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

We consider the Heisenberg uncertainty principle of position and momentum in 3-dimensional spaces of constant curvature K. The uncertainty of position is defined coordinate independent by the geodesic radius of spherical domains in which the particle is localized after a von Neumann–Lüders projection. By applying mathematical standard results from spectral analysis on manifolds, we obtain the largest lower bound of the momentum deviation in terms of the geodesic radius and K. For hyperbolic spaces, we also obtain a (...) global lower bound \, which is non-zero and independent of the uncertainty in position. Finally, the lower bound for the Schwarzschild radius of a static black hole is derived and given by \, where \ is the Planck length. (shrink)

The research has three objectives: 1) to study the concept of Heisenberg’s uncertainty principle, 2) to study the concept of reality and knowledge in Buddhist philosophy, and 3) to analyze the concept of Heisenberg’s uncertainty principle in Buddhist philosophical perspective. This is documentary research. In this research, it was found that Heisenberg's uncertainty principle refers to the experiment of thought while studying physical reality on smaller particles than atoms where at the present no theory (...) of Physics can clearly explain such properties. In this respect, the mentioned principle is utilized to predict the pairs of a certain attribute of physics, position, and momentum, for instance. The accuracy of position, however, cannot be precisely yielded in advance by such a principle. In other words, it is impossible to measure the position and momentum of a quantum particle at the same time. In the study of the ultimate reality on the matter in the Buddhist philosophy, it showed that corporeality in nature is conditioned by cause and effect and thereby falling under the three common characteristics: 1) impermanence, 2) state of suffering, and 3) state of non-substantiality. In the study of Heisenberg’s uncertainty principle in the Buddhist philosophical perspective, this research was found that the processes in acquiring certain knowledge of Heisenberg and Buddhist philosophy are by one another in the sense that such knowledge is methodologically acquired through experience, rationality, and intuition because both see the Reality in the same manners, that is, the physical reality is viewed by Heisenberg as the thing that goes under changing state of wave-particle all the times, and the matter is seen by Buddhist philosophy as the impermanence and change depending upon its factors involved and thereby is not-self. However, in the different aspect, on the one hand, Buddhist philosophy utilizes the knowledge on the matter to develop the morality and ethics by which the cessation of suffering could be respectively made, but on the other hand, Heisenberg somehow applies the certain knowledge on physical objects into quantum technology to accommodate the physical comfortability in living life. Suggestions in the application of knowledge gained from this research into benefit were that while Buddhist philosophy can make use of Heisenberg’s uncertainty principle to provide certain help at the time of explanation of three common characteristics being done through the scientific method, science also can utilize knowledge gained from Buddhist philosophy to expand the framework of scientific knowledge which is aimed at studying only the physical objects to be able to study the mental objects through the integration of three epistemological methods as well. (shrink)

Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a condition ensuring that mutually exclusive experimental options can be reconciled if an appropriate trade-off is accepted. The uncertainty principle is shown to appear in three manifestations, in the form of uncertainty relations: for the widths of the position and momentum distributions (...) in any quantum state; for the inaccuracies of any joint measurement of these quantities; and for the inaccuracy of a measurement of one of the quantities and the ensuing disturbance in the distribution of the other quantity. Whilst conceptually distinct, these three kinds of uncertainty relations are shown to be closely related formally. Finally, we survey models and experimental implementations of joint measurements of position and momentum and comment briefly on the status of experimental tests of the uncertainty principle. (shrink)

In this paper we critically analyse W. Heisenberg’s arguments against the ontology of point particles following trajectories in quantum theory, presented in his famous 1927 paper and in his Chicago lectures (1929). Along the way, we will clarify the meaning of Heisenberg’s uncertainty relation and help resolve some confusions related to it.

We consider a space with Generalized Uncertainty Principle which can be obtained in the frame of the deformed commutation relations. In the space with GUP we have found transformations relating coordinates and times of moving and rest frames of reference in the first order over the parameter of deformation. In the non-relativistic case we find the deformed Galilean transformation which is rotation in Euclidian space–time. This transformation is similar to the Lorentz one but written for Euclidean space–time where (...) the speed of light is replaced by some velocity related to the parameter of deformation. We show that for relativistic particle in the space with GUP the coordinates of the rest and moving frames of reference satisfy the Lorentz transformation with some effective speed of light. (shrink)

Heisenberg’s uncertainty principle is a milestone of twentieth-century physics. We sketch the history that led to the formulation of the principle, and we recall the objections of Grete Hermann and Niels Bohr. Then we explain that there are in fact two uncertainty principles. One was published by Heisenberg in the Zeitschrift für Physik of March 1927 and subsequently targeted by Bohr and Hermann. The other one was introduced by Earle Kennard in the same journal a couple (...) of months later. While Kennard’s principle remains untarnished, the principle of Heisenberg has recently been criticized in a way that is very different from the objections by Bohr and Hermann: there are reasons to believe that Heisenberg’s formula is not valid. Experimental results seem to support this claim. -/- . (shrink)

