Firearm violence is a major public health problem in the United States. In 2000, firearms were used in 10,801 homicides – two-thirds of all homicides in the U.S. – and 533,470 non-fatal criminal victimizations including rapes, robberies, and assaults. The social costs of gun violence in the United States are also staggering, and have been estimated to be on the order of $100 billion per year.Illegal gun carrying, usually concealed, in public places is an important risk factor for firearm-related crime. (...) In the 1980s and 1990s, police departments across the country began to develop and implement strategies to address illegal weapons carrying. Often these strategies have involved aggressive efforts to identify and physically search individuals suspected of illegally carrying a firearm. (shrink)

Firearm violence is a major public health problem in the United States. In 2000, firearms were used in 10,801 homicides – two-thirds of all homicides in the U.S. – and 533,470 non-fatal criminal victimizations including rapes, robberies, and assaults. The social costs of gun violence in the United States are also staggering, and have been estimated to be on the order of $100 billion per year.Illegal gun carrying, usually concealed, in public places is an important risk factor for firearm-related crime. (...) In the 1980s and 1990s, police departments across the country began to develop and implement strategies to address illegal weapons carrying. Often these strategies have involved aggressive efforts to identify and physically search individuals suspected of illegally carrying a firearm. (shrink)

ABSTRACT:While the literature on psychedelic medicine emphasizes the importance of set and setting alongside the quality of subjective drug effects for therapeutic efficacy, few scholars have explored the therapeutic frameworks that are used alongside psychedelics in the lab or in the clinic. Based on a narrative analysis of the treatment manual and post-session experience reports from a pilot study of psilocybin-assisted treatment for tobacco smoking cessation, this article examines how therapeutic frameworks interact with the psychedelic substance in ways that can (...) rapidly reshape participants' identity and sense of self. We identified multiple domains relating to identity shift that appear to serve as smoking cessation mechanisms during psilocybin sessions, each of which had an identifiable presence in the manualized treatment. As psychedelic medicine becomes mainstream, consensual and evidence-based approaches to psychedelic-assisted identity shift that respect patient autonomy and encourage empowerment should become areas of focus in the emergent field of psychedelic bioethics. (shrink)

Blair articulates a concept of argument that suggests, as he puts it, that argument is a normative concept (Blair, Informal Logic 24:137–151, 2004, p. 190). Put roughly, the idea is that a collection of propositions doesn’t constitute an argument unless some taken together constitute a reason for the remaining proposition and thereby support it enough to provide at least prima facie justification for it (Blair, in: Blair, Johnson, Hansen, Tindale (eds) Informal Logic at 25, Proceedings of the 25th anniversary (...) conference, Ontario Society for the Study of Argumentation, 2003, p.173). My primary task in this paper is to advance an understanding of the illative unit of argument and the reasons associated with it that provides an intuition pump for a normative concept of argument. My aim is to advance a positive consideration in favor of a normative concept of argument that motivates its further development. I take the normative concept of argument I defend here to be in the same ballpark as the one Blair characterizes. (shrink)

Cognitive Science, Volume 46, Issue 6, June 2022.

We estimate that 208,000 deep brain stimulation (DBS) devices have been implanted to address neurological and neuropsychiatric disorders worldwide. DBS Think Tank presenters pooled data and determined that DBS expanded in its scope and has been applied to multiple brain disorders in an effort to modulate neural circuitry. The DBS Think Tank was founded in 2012 providing a space where clinicians, engineers, researchers from industry and academia discuss current and emerging DBS technologies and logistical and ethical issues facing the field. (...) The emphasis is on cutting edge research and collaboration aimed to advance the DBS field. The Eighth Annual DBS Think Tank was held virtually on September 1 and 2, 2020 (Zoom Video Communications) due to restrictions related to the COVID-19 pandemic. The meeting focused on advances in: (1) optogenetics as a tool for comprehending neurobiology of diseases and on optogenetically-inspired DBS, (2) cutting edge of emerging DBS technologies, (3) ethical issues affecting DBS research and access to care, (4) neuromodulatory approaches for depression, (5) advancing novel hardware, software and imaging methodologies, (6) use of neurophysiological signals in adaptive neurostimulation, and (7) use of more advanced technologies to improve DBS clinical outcomes. There were 178 attendees who participated in a DBS Think Tank survey, which revealed the expansion of DBS into several indications such as obesity, post-traumatic stress disorder, addiction and Alzheimer’s disease. This proceedings summarizes the advances discussed at the Eighth Annual DBS Think Tank. (shrink)

In this issue of the American Journal of Bioethics, manuscripts focus on the obligations of clinicians and researchers in pragmatic clinical trials (Garland, Morain, and Sugarman 2023; Morain and L...

