I show that the Lottery Paradox is just a version of the Sorites, and argue that this should modify our way of looking at the Paradox itself. In particular, I focus on what I call “the Cut-off Point Problem” and contend that this problem, well known by Sorites scholars, ought to play a key role in the debate on Kyburg’s puzzle. Very briefly, I show that, in the Lottery Paradox, the premises “ticket n°1 will lose”, “ticket n°2 will lose”… (...) “ticket n°1000 will lose” are equivalent to soritical premises of the form “~(the winning ticket is in {…, (tn)}) ⊃ ~(the winning ticket is in {…, tn, (tn + 1)})” (where “⊃” is the material conditional, “~” is the negation symbol, “tn” and “tn + 1” are “ticket n°n” and “ticket n°n + 1” respectively, and “{}” identify the elements of the lottery tickets’ set. The brackets in “(tn)” and “(tn + 1)” are meant to point out that in the antecedent of the conditional we do not always have a “tn” (and, as a result, a “tn + 1” in the consequent): consider the conditional “~(the winning ticket is in {}) ⊃ ~(the winning ticket is in {t1})”). As a result, failing to believe, for some ticket, that it will lose comes down to introducing a cut-off point in a chain of soritical premises. In this paper I explore the consequences of the different ways of blocking the Lottery Paradox with respect to the Cut-off Point Problem. A heap variant of the Lottery Paradox is especially relevant for evaluating the different solutions. One important result is that the most popular way out of the puzzle, i.e., denying the Lockean Thesis, becomes less attractive. Moreover, I show that, along with the debate on whether rational belief is closed under classical logic, the debate on the validity of modus ponens should play an important role in discussions on the Lottery Paradox. -/- . (shrink)

In ‘Towards a Solution to the Sorites Paradox’, Graham Priest gives us a new account of the sorites based on fuzzy logic. The novelty lies in the suggestion that truth-value assignments should themselves be treated as fuzzy objects, i.e., objects about which we can make fuzzy identity statements. I argue that Priest’s solution does not have the explanatory force that Priest advocates. That is, it does not explain why we find the existence of a cut-off point counter-intuitive. I also (...) argue that this sort of explanation calls for a general theory that goes beyond the special case of linguistic vagueness, for the phenomenon is at bottom not linguistic. (shrink)

The rising demographic of older adults worldwide has led to an increase in dementia cases. In order to ensure the proper allocation of care and resources to this clinical group, it is necessary to correctly distinguish between simulated versus bona-fide cognitive deficits typical of dementia. Performance Validity Tests are specifically designed to assess a lack of effort and the possible simulation of cognitive impairment. Previous research demonstrates that PVTs may be sensitive to dementia, thus inaccurately classifying real memory impairment as (...) simulation. Here, we analyzed the sensitivity of PVTs in discriminating between dementia and simulation using receiver operating characteristic curve analyses. Further, we examined the potential need for adjusting cut-off scores for three stand-alone and one embedded PVT for Portuguese older adults with dementia. The results showed that all measures, except for the Coin in Hand— Extended version, were sensitive to one or more sociodemographic and/or cognitive variables, and it was necessary to adjust cut-off points for all measures. Additionally, the Rey-15 Item Memory Test did not demonstrate sufficient discriminating capacity for dementia. These results present important implications for clinical practice and the daily life of patients, as the use of incorrect cut-off points could impede patients from getting the resources they need. (shrink)

Psychopathology is the study of the signs and symptoms of psychiatric disorders - delusions, hallucinations, phobias, depression, for example. This book gives an account of the terms currently in use and attempts an in-depth analysis of the nature of each. The matter is examined both from a philosophical perspective and from the point of view of what is known about the function of the hemispheres of the brain.