Drawing from field theory, Gestalt therapy conceives psychological suffering and psychotherapy as two intentional field phenomena, where unprocessed and chaotic experiences seek the opportunity to emerge and be assimilated through the contact between the patient and the therapist (i.e., the intentionality of contacting). This therapeutic approach is based on the therapist’s aesthetic experience of his/her embodied presence in the flow of the healing process because (1) the perception of beauty can provide the therapist with feedback on the assimilation of unprocessed (...) experiences; (2) the therapist’s attentional focus on intrinsic aesthetic diagnostic criteria can facilitate the modification of rigid psychopathological fields by supporting the openness to novel experiences. The aim of the present manuscript is to review recent evidence from psychophysiology, neuroaesthetic research, and neurocomputational models of cognition, such as the free energy principle (FEP), which support the notion of the therapeutic potential of aesthetic sensibility in Gestalt psychotherapy. Drawing from neuroimaging data, psychophysiology and recent neurocognitive accounts of aesthetic perception, we propose a novel interpretation of the sense of beauty as a self-generated reward motivating us to assimilate an ever-greater spectrum of sensory and affective states in our predictive representation of ourselves and the world and supporting the intentionality of contact. Expecting beauty, in the psychotherapeutic encounter, can help therapists tolerate uncertainty avoiding impulsive behaviours and to stay tuned to the process of change. (shrink)

We study uncertainty relations for a general class of canonically conjugate observables. It is known that such variables can be approached within a limiting procedure of the Pegg–Barnett type. We show that uncertainty relations for conjugate observables in terms of generalized entropies can be obtained on the base of genuine finite-dimensional consideration. Due to the Riesz theorem, there exists an inequality between norm-like functionals of two probability distributions in finite dimensions. Using a limiting procedure of the Pegg–Barnett type, (...) we take the infinite-dimensional limit right for this inequality. Hence, uncertainty relations are derived in terms of generalized entropies. In particular, the case of measurements with a finite precision is addressed. It takes into account that in any experiment an accuracy of performed measurements is always limited. (shrink)

In this essay, we explore an issue of moral uncertainty: what we are permitted to do when we are unsure about which moral principles are correct. We develop a novel approach to this issue that incorporates important insights from previous work on moral uncertainty, while avoiding some of the difficulties that beset existing alternative approaches. Our approach is based on evaluating and choosing between option sets rather than particular conduct options. We show how our approach is particularly well-suited (...) to address this issue of moral uncertainty with respect to agents that have credence in moral theories that are not fully consequentialist. (shrink)

Defenders of deontological constraints in normative ethics face a challenge: how should an agent decide what to do when she is uncertain whether some course of action would violate a constraint? The most common response to this challenge has been to defend a threshold principle on which it is subjectively permissible to act iff the agent's credence that her action would be constraint-violating is below some threshold t. But the threshold approach seems arbitrary and unmotivated: what would possibly determine (...) where the threshold should be set, and why should there be any precise threshold at all? Threshold views also seem to violate ought agglomeration, since a pair of actions each of which is below the threshold for acceptable moral risk can, in combination, exceed that threshold. In this paper, I argue that stochastic dominance reasoning can vindicate and lend rigor to the threshold approach: given characteristically deontological assumptions about the moral value of acts, it turns out that morally safe options will stochastically dominate morally risky alternatives when and only when the likelihood that the risky option violates a moral constraint is greater than some precisely definable threshold (in the simplest case, .5). I also show how, in combination with the observation that deontological moral evaluation is relativized to particular choice situations, this approach can overcome the agglomeration problem. This allows the deontologist to give a precise and well-motivated response to the problem of uncertainty. (shrink)

Moral uncertainty and disagreement pervade our lives. Yet we still need to make decisions and act, both individually and politically. So, what should we do? Moral uncertainty theorists provide a theory of what individuals should do when they are uncertain about morality. Public reason liberals provide a theory of how societies should deal with reasonable disagreements about morality. They defend the public justification principle: state action is permissible only if it can be justified to all reasonable people. (...) In this article, we bring these two approaches together. Specifically, we investigate whether considerations of moral uncertainty support public reason liberalism: given moral uncertainty, should we favor public justification? We argue that while moral uncertainty theory cannot vindicate an exceptionless public justification principle, it supports adopting public justification as a pro tanto principle – albeit one that can be overridden when the moral stakes are high. It also provides new answers to some intramural debates among public reason liberals and new responses to some common objections. (shrink)