Recent work has defended “Euclidean” theories of set size, in which Cantor’s Principle (two sets have equally many elements if and only if there is a one-to-one correspondence between them) is abandoned in favor of the Part-Whole Principle (if A is a proper subset of B then A is smaller than B). It has also been suggested that Gödel’s argument for the unique correctness of Cantor’s Principle is inadequate. Here we see from simple examples, not that Euclidean theories of set (...) size are wrong, but that they must be either very weak and narrow or largely arbitrary and misleading. (shrink)

This paper examines one of the historical antecedents of Big Data, the social physics movement. Its origins are in the scientific revolution of the 17th century in Western Europe. But it is not named as such until the middle of the 19th century, and not formally institutionalized until another hundred years later when it is associated with work by George Zipf and John Stewart. Social physics is marked by the belief that large-scale statistical measurement of social variables reveals underlying relational (...) patterns that can be explained by theories and laws found in natural science, and physics in particular. This larger epistemological position is known as monism, the idea that there is only one set of principles that applies to the explanation of both natural and social worlds. Social physics entered geography through the work of the mid-20th-century geographer William Warntz, who developed his own spatial version called “macrogeography.” It involved the computation of large data sets, made ever easier with the contemporaneous development of the computer, joined with the gravitational potential model. Our argument is that Warntz's concerns with numeracy, large data sets, machine-based computing power, relatively simple mathematical formulas drawn from natural science, and an isomorphism between natural and social worlds became grounds on which Big Data later staked its claim to knowledge; it is a past that has not yet passed. (shrink)

Recent research in ethics education shows a potentially problematic variation in content, curricular materials, and instruction. While ethics instruction is now widespread, studies have identified significant variation in both the goals and methods of ethics education, leaving researchers to conclude that many approaches may be inappropriately paired with goals that are unachievable. This paper speaks to these concerns by demonstrating the importance of aligning classroom-based assessments to clear ethical learning objectives in order to help students and instructors track their progress (...) toward meeting those objectives. Two studies at two different universities demonstrate the usefulness of classroom-based, formative assessments for improving the quality of students’ case responses in computational modeling and research ethics. (shrink)

Even with the lack of consensus on the nature of an argument, the thesis that explanations and arguments are distinct is near orthodoxy in well-known critical thinking texts and in the more advanced argumentation literature. In this paper, I reconstruct two rationales for distinguishing arguments from explanations. According to one, arguments and explanations are essentially different things because they have different structures. According to the other, while some explanations and arguments may have the same structure, they are different things because (...) explanations are used for different purposes than arguments. I argue that both rationales fail to motivate a distinction between arguments and explanations. Since these are the only rationales for distinguishing arguments from explanations that I am prepared to take seriously, I don’t see why we should exclude explanations from being arguments. (shrink)

A probability distribution is regular if it does not assign probability zero to any possible event. While some hold that probabilities should always be regular, three counter-arguments have been posed based on examples where, if regularity holds, then perfectly similar events must have different probabilities. Howson and Benci et al. have raised technical objections to these symmetry arguments, but we see here that their objections fail. Howson says that Williamson’s “isomorphic” events are not in fact isomorphic, but Howson is speaking (...) of set-theoretic representations of events in a probability model. While those sets are not isomorphic, Williamson’s physical events are, in the relevant sense. Benci et al. claim that all three arguments rest on a conflation of different models, but they do not. They are founded on the premise that similar events should have the same probability in the same model, or in one case, on the assumption that a single rotation-invariant distribution is possible. Having failed to refute the symmetry arguments on such technical grounds, one could deny their implicit premises, which is a heavy cost, or adopt varying degrees of instrumentalism or pluralism about regularity, but that would not serve the project of accurately modelling chances. (shrink)