In West Germany, there is a good deal of disagreement among leading political groups, economic decision makers and scientific experts concerning both the future of the labor market and the role of labor in society. This disagreement bears on all of the three relevant points: the prognosis of the likely future development, the policy most suited to this development, and the criteria and objectives that determine whether, in fact, a development could be judged as positive or indeed desirable. In this (...) discussion, the first of these three points is the least controversial. Quite a number of contemporary publications in Germany feature the famous graph, developed in 1982 by the Federal Labor Agency's Institute for Labor Market and Vocational Research, which depicts labor market trends for the years 1965 to 2000. (shrink)

What is knowledge? What makes me, me? Do we have free will? People have been asking such fundamental questions about the nature of reality for centuries, but how can they help us make sense of our existence in a 21st-century world of social media, cyber wars, cloning, artificial intelligence and virtual reality? Short Cuts: Philosophy provides the map you need to travel beyond traditional foundations and explore a diverse array of deep thinkers. Soul-searching questions prompt 'short cut' answers written by (...) experts in their field, with each one the setting-off point for instructions that plot a path through the philosophical landscape. With 'one-stop' graphics visualizing a memorable theory or idea for each concept, and 'route map' glossaries explaining key words and their connections, Short Cuts: Philosophy will help you wrestle with the meaning of ancient and modern philosophical thought. (shrink)

Despite the many successes of the relativistic quantum theory developed by Horwitz et al., certain difficulties persist in the associated covariant classical mechanics. In this paper, we explore these difficulties through an examination of the classical. Coulomb problem in the framework of off-shell electrodynamics. As the local gauge theory of a covariant quantum mechanics with evolution paratmeter τ, off-shell electrodynamics constitutes a dynamical theory of ppacetime events, interacting through five τ-dependent pre-Maxwell potentials. We present a straightforward solution of the classical (...) equations of motion, for a test event traversing the field induced by a “fixed” event (an event moving uniformly along the time axis at a fixed point in space). This solution is seen to be unsatisfactory, and reveals the essential difficulties in the formalism at the classical levels. We then offer a new model of the particle current—as a certain distribution of the event currents on the worldline—which eliminates these difficulties and permits comparison of classisical off-shell electrodynamics with the standard Maxwell theory. In this model, the “fixed” event induces a Yukawa-type potential, permitting a semiclassical identification of the pre-Maxwell time scale λ with the inverse mass of the intervening photon. Numerical solutions to the equations of motion are compared with the standard Maxwell solutions, and are seen to coincide when λ≳10−6 seconds, providing an initial estimate of this parameter. It is also demonstrated that the proposed model provides a natural interpretation for the photon mass cut-off required for the renormalizability of the off-shell quantum electrodynamics. (shrink)

This piece is a response to Marilyn Strathern's article, “Binary License,” in the Common Knowledge symposium on “comparative relativism.” Arguing that, across noncoherent practices, there is room for different natures, the essay suggests that modes of relating (the briefly invoked example given is of divergent counting practices) do not need a shared conceptual apparatus in order to be combined. What is held in the juxtaposition of acts and practices seems to be the sense in which acts are not affected by (...) how they are described. The main example given is of surgery, and the emphasis placed on how splitting open part of patient's body is never a matter of a point of view. But to know exactly what is going on in the operating theater, we might wish to ask how this act speaks to the act of intellectual bifurcation, splitting open what up to then had been a seamless argument. To know exactly what is going on in the operating theater, we might also wish to ask how this act speaks to persons cutting themselves off from one another. (shrink)

At the beginning of Book 5 Plato catalogues the ways in which men ‘dishonour’ their souls, and at 728 ab sums up by saying that any man who does not practise what the lawgiver describes as noble and good is treating his soul dishonourably. He goes on to say that hardly anyone takes account of, which is to cut oneself off from good men and be completely assimilated to the bad. We the n read.

At the beginning of Book 5 Plato catalogues the ways in which men ‘dishonour’ ([Greek text] 727 c 3) their souls, and at 728 ab sums up by saying that any man who does not practise what the lawgiver describes as noble and good is treating his soul dishonourably. He goes on to say that hardly anyone takes account of [Greek text] (728 b 2), which is to cut oneself off from good men and be completely assimilated to the bad (...) [Greek text]. We the n read. (shrink)

At the beginning of Book 5 Plato catalogues the ways in which men ‘dishonour’ their souls, and at 728 ab sums up by saying that any man who does not practise what the lawgiver describes as noble and good is treating his soul dishonourably. He goes on to say that hardly anyone takes account of, which is to cut oneself off from good men and be completely assimilated to the bad. We the n read.