In contemporary science uncertainty is often represented as an intrinsic feature of natural and of human phenomena. As an example we need only think of two important conceptual revolutions that occurred in physics and logic during the first half of the twentieth century: (1) the discovery of Heisenberg’s uncertainty principle in quantum mechanics; (2) the emergence of many-valued logical reasoning, which gave rise to so-called ‘fuzzy thinking’. I discuss the possibility of applying the notions of uncertainty, (...) developed in the framework of quantum mechanics, quantum information and fuzzy logics, to some problems of political and social sciences. (shrink)

The precautionary principle is invoked in a number of important personal and policy decision contexts. Peterson shows that certain ways of making the principle precise are inconsistent with other criteria of decision-making. Some object that the results do not apply to cases of deep uncertainty or value incommensurability which are alleged to be in the principle’s wheelhouse. First, I show that Peterson’s impossibility results can be generalized considerably to cover cases of both deep uncertainty and (...) incommensurability. Second, I contrast an alternative way of giving voice to the precautionary impulse. (shrink)

While ordinary decision theory focuses on empirical uncertainty, real decision-makers also face normative uncertainty: uncertainty about value itself. From a purely formal perspective, normative uncertainty is comparable to (Harsanyian or Rawlsian) identity uncertainty in the 'original position', where one's future values are unknown. A comprehensive decision theory must address twofold uncertainty -- normative and empirical. We present a simple model of twofold uncertainty, and show that the most popular decision principle -- maximising (...) expected value (`Expectationalism') -- has different formulations, namely Ex-Ante Expectationalism, Ex-Post Expectationalism, and hybrid theories. These alternative theories recommend different decisions, reasoning modes, and attitudes to risk. But they converge under an interesting (necessary and sufficient) condition. (shrink)

We investigate the conflict between the ex ante and ex post criteria of social welfare in a new framework of individual and social decisions, which distinguishes between two sources of uncertainty, here interpreted as an objective and a subjective source respectively. This framework makes it possible to endow the individuals and society not only with ex ante and ex post preferences, as is usually done, but also with interim preferences of two kinds, and correspondingly, to introduce interim forms of (...) the Pareto principle. After characterizing the ex ante and ex post criteria, we present a first solution to their conflict that extends the former as much possible in the direction of the latter. Then, we present a second solution, which goes in the opposite direction, and is also maximally assertive. Both solutions translate the assumed Pareto conditions into weighted additive utility representations, and both attribute to the individuals common probability values on the objective source of uncertainty, and different probability values on the subjective source. We discuss these solutions in terms of two conceptual arguments, i.e., the by now classic spurious unanimity argument and a novel informational argument labelled complementary ignorance. The paper complies with the standard economic methodology of basing probability and utility representations on preference axioms, but for the sake of completeness, also considers a construal of objective uncertainty based on the assumption of an exogeneously given probability measure. JEL classification: D70; D81. (shrink)

According to John Broome, akrasia consists in a failure to intend to do something that one believes one ought to do, and such akrasia is necessarily irrational. In fact, however, failing to intend something that one believes one ought to do is only guaranteed to be irrational if one is certain of a maximally detailed proposition about what one ought to do; if one is uncertain about any part of the full story about what one ought to do, it could (...) be perfectly rational not to intend to do something that one believes one ought to do. This paper seeks to remedy this problem, by proposing an anti-akrasia principle that covers cases of uncertainty (as well as cases of such complete certainty). It is argued that this principle is in effect the fundamental principle of practical rationality. (shrink)

The book provides a comprehensive and principled account of the uncertainty problem that arises in tort litigation. It presents and critically examines the existing doctrinal solutions of the problem, as evolved in England, the United States, Canada, and Israel, and also offers a number of original solutions, such as imposition of collective liability and liability for evidential damage. Among the issues dealt with by the book are rapidly developing areas of tort law, such as mass torts, liability for imposing (...) risk and the like. The book combines the traditional doctrinal depiction of the law with general theoretical insights that include economic analysis. (shrink)

Decision-makers face severe uncertainty when they are not in a position to assign precise probabilities to all of the relevant possible outcomes of their actions. Such situations are common—novel medical treatments and policies addressing climate change are two examples. Many decision-makers respond to such uncertainty in a cautious manner and are willing to incur a cost to avoid it. There are good reasons for taking such an uncertainty-averse attitude to be permissible. However, little work has been done (...) to incorporate it into an egalitarian theory of distributive justice. We aim to remedy this lack. We put forward a novel, uncertainty-averse egalitarian view. We analyse when the aims of reducing inequality and limiting the burdens of severe uncertainty are congruent and when they conflict, and highlight practical implications of the proposed view. We also demonstrate that if uncertainty aversion is permissible, then utilitarians must relinquish a favourite argument against egalitarianism. (shrink)