There is no uniquely standard concept of an effectively decidable set of real numbers or real n-tuples. Here we consider three notions: decidability up to measure zero [M.W. Parker, Undecidability in Rn: Riddled basins, the KAM tori, and the stability of the solar system, Phil. Sci. 70(2) (2003) 359–382], which we abbreviate d.m.z.; recursive approximability [or r.a.; K.-I. Ko, Complexity Theory of Real Functions, Birkhäuser, Boston, 1991]; and decidability ignoring boundaries [d.i.b.; W.C. Myrvold, The decision problem for entanglement, in: R.S. (...) Cohen et al. (Eds.), Potentiality, Entanglement, and Passion-at-a-Distance: Quantum Mechanical Studies fo Abner Shimony, Vol. 2, Kluwer Academic Publishers, Great Britain, 1997, pp. 177–190]. Unlike some others in the literature, these notions apply not only to certain nice sets, but to general sets in Rn and other appropriate spaces. We consider some motivations for these concepts and the logical relations between them. It has been argued that d.m.z. is especially appropriate for physical applications, and on Rn with the standard measure, it is strictly stronger than r.a. [M.W. Parker, Undecidability in Rn: Riddled basins, the KAM tori, and the stability of the solar system, Phil. Sci. 70(2) (2003) 359–382]. Here we show that this is the only implication that holds among our three decidabilities in that setting. Under arbitrary measures, even this implication fails. Yet for intervals of non-zero length, and more generally, convex sets of non-zero measure, the three concepts are equivalent. (shrink)

A probability distribution is regular if no possible event is assigned probability zero. While some hold that probabilities should always be regular, three counter-arguments have been posed based on examples where, if regularity holds, then perfectly similar events must have different probabilities. Howson (2017) and Benci et al. (2016) have raised technical objections to these symmetry arguments, but we see here that their objections fail. Howson says that Williamson’s (2007) “isomorphic” events are not in fact isomorphic, but Howson is speaking (...) of set-theoretic representations of events in a probability model. While those sets are not isomorphic, Williamson’s physical events are, in the relevant sense. Benci et al. claim that all three arguments rest on a conflation of different models, but they do not. They are founded on the premise that similar events should have the same probability in the same model, or in one case, on the assumption that a single rotation-invariant distribution is possible. Having failed to refute the symmetry arguments on such technical grounds, one could deny their implicit premises, which is a heavy cost, or adopt varying degrees of instrumentalism or pluralism about regularity, but that would not serve the project of accurately modelling chances. (shrink)

What are the effects of word-by-word predictability on sentence processing times during the natural reading of a text? Although information complexity metrics such as surprisal and entropy reduction have been useful in addressing this question, these metrics tend to be estimated using computational language models, which require some degree of commitment to a particular theory of language processing. Taking a different approach, this study implemented a large-scale cumulative cloze task to collect word-by-word predictability data for 40 passages and compute surprisal (...) and entropy reduction values in a theory-neutral manner. A separate group of participants read the same texts while their eye movements were recorded. Results showed that increases in surprisal and entropy reduction were both associated with increases in reading times. Furthermore, these effects did not depend on the global difficulty of the text. The findings suggest that surprisal and entropy reduction independently contribute to variation in reading times, as these metrics seem to capture different aspects of lexical predictability. (shrink)

In standard probability theory, probability zero is not the same as impossibility. But many have suggested that only impossible events should have probability zero. This can be arranged if we allow infinitesimal probabilities, but infinitesimals do not solve all of the problems. We will see that regular probabilities are not invariant over rigid transformations, even for simple, bounded, countable, constructive, and disjoint sets. Hence, regular chances cannot be determined by space-time invariant physical laws, and regular credences cannot satisfy seemingly reasonable (...) symmetry principles. Moreover, the examples here are immune to the objections against Williamson’s infinite coin flips. (shrink)

On the first page of “What is Cantor's Continuum Problem?”, Gödel argues that Cantor's theory of cardinality, where a bijection implies equal number, is in some sense uniquely determined. The argument, involving a thought experiment with sets of physical objects, is initially persuasive, but recent authors have developed alternative theories of cardinality that are consistent with the standard set theory ZFC and have appealing algebraic features that Cantor's powers lack, as well as some promise for applications. Here we diagnose Gödel's (...) argument, showing that it fails in two important ways: Its premises are not sufficiently compelling to discredit countervailing intuitions and pragmatic considerations, nor pluralism, and its final inference, from the superiority of Cantor's theory as applied to sets of changeable physical objects to the unique acceptability of that theory for all sets, is irredeemably invalid. (shrink)