Background and aims: Recent investigations have highlighted the value of neuropsychological testing for the assessment and screening of Alcohol-Related Brain Damage. The aim of the present study was to evaluate the suitability of the Addenbrooke’s Cognitive Examination and the Repeatable Battery for the Assessment of Neuropsychological Status for this purpose. Methods: Comparing 28 participants with ARBD and 30 alcohol-dependent participants without ARBD we calculated Area Under the Curve statistics, sensitivity and specificity values, base-rate adjusted predictive values, and likelihood ratios for (...) both tests. Results: High levels of screening accuracy were found for the total scores of both the ACE-III and RBANS at multiple cut-off points. Removing participants with a history of polysubstance from the samples improved the diagnostic capabilities of the RBANS substantially, while only minor improvements to the ACE-III’s accuracy were observed. Conclusions: Overall, both the ACE-III and RBANS are suitable tools for ARBD screening within an alcohol-dependent population, though the RBANS is the superior of the two. Clinicians using these tools for ARBD screening should be cautious of false-positive outcomes and should therefore combine them with other assessment methods and more detailed neuropsychological testing before reaching diagnostic decisions. (shrink)

This paper explores the link between number marking and(in)definiteness in nominals and their interpretation. Differencesbetween bare singulars and plurals in languages without determinersare explained by treating bare nominals as kind terms. Differencesarise, it is argued, because singular and plural kinds relatedifferently to their instantiations. In languages with determiners,singular kinds typically occur with the definite determiner, butplural/mass kinds can be bare in some languages and definite inothers. An account of singular kinds in terms of taxonomic readingsis proposed, with number marking playing (...) a crucial role inexplaining the obligatory presence of the determiner. The variationbetween languages with respect to plural/mass kinds is explained bypositing a universal scale of definiteness, with individual languageschoosing different cut-off points for lexicalization of the definitedeterminer. The possibility of further cross-linguistic variation isalso considered. (shrink)

According to the naive theory of vagueness, the vagueness of an expression consists in the existence of both positive and negative cases of application of the expression and in the non- existence of a sharp cut-off point between them. The sorites paradox shows the naive theory to be inconsistent in most logics proposed for a vague language. The paper explores the prospects of saving the naive theory by revising the logic in a novel way, placing principled restrictions on the (...) transitivity of the consequence relation. A lattice-theoretical framework for a whole family of “tolerant logics” is proposed and developed. Particular care is devoted to the relation between the salient features of the formal apparatus and the informal logical and semantic notions they are supposed to model. A suitable non-transitive counterpart to classical logic is defined. Some of its properties are studied, and it is eventually shown how an appropriate regimentation of the naive theory of vagueness is consistent in such a logic. (shrink)

According to some collectivists, purposive groups that lack decision-making procedures such as riot mobs, friends walking together, or the pro-life lobby can be morally responsible and have moral duties. I focus on plural subject- and we-mode-collectivism. I argue that purposive groups do not qualify as duty-bearers even if they qualify as agents on either view. To qualify as a duty-bearer, an agent must be morally competent. I develop the Update Argument. An agent is morally competent only if the agent has (...) sufficient positive and negative control over updating their goal-seeking states. Positive control involves the general ability to update one’s goal-seeking states, whereas negative control involves the absence of other agents with the capacity to arbitrarily interfere with updating one’s goal-seeking states. I argue that even if purposive groups qualify as plural subjects or we-mode group agents, these groups necessarily lack negative control over updating their goal-seeking states. This creates a cut-off point for groups as duty-bearers: Organized groups may qualify as duty-bearers, whereas purposive groups cannot qualify as duty-bearers. (shrink)

A number of arguments purport to show that vague properties determine sharp boundaries at higher orders. That is, although we may countenance vagueness concerning the location of boundaries for vague predicates, every predicate can instead be associated with precise knowable cut-off points deriving from precision in their higher order boundaries. I argue that this conclusion is indeed paradoxical, and identify the assumption responsible for the paradox as the Brouwerian principle B for vagueness: that if p then it's determinate that it's (...) not determinate that not p. Other paradoxes which do not appear to turn on B turn instead on some subtle issues concerning the relation between assertion, belief and higher order vagueness. In this paper a theory of assertion, knowledge and logic is outlined which allows one to avoid any kind of higher order precision. A class of realistic models containing counterexamples to B and a number of weakenings of B are introduced and its logic is shown to support vagueness at every order. (shrink)

