Jeff McMahan appeals to what he calls the “Time-relative Interest Account of the Wrongness of Killing ” to explain the wrongness of killing individuals who are conscious but not autonomous. On this account, the wrongness of such killing depends on the victim’s interest in his or her future, and this interest, in turn, depends on two things: the goods that would have accrued to the victim in the future; and the strength of the (...) prudential relations obtaining between the victim at the time of the killing and at the times these goods would have accrued to him or her. More precisely, when assessing this interest, future goods should be discounted to reflect reductions in the strength of such relations. Against McMahan’s account I argue that it relies on an implausible “actualist” view of the moral importance of interests according to which satisfactions of future interests only have moral significance if they are satisfactions of actual interests. More precisely, I aim to show that the Time-relative Interest Account does not have the implications for the morality of killing that McMahan takes it to have, and implies, implausibly, that certain interest satisfactions which seem to be morally significant are morally insignificant because they are not satisfactions of actual interests. (shrink)

The concept of a time-relative interest is introduced by Jeff McMahan to solve certain puzzles about the badness of death. Some people (e.g. McMahan and David DeGrazia) believe that this concept can also be used to show that abortion is permissible. In this paper, I first argue that if the Time-Relative Interest Account permits abortion, then it would also permit infanticide.

Don Marquis has argued most abortions are immoral, for the same reason that killing you or me is immoral: abortion deprives the fetus of a valuable future. Call this account the FLOA. A rival account is Jeff McMahan’s, time-relative interest account of the wrongness of killing. According to this account, an act of killing is wrong to the extent that it deprives the victim of future value and the relation of psychological unity would (...) have held between the victim at the time of death and herself at a later time if she had lived. The TRIA supposedly has two chief advantages over Marquis’s FLOA. First, unlike the FLOA, the TRIA does not rely on the controversial thesis that identity is what matters in survival. Second, the TRIA yields more plausible verdicts about cases. Proponents of the TRIA use the account to argue that abortion is generally permissible, because there would be little to no psychological unity between the fetus and later selves if it lived. I argue that advocates of the TRIA have failed to establish its superiority to the FLOA, for two reasons. First, the two views are on a par with respect to the thesis that identity is what matters in survival. Second, Marquis’s FLOA does not yield the counterintuitive implications about cases that advocates of the TRIA have attributed to it, and the TRIA yields its own share of implausible judgments about cases. (shrink)

Regarding the sinking lifeboat scenario involving several human beings and a dog, nearly everyone agrees that it is right to sacrifice the dog. I suggest that the best explanation for this considered judgment, an explanation that appears to time-relative interests, contains a key insight about prudential value. This insight, I argue, also provides perhaps the most promising reply to the future-like-ours argument, which is widely regarded as the strongest moral argument against abortion. Providing a solution to a longstanding (...) puzzle in value theory across species while illuminating the morality of abortion, the time-relative interest account proves worthy of sustained theoretical attention. (shrink)

The substance view is an account of personhood that regards all human beings as possessing instrinsic value and moral status equivalent to that of an adult human being. Consequently, substance view proponents typically regard abortion as impermissible in most circumstances. The substance view, however, has difficulty accounting for certain intuitions regarding the badness of death for embryos and fetuses, and the wrongness of killing them. Jeff McMahan’s time-relative interest account is designed to cater for such (...) intuitions, and so I present a proposal for strengthening the substance view by incorporating McMahan’s account – the Dual-Aspect Account of the morality of killing. I show that it resolves some important issues for the substance view while preserving its central premise of moral equality for all human beings. I then compare the Dual-Aspect Account with McMahan’s Two-Tiered Account of the morality of killing, which he derives from his time-relative interest account. (shrink)

Implicit in our everyday attitudes and practices is the assumption that death ordinarily harms a person who dies. A far more contested matter is whether death harms sentient individuals who are not persons, a category that includes many animals and some human beings. On the basis of the deprivation account of the harm of death, I argue that death harms sentient nonpersons. I next consider possible bases for the commonsense judgment that death ordinarily harms persons more than it harms (...) sentient nonpersons. Contrary to what some philosophers believe, it is doubtful that the familiar resources of prudential value theory can vindicate this judgment. I show that the approach that at first glance seems most promising for supporting this judgment – namely, invoking an objective account of well-being – faces substantial challenges, before arguing that McMahan's time-relative interest account supplies the needed theoretical basis. I then go on to extract a significant practical implication of the first thesis, that death ordinarily harms sentient nonpersons: We should find a way to discontinue the routine killing of animal subjects following their use in experiments. (shrink)

According to Interest-Relative Invariantism, whether an agent knows that p, or possesses other sorts of epistemic properties or relations, is in part determined by the practical costs of being wrong about p. Recent studies in experimental philosophy have tested the claims of IRI. After critically discussing prior studies, we present the results of our own experiments that provide strong support for IRI. We discuss our results in light of complementary findings by other theorists, and address the challenge posed (...) by a leading intellectualist alternative to our view.Send article to KindleTo send this article to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle. Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply. Find out more about the Kindle Personal Document Service.EMPIRICAL TESTS OF INTEREST-RELATIVE INVARIANTISMVolume 9, Issue 1Chandra Sekhar Sripada and Jason StanleyDOI: https://doi.org/10.1017/epi.2011.2Your Kindle email address Please provide your Kindle [email protected]@kindle.com Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Dropbox To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox. EMPIRICAL TESTS OF INTEREST-RELATIVE INVARIANTISMVolume 9, Issue 1Chandra Sekhar Sripada and Jason StanleyDOI: https://doi.org/10.1017/epi.2011.2Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Google Drive To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive. EMPIRICAL TESTS OF INTEREST-RELATIVE INVARIANTISMVolume 9, Issue 1Chandra Sekhar Sripada and Jason StanleyDOI: https://doi.org/10.1017/epi.2011.2Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Export citation Request permission. (shrink)