Introduction -- The concept of logical consequence -- Tarski's characterization of the common concept of logical consequence -- The logical consequence relation has a modal element -- The logical consequence relation is formal -- The logical consequence relation is A priori -- Logical and non-logical terminology -- The meanings of logical terms explained in terms of their semantic properties -- The meanings of logical terms explained in terms of their inferential properties -- Model-theoretic and deductive-theoretic conceptions of logic -- Linguistic (...) preliminaries : the language M -- Syntax of M -- The definition of a well formed formula of M -- Semantics for M -- The sentential connectives are defined -- The notion of satisfaction is introduced and the quantifiers are defined -- Model-theoretic consequence -- Truth in a structure -- Satisfaction revisited -- Formalized definition of truth -- Model-theoretic consequence defined -- The model-theoretic definition and the concept of logical consequence -- Does the model theoretic consequence relation reflect the salient features of the common concept of logical consequence? -- What is a logical constant? -- Deductive consequence -- Deductive system n -- The deductive theoretic definition and the concept of logical consequence -- Tarski's criticism of the deductive theoretic definition -- Is N a correct deductive system? (shrink)

Executive speechwriting is a common practice in most large organizations. This activity, however, raises a number of ethical questions about responsibility and about audience deception. This essay explores the ethics of speechwriting from three perspectives and offers some general guidelines for maintaining ethical standards when using speechwriters.

The least infringement principle has been widely endorsed by public health scholars. According to this principle, public health policies may infringe upon “general moral considerations” in order to achieve a public health goal, but if two policies provide the same public health benefit, then policymakers should choose the one that infringes least upon “general moral considerations.” General moral considerations can encompass a wide variety of goals, including fair distribution of burdens and benefits, protection of privacy and confidentiality, and respect for (...) autonomy.In this article, we argue that the Center for Disease Control and Prevention's 2006 HIV screening recommendations may violate the least infringement principle. This is a concern because, although not legally binding, the Recommendations appear to have already influenced state laws and will likely continue to do so as legislative proposals continue to be passed. At a minimum, therefore, the Recommendations have important implications for HIV screening within the United States. (shrink)

As an application of his Material Theory of Induction, Norton (2018; manuscript) argues that the correct inductive logic for a fair infinite lottery, and also for evaluating eternal inflation multiverse models, is radically different from standard probability theory. This is due to a requirement of label independence. It follows, Norton argues, that finite additivity fails, and any two sets of outcomes with the same cardinality and co-cardinality have the same chance. This makes the logic useless for evaluating multiverse models based (...) on self-locating chances, so Norton claims that we should despair of such attempts. However, his negative results depend on a certain reification of chance, consisting in the treatment of inductive support as the value of a function, a value not itself affected by relabeling. Here we define a purely comparative infinite lottery logic, where there are no primitive chances but only a relation of ‘at most as likely’ and its derivatives. This logic satisfies both label independence and a comparative version of additivity as well as several other desirable properties, and it draws finer distinctions between events than Norton's. Consequently, it yields better advice about choosing between sets of lottery tickets than Norton's, but it does not appear to be any more helpful for evaluating multiverse models. Hence, the limitations of Norton's logic are not entirely due to the failure of additivity, nor to the fact that all infinite, co-infinite sets of outcomes have the same chance, but to a more fundamental problem: We have no well-motivated way of comparing disjoint countably infinite sets. (shrink)

Matthew W. Slaboch examines the work of German philosophers Arthur Schopenhauer and Oswald Spengler, Russian novelists Leo Tolstoy and Aleksandr Solzhenitsyn, and American historians Henry Adams and Christopher Lasch—rare skeptics of the idea of progress who have much to offer political theory, a field dominated by historical optimists.

RESUMEN Una vez que el foco de la reflexión pasa de las teorías ideales a la aplicación de la justicia social, centrada en las instituciones de las sociedades democráticas, se requiere prestar especial atención a los estilos de vida. Estos tienen una alta incidencia en cómo la justicia es realizada y afectan tanto a la desigualdad económica como a la disponibilidad de los recursos naturales. En nuestras sociedades es posible establecer restricciones a los estilos de vida, especialmente en aquellos casos (...) en que, por el efecto de algunas dinámicas sociales, aquellos se desacoplan de las concepciones del bien. Se defiende que, en tales casos, la base normativa que permite exigir el respeto a los estilos de vida se disuelve y por ello es posible justificar su restricción. ABSTRACT Now that the focus of reflection has shifted from ideal theories to the application of social justice, centered on the institutions of democratic societies, it is necessary to pay special attention to lifestyles, since they not only influence the realization of justice, but also have an effect on economic inequality and the availability of natural resources. In our societies, it is possible to place restrictions on lifestyles, especially in those cases in which, influenced by certain social dynamics, they disengage from conceptions of the good. The article argues that, in those cases, the normative base grounding the demand that lifestyles be respected is dissolved, thus justifying their restriction. (shrink)