The concepts of uncertainty in prediction and inference are introduced and illustrated using the diffraction of light as an example. The close relationship between the concepts of uncertainty in inference and resolving power is noted. A general quantitative measure of uncertainty in inference can be obtained by means of the so-called statistical distance between probability distributions. When applied to quantum mechanics, this distance leads to a measure of the distinguishability of quantum states, which essentially is the absolute (...) value of the matrix element between the states. The importance of this result to the quantum mechanical uncertainty principle is noted. The second part of the paper provides a derivation of the statistical distance on the basis of the so-called method of support. (shrink)

The main purpose of the paper is to develop a concept of _model uncertainty_ as opposed to the existing and well-established concept of model risk. Up to date the broad literature on probability not only developed complete probability systems, but also correctly noticed limitations of probability calculus. Despite the acknowledgement of such probability restrictions, drawbacks of modeling are often related to model risk. We present an argument here to distinguish a feature limiting models even further: model uncertainty. The tenets (...) of it already exist in the literature on probability, but were not properly emphasized while the idea of model risk was developed. Our plan it to start with a broad overview of the existing knowledge about probability in order to start with fundamental principles. From them we are deriving a new concept of model uncertainty. (shrink)

In ‘Patients, doctors and risk attitudes,’ Makins argues that, when physicians must decide for, or act on behalf of, their patients they should defer to patient risk attitudes for many of the same reasons they defer to patient values, although with a caveat: physicians should defer to the higher-order desires of patients when considering their risk attitudes. This modification of what Makins terms the ‘deference principle’ is primarily driven by potential counterexamples in which a patient has a first-order desire (...) with one risk attitude (either risk-seeking or averse) and a second-order desire that this risk attitude not be effective in guiding their choices.1 There are two reasons we might think people with obsessive–compulsive disorder (OCD) are particularly relevant patients for evaluating Makins’ proposal. Not only might their first-order risk attitudes be irrational, but many people with OCD also judge their own OCD behaviours to be excessive or unwarranted making them structurally similar to the counterexamples outlined above. Yet, I argue that recent research about risk and decision-making under uncertainty for those with OCD complicates Makins’ proposal by raising questions of whether and to what degree their risk attitudes are irrational such that they should not play a part in the surrogate decisions made by physicians. This places more …. (shrink)

This paper explores the intertwining of uncertainty and values. We consider an important but underexplored field of fundamental uncertainty and values in decision-making. Some proposed methodologies to deal with fundamental uncertainty have included potential surprise theory, scenario planning and hypothetical retrospection. We focus on the principle of uncertainty transduction in hypothetical retrospection as an illustrative case of how values interact with fundamental uncertainty. We show that while uncertainty transduction appears intuitive in decision contexts (...) it nevertheless fails in important ranges of strategic game-theoretic cases. The methodological reasons behind the failure are then examined. (shrink)

In this thesis I investigate the behaviour of uncertainty about vague matters. It is a fairly common view that vagueness involves uncertainty of some sort. However there are many fundamental questions about this kind of uncertainty that are left open. Could you be genuinely uncertain about p when there is no matter of fact whether p? Could you remain uncertain in a vague proposition even if you knew exactly which possible world obtained? Should your degrees of belief (...) be probabilistically coherent? Should your beliefs in the vague be fixed by your beliefs in the precise? Could one in principle tell what credences a person has in the vague? (shrink)

If an agent is unsure about which moral theory or principle should guide her action in a decision situation, she faces moral uncertainty. In recent years, various strategies have been explored to deal with this type of uncertainty. In this paper, we briefly mention two strategies from the literature that make use of credence distributions over moral theories, namely “my favourite theory” and “maximizing expected choice-worthiness”. As an alternative, we propose a two-step procedure which uses the concept (...) of aggregation over structural properties. It is standard in the theory of collective choice and has recently been applied to the Kuhnian problem of theory choice as well. The idea is to explore how a morally-motivated rational agent may assess different moral theories on the basis of fundamental properties. These properties are ranked on a common scale of qualitative verdicts. This method enables an outside observer to make comparisons across competing moral theories and then conclude to what degree these theories fulfil a set of postulated properties. By doing so, we try to render the reasons more transparent that lie behind different types of credence ascriptions. (shrink)

According to the sufficiency principle, distributive justice requires that everyone have some sufficient level of resources or well-being, but inequalities above this threshold have no moral significance. This paper defends a version of the sufficiency principle as the appropriate response to moral uncertainty about distributive justice. Assuming that the appropriate response to moral uncertainty is to maximize expected choiceworthiness, and given a reasonable distribution of credence in some familiar views about distributive justice, a version of the (...) sufficiency principle strikes the optimal balance between the competing moral risks posed by implementing these views. In particular, it avoids the moral risk posed by views like Nozick’s libertarianism, which forbid redistributive taxation even for the sake of helping to provide for people’s basic needs: failing to do the latter, if it turns out that justice does require it, would be very morally wrong. This “uncertainty argument” has the advantage of minimizing reliance on controversial intuitions about distributive justice, helps to specifying a non-arbitrary threshold for sufficiency, and shows that the substantive moral implications of moral uncertainty are not limited to high-stakes applied ethics issues such as abortion and vegetarianism but instead extend to an issue at the heart of political philosophy. (shrink)