In this paper I draw the distinction between intuitive and theory-relative accounts of the time reversal symmetry and identify problems with each. I then propose an alternative to these two types of accounts that steers a middle course between them and minimizes each account’s problems. This new account of time reversal requires that, when dealing with sets of physical theories that satisfy certain constraints, we determine all of the discrete symmetries of the physical laws we (...) are interested in and look for involutions that leave spatial coordinates unaffected and that act consistently across our physical laws. This new account of time reversal has the interesting feature that it makes the nature of the time reversal symmetry an empirical feature of the world without requiring us to assume that any particular physical theory is time reversal invariant from the start. Finally, I provide an analysis of several toy cases that reveals differences between my new account of time reversal and its competitors. (shrink)

At what stage of life is death worst for its victim? I hold that, typically, death is worse the earlier it occurs. Others, including Jeff McMahan and Christopher Belshaw, have argued that it is worst to die in early adulthood. In this paper I show that McMahan and Belshaw are wrong; I show that views that entail that Student’s death is worse face fatal objections. I focus in particular on McMahan’s time-relative interest account (TRIA) of the (...) badness of death. Manuscript in progress. (shrink)

This thesis consists of several independent papers in population ethics. I begin in Chapter 1 by critiquing some well-known 'impossibility theorems', which purport to show there can be no intuitively satisfactory population axiology. I identify axiological vagueness as a promising way to escape or at least mitigate the effects of these theorems. In particular, in Chapter 2, I argue that certain of the impossibility theorems have little more dialectical force than sorites arguments do. From these negative arguments I move to (...) positive ones. In Chapter 3, I justify the use of a 'veil of ignorance', starting from three more basic normative principles. This leads to positive arguments for various kinds of utilitarianism - the best such arguments I know. But in general the implications of the veil depend on how one answers what I call 'the risky existential question': what is the value to an individual of a chance of non-existence? I chart out the main options, and raise some puzzles for non-comparativism, the view that life is incomparable to non-existence. Finally, in Chapter 4, I consider the consequences for population ethics of the idea that what is normatively relevant is not personal identity, but a degreed relation of psychological connectedness. In particular, I pursue a strategy based in population ethics for understanding the controversial 'time-relative interests' account of the badness of death. (shrink)

Michael Tooley presents a major new philosophical theory of the nature of time, offering a powerful alternative to the traditional "tensed" and recent "tenseless" accounts of time. He argues for a dynamic conception of the universe, in which past, present, and future are not merely subjective features of experience. He claims that the past and the present are real, while the future is not. Tooley's approach accounts for time in terms of causation. He therefore claims that the (...) key to understanding the dynamic nature of the universe is to understand the nature of causation. Time, Tense, and Causation is a landmark treatment of one of the oldest and most perplexing intellectual problems, and will be fascinating reading for anyone interested in the character of time. (shrink)

Appealing to reason rather than religious belief, this book is the most comprehensive case against the choice of abortion yet published. This _Second Edition_ of _The Ethics of Abortion _critically evaluates all the major grounds for denying fetal personhood, including the views of those who defend not only abortion but also post-birth abortion. It also provides several justifications for the conclusion that all human beings, including those in utero, should be respected as persons. This book also critiques the view that (...) abortion is not wrong even if the human fetus is a person. _The Ethics of Abortion _examines hard cases for those who are prolife, such as abortion in cases of rape or in order to save the mother’s life, as well as hard cases for defenders of abortion, such as sex selection abortion and the rationale for being "personally opposed" but publically supportive of abortion. It concludes with a discussion of whether artificial wombs might end the abortion debate. Answering the arguments of defenders of abortion, this book provides reasoned justification for the view that all intentional abortions are ethically wrong and that doctors and nurses who object to abortion should not be forced to act against their consciences. Updates and Revisions to the Second Edition include: -A response to Alberto Giubilini’s and Francesca Minerva’s now famous 2012 article, "After-Birth Abortion" in the _Journal of Medical Ethics _ -Responses to new defenses of Judith Jarvis Thomson’s violinist argument -The addition of a new chapter on gradualist views of fetal moral worth, including Jeff McMahan’s Time-Relative Interest Account -The addition of a new chapter on the conscience protection for health care workers who are opposed to abortion -Responses to many critiques of the first edition, including those made by Donald Marquis, David DeGrazia, and William E. May. (shrink)

Citing some recent experimental findings, I argue for the surprising claim that in some cases the less time you have the more you know. More specifically, I present some evidence to suggest that our ordinary knowledge ascriptions are sometimes sensitive to facts about an epistemic subject's truth-irrelevant time constraints such that less is more. If knowledge ascriptions are sensitive in this manner, then this is some evidence of pragmatic encroachment. Along the way, I consider comments made by Jonathan (...) Schaffer and Jennifer Nagel to construe a purist contextualist and a strict invariantist explanation of the data respectively, before giving reasons to resist them in favor of an account that indicates pragmatic encroachment. If successful, this may suggest a new way to argue for the controversial thesis that there is pragmatic encroachment on knowledge. (shrink)

The scientific conception of change and motion raises two fundamental questions: Is there any evidence that the temporal order of events cannot legitimately be postulated to be continuous in Cantor's sense? Is it possible to account for such distinguishing properties of time as its possession of an "arrow" on the basis of assuming that events constitute a continuous type of order in Cantor's sense, and providing a coordinating definition for the ordering relation "later than"? We must raise these (...) questions, since at least four philosophers of the present century have denied the compatibility of the temporal structure of actual events with the order defined by Cantor's linear continuum and have held that a description of physical change which is based on the latter type of order is incompetent to account for the "arrow" of time and for such features of actual events as the latter involves. The philosophers in question are Henri Bergson, William James, Alfred North Whitehead and Paul Weiss. Each of these thinkers makes reference to Zeno's paradoxes of motion in setting forth his arguments. (shrink)

According to John Martin Fischer and Anthony Brueckner’s unique version of the deprivation approach to accounting for death’s badness, it is rational for us to have asymmetric attitudes toward prenatal and posthumous nonexistence. In previous work, I have defended this approach against a criticism raised by Jens Johansson by attempting to show that Johansson’s criticism relies on an example that is incoherent. Recently, Duncan Purves has argued that my defense reveals an incoherence not only in Johansson’s example but also in (...) Fischer and Brueckner’s approach itself. Here I argue that by paying special attention to a certain feature of Fischer and Brueckner’s approach, we can dispense of not only Johansson’s criticism but also of Purves’s objection to Fischer and Brueckner’s approach. (shrink)

