correlations violate relativistic causality in the classical limit-then the argument must be incorrect (since GHZ correlations do respect relativistic causality in the (...) classical limit.) However, we find that the argument does not extend to GHZ correlations. We also show that both PR-box correlations and GHZ correlations can be retrocausal, but the retrocausality of PR-box correlations leads to self-contradictory causal loops, while the retrocausality of GHZ correlations does not. (shrink)

Here is a simple, clear, useful proof that quantum mechanics contradicts Einstein, Podolsky, and Rosen's local realistic assumptions. It is a variant of the powerful argument first worked out by Daniel Mordechai Greenberger, Michael A. Horne, and Anton Zeilinger. This version uses the eigenstates of two orthogonal spin components for three spin-1/2 particles. No operator or matrix algebra is necessary. A novel discussion of the background and history serves to introduce this proof and to place it in the (...) context of Danny's work. (shrink)

In this book, Yael Greenberg discusses and clarifies a number of controversial issues and phenomena in the generic literature, including the existence of ...

This paper deals with the exceptions-tolerance property of generic sentences with indefinite singular and bare plural subjects (IS and BP generics, respectively) and with the way this property is connected to some well-known observations about felicity differences between the two types of generics (e.g. Lawler's 1973, Madrigals are popular vs. #A madrigal is popular). I show that whereas both IS and BP generics tolerate exceptional and contextually irrelevant individuals and situations in a strikingly similar way, which indicates the existence of (...) a basically equivalent tolerance mechanism, there is also a difference between them, unnoticed so far, which concerns the degree to which the properties of the legitimate exceptions can be characterized in advance. Following claims in Greenberg (2003), I argue that both this newly observed difference as well as the traditional felicity differences result from an underlying contrast in the type of ‘non-accidentalness’ expressed by the two types of generic sentences, and more formally, in the accessibility relations that their generic quantifier (Gen) is compatible with. To capture the new difference in tolerance of exceptions, I develop an improved version of the exceptions-tolerance mechanism for generic sentences suggested in Kadmon & Landman (1993), namely, a restriction on the set of individuals and situations quantified by Gen, which is partially vague to two different degrees using supervaluationist methods. The different degrees of vagueness in this restriction are shown to be systematically dependent on the two types of accessibility relations that IS and BP generics are compatible with, which are redefined as precise and vague restrictions on the generic quantification over worlds. (shrink)

It is common to hear talk of the aim of belief and to find philosophers appealing to that aim for numerous explanatory purposes. What belief 's aim explains depends, of course, on what that aim is. Many hold that it is somehow related to truth, but there are various ways in which one might specify belief 's aim using the notion of truth. In this article, by considering whether they can account for belief 's standard of correctness and the epistemic (...) norms governing belief, I argue against certain prominent specifications of belief 's aim given in terms of truth, and advance a neglected alternative. (shrink)