In this paper I argue that the rationality of law and legal decision making would be enhanced by a systematic attempt to recognize and respond to the implications of empirical uncertainty for policy making and decision making. Admission of uncertainty about the accuracy of facts and the validity of assumptions relied on to make inferences of fact is commonly avoided in law because it raises the spectre of paralysis of the capacity to decide issues authoritatively. The roots of (...) this short-sighted view are found in primitive mechanical models of relationships in the empirical and social world – those of objective causality and determinism. Insofar as it is believed that if we had sufficient data a clear and unequivocal answer would be available to each question, admission of uncertainty is seen as a sign of insufficiency, incompetence, impotence, and is avoided whenever a decision that must be seen to be based on valid reasons, cannot be avoided. Avoidance of some decisions, duplicity in others, is the result. -/- Decision-making must be restructured to recognize the provisional and context-bound validity and relevance of the models we use to conceptualize and order our understanding of phenomena, and to utilize this awareness as an instrument in the production of legal policies and decisions that will be authoritative precisely because they are honestly accurate and socially responsible. The paper makes a start on such a re-structuring of the legal process by exploring the implications of the observation that if law is to be “just”: 1) legal policy must be based on accurate information and rationally related to social goals; and 2) decisions applying policy to individual fact situations must be based on assumptions that are both relevant and accurate. -/- Reasons for determinations of fact must be given, otherwise the presumption that the trier of fact is “reasonable” is an unconditional licence to use private modes of logic and theories of social and natural science. What is not disclosed cannot be challenged on grounds of invalidity or irrelevance. Use of “objective validity” as a standard to evaluate conclusions made by the trier of fact in contentious cases would only serve to beg all important questions by concealing: 1) fundamental normative conflict, and 2) the limited nature and applicability of many validity claims. -/- Our use of the phrases “undue risk,” “public interest,” “reasonable,” and “necessary,” reflects the weight we choose to give conflicting social values and goals when we must make decisions in relative ignorance of all the consequences. “Objective criteria” are of limited utility in legal decision-making because their social meaning is derivative. Policy generation in the absence of any coherent conceptual-normative framework, use of vague terminology in legislation stating policy, and the absence of rational means to distinguish between individual cases to which decision-makers are required by law to apply policy, make it inevitable that many legal “decisions” made in the guise of determinations of objective fact, are charades, an arbitrary, capricious, intuitive, subjective (and thus private) use of public decision-making power. -/- Law must alter its aspirations and recognize that rational decision-making is a process that can occur only within parameters set by present knowledge and societal preference structures. Only by working with the constraints imposed by these parameters is it possible to achieve “just” decisions. Where no rational basis for differentiating cases exists, “individualized justice” must be avoided and public policy articulated in law applied uniformly to all cases in a class. The terms “reasonable” and “necessary,” used to describe policy and its consequences for specific cases, must be understood to represent provisional societal assessments, attempts to implement societal preference structures in the face of limited knowledge. Heightened awareness of the limited nature of our knowledge can only result in legal policies that have a more explicit normative basis. (shrink)

Quantum uncertainty relations have deep-rooted significance in the formalism of quantum mechanics. Heisenberg’s uncertainty relations attracted a renewed interest for its applications in quantum information science. Following the discovery of the Heisenberg uncertainty principle, Robertson derived a general form of Heisenberg’s uncertainty relations for a pair of arbitrary observables represented by Hermitian operators. In the present work, we discover a temporal version of the Heisenberg–Robertson uncertainty relations for the measurement of two observables at two (...) different times, where the dynamical uncertainties crucially depend on the time evolution of the observables. The uncertainties not only depend on the choice of observables but also depend on the times at which the physical observables are measured. The time correlated two-time commutator dictates the trade-off between the dynamical uncertainties. We demonstrate the dynamics of these uncertainty relations for a spin-1/2 quantum system and for a quantum harmonic oscillator. We also present the dynamical uncertainty relation in terms of entropies, where the temporal entropic uncertainties are restricted by a time-dependent complementarity factor. The temporal uncertainty relations explored in this work can be experimentally verified with the present quantum technology. (shrink)