David Albert claims that classical electromagnetic theory is not time reversal invariant. He acknowledges that all physics books say that it is, but claims they are ``simply wrong" because they rely on an incorrect account of how the time reversal operator acts on magnetic fields. On that account, electric fields are left intact by the operator, but magnetic fields are inverted. Albert sees no reason for the asymmetric treatment, and insists that neither field should be inverted. (...) I argue, to the contrary, that the inversion of magnetic fields makes good sense and is, in fact, forced by elementary geometric considerations. I also suggest a way of thinking about the time reversal invariance of classical electromagnetic theory -- one that makes use of the invariant (four-dimensional) formulation of the theory -- that makes no reference to magnetic fields at all. It is my hope that it will be of interest in its own right, Albert aside. It has the advantage that it allows for arbitrary curvature in the background spacetime structure, and is therefore suitable for the framework of general relativity. (The only assumption one needs is temporal orientability.). (shrink)

The encounter between Bergson and Einstein that took place at the 1922 meeting of the Philosophical Society at the Collège de France gave rise to a lively debate about the relative merits of Bergson’s contribution to the understanding of time in relativity. In this paper, I argue that despite some serious shortcomings, Bergson’s philosophical intervention in the interpretation of relativity makes a novel and valuable contribution to the understanding of time in relativity. With reference to the so-called (...) ‘paradox’ of the twins, I begin by arguing that Bergson offers a corrective for the fallacious view that temporal passage is illusory. In the second section, I explain what Bergson means by a single, universal time. Given the fact that in relativity there is a plurality of times, this idea seems inconsistent with relativity, but I argue that Bergson’s single time is just duration, a time that is dependent on the temporal passage in a particular inertial frame. In a third section, I show that despite his failure to see it, Bergsonian duration is actually consistent with proper time, a time that is invariant regardless of which frame is used to perform the calculation. Once we make this connection between duration and proper time, we can see what Bergson’s intervention is really meant to accomplish; namely, to attach a concrete sense of the passage of time to relativity, thus ‘completing’ the theory of relativity so that it can account for the duration that we all feel and know with inimitable intimacy. In the end, my position is that Bergson helps us to see that time lapse is what it is not because it is measured as such, but rather because it is the lived time of a particular process that is invariant to change of inertial frame. (shrink)

This concise book introduces nonphysicists to the core philosophical issues surrounding the nature and structure of space and time, and is also an ideal resource for physicists interested in the conceptual foundations of space-time theory. Tim Maudlin's broad historical overview examines Aristotelian and Newtonian accounts of space and time, and traces how Galileo's conceptions of relativity and space-time led to Einstein's special and general theories of relativity. Maudlin explains special relativity using a geometrical approach, emphasizing intrinsic (...) space-time structure rather than coordinate systems or reference frames. He gives readers enough detail about special relativity to solve concrete physical problems while presenting general relativity in a more qualitative way, with an informative discussion of the geometrization of gravity, the bending of light, and black holes. Additional topics include the Twins Paradox, the physical aspects of the Lorentz-FitzGerald contraction, the constancy of the speed of light, time travel, the direction of time, and more.Introduces nonphysicists to the philosophical foundations of space-time theory Provides a broad historical overview, from Aristotle to Einstein Explains special relativity geometrically, emphasizing the intrinsic structure of space-time Covers the Twins Paradox, Galilean relativity, time travel, and more Requires only basic algebra and no formal knowledge of physics. (shrink)

BackgroundThe state of the world is one with scarce medical resources where longevity is not equally distributed. Given such facts, setting priorities in health entails making difficult yet unavoidable decisions about which lives to save. The business of saving lives works on the assumption that longevity is valuable and that an early death is worse than a late death. There is a vast literature on health priorities and badness of death, separately. Surprisingly, there has been little cross-fertilisation between the academic (...) fields of priority setting and badness of death. Our aim is to connect philosophical discussions on the badness of death to contemporary debates in health priorities.DiscussionTwo questions regarding death are especially relevant to health priorities. The first question is why death is bad. Death is clearly bad for others, such as family, friends and society. Many philosophers also argue that death can be bad for those who die. This distinction is important for health priorities, because it concerns our fundamental reasons for saving lives. The second question is, ‘When is the worst time to die?’ A premature death is commonly considered worse than a late death. Thus, the number of good life years lost seems to matter to the badness of death. Concerning young individuals, some think the death of infants is worse than the death of adolescents, while others have contrary intuitions. Our claim is that to prioritise between age groups, we must consider the question of when it is worst to die.ConclusionsDeprivationism provides a more plausible approach to health priorities than Epicureanism. If Deprivationism is accepted, we will have a firmer basis for claiming that individuals, in addition to having a health loss caused by morbidity, will have a loss of good life years due to mortality. Additionally, Deprivationism highlights the importance of age and values for health priorities. Regarding age, both variants of Deprivationism imply that stillbirths are included in the Global Burden of Disease. Finally, we suggest that the Time-Relative Interest Account may serve as an alternative to the discounting and age weighting previously applied in the Global Burden of Disease. (shrink)

I argue that excessive reliance on the notion of “the badness of death” tends to lead theorists astray when thinking about healthcare prioritisation. I survey two examples: the confusion surrounding the “time-relative interests account” of the badness of death, and a confusion in the recent literature on cost-benefit analyses for family planning interventions. In both cases, the confusions in question would have been avoided if (instead of attempting to theorise in terms of the badness of death) theorists (...) had forced themselves first to write down an appropriate value function, and then focused on the question of how to maximize value. (shrink)

The frequency of death from miscarriage is very high, greater than the number of deaths from induced abortion or major diseases.Berg (2017, Philosophical Studies 174:1217–26) argues that, given this, those who contend that personhood begins at conception (PAC) are obliged to reorient their resources accordingly—towards stopping miscarriage, in preference to stopping abortion or diseases. This argument depends on there being a basic moral similarity between these deaths. I argue that, for those that hold to PAC, there are good reasons to (...) think that there is no such similarity. There is a morally relevant difference between preventing killing and letting die, giving PAC supporters reasons to prioritize reducing abortion over reducing miscarriage. And the time-relative interest account provides a morally relevant difference in the badness of death of miscarriages and deaths of born adults, justifying attempts to combat major diseases over attempts to combat miscarriage. I consider recent developments in the literature and contend that these new arguments are unsuccessful in establishing moral similarities between deaths from miscarriage and abortion, and deaths from miscarriage and disease. (shrink)