The study area was a small lowland river valley (the Łęg river) located in the south-east of Poland. The object of investigation was the macrophytes of 10 river lakes with corresponding active river channel stretches of the same length as the cut-offs. The aim was to check the difference in species diversity between cut-off and active river channels. The second aim was to test the following hypothesis: vegetation of river lake has been shaped under the influence of contiguous river stretch (...) which has left a measurable mark in species abundance and composition. To test this, we checked whether a cut-off channel’s flora is more similar to flora of the contiguous river stretch, than to flora of a farther river stretch. During the course of the study it was found that the average species richness was approximately two times higher in the cut-off channels than in the river stretches. The number of the species exclusive for the river lakes was nine times higher in comparison with the river’s exclusives (not found in the cut-offs). The Shannon diversity index definitely spoke in favor of the river lakes. These results clearly show the significance of river lakes in maintaining biodiversity of aquatic ecosystems in a small river valley. We did not confirm our hypothesis concerning floristic relation between an active channel and its cut-offs. The floristic similarity between a given cut-off channel and the contiguous active river channel stretch is not stronger than the similarity between this lake and more distant river stretches. The cause of such a state of affairs may be high natural dynamics of investigated habitats and anthropogenic transformation of the river valley. (shrink)

Public health emergencies such as pandemics can put health systems in a position where they need to ration medical equipment and interventions because the resources available are not sufficient to meet demand. In public health management, the fair allocation of resources is a permanent and cross-sector issue since resources, and especially economic resources, are not infinite. During the COVID-19 pandemic resources need to be allocated under conditions of extreme urgency and uncertainty. One very problematic aspect has concerned intensive care medicine (...) and age discrimination has been among the most hotly discussed issues, as age has been touted as a probable criterion for selection. In this paper we analyse some documents originating from scientific societies and medical associations, mainly related to EU sphere and available in English, French, Spanish and Italian, concerning the criteria for admission to the intensive care units. We highlights how, in most of these documents, it is explicitly stated that “age itself” is not a criterion for patient selection. Our conclusion is that these criteria should be defined in advance of a crisis situation and be grounded in clinical indicators. Establishing “cut-off” policies with regard to criteria such as age or chronic disability is definitely an unjustifiable form of discrimination even in the context of a public health emergency. (shrink)

Vague predicates, on a paraconsistent account, admit overdetermined borderline cases. I take up a new line on the paraconsistent approach, to show that there is a close structural relationship between the breakdown of soritical progressions, and contradiction. Accordingly, a formal picture drawn from an appropriate logic shows that any cut-off point of a vague predicate is unidentifiable, in a precise sense. A paraconsistent approach predicts and explains many of the most counterintuitive aspects of vagueness, in terms of a more (...) fundamental inconsistency. (shrink)

This paper considers a generalisation of the sorites paradox, in which only topological notions are employed. We argue that by increasing the level of abstraction in this way, we see the sorites paradox in a new, more revealing light—a light that forces attention on cut-off points of vague predicates. The generalised sorites paradox presented here also gives rise to a new, more tractable definition of vagueness.

Research has demonstrated that policing is a stressful occupation and has a negative impact on police officers’ mental and physical health, performance, and interactions with citizens. Mental health at the workplace has become a concern due to the costs of depression, anxiety, burnout, and even suicide, which is high among police officers.To ameliorate occupational health, it is crucial therefore to identify stress and burnout levels on a regular basis. However, the instruments frequently used to measure stress have not valorized the (...) specificity of policing tasks. This study aims: i) conducting a literature review, to identify questionnaires used to assess occupational stress and burnout among police officers; ii) to analyze the psychometric characteristics of a Portuguese version of Operational Police Stress Questionnaire (PSQ-Op); and, using the PSQ-op and other questionnaires, iii) to identify operational stress, burnout, and distress levels among Portuguese police officers. The literature review identified 108 studies, which use a multiplicity of questionnaires to measure burnout or occupational stress among police officers, but few studies use specific police stress questionnaires. Sample sizes were mostly below 500 participants and studies were mainly developed in the last decade in the USA and Brazil, but also in another 24 countries, showing the extent of the interest in this topic. This study applied to 2057 police officers from National Portuguese Police, a force policing urban centers, the PSQ-Op, as well the Spanish Burnout Inventory and the Kessler Psychological Distress Scale.The results show that the psychometric properties of the Portuguese version of PSQ-Op are adequate. Factorial analysis revealed two dimensions defined as social and work issues, which were associated with measures of distress and burnout.Fit indices suggested a second-order solution called operational police stress. Overall, and considering the scale range of each questionnaire, the results showed moderate values of operational stress, distress, and burnout. However, considering their cut-off points, 85% of the sample presented high operational stress levels, 11% critical values for burnout, and 28% high distress levels, with 55% of the sample at risk of psychological disorder. These results reinforce the need to prevent stress and to invest in police officers’ occupational health. (shrink)