The article deals with some implications of radical uncertainty for participatory democracy, and more precisely for Participatory Technology Assessment. Two main forms of PTA are discussed. One is aimed at involving lay citizens and highlighting public opinion. The other is addressed to stakeholder groups and organisations, not only in terms of interest mediation but also of inclusion of their insight into a problem. Radical uncertainty makes 'intractable' many environmental and technological issues and brings into question traditional and new (...) approaches to policymaking. Its consequences are explored from the viewpoint of new science, deliberative democracy, and network governance. Radical uncertainty calls for a rethinking of the aims of public deliberation, and a reinterpretation of the divide between opinion- and position-oriented PTA. To look for a public opinion, understood as a shared principled view, can prove misleading, as can thinking of stakeholder participatory arrangements in the usual way. When facts and values overlap, and are deeply controversial, the only opportunity for mutual understanding may be to look for practical, 'local' answers, based on different positional insights. Moreover, radical uncertainty also affects interest determination and pursuit, and may enhance the opportunity of joint, inclusive, non-strategic issue definition and solution-devising. This vision of public deliberation is consistent with the idea of network governance. However, fragmentation can affect the effectiveness and legitimacy of participatory policies. Trying to handle fragmentation from the top, as many suggest, is unlikely to be successful. A more promising endeavour is to foster deliberative settings which, although positioned at the level of 'local' and often contingent networks and commonalities, are open to include 'Otherness' – other contexts, other problem definitions, other concerns. (shrink)

The Babylonian Talmud, compiled from the 2nd to 7th centuries C.E., is the primary source for all subsequent Jewish laws. It is not written in apodeictic style, but rather as a discursive record of (real or imagined) legal (and other) arguments crossing a wide range of technical topics. Thus, it is not a simple matter to infer general methodological principles underlying the Talmudic approach to legal reasoning. Nevertheless, in this article, we propose a general principle that we believe helps (...) to explain the variety of methods used by the Rabbis of the Talmud for resolving uncertainty in matters of Jewish Law (henceforth: Halakhah). Such uncertainty might arise either if the facts of a case are clear but the relevant law is debatable or if the facts themselves are unclear. (shrink)

One of the central arguments against redistribution through private law is its inefficiency due to the double-distortion phenomenon that accompanies it. I argue that in a subset of cases—in which there is uncertainty regarding the fairness principle that should be accepted in the realm of private law—it may be required to take into account redistributive considerations even if one generally accepts the double-distortion argument. I assert that while side-constraints may apply to direct redistribution, they do not apply to (...) the role of redistributive considerations in determining which of the fairness principles should be accepted in the realm of private law. As a consequence, some distributive patterns could be achieved only by taking into account redistributive considerations in the realm of private law. I argue that redistributive considerations may tilt the scales toward accepting the fairness principle with the lower credence of being true. (shrink)

lNTRODUCTlON ln itself the world is neither governed by a principle of order, irremediably abandoned to disorder, structured with iron determinism, ...

How might an agent's moral uncertainty affect what they ought to do? One approach posits principles independent of all first-order moral theories to provide impartial guidance to those uncertain about which moral theory is true; a popular candidate is the principle of maximizing expected choiceworthiness (MEC). Another approach focuses on what first-order moral theories themselves might say about the moral implications of moral uncertainty. This paper considers the latter question in the context of consequentialism by exploring how (...) two consequentialist strategies for dealing with non-moral uncertainty could be extended to moral uncertainty. My conclusion is that a consequentialist could plausibly adopt maximizing expected goodness as a standard of rightness, but not MEC, and that neither is likely to be part of the best consequentialist decision procedure. This result refutes the common suspicion that MEC represents a distinctively consequentialist approach to moral uncertainty. (shrink)

All logic instruments and tools in possession of, and used by researchers are generally considered as the results of bivalent logic. A common error to people interested in science is that, usually, they don’t known with certainty which things are true and which are false. But they are sure that things are true or false. No ways in the middle. The fuzzy principle asserts that this is completely a question of measure. Fuzziness is the opposite concept to bivalency, while (...) fuzzy quality means polyvalency. Fuzzy logic is able to manage uncertain knowledge and, more precisely, to manage those rules difficult to formalize. In many cases, such rules haven’t got, or cannot have, the necessary precision, required for a whole formalization. (shrink)

In this contribution in honour of Paul Busch, we criticise the claims of many expositions that the time-energy uncertainty principle allows both a violation of energy conservation and particle creation, provided that this happens for a sufficiently short time. But we agree that there are grains of truth in these claims: which we make precise and justify using perturbation theory.

Using climate policy debates as a case study, I argue that a certain response to the argument from inductive risk, the hedging defense, runs afoul of a reasonable ethical principle: the no-passing-...