The paper proposes a re-assessment of Reichenbach’s ‘causal’ theory of time. Reichenbach’s version of the theory, first proposed in 1921, is interesting because it is one of the first attempts to construct a causal theory as a relational theory of time, which fully takes the results of the Special theory of relativity into account. The theory derives its name from the cone structure of Minkowski space–time, in particular the emission of light signals. At first Reichenbach defines (...) an ‘order’ of time, a ‘before-after’ relationship between mechanical events. In his later work, he comes to the conclusion that the ‘order’ of time needs to be distinguished from the ‘direction’ of time. He therefore abandons the sole focus on light geometry and turns to Boltzmann’s statistical version of thermodynamics. However, as Einstein pointed out, the emission and reception of light signals have thermodynamic aspects. When this is taken into account, Reichenbach’s ‘causal’ theory turns out to be an entropic theory of time. It also emerges that Reichenbach discusses phase space and typicality arguments in support of his dynamic view of time. They provide a better understanding of the notion of entropy. This unifies his approach and helps to answer some of the standard objections against a causal theory of time. (shrink)

The idea of a ‘global’ concept of art might suggest a transcending of the categories which would locate an artwork relative to one place and one time. Is this possible? If we answer in the negative, this suggests that a global concept of art is not possible, but on the positive side, the significance of the particular is kept intact. If we answer in the affirmative, then a global concept of art is possible, but we lose the very (...) aspect that defines art: its particularity. I will argue that we can limit the damage all round by construing art in a way that allows the particular features of an artwork’s time and place to feature within the broader placeholders of a global concept of art. According to the global concept of art I will present here, art is a normative system. Its place holders could be a narrative, representation, expression of emotion or perceptual experience but what in each case explains our engagement with it as art rather than say a scientific experiment or an historical record is the particular kind of reflection that the form of the work gives rise to. Hence the form of the work or the form that our engagement with it takes is what qualifies the narrative, representation, expression of emotion or perceptual experience as art. The damage referred to above is not eliminated entirely though. The norms in a system are taken on board through day to day interaction with others who engage these norms. As such, when art is construed according to such systems, the meanings it embodies as art may be inaccessible to those not acculturated into the relevant norms. A theory of art for a global concept of art, then, must identify in what sense art is a normative system and it must provide some account of how we engage with it when we engage with it as art. For the former, I draw upon philosophical analyses of moral judgment, and for the latter, I turn to that much maligned, indeed bogus, divide between the aesthetic and the antiaesthetic. I conclude that a global concept of art is one that maintains the integrity of the artwork, and that writing is art historical rather than merely historical when it is conducted from within the culture that grounds the art under discussion. (shrink)

Según la concepción del daño de la muerte en función del interés relativo al momento, propuesta por Jeff McMahan, nuestro interés en vivir no viene determinado sólo por el valor de nuestra vida futura, sino también por los vínculos prudenciales que nos atan a ésta. McMahan sostiene que tales relaciones dependen de nuestra complejidad psicológica. Esta propuesta respalda algunas asunciones comunes acerca del daño de la muerte. Pero también cuestiona los planteamientos antropocéntricos acerca del valor comparativo de las vidas de (...) los seres humanos, pues toda una serie de seres humanos (como los bebés y aquellos con diversidad funcional intelectual notable) tienen unas capacidades psicológicas inferiores a las de muchos animales no humanos. Por otra parte, no está claro que la fuerza de las relaciones prudenciales venga de hecho determinada por la complejidad psicológica. According to the Time-relative Interest Account of the harm of death, which Jeff McMahan has proposed, our interest in living is not only determined by the value of our future life, but also by the prudential ties which bind us to it. McMahan maintains that such relations depend significantly on our psychological complexity. This proposal backs up some common assumptions as regards the harm of death. But it also questions anthropocentric views regarding the comparative value of the lives of human beings, since a number of humans (such as babies and those with significant intellectual disabilities) have psychological capacities below those of many nonhuman animals. Apart from this, it is not clear whether the strength of prudential relations is actually determined by psychological complexity. (shrink)

Donors to global health programs and policymakers within national health systems have to make difficult decisions about how to allocate scarce health care resources. Principled ways to make these decisions all make some use of summary measures of health, which provide a common measure of the value (or disvalue) of morbidity and mortality. They thereby allow comparisons between health interventions with different effects on the patterns of death and ill health within a population. The construction of a summary measure of (...) health requires that a number be assigned to the harm of death. But the harm of death is currently a matter of debate: different philosophical theories assign very different values to the harm of death at different ages. This chapter considers how we should assign numbers to the harm of deaths at different ages in the face of uncertainty and disagreement. (shrink)

“Intuitive time,” Gödel says, “is what everyone understood by time before relativity theory.” Such an understanding includes the perception or experience of objective lapse of time, presupposing a layer of successive “nows,” and a change in the existing. The notion of temporality that Gödel came up with in his work on the general theory of relativity has, in contrast, often been taken to demonstrate the impossibility of such a theory to account for the intuitive notion of (...) time, and even be inconsistent with it. So instead, what Gödel suggested is temporal idealism, that intuitive time is an illusion. (shrink)

The past six decades have seen rising interest in the philosophy of time, driven in large measure by the metaphysical implications of the physical theories of relativity and quantum mechanics. Philosophical theology has only recently begun serious interaction with contemporary metaphysics of time. In particular, the issue of God's temporal mode of being has come under investigation In Part 1, I begin with the metaphysics of time, explicating and defending a causal account of dynamic (...) class='Hi'>time. I then consider objections that can be brought against this account from the standpoint of the Special and General Theories of Relativity and Quantum Mechanics, and conclude that one of the objections are compelling. In Part II, I consider the evidence from Scripture relative to God's temporal mode of being, and find that it is neutral between a temporal and an atemporal conception. The arguments upholding the medieval consensus in philosophical theology of divine timelessness are evaluated, along with contemporary arguments for atemporality. Openness to divine temporality is discernible in some medieval philosophers; their arguments, along with contemporary arguments for temporality, are investigated. I then offer an analysis of the concept of omnitemporality which I take to be the form of temporality most appropriate to expressing God's temporal mode of being. Finally I argue that objections to omnitemporality are not forceful, and that the concept has in its favor greater explanatory power for a range of issues in philosophical theology. (shrink)