In this paper I offer a counterexample to the so called vagueness argument against restricted composition. This will be done in the lines of a recent suggestion by Trenton Merricks, namely by challenging the claim that there cannot be a sharp cut-off point in a composition sequence. It will be suggested that causal powers which emerge when composition occurs can serve as an indicator of such sharp cut-off points. The main example will be the case of a heap. It (...) seems that heaps might provide a very plausible counterexample to the vagueness argument if we accept the idea that four grains of sand is the least number required to compose a heap—the case has been supported by W. D. Hart. My purpose here is not to put forward a new theory of composition, I only wish to refute the vagueness argument and point out that we should be wary of arguments of its form. (shrink)

Timothy Williamson’s potentially most important contribution to epistemicism about vagueness lies in his arguments for the basic epistemicist claim that the alleged cut-off points of vague predicates are not knowable. His arguments for this are based on so-called ‘margin for error principles’. This paper argues that these principles fail to provide a good argument for the basic claim. Williamson has offered at least two kinds of margin for error principles applicable to vague predicates. A certain fallacy of equivocation seems to (...) underlie his justification for both kinds of principles. Besides, the margin for error principles of the first kind can be used in the derivation of unacceptable consequences, while the margin for error principles of the second kind can be shown to be compatible with the falsity of epistemicism, under a number of assumptions acceptable to the epistemicist. (shrink)

The paper challenges Williamson’s safety based explanation for why we cannot know the cut-off point of vague expressions. We assume throughout (most of) the paper that Williamson is correct in saying that vague expressions have sharp cut-off points, but we argue that Williamson’s explanation for why we do not and cannot know these cut-off points is unsatisfactory. -/- In sect 2 we present Williamson's position in some detail. In particular, we note that Williamson's explanation relies on taking a particular (...) safety principle ('Meta-linguistic belief safety' or 'MBS') as a necessary condition on knowledge. In section 3, we show that even if MBS were a necessary condition on knowledge, that would not be sufficient to show that we cannot know the cut-off points of vague expressions. In section 4, we present our main case against Williamson's explanation: we argue that MBS is not a necessary condition on knowledge, by presenting a series of cases where one's belief violates MBS but nevertheless constitutes knowledge. In section 5, we present and respond to an objection to our view. And in section 6, we briefly discuss the possible directions a theory of vagueness can take, if our objection to Williamson's theory is taken on board. (shrink)

Several types of definitions and means of assessing welfare are discussed in an attempt to reconcile differences which may be counter-productive in addressing welfare issues. Various groups should use similar terminology and it is suggested that well-being be used in the context of the current state of the animal, while welfare refer to a more general concept including past, present and future implications for the animal's well-being. Legal, public and technical definitions of welfare serve different purposes and will necessarily differ. (...) All of these definitions are interdependent and are affected by, and affect, each other. It is suggested that all definitions should attempt to reflect the animals' perspective on their own welfare. Although the ideal means of assessing welfare may lie in determining animals' mental experiences, our ability to do this is limited at this time. A more practical approach is to assess several behavioural, physiological and pathological variables. Reliance on a specific variable or a "cut-off" point may be appropriate in a legal definition of welfare, but should be avoided in scientific studies. The study of animal welfare should not focus only on assessing well-being or the effects of poor welfare, but should also determine behavioural, physiological and pathological factors which predispose animals to environmental stressors. Only then can we focus on developing improved management systems rather than eliminating poor ones. (shrink)