We consider an approach to some philosophical problems that I call the Method of Conceptual Articulation: to recognize that a question may lack any determinate answer, and to re-engineer concepts so that the question acquires a definite answer in such a way as to serve the epistemic motivations behind the question. As a case study we examine “Galileo’s Paradox”, that the perfect square numbers seem to be at once as numerous as the whole numbers, by one-to-one correspondence, and yet less (...) numerous, being a proper subset. I argue that Cantor resolved this paradox by a method at least close to that proposed—not by discovering the true nature of cardinal number, but by articulating several useful and appealing extensions of number to the infinite. Galileo was right to suggest that the concept of relative size did not apply to the infinite, for the concept he possessed did not. Nor was Bolzano simply wrong to reject Hume’s Principle (that one-to-one correspondence implies equal number) in the infinitary case, in favor of Euclid’s Common Notion 5 (that the whole is greater than the part), for the concept of cardinal number (in the sense of “number of elements”) was not clearly defined for infinite collections. Order extension theorems now suggest that a theory of cardinality upholding Euclid’s principle instead of Hume’s is possible. Cantor’s refinements of number are not the only ones possible, and they appear to have been shaped by motivations and fruitfulness, for they evolved in discernible stages correlated with emerging applications and results. Galileo, Bolzano, and Cantor shared interests in the particulate analysis of the continuum and in physical applications. Cantor’s concepts proved fruitful for those pursuits. Finally, Gödel was mistaken to claim that Cantor’s concept of cardinality is forced on us; though Gödel gives an intuitively compelling argument, he ignores the fact that Euclid’s Common Notion is also intuitively compelling, and we are therefore forced to make a choice. The success of Cantor’s concept of cardinality lies not in its truth (for concepts are not true or false), nor its uniqueness (for it is not the only extension of number possible), but in its intuitive appeal, and most of all, its usefulness to the understanding. (shrink)

Name der Zeitschrift: Semiotica Jahrgang: 2017 Heft: 216 Seiten: 363-381.

This article stages a new encounter between rhetoric and the philosophy of Karl Marx. We argue that the configuration of two major tropes in Marx’s 1852 pamphlet The Eighteenth Brumaire of Louis Bonaparte renders explicit the operative but implicit logics of Marxian historical materialism. Our reading therefore makes available a novel and untimely dimension of Marx’s conceptual labor where we least expect to find it: in a text that has been largely, but not exclusively, understood as a history of counterrevolution (...) that was meant to intervene within its own context in particular ways. While we do not wish to lose sight of that context, our aim is to demonstrate that The Eighteenth Brumaire is suggestive of the.. (shrink)

This dialogue discusses a proposal for the legalization of torture under specific circumstances and contrasts it with arguments for a total ban on torture. We consider three types of objection: first, that the difficulty of having adequate knowledge renders the stock “ticking bomb” scenario such a low-probability hypothetical as to present no realistic threat to a policy banning all torture; second, that empirically the information gleaned from torture is so unlikely to be reliable that it could not justify the moral (...) risk; and third, that sanctioning torture, even if only under the most extreme circumstances, would generate a ‘culture of torture,’ hence undermining fragile advances in international human rights rooted in unwavering commitment to human dignity. Compelling as these arguments appear, not all the conversants are wholly convinced by them; to this extent the dialogue ends aporetically. (shrink)

The behavior of some systems is non-computable in a precise new sense. One infamous problem is that of the stability of the solar system: Given the initial positions and velocities of several mutually gravitating bodies, will any eventually collide or be thrown off to infinity? Many have made vague suggestions that this and similar problems are undecidable: no finite procedure can reliably determine whether a given configuration will eventually prove unstable. But taken in the most natural way, this is trivial. (...) The state of a system corresponds to a point in a continuous space, and virtually no set of points in space is strictly decidable. A new, more pragmatic concept is therefore introduced: a set is decidable up to measure zero (d.m.z.) if there is a procedure to decide whether a point is in that set and it only fails on some points that form a set of zero volume. This is motivated by the intuitive correspondence between volume and probability: we can ignore a zero-volume set of states because the state of an arbitrary system almost certainly will not fall in that set. D.m.z. is also closer to the intuition of decidability than other notions in the literature, which are either less strict or apply only to special sets, like closed sets. Certain complicated sets are not d.m.z., most remarkably including the set of known stable orbits for planetary systems (the KAM tori). This suggests that the stability problem is indeed undecidable in the precise sense of d.m.z. Carefully extending decidability concepts from idealized models to actual systems, we see that even deterministic aspects of physical behavior can be undecidable in a clear and significant sense. (shrink)