These arguments are fairly well known today. It is interesting to note that v. Kries already knew them, and that they have been ignored by Reichenbach and v. Mises in their original account of probability.2This observation leads to the interesting question why the frequency theory of probability has been adopted by many people in our century in spite of severe counterarguments. One may think of a change in scientific attitude, of a scientific revolution put forward by Feyerabendarian propaganda- and (...) who would deny that Reichenbach was an excellent propagandist!My suggested explanation is the following:J. v. Kries is still a mentalist in the tradition of Descartes and Locke. This can be shown very well from his logic, which he wrote even much later (1916). A mentalist does not pose semantical questions in a proper sense: he rather asks which ideas in the human mind make up a concept. And studying probability in this way, he will find in any case that what is in the human mind is first of all an expectation. Therefore, his analysis of the concept of probability will be centered around the concept of expectation.People tended to approach the problem in quite a different way after the scientific revolution which led from mentalism to lingualism. They tended in many cases to use operationalism and to ask how probabilities are determined in science, if they wanted to clear up the meaning of probability. This new aspect of probability, which was caused by looking at it from a new position or standpoint, suggested it to be the limit of relative frequencies in the first instance. This suggestion was so strong that all objections were ignored, and all counterarguments encountered deaf ears.Of course I have used here an oversimplification. Neither was J. v. Kries untouched by Poincaré's conventionalism, which is essentially a movement leading to the breakdown of mentalism; nor was Reichenbach, when he wrote his thesis in 1915, already a lingualist in any respect.Nevertheless, I think that the lingualist revolution, which took place particularly in mathematics and physics, has also changed the attitude towards probability. It would be interesting to corroborate this thesis by extensive study of the history of science in the late 19th century.Besides this historical aspect of v. Kries' theory, there is a systematic one which should be noticed. Though his theory still has a mentalist outlook, many of v. Kries' statements can be translated into the present lingualist idiom and then become most interesting contributions to the present discussion. We shall then state that for v. Kries probabilities appear first of all in probabilistic hypotheses which may or may not be confirmed by empirical data. Therefore, they have a role similar to theoretical concepts.3But that is not the only predominant feature of v. Kries' theory. He is approaching objective probability in a way which is quite unfamiliar to present day philosophers or mathematicians. Objective probabilities are connected with other concepts in three different ways. First of all, probabilistic hypotheses are confirmed by empirically found relative frequencies in a finite series of events. Secondly, they serve as an aid for decisions. And finally, there is a third relationship. Probabilities have to be explained by theories which are in many cases not formulated in probabilistic terms themselves. We can try to understand probability in one of the first two ways via their connection to other concepts. That is what is usually done by interpretations in terms of frequencies or decisions. A third approach, however, is to understand the nature of probability by the way probabilities are explained, and that is what v. Kries does. Such an approach does not seem unusual at all. In many cases the nature of a kind of objects is characterized by giving an explanation. If somebody asks what an eclipse of the moon is, we shall answer - as Aristotle already proposed - by giving an explanation of it. Thus it is quite natural to answer a question as to the nature of probability by describing the general type of explanation of probability distributions in natural or social science. The answer given by v. Kries is - as we know today — of limited validity. Quantum mechanical probabilities are not explainable by Spielräume. V. Kries solution, however, is remarkable in one important respect. It accounts for the time direction of objective probabilities, which are always predictive or forward probabilities, while retrodictive or backward probabilities are always subjective. The relation of objective probabilities to time direction is surely of utmost importance for natural philosophy. I do not know of any other philosophical foundation of probability which takes into account this deep-rooted relation. Therefore, v. Kries' interpretation may help us to understand one of the most intricate puzzles of philosophy. It may be nearly one hundred years old, but is by no means out of date. (shrink)

Physical Relativity explores the nature of the distinction at the heart of Einstein's 1905 formulation of his special theory of relativity: that between kinematics and dynamics. Einstein himself became increasingly uncomfortable with this distinction, and with the limitations of what he called the 'principle theory' approach inspired by the logic of thermodynamics. A handful of physicists and philosophers have over the last century likewise expressed doubts about Einstein's treatment of the relativistic behaviour of rigid bodies and clocks in motion in (...) the kinematical part of his great paper, and suggested that the dynamical understanding of length contraction and time dilation intimated by the immediate precursors of Einstein is more fundamental. Harvey Brown both examines and extends these arguments, after giving a careful analysis of key features of the pre-history of relativity theory. He argues furthermore that the geometrization of the theory by Minkowski in 1908 brought illumination, but not a causal explanation of relativistic effects. Finally, Brown tries to show that the dynamical interpretation of special relativity defended in the book is consistent with the role this theory must play as a limiting case of Einstein's 1915 theory of gravity: the general theory of relativity.Appearing in the centennial year of Einstein's celebrated paper on special relativity, Physical Relativity is an unusual, critical examination of the way Einstein formulated his theory. It also examines in detail certain specific historical and conceptual issues that have long given rise to debate in both special and general relativity theory, such as the conventionality of simultaneity, the principle of general covariance, and the consistency or otherwise of the special theory with quantum mechanics. Harvey Brown' s new interpretation of relativity theory will interest anyone working on these central topics in modern physics. (shrink)