This paper introduces taxonomy of clinical uncertaintes and argues that the choice of scientific method should match the underlying level of uncertainty. Clinical trial is one of these methods aiming to resolve clinical uncertainties. Whenever possible these uncertainties should be quantified. The paper further shows that the still ongoing debate about the usage of "equipoise" vs. "uncertainty principle" vs. "indifference" as an entry criterion to clinical trials actually refers to the question "whose uncertainty counts". This question (...) is intimately linked to the control of research agenda, which is not quantifiable and hence is not solvable to equal acceptability to all interested parties. The author finally shows that there is a predictable relation between [acknowledgement of] uncertainty (the moral principle) on which trials are based and the ultimate outcomes of clinical trials. That is, [acknowledgement of] uncertainty determines a pattern of success in medicine and drives clinical discoveries. (shrink)

We typically have to act under uncertainty. We can be uncertain about the relevant descriptive facts, but also about the relevant normative facts. However, the search for a theory of decision-making under normative uncertainty is doomed to failure. First, the most natural proposal for what to do given normative uncertainty faces two devastating problems. Second, the motivations for wanting a theory of what to do given descriptive uncertainty do not carry over to normative uncertainty. Descriptive (...) facts may be inaccessible even in principle, and ignorance of them excuses one from blame, but normative facts are in principle accessible, and ignorance of them arguably is no excuse. Normative facts differ from descriptive facts: normative facts affect what we ought to do no matter what, while descriptive facts affect what we ought to do only insofar as we are aware of them. (shrink)

A coherent account of the connections and contrasts between the principles of complementarity and uncertainty is developed starting from a survey of the various formalizations of these principles. The conceptual analysis is illustrated by means of a set of experimental schemes based on Mach-Zehnder interferometry. In particular, path detection via entanglement with a probe system and (quantitative) quantum erasure are exhibited to constitute instances of joint unsharp measurements of complementary pairs of physical quantities, path and interference observables. The analysis (...) uses the representation of observables as positive-operator-valued measures (POVMs). The reconciliation of complementary experimental options in the sense of simultaneous unsharp preparations and measurements is expressed in terms of uncertainty relations of different kinds. The feature of complementarity, manifest in the present examples in the mutual exclusivity of path detection and interference observation, is recovered as a limit case from the appropriate uncertainty relation. It is noted that the complementarity and uncertainty principles are neither completely logically independent nor logical consequences of one another. Since entanglement is an instance of the uncertainty of quantum properties (of compound systems), it is moot to play out uncertainty and entanglement against each other as possible mechanisms enforcing complementarity. (shrink)

How does it come about then, that great scientists such as Einstein, Schrödinger and De Broglie are nevertheless dissatisfied with the situation? Of course, all these objections are levelled not against the correctness of the formulae, but against their interpretation. [...] The lesson to be learned from what I have told of the origin of quantum mechanics is that probable refinements of mathematical methods will not suffice to produce a satisfactory theory, but that somewhere in our doctrine is hidden a (...) concept, unjustified by experience, which we must eliminate to open up the road. (Born [ 1954 ], pp. 8, 11) It is truly surprising how little difference all this makes. Most physicists use quantum mechanics every day in their working lives without needing to worry about the fundamental problem of its interpretation. (Weinberg [ 1992 ], p. 66) I endorse the view that it may be of no relevance to the acceptability of the Everett interpretation of quantum mechanics as a physical theory whether or not an informed observer can be uncertain about the outcome of a quantum measurement prior to its having occurred. However, I suggest that the very possibility of post-measurement, pre-observation uncertainty has an essential role to play in both confirmation theory and decision theory in a branching universe. This is supported by arguments which do not appeal to van Fraassen’s Reflection Principle. (shrink)

We show that the strong form of Heisenberg’s inequalities due to Robertson and Schrödinger can be formally derived using only classical considerations. This is achieved using a statistical tool known as the “minimum volume ellipsoid” together with the notion of symplectic capacity, which we view as a topological measure of uncertainty invariant under Hamiltonian dynamics. This invariant provides a right measurement tool to define what “quantum scale” is. We take the opportunity to discuss the principle of the symplectic (...) camel, which is at the origin of the definition of symplectic capacities, and which provides an interesting link between classical and quantum physics. (shrink)

A shared presumption among practice-dependent theorists is that a principle of justice is dependent on the function or aim of the practice to which it is supposed to be applied. In recent contributions to this debate, the condition of epistemic uncertainty plays a significant role for motivating and justifying a practice-dependent view. This paper analyses the role of epistemic uncertainty in justifying a practice-dependent approach. We see two kinds of epistemic uncertainty allegedly playing this justificatory role. (...) What we call ‘normative epistemic uncertainty’ emerges from dealing with the problem of value uncertainty in justifying applied principles when our higher-level principles are open-textured, that is, when their content is too vague or unclear to generate determinate prescriptions. What we call ‘descriptive epistemic uncertainty’ emerges from dealing with uncertainty about empirical facts, such as the problem of moral assurance, that is, the problem that the requirements of justice cannot go beyond arrangements that we can know with reasonable confidence that we can jointly establish and maintain. In both cases, practice-dependent theorists conclude that the condition of epistemic uncertainty justifies a practice-dependent approach, which puts certain restrictions on theorizing regulative principles and has wide-ranging practical implications for the scope of justice. Our claim in this paper is that neither kind of epistemic uncertainty justifies a practice-dependent approach. (shrink)

