A course focusing on ethical issues in physics has been taught to undergraduate students at Eastern Michigan University since 1988. The course covers both responsible conduct of research and ethical issues associated with how physicists interact with the rest of society. Since most undergraduate physics majors will not have a career in academia, it is important that a course such as this address issues that will be relevant to physicists in a wide range of job situations. There is a wealth (...) of published work that can be drawn on for reading assignments. (shrink)

This paper attempts to elucidate on Jacques Derrida’s concept of deconstruction and its difficult elements, viz., differance, dissemination, destinerrance, and geocatasthrophe. These basic ideas need elaboration for their proper understanding. Once successfully achieved, then here lies the significance of this paper.

This paper looks at the issues and controversies that led to creation of the Office of Research Integrity (ORI) and that dominated its agenda in the early years. The successes and failures of ORI are described and new problems identified. This paper then looks ahead to the future, considering what issues will dominate ORI’s agenda and affect the research institutions, individual scientists, and the scientific community in the next several years.

We highlight recent progress in neuroimaging and neuropsychological research on memory mechanisms in the medial temporal lobe that speaks to the involuntary nature of memory retrieval processes. We suggest that evidence form these studies supports Barzykowski and Moulin's proposal that memory signals involved in experiences of familiarity and déjà vu can be generated in the absence of retrieval intentionality.

In this paper we provide a new arithmetic characterization of the levels of the og-time hierarchy . We define arithmetic classes equation image and equation image that correspond to equation image-LOGTIME and equation image-LOGTIME, respectively. We break equation image and equation image into natural hierarchies of subclasses equation image and equation image. We then define bounded arithmetic deduction systems equation image′ whose equation image-definable functions are precisely B. We show these theories are quite strong in that LIOpen proves for any (...) fixed m that equation image, TAC, a theory that is slightly stronger than equation image′ whose equation image-definable functions are LH, proves LH is not equal to equation image-TIME for any m> 0, where 2s ∈L, s ∈ ω, and TAC proves LH ≠ equation image for all k and m. We then show that the theory TAC cannot prove the collapse of the polynomial hierarchy. Thus any such proof, if it exists, must be argued in a stronger systems than ours. (shrink)

Mohism was an ancient Chinese philosophical movement founded in the fifth century B.C.E. by the charismatic artisan Mozi, or "Master Mo." The Mohists advanced a consequentialist ethics that anticipated Western utilitarianism by more than two thousand years and developed fascinating logical, epistemological, and political theories that set the terms of philosophical debate in China for generations. They were the earliest thinkers to outline a just war doctrine and to explain the origin of government from a state of nature. Their epistemology (...) and psychology provide intriguing alternatives to contemporary Western mentalism. The Philosophy of the Mozi is an extensive study of Mohism that immerses readers in the Mohist worldview, situates the movement's rise and decline within Chinese history, and highlights its relevance to modern thought. (shrink)

In this paper, we examine critically the notion of “Triple Bottom Line” accounting. We begin by asking just what it is that supporters of the Triple Bottom Line idea advocate, and attempt to distil specific, assessable claims from the vague, diverse, and sometimescontradictory uses of the Triple Bottom Line rhetoric. We then use these claims as a basis upon which to argue (a) that what issound about the idea of a Triple Bottom Line is not novel, and (b) that what (...) is novel about the idea is not sound. We argue on bothconceptual and practical grounds that the Triple Bottom Line is an unhelpful addition to current discussions of corporate social responsibility. Finally, we argue that the Triple Bottom Line paradigm cannot be rescued simply by attenuating its claims: the rhetoric isbadly misleading, and may in fact provide a smokescreen behind which firms can avoid truly effective social and environmental reporting and performance. (shrink)

Inflationary cosmology has been widely accepted due to its successful predictions: for a “generic” initial state, inflation produces a homogeneous, flat, bubble with an appropriate spectrum of density perturbations. However, the discovery that inflation is “generically eternal,” leading to a vast multiverse of inflationary bubbles with different low-energy physics, threatens to undermine this account. There is a “predictability crisis” in eternal inflation, because extracting predictions apparently requires a well-defined measure over the multiverse. This has led to discussions of anthropic predictions (...) based on a measure over the multiverse, and an assumption that we are typical observers. I will give a pessimistic assessment of attempts to make predictions in this sense, emphasizing in particular problems that arise even if a unique measure can be found. (shrink)