If you were to list the perennial issues in philosophy, the nature of time would no doubt be on that list. The essays in the present volume all touch upon the problem of time. The volume includes four contributions from different perspectives within the history of philosophy of time.Jani Hakkarainen and Todd Ryan delve into David Hume's account of time. Hume thinks there can be no time without succession. Consequently, unchanging, steadfast objects do not (...) have a duration. They are stationary, not subject to any change. Although they lack a duration, they coexist with a temporal succession. This introduces a problem: What is the relation between unchanging objects and time? Hakkarainen and Ryan draw on what they call Hume's Principle of Quantitative Comparison. Each indivisible temporal extent is equal to any other temporal extent; differences in duration are due to the different number of temporal parts. Steadfast objects may be thought to undergo a certain number of calculable changes when they are compared to ordinary successions we experience. This experience is provided, for example, by the ticking of a clock. We have the capacity to think that steadfast objects have precise durations. We humans nevertheless cannot give any deep explanation as how we come to this conclusion.Emily Thomas focuses on the graphic representation of time. Whereas the visual representation of time has typically been done with matrices or grids, Joseph Priestley represented time in a line in 1765. Priestley's line divides time “by an equal scale” into centuries. Many have interpreted this as being evidence of a Newtonian influence, as if there is an absolute time flowing equably. Thomas situates Priestley's position in the modern debates on the nature of our ideas. She argues that the absolutist reading does not have merit. Thomas thinks rather that Priestley sides with David Hartley, who explained how we acquire the ideas of duration and time from sensation. Thomas's essay advances our understanding of the history of space-time parallelism. With timelines, the analogy between time and space becomes a possibility. In my essay I assess Ernst Mach's criticism of Isaac Newton's substantivalist account of time. Newton's argument for absolute time relates to his mathematical-empirical physics and theology. In his Science of Mechanics, Mach largely neglects the laws of motion, calculus and the omnipresence theology that is at the background of Newton's concept of time. Mach did however criticize Newton's absolutist argument on the basis that the self-existing flow cannot be observed, measured, or experimented with, and he provided an alternative relational account of time. I point out that this was not only extreme positivism or phenomenalism, but an epistemology and ontology suited for the subsequent physical theories of relativity. Finally, I argue that Mach's denial of the independent atomic structure of matter should not be entirely assimilated to his denial of substantivalism about time. The two phenomena are different, so we should evaluate Mach's reasoning concerning them accordingly. Matyáš Moravec and Peter West go through Susan Stebbing's criticism of Arthur Eddington's popular account of the passage of time. Stebbing's target, Moravec and West argue, is Eddington's largely Bergsonian view on time. She objects to the view that our minds have “a private door” to the physical reality which no measurements can disclose. Stebbing believes that our experience of the passage of time belongs to our ordinary, every-day experience, and she thinks Eddington mystifies the whole idea by leaning on a peculiar form of introspection. Moravec and West build a case for Bergson's influence on Eddington, arguing that Bergson probably did contribute to Eddington's idea of “the intuition of becoming.” Both seem to think that we may access the dynamic temporal reality in ways not captured by scientific investigation, by means of an introspective internal experience of duration. As a final remark, I think I should note, with regret, that out of the six authors in this volume only one is a woman. Let the reader know that as an editor I tried to strike a better balance. I still trust that the quality of the articles is high, and most importantly, worthwhile for readers interested in the history of philosophy of time. (shrink)

This volume explores the opportunities and challenges facing the accounting profession in an increasingly globalized business and financial reporting environment. It looks back at past experiences of the profession in attempting to meet its public interest obligation. It examines the role and responsibilities of accounting to society including regulatory requirements, increased emphasis on corporate social responsibility, accounting fraud and whistle-blowing implications, internationalization of public interest obligations, and providing the education needed to be successful. The book incorporates an ethical (...) dimension in making these assessments. Its focus is a conceptual, theoretical one drawing on classical philosophy, the sociology of professions, economic theory, and the public interest dimension of accountants as professionals. The authors of papers are long-time contributors to the annual symposium on Research in Accounting Ethics sponsored by the Public Interest Section of the AAA.. (shrink)

When addressing the notion of proper time in the theory of relativity, it is usually taken for granted that the time read by an accelerated clock is given by the Minkowski proper time. However, there are authors like Harvey Brown that consider necessary an extra assumption to arrive at this result, the so-called clock hypothesis. In opposition to Brown, Richard TW Arthur takes the clock hypothesis to be already implicit in the theory. In this paper I will (...) present a view different from these authors by taking into account Einstein’s notion of natural clock and showing its relevance to the debate. (shrink)

The aim of this book is to give an account of Einstein's work without introducing anything very technical in the way of mathematics, physics, or philosophy.

I propose a measure of dependence that relates a set of items of evidence to an hypothesis H and to H's negation. I dub this measure relative consilience and propose a method for using it as a correction factor for dependence among items of evidence. Using RC, I examine collusion and testimonial independence, the value of diverse evidence, and the strengthening of otherwise weak or non-existent cases. RC provides a valuable tool for formal epistemologists interested in analyzing cumulative case (...) arguments. (shrink)

According to what I will call a contextualist solution to the sorites paradox, vague terms are context-sensitive, and one can give a convincing dissolution of the sorites paradox in terms of this context-dependency. The reason, according to the contextualist, that precise boundaries for expressions like “heap” or “tall for a basketball player” are so difficult to detect is that when two entities are sufficiently similar (or saliently similar), we tend to shift the interpretation of the vague expression so that if (...) one counts as falling in the extension of the property expressed by that expression, so does the other. As a consequence, when we look for the boundary of the extension of a vague expression in its penumbra, our very looking has the effect of changing the interpretation of the vague expression so that the boundary is not where we are looking. This accounts for the persuasive force of sorites arguments. (shrink)

This book is a contribution to both the study of the logical and philosophical foundations of physics, and the investigation of applied formal axiomatic systems. Basri uses the techniques of logic and set theory in order to construct a rigorous physical theory whose theorems turn out to be those of the general theory of relativity or else arbitrarily close approximations thereof. Whether Basri's approach turns out to be fruitful for the analysis of foundational problems in physics remains to be seen, (...) but he has clearly rendered an important service in providing at least one rigorously unified way of talking about such things as particles, events, signals, clocks, rigid measuring instruments, etc. A novel feature of the book is that the basis of Basri's system is rather phenomenalistic: he uses primitives like "the class of unbiased human observers" and "the class of simultaneous sensations of observer H." The obvious philosophical problems about perception and the external world which are consequent upon this sort of approach are not treated by Basri, but he is certainly not to be faulted on this account. There are, however, a number of errors and imprecisions in the underlying logistic system, some of which are more serious than others. But in general, this book deserves to be read and its thesis considered by all students interested in serious and responsible efforts in the philosophy of physics.—H. P. K. (shrink)