Ten years ago, researchers using event-related brain potentials to study language comprehension were puzzled by what looked like a Semantic Illusion: Semantically anomalous, but structurally well-formed sentences did not affect the N400 component—traditionally taken to reflect semantic integration—but instead produced a P600 effect, which is generally linked to syntactic processing. This finding led to a considerable amount of debate, and a number of complex processing models have been proposed as an explanation. What these models have in common is that they (...) postulate two or more separate processing streams, in order to reconcile the Semantic Illusion and other semantically induced P600 effects with the traditional interpretations of the N400 and the P600. Recently, however, these multi-stream models have been called into question, and a simpler single-stream model has been proposed. According to this alternative model, the N400 component reflects the retrieval of word meaning from semantic memory, and the P600 component indexes the integration of this meaning into the unfolding utterance interpretation. In the present paper, we provide support for this “Retrieval–Integration ” account by instantiating it as a neurocomputational model. This neurocomputational model is the first to successfully simulate the N400 and P600 amplitude in language comprehension, and simulations with this model provide a proof of concept of the single-stream RI account of semantically induced patterns of N400 and P600 modulations. (shrink)

Old habits die hard; so, it seems, do old arguments. Proponents of thoracoabdominal normothermic regional perfusion (TA-NRP, but more commonly referred to as NRP) continue to proffer arguments and...

In a fictional conversation designed to appeal to both working teachers and social philosophers, three educators take up the question of whether critical thinking itself can, or should, be taught independently of an explicit consideration of issues related to social justice. One, a thoughtful but somewhat traditional Enlightenment rationalist, sees critical thinking as a neutral set of skills and dispositions, essentially unrelated to the conclusions of morality, problems of social organization, or the content of any particular academic discipline. A second (...) interlocutor, steeped in “critical” pedagogy of Paulo Freire, insists that the problem is the pose of neutrality itself. On this view, all honest and effective approaches to teaching must confront the hegemony of unjust relationships, institutions, and conceptual schemes. The third character attempts to resolve the tension between these two opposed camps. (shrink)

In a fictional conversation designed to appeal to both working teachers and social philosophers, three educators take up the question of whether critical thinking itself can, or should, be taught independently of an explicit consideration of issues related to social justice. One, a thoughtful but somewhat traditional Enlightenment rationalist, sees critical thinking as a neutral set of skills and dispositions, essentially unrelated to the conclusions of morality, problems of social organization, or the content of any particular academic discipline. A second (...) interlocutor, steeped in “critical” pedagogy of Paulo Freire, insists that the problem is the pose of neutrality itself. On this view, all honest and effective approaches to teaching must confront the hegemony of unjust relationships, institutions, and conceptual schemes. The third character attempts to resolve the tension between these two opposed camps. (shrink)

We examine a case in which non-computable behavior in a model is revealed by computer simulation. This is possible due to differing notions of computability for sets in a continuous space. The argument originally given for the validity of the simulation involves a simpler simulation of the simulation, still further simulations thereof, and a universality conjecture. There are difficulties with that argument, but there are other, heuristic arguments supporting the qualitative results. It is urged, using this example, that absolute validation, (...) while highly desirable, is overvalued. Simulations also provide valuable insights that we cannot yet (if ever) prove. (shrink)

Some have suggested that certain classical physical systems have undecidable long-term behavior, without specifying an appropriate notion of decidability over the reals. We introduce such a notion, decidability in (or d- ) for any measure , which is particularly appropriate for physics and in some ways more intuitive than Ko's (1991) recursive approximability (r.a.). For Lebesgue measure , d- implies r.a. Sets with positive -measure that are sufficiently "riddled" with holes are never d- but are often r.a. This explicates Sommerer (...) and Ott's (1996) claim of uncomputable behavior in a system with riddled basins of attraction. Furthermore, it clarifies speculations that the stability of the solar system (and similar systems) may be undecidable, for the invariant tori established by KAM theory form sets that are not d-. (shrink)