BackgroundHealth care professionals face a number of problems during crises, such as the COVID-19. Studies addressed the prevalence of moral injury among healthcare professionals during the COVID-19 outbreak. Lack of a valid standard of moral injury among health care professionals is one of the factors that has made it difficult to identify and treat this complication. This study aimed to evaluate the psychometric properties of the Moral Injury Symptoms Scale-Health Care Professionals among health care professionals in Iran.MethodsThis study was conducted (...) to evaluate the validity and reliability of the MISS-HP. The sample included 455 healthcare professionals working in four teaching hospitals in Kerman, who were in direct contact with patients. In this study, face validity, content validity, construct validity, and internal reliability of the MISS-HP were evaluated. Demographic information questionnaire, the Moral Injury Symptoms Scale-HealthCare Professionals, General Health Questionnaire, and Impact of Event Scale were administered to study participants.ResultsThe MISS-HP was evaluated using translation-back translation technique. The content validity index of the items and the scale were 0.9 and 0.99, respectively. Exploratory factor analysis showed a three-factor structure in the MISS-HP that explained 57.49% of the variance. Confirmatory factor analysis indices were acceptable. The cut-off point of the questionnaire was 36.5. There was a positive and moderate correlation between the Persian version of MISS-HP, GHQ, and IES-R. The Cronbach’s alpha coefficient of the Persian version of MISS-HP was 0.70.ConclusionThis study found that the MISS-HP is a concise, comprehensive, valid and reliable scale for assessing moral injury among health care professionals in clinical or research settings. This scale will be helpful for managers and researchers to identify and plan health policies and improve the psychological state of health care professionals. (shrink)

It is commonly claimed that rule consequentialism (utilitarianism) collapses into act consequentialism, because sometimes there are benefits from breaking the rules. I suggest this argument is less powerful than has been believed. The argument requires a commitment to a very particular (usually implicit) account of feasibility and constraints. It requires the presupposition that thinking of rules as the relevant constraint is incorrect. Supposedly we should look at a smaller unit of choice—the single act—as the relevant choice variable. But once we (...) see feasibility as a matter of degree, there is no obvious cut-off point for how broadly we should think about the constraints on our choices. Treating “a bundle of choices” as a relevant free variable is no less defensible than treating “a single act” as the relevant free variable. Rule utilitarianism, rule consequentialism, and other rules-based approaches are stronger than their current reputation. (shrink)

ExtractDuring the second half of the twentieth century an attention of historians of mathematics shifted to mathematics of the Late Antiquity and its subsequent development by mathematicians of the Arabic world. Many critical editions of works of mathematicians of the Hellenistic era have made their appearance, giving rise to a new, more detailed historical picture. Among these are the critical editions of the works of Diophantus, Apollonius, Archimedes, Pappus, Diocles, and others.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.The Readings of Apollonius' On the Cutting off of a RatioVolume 22, Issue 1Ioannis M. Vandoulakis DOI: https://doi.org/10.1017/S0957423911000130Your 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. The Readings of Apollonius' On the Cutting off of a RatioVolume 22, Issue 1Ioannis M. Vandoulakis DOI: https://doi.org/10.1017/S0957423911000130Available 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. The Readings of Apollonius' On the Cutting off of a RatioVolume 22, Issue 1Ioannis M. Vandoulakis DOI: https://doi.org/10.1017/S0957423911000130Available 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)

It is demonstrated that in quantized general relativity one is led to Jordan-Fock type uncertainty relations implying the occurrence of cut-off lengths. We argue that these lengths (i) represent limitations on the measurability of quantum effects of general relativity and (ii) provide a cut-off length of quantum divergences.

Value capture occurs when an agent’s values are rich and subtle; they enter a social environment that presents simplified — typically quantified — versions of those values; and those simplified articulations come to dominate their practical reasoning. Examples include becoming motivated by FitBit’s step counts, Twitter Likes and Re-tweets, citation rates, ranked lists of best schools, and Grade Point Averages. We are vulnerable to value capture because of the competitive advantage that such crisp and clear expressions of value have (...) in our private reasoning and our public justification. There is, however, a price. In value capture, we take a central component of our autonomy — our ongoing deliberation over the exact articulation of our values — and we outsource it. And the metrics to which we outsource usually engineered for the interests of some external force, like a large-scale institution’s interest in cross-contextual comprehensibility and quick aggregability. That outsourcing cuts off one of the key benefits to personal deliberation. In value capture, we no longer adjust our values and their articulations in light of own rich experience of the world. Our values should often be carefully tailored to our particular selves or our small-scale communities, but in value capture, we buy our values off the rack. In some cases – like decreasing CO2 emissions – the costs of non-tailored values are outweighed by the benefit of precise collective coordination. In other cases, like in our aesthetic lives, they are not. This suggests that we should want different values suited to different scales. We should want value federalism. Some values are perhaps best pursued at the largest-scale level, others at smaller scales. The problem occurs when we exhibit an excess preference for the largest-scale values – when we consistently let the universal metrics swamp our quieter interests. (shrink)