The picture which one naturally presents of the situation is that which would arise before an observer placed outside the earth, who could watch the light wave starting from the central mirror and pursuing the distant mirror, catching up with it at some distance beyond the point at which it was when the light wave started. In this case the observer is able to locate the points at which the parts of the apparatus were at different moments and to measure (...) the distances between. We could simulate this situation on the earth by assuming an enclosed square car, from some point in which two balls were shot out in directions at right angles to each other to the walls of the car, bounding back to the point at which they started. We will assume that the balls move with uniform velocity going and coming, and we will assume that the car is moving. An observer outside the car who marked the point on the rail directly over the starting point and the points reached by the balls when they struck the sides of the car, and then measured the distances which the balls travelled, would find that the ball which travelled with the car covered a greater distance than that traversed by the ball which went at right angles to the direction of the train, and yet the balls would return to the starting point at the same moment, provided they travelled over both their paths at the same velocity during their entire trajects, i.e., the same velocity measured within the car. The observer would be at no difficulty to explain this, for he would see that the velocity in the direction of its motion of the car had to be added to that of balls within the car. That is not the case of the light wave. The velocity of a moving shining body is not added to that of the light wave. The wave motion being set up in ether travels with its own uniform velocity of approximately 300,000 kilometers a second. The light waves then, from the standpoint of the observer outside the earth, traverse through the stagnant ether different distances at a uniform velocity and yet the ether waves exhibit on their return none of the evidence which they should exhibit in the interferometer. (shrink)

This thesis presents a novel theory of temporal experience. While time as measured by the clock is a perennially popular topic, the time of experience remains relatively neglected and poorly understood despite its centrality to our existence. This thesis therefore sets out to address the following questions: 1) How should we characterize experiential time and the experienced present? 2) How might such distinctively temporal experience arise in the first place? While the first of these is a “what (...) is it like” question, and thus in the realm of phenomenological analysis, the second is ostensibly closer to the realm of scientific inquiry in that it concerns an empirical phenomenon. The goal of this thesis is to synthesize plausible answers to both of these questions. As to the first question, there is already a lively debate ongoing in the philosophy of mind between various camps, each offering what they see as the most plausible analysis of the phenomenology of time. Regarding the second, there is an interdisciplinary investigation of mechanisms at various levels of abstraction, notably the levels of neurophysiology and information processing. This thesis proposes, among other contentions, that the time of experience is best characterized by a combination of retentional and extensional phenomenological analyses. This means the actual temporal extension of experience and its correlates determines, to some degree, the felt temporal character of experience. At the same time, perhaps the greater part of temporal phenomenology is determined by content: mental processes can be about temporal properties in addition to their primary contents and the way they are so partially determines the temporal character of experience as well. This analysis dovetails nicely with contemporary theories of consciousness that maintain the brain is fundamentally a complex predictive engine actively and adaptively guiding behavior. The thesis thus represents a multi-level framework for understanding the experience of time and the mechanisms underpinning it. It is my hope this perspective advances the debate on time-consciousness and can guide further work towards understanding this most fundamental aspect of our lives. (shrink)

The history of the theory of general relativity presents unique features. After its discovery, the theory was immediately confirmed and rapidly changed established notions of space and time. The further implications of general relativity, however, remained largely unexplored until the mid 1950s, when it came into focus as a physical theory and gradually returned to the mainstream of physics. This essay presents a historiographical framework for assessing the history of general relativity by taking into account in an integrated (...) narrative intellectual developments, epistemological problems, and technological advances; the characteristics of post–World War II and Cold War science; and newly emerging institutional settings. It argues that such a framework can help us understand this renaissance of general relativity as a result of two main factors: the recognition of the untapped potential of general relativity and an explicit effort at community building, which allowed this formerly disparate and dispersed field to benefit from the postwar changes in the scientific landscape. (shrink)

This book is an attempt to get to the bottom of an acute and perennial tension between our best scientific pictures of the fundamental physical structure of the world and our everyday empirical experience of it. The trouble is about the direction of time. The situation (very briefly) is that it is a consequence of almost every one of those fundamental scientific pictures--and that it is at the same time radically at odds with our common sense--that whatever can (...) happen can just as naturally happen backwards. Albert provides an unprecedentedly clear, lively, and systematic new account--in the context of a Newtonian-Mechanical picture of the world--of the ultimate origins of the statistical regularities we see around us, of the temporal irreversibility of the Second Law of Thermodynamics, of the asymmetries in our epistemic access to the past and the future, and of our conviction that by acting now we can affect the future but not the past. Then, in the final section of the book, he generalizes the Newtonian picture to the quantum-mechanical case and (most interestingly) suggests a very deep potential connection between the problem of the direction of time and the quantum-mechanical measurement problem. The book aims to be both an original contribution to the present scientific and philosophical understanding of these matters at the most advanced level, and something in the nature of an elementary textbook on the subject accessible to interested high-school students. Table of Contents: Preface 1. Time-Reversal Invariance 2. Thermodynamics 3. Statistical Mechanics 4. The Reversibility Objections and the Past-Hypothesis 5. The Scope of Thermodynamics 6. The Asymmetries of Knowledge and Intervention 7. Quantum Mechanics Appendix: Gedankenexperiments with Heat Engines Index Reviews of this book: The foundations of statistical mechanisms are often presented in physics textbooks in a rather obscure and confused way. By challenging common ways of thinking about this subject, Time and Chance can do quite a lot to improve this situation. --Jean Bricmont, Science Albert is perfecting a style of foundational analysis that is uniquely his own...It has a surgical precision...and it is ruthless with pretensions. The foundations of thermodynamics is a topic that has accumulated a good deal of dead wood; this is a fire that will burn and burn. --Simon W. Saunders, Oxford University As usual with Albert's work, the exposition is brisk and to the point, and exceptionally clear...The book will be an extremely valuable contribution to the literature on the subject of philosophical issues in thermodynamics and statistical mechanics, a literature which has been thin on the ground but is now growing as it deserves to. --Lawrence Sklar, University of Michigan. (shrink)

I discuss the interest-relative account of vagueness and argue for a distinction between relational vague predicates and non-relational vague predicates depending on the kind of properties expressed by them. The strategy rests on three arguments arising from the existence of clear cases of a vague predicate, from contexts in which a different answer is required for questions about whether a vague predicate applies to an item, and whether such an item satisfies the interest of an agent, (...) and from cases where an object changes up to the point of becoming P, where P is a vague predicate. In the second part of the paper, I distinguish between relational properties and non-relational properties, and I argue for the view that some vague predicates can express non-relational properties, comparative relational properties and interest-relative properties. On the basis of these arguments, I conclude that vagueness cannot be reduced to interest-relativity. (shrink)

An interesting connection between special relativity and quantum mechanics was put forward by Louis de Broglie, about 60 years ago, who focused on the link between synchronization in a rotating frame and the quantization of the angular momentum. Here we generalise his approach to curved spacetime, using the gravitoelectromagnetic analogy, which can be applied to describe the weak gravitational field around rotating sources, and give a new interpretation of the results.

