First steps are taken toward a formulation of quantum mechanics which avoids the use of probability amplitudes and is expressed entirely in terms of observable probabilities. Quantum states are represented not by state vectors or density matrices but by “probability tables,” which contain only the probabilities of the outcomes of certain special measurements. The rule for computing transition probabilities, normally given by the squared modulus of the inner product of two state vectors, is re-expressed in terms of probability tables. The (...) new version of the rule is surprisingly simple, especially when one considers that the notion of complex phases, so crucial in the evaluation of inner products, is entirely absent from the representation of states used here. (shrink)

This paper examines the statistical properties of random quantum states, for four different kinds of random state:(1) a pure state chosen at random with respect to the uniform measure on the unit sphere in a finite-dimensional Hilbert space;(2) a random pure state in a real space;(3) a pure state chosen at random except that a certain expectation value is fixed;(4) a random mixed state with fixed eigenvalues. For the first two of these, we give examples of simple states of a (...) model system, the kicked top, which have the statistical properties of random states. Interestingly, examples of both kinds of randomness can be found in the same system. In studying the last two kinds of random state, we obtain new results concerning the application of information theory to quantum systems. (shrink)

The limitation on the sharing of entanglement is a basic feature of quantum theory. For example, if two qubits are completely entangled with each other, neither of them can be at all entangled with any other object. In this paper we show, at least for a certain standard definition of entanglement, that this feature is lost when one replaces the usual complex vector space of quantum states with a real vector space. Moreover, the difference between the two theories is extreme: (...) in the real-vector-space theory, there exist states of arbitrarily many binary objects, “rebits,” in which every rebit in the system is maximally entangled with each of the other rebits. (shrink)

Let us accept the quantum mechanical description of a free particle and one fact from special relativity: rest mass contributes to energy. If we add to this bare framework one additional fact—that time runs slower near the earth—we can account for our everyday experience of gravity.

Quantum theory has the property of “local tomography”: the state of any composite system can be reconstructed from the statistics of measurements on the individual components. In this respect the holism of quantum theory is limited. We consider in this paper a class of theories more holistic than quantum theory in that they are constrained only by “bilocal tomography”: the state of any composite system is determined by the statistics of measurements on pairs of components. Under a few auxiliary assumptions, (...) we derive certain general features of such theories. In particular, we show how the number of state parameters can depend on the number of perfectly distinguishable states. We also show that real-vector-space quantum theory, while not locally tomographic, is bilocally tomographic. (shrink)

Normative theories of obligation, moral and nonmoral value, and meta-ethical issues and theories are considered.

Taking reduction in the traditional deductive sense, the programmatic claim that most of genetics can be reduced by molecular genetics is defended as feasible and significant. Arguments by Ruse and Hull that either the relationship is replacement or at best a weaker form of reduction are shown to rest on a mixture of historical and logical confusions about the nature of the theories involved.

This paper argues for the importance of approaching medicine, as a theoretical science, through values. The normative concepts of benefit and harm are held to provide a framework for the analysis of medicine which reflects the obligations of the doctor-patient relationship, suffices to define the key concept of medical relevance, yields a general necessary condition for the basic concepts of medicine, explains the role of such nonnormative conceptions as discomfort, dysfunction, and incapacity, and avoids the mistakes of other normative approaches (...) which hold that unhealthy conditions are disvaluable or should be treated. Neutralist analyses are criticized, especially those approaching health through proper functioning. (shrink)

I critically examine an argument, due to howard wettstein, purporting to show that sentences containing definite descriptions are semantically ambiguous between referential and attributive readings. Wettstein argues that many sentences containing nonidentifying descriptions--descriptions that apply to more than one object--cannot be given a Russellian analysis, and that the descriptions in these sentences should be understood as directly referential terms. But because Wettstein does not justify treating referential uses of nonidentifying descriptions differently than attributive uses of nonidentifying descriptions, his argument fails.