John Rawls argued in The Law of Peoples that we should reject any principle of international distributive justice, whether in ideal theory or nonideal theory. Instead, he advocated a duty of assistance on the part of well‐ordered societies toward burdened societies. I argue that Rawls is correct that we should endorse a principle with a target and cut‐off point rather than a principle of international distributive justice. But the target and cut‐off point he favors is too (...) undemanding, because it can be met by assisting a burdened society to become a decent people. Instead, only a society that respects the right to an adequate standard of living, and not simply a right to subsistence, can be an acceptable target. Rawls is prevented from drawing this conclusion by a failure to disentangle issues of intervention and assistance, a failure bound up with his flawed, intervention‐driven account of human rights in defining a decent people. (shrink)

To examine the ethical issues involved in governmental decisions with potential health risks, we review the history of the decision to raise the interurban speed limit in Israel in light of its impact on road death and injury. In 1993, the Israeli Ministry of Transportation initiated an “experiment” to raise the interurban speed limit from 90 to 100 kph. The “experiment” did not include a protocol and did not specify cut-off points for early termination in the case of adverse results. (...) After the raise in the speed limit, the death toll on interurban roads rose as a result of a sudden increase in speeds and case fatality rates. The committee's decision is a case study in unfettered human experimentation and public health risks when the setting is non-medical and lacks a defined ethical framework. The case study states the case for extending Helsinki type safeguards to experimentation in non-medical settings. (shrink)

Children and young people under 18 years old should no longer be regarded as incompetent to give or withhold consent in decisions involving their health care, Recent research suggests a functional test of cognitive and emotional maturity, rather than a strict age cut-off point. However, it is often difficult to implement these recommendations in practice, not least because the law is, if anything, increasingly 'hard-line' about children's autonomy.

It is uncontroversial that, on any run through a Sorites series, a subject, at some point, switches from an ‘F’ verdict on one exhibit to a non-‘F’ verdict on the next. (Where this ‘cut-off’ point occurs tend to differ from trial to trial.) It is a fallacy to infer that there must be a cut-off point simpliciter between F items and non-F items. The transition is from firm ground to swamp. In the Sorites reasoning, some conditionals of (...) the form ‘If Item n is F, then Item n + 1 is F’ are not false but nonsensical. This solution respects boundarylessness. (shrink)

In the literature on global justice, there has been a lengthy debate about what the world’s rich owe to the world’s poor. Some have argued that rich individuals have positive duties of beneficence to help the poor, while others have argued that rich individuals only have negative duties not to harm them. A common objection to the former view is that once it is accepted that positive duties exist, fulfilling these duties will be overdemanding since rich individuals can almost always (...) help a little more. Some have tried to overcome this overdemandingness objection by setting cut-off points for how demanding morality is. In this article, we aim to show that it is problematic to be committed to the following propositions: (1) Positive duties to aid exist; (2) The overdemandingness objection is a serious challenge for anyone who accepts that positive duties to aid exist; and (3) Setting cut-off points for how demanding morality is constitutes a plausible way to overcome the overdemandingness objection. Showing that a commitment to (1), (2) and (3) is problematic is of interest given that several influential theorists are committed to this set of views. This set of views is simply a bad theoretical cocktail. (shrink)

In this paper I explore a neglected discussion of vagueness put forward by Wittgenstein in his Philosophical Grammar (1932–34). In this work, unlike Philosophical Investigations (1953), Wittgenstein not only discusses the venerable Sorites paradox but provides a novel conception of vagueness using an analogy with coin tossing and converging intervals. As he sees it, the problematic picture of vagueness arises because we conflate aspects of the functioning of vague concepts with those of non-vague ones. Thus, while we accept that vague (...) concepts have no sharp cut-off points (are boundaryless), we nevertheless retain the idea that we can progress towards the penumbra the way we progress towards the cut-off points of non-vague concepts. As a potential remedy, Wittgenstein's analogy with coin tossing and converging intervals replaces this picture and provides an understanding of the functioning of vague concepts in which no notion of a progression arises. (shrink)