An often repeated account of the genesis of special relativity tells us that relativity theory was to a considerable extent the fruit of an operationalist philosophy of science. Indeed, Einstein’s 1905 paper stresses the importance of rods and clocks for giving concrete physical content to spatial and temporal notions. I argue, however, that it would be a mistake to read too much into this. Einstein’s operationalist remarks should be seen as serving rhetoric purposes rather than as attempts to promulgate (...) a particular philosophical position --- in fact, Einstein never came close to operationalism in any of his philosophical writings. By focussing on what could actually be measured with rods and clocks Einstein shed doubt on the empirical status of a number of pre-relativistic concepts, with the intention to persuade his readers that the applicability of these concepts was not obvious. This rhetoric manoeuvre has not always been rightly appreciated in the philosophy of physics. Thus, the influence of operationalist misinterpretations, according to which associated operations strictly define what a concept means, can still be felt in present-day discussions about the conventionality of simultaneity. The standard story continues by pointing out that Minkowski in 1908 supplanted Einstein’s approach with a realist spacetime account that has no room for a foundational role of rods and clocks: relativity theory became a description of a four-dimensional ‘absolute world’. As it turns out, however, it is not at all clear that Minkowski was proposing a substantivalist position with respect to spacetime. On the contrary, it seems that from a philosophical point of view Minkowski’s general position was not very unlike the one in the back of Einstein’s mind. However, in Minkowski’s formulation of special relativity it becomes more explicit that the content of spatiotemporal concepts relates to considerations about the form of physical laws. If accepted, this position has important consequences for the discussion about the conventionality of simultaneity. (shrink)

Philosopher William Lane Craig of the Talbot School of Theology has published three other Kluwer books on time and eternity and God’s relationship to them. In this book, Craig draws some important strands together regarding the concept of God and relativity theory. He notes the striking “paucity of integrative literature” in this regard: “I am convinced that this lack is largely due to the fact that theologians and philosophers of religion do not understand Einstein’s theories and so are reduced (...) to merely parroting what they read in scientific popularizations,” resulting in “a superficial and uncritical interaction”. (shrink)

This volume offers an integrated understanding of how the theory of general relativity gained momentum after Einstein had formulated it in 1915. Chapters focus on the early reception of the theory in physics and philosophy and on the systematic questions that emerged shortly after Einstein's momentous discovery. They are written by physicists, historians of science, and philosophers, and were originally presented at the conference titled Thinking About Space and Time: 100 Years of Applying and Interpreting General Relativity, held at (...) the University of Bern from September 12-14, 2017. By establishing the historical context first, and then moving into more philosophical chapters, this volume will provide readers with a more complete understanding of early applications of general relativity and of related philosophical issues. Because the chapters are often cross-disciplinary, they cover a wide variety of topics related to the general theory of relativity. These include: Heuristics used in the discovery of general relativity Mach's Principle The structure of Einstein's theory Cosmology and the Einstein world Stability of cosmological models The metaphysical nature of spacetime The relationship between spacetime and dynamics The Geodesic Principle Symmetries Thinking About Space and Time will be a valuable resource for historians of science and philosophers who seek a deeper knowledge of the uses of general relativity, as well as for physicists and mathematicians interested in exploring the wider historical and philosophical context of Einstein's theory. (shrink)

BETWEEN St. Augustine and Plato, as between St. Thomas and Aristotle, there are significant analogies. If Whitehead exaggerated only pardonably little in describing Western philosophy as a series of footnotes to Plato, one could point to a similar relationship between Christian thought and Augustine. Plato and Augustine were fertile in inspiration, Aristotle and Aquinas were systematizers on the grandest scale. Augustine is often styled the Christian Plato; this is true in part because he was a Platonist, but perhaps even more (...) because both men were great artists, who have scarcely had rivals in the whole of Western philosophical history. Even in their manner of artistry they agree, for both were censorious of art, and indeed for analogous reasons; yet each manifested in his writings an artistry that somehow achieved the goal for the attainment of which he disputed with art itself. The difficulty of disengaging from the thought of Plato, or of Augustine, a series of views, a synthesis of arguments, a statement of acquired conclusions, is notorious; the expositor who, like myself, undertakes to explain the Augustinian view of time cannot hope simply by excerpting a series of propositions from the living dialectic of the Confessions to present them as a remainderless rendering of the original, any more than one can translate poetry into prose and expect to retain its meaning, without remainder. If the attempt is made, there remains, despite all disclaimers and warnings, an ineluctable element of betrayal. I offer what I do, neither in the guise of an accurate summary of Augustine's views on time, nor as a rebuttal of other interpretations of Augustine's mind, but simply as an incitement to the reading of the Confessions, and as a provocation or stimulus to philosophical mimesis. (shrink)

The two books discussed here make important contributions to our understanding of the role of spacetime concepts in physical theories and how that understanding has changed during the evolution of physics. Both emphasize what can be called a ‘dynamical’ account, according to which geometric structures should be understood in terms of their roles in the laws governing matter and force. I explore how the books contribute to such a project; while generally sympathetic, I offer criticisms of some historical claims (...) concerning Newton, and argue that the dynamical account does not undercut ontological issues as the books claim. *Received January 2009; revised March 2009. †To contact the author, please write to: Department of Philosophy, 1423 University Hall MC 267, University of Illinois at Chicago, 601 S. Morgan Street, Chicago, IL 60607; e‐mail: [email protected]. (shrink)