I begin with a note about moral goodness as a quality, disposition, or trait of a person or human being. This has at least two different senses, one wider and one narrower. Aristotle remarked that the Greek term we translate as justice sometimes meant simply virtue or goodness as applied to a person and sometimes meant only a certain virtue or kind of goodness. The same thing is true of our word “goodness.” Sometimes being a good person means having all (...) the virtues, or at least all the moral ones; then goodness equals the whole of virtue. But sometimes, being a good person has a narrower meaning, namely, being kind, generous, and so forth. Thus, my OED sometimes equates goodness with moral excellence as a whole and sometimes with a particular moral excellence, viz., kindness, beneficence, or benevolence; and the Bible, when it speaks of God as being good sometimes means that God has all the virtues and sometimes only that he is kind, mereiful, or benevolent. When Jesus says, “Why callest thou me good: None is good, save one, that is God,” he seems to be speaking of goodness in the inclusive sense, but when the writer of Exodus has God himself say that he is “merciful and gracious, long-suffering, and abundant in goodness and truth,” God is using “goodness” in the narrower sense in which it means benevolence, for he goes on to make it clear that he is also just and severe. Similarly, “good will” may mean either “morally good will” in general, as it does in Kant, or it may mean only “benevolent will,” as it usually does; in “men of good will” it is perhaps ambiguous. (shrink)

This essay, one of the last that Frankena wrote, provides a scrupulously detailed exploration of the various possible meanings of one of Sidgwick's most famous footnotes in the Methods Long intrigued by what Sidgwick had in mind when he said that he would explain how it came about that for moderns it is not tautologous to claim that one's own good is one's only reasonable ultimate end, Frankena uses this note as a point of departure for a penetrating review of (...) Sidgwick's insights and ambiguities on the differences between ancient and modern ethics. (shrink)

This paper analyzes in some detail what an ethics of love would be like if interpreted rigorously as an ethics of being rather than of doing. It delineates the metaethical structure of such an ethics and suggests the characteristics of love appropriate to the structure. The author then indicates some problems that arise for such an ethical theory.

It is well known that Sidgwick finished his examination of “the methods of ethics” in some difficulty. Just what that difficulty was and how he came to be in it, we shall see in due course. This paper is written in the conviction that what he was doing is worth looking at again in the context of contemporary discussion.

Japan’s economy has stagnated since the bursting of the twin real estate and stock bubbles in 1990. Construction employment rose after the bubbles burst despite a real estate glut.Systemic corruption is delaying recovery. The key is the dango—Japan’s system of bid rigging, which is pervasive in public construction. The firms rotate who will win the “competitive” bid. The bureaucrats leak the highest price bid that will be accepted in return for favors from the industry and lucrative sinecures when they retire (...) (amakudari—“descent from heaven”). The ruling politicians (the “construction tribes”) get kickbacks and ensure the adoption of enormous public construction programs.The result is that Japanese public and private capital flows are corruptly routed to uses that are not simply inefficient, but outright harmful to society. Pervasive corruption is the primary obstacle to Japanese economic (and environmental) health and political reform. (shrink)

In this paper I tee off from a footnote in prichard's article, "is moral philosophy based on a mistake?" in it he contrasts living under the aegis of moral obligation and moral goodness with living under the aegis of virtue. Using prichard's terms I try to say what an ethics of virtue as versus one of duty and moral goodness would be like. Then I try to see what prichard's case against the former and for the latter would be like, (...) And to indicate my own sympathies in the matter. (shrink)

Adolf Grünbaum, [1], and Philip Quinn, [7], have proposed two problems as sharpened versions of theses suggested by Pierre Duhem. Can an hypothesis which in itself has no observational consequences ever be falsified by the evidence? When a theory has observational consequences only in conjunction with auxiliary hypotheses and some of these consequences fail, can the theory always be reasonably defended by constructing alternative auxiliary hypotheses?

New discoveries about materials and solar energy raise the possibility of a long-tenn shift of mining, refining, and manufacturing from Earth’s surface to locations outside Earth’s ecosphere, allowing Earth to begin to relax back toward its natural state. A little-discussed ambivalence toward the potential of space exploration exists among environmentalists. One camp sees it as a human adventure that may allow a bold initiative to improve Earth; another camp shies away from “heavy technology” and thus distrusts efforts as massive as (...) space exploration or utilization. Due to impending resource depletion on Earth, we may have only until the mid-twenty-first century to pursue the promising potential of space exploration to alleviate environmental problems of Earth. Subsequently, there may be too litde industlial base to support vigorous exploration and exploitation of resources in space. (shrink)

An expansion of 3 lectures presented by the author in 1978 at the University of Michigan.

This is the text of The Lindley Lecture for 1961, given by William K. Frankena, an American philosopher.