This paper describes a cubic water tank equipped with a movable partition receiving various amounts of liquid used to represent joint probability distributions. This device is applied to the investigation of deductive inferences under uncertainty. The analogy is exploited to determine by qualitative reasoning the limits in probability of the conclusion of twenty basic deductive arguments (such as Modus Ponens, And-introduction, Contraposition, etc.) often used as benchmark problems by the various theoretical approaches to reasoning under uncertainty. The probability (...) bounds imposed by the premises on the conclusion are derived on the basis of a few trivial principles such as "a part of the tank cannot contain more liquid than its capacity allows", or "if a part is empty, the other part contains all the liquid". This stems from the equivalence between the physical constraints imposed by the capacity of the tank and its subdivisions on the volumes of liquid, and the axioms and rules of probability. The device materializes de Finetti's coherence approach to probability. It also suggests a physical counterpart of Dutch book arguments to assess individuals' rationality in probability judgments in the sense that individuals whose degrees of belief in a conclusion are out of the bounds of coherence intervals would commit themselves to executing physically impossible tasks. (shrink)

Something is not working in ethics consultation: in certain situations, relationships within families and with careproviders and surrogates have become so emotionally charged and destabilized that attention is dominated by conflict and misunderstanding, foreshadowing a loss of dignity and hope. In a compelling, urgent article, informed by events in the Schiavo case, with examples from the literature on theory, practice, and outcomes, Caplan and Bergman address this situation: redirecting our attention to what they see as “a lack of effective mechanisms” (...) for dealing with a “painful class of disputes in which families disagree with one another, or with doctors, about the care of those who cannot communicate.”1 It is no small matter that many of these cases are situated in the immediate, intense environment of end-of-life decision making. -/- How might we understand these encounters, and their limits? What can we hope? Following the tack of Caplan and Bergman, I will extend the discussion of the complex relationships between patients, families, surrogates, and physicians, and “hope for consensual resolution,” offering a somewhat different account of what is lacking. While Caplan and Bergman foreground an apparent irreconcilability of appeals to competing biomedical principles as what is lacking, I will suggest that a “salient characteristic” among participants, what Caplan and Bergman identify as a common concern for the patient’s best interests, may be far less stable and more complex, and thereby less directive, than first imagined. When Caplan and Bergman sketch their expectations for mediation and for mediators, they are right in noting that abstract principles “articulated as dispositive by designated ‘experts’ fail to capture, and arguably respect, the unique and complex nature of each such individual decision-making process,” and that “patients and families are at the extreme end of a power imbalance.” It is less clear that their descriptions — or their hope for mediation — capture this enormous challenge. (shrink)

This article argues that a manuscript dated to the summer of 1927 by the editors of Bohr’s Collected Works was written a year earlier. The re-dating allows the conclusion that Bohr was well on his way to complementarity before his famous fight with Heisenberg over the uncertainty principle early in 1927. The literature that assumes that complementarity was Bohr’s response to Heisenberg is therefore in error. The editors of the Collected Works assigned the document the date of 1927 (...) because it refers to electron-diffraction experiments by Davisson and Germer, which were published in 1927. But as the article points out, Bohr and other leading physicists such as Max Born met Davisson in Britain in 1926 and discussed the experiments with him then. That demolished the basis of the earlier dating. Finally, the article argues that when the document takes its place between the Bohr–Kramers–Slater theory (1924) and the 1927 drafts of complementarity, everything falls neatly into place. (shrink)

Intuitive predictions and judgements under uncertainty are often mediated by judgemental heuristics that sometimes lead to biases. Our micro-developmental study suggests that a presumption of rationality is justified for adult subjects, in so far as their systematic judgemental biases appear to be due to a specific executive-inhibition failure in working memory, and not necessarily to a lack of understanding of the fundamental principles of probability. This hypothesis was tested using an experimental procedure in which 60 adult subjects were trained (...) to inhibit the classical conjunction bias on a frequency judgement task derived from Tversky and Kahneman's work. Pre- and post-test performance was assessed via a probability judgement task. The data indicated a training effect, suggesting that subjects traditionally labelled as "irrational" with respect to the classical rules of inductive reasoning are in fact "inefficient inhibitors". These findings are discussed in terms of a polymorphous view of rationality. (shrink)