This paper explores how fair trade social enterprises manage paradoxes in stakeholder-oriented governance models. We use narrative accounts from board members, at governance events and board documents to report an exploratory study of paradoxes in three FTSEs which are partly farmer-owned. Having synthesized the key social enterprise governance literature and framed it alongside the broader paradox theory, we used narratives to explore how tensions are articulated, how they can be applied within an adapted paradox framework, and how governance actors seek (...) to mitigate paradoxes. The paper contributes to current debates in social enterprise scholarship concerning hybridity :455–476, 2010; in Institutional logics in action, Part B, 2012), hybrid organizing :397–441, 2014) and operational tensions :407–442, 2013) by illustrating empirically how the central social/enterprise paradox manifests in FTSEs governance arrangements. We build on the paradox categories proposed by Lüscher and Lewis :221–240, 2008) and adapted in Smith et al. :407–442, 2013) by developing a recursive model of legitimacy-seeking governance processes, conceptualizing how boards seek to mitigate, but not necessarily resolve, paradoxes. (shrink)

Some children living with life-shortening medical conditions may wish to attend school without the threat of having resuscitation attempted in the event of cardiopulmonary arrest on the school premises. Despite recent attention to in-school do-not-attempt-resuscitation (DNAR) orders, no assessment of state laws or school policies has yet been made. We therefore sought to survey a national sample of prominent school districts and situate their policies in the context of relevant state laws. Most (80%) school districts sampled did not have policies, (...) regulations, or protocols for dealing with student DNARs. A similar majority (76%) either would not honor student DNARs or were uncertain about whether they could. Frequent contradictions between school policies and state laws also exist. Consequently, children living with life-shortening conditions who have DNARs may not have these orders honored if cardiopulmonary arrest were to occur on school premises. Coordinated efforts are needed to harmonize school district, state, and federal approaches in order to support children and families' right to have important medical decisions honored. (shrink)

In the Western philosophical tradition, the earliest recognized paradoxes are attributed to Zeno of Elea (ca. 490–430 B.C.E.) and to Eubulides of Miletus (fl. 4th century B.C.E.). In the Chinese tradition, the earliest and most well-known paradoxes are ascribed to figures associated with the “School of Names” (ming jia 名家), a diverse group of Warring States (479–221 B.C.E.) thinkers who shared an interest in language, logic, and metaphysics. Their investigations led some of these thinkers to propound puzzling, paradoxical statements such (...) as “Today go to Yue but arrive yesterday,” “White horses are not horses,” and “Mountains and gorges are level.” Such paradoxes seem to have been intended to highlight fundamental features of reality or subtleties in semantic relations between words and things. Why were thinkers who advanced paradoxes categorized as a school of “names”? In ancient China, philosophical inquiry concerning language and logic focused on the use of “names” (ming 名, also terms, labels, or reputation) and their semantic relations to “stuff” (shi 實, also objects, features, events, or situations). Hence for classificatory purposes, second-century B.C.E. Han-dynasty archivists grouped together assorted pre-Han figures whose most prominent ideas seemed to concern the relation between names and stuff—or at least strange, unorthodox uses of names—and dubbed them a school or lineage (jia 家) devoted to the study of names. Unfortunately, both the label and the grouping are misleading. Historically, the school was a retrospective, taxonomical fiction. The figures classified under the “School of Names” never formed a distinct circle, movement, tradition, or line of influence devoted to any particular doctrine, theme, method, or way of life. Their intellectual interests overlapped at most only partly, while also overlapping extensively with those of texts associated with other schools or traditions, such as the Mohist “Dialectics” 墨辯, the Zhuangzi 莊子, the Xunzi 荀子, and the Annals of Lü Buwei 呂氏春秋. What perhaps does set the School of Names apart is that some (though not all) of the figures associated with it apparently delighted in propounding paradoxical or preposterous sayings, while the other texts just mentioned generally (though not exclusively) seek to explain and debunk such utterances. (shrink)

A typical theorem of conaexive logics is Aristotle''s Thesis(A), (AA).A cannot be added to classical logic without producing a trivial (Post-inconsistent) logic, so connexive logics typically give up one or more of the classical properties of conjunction, e.g.(A & B)A, and are thereby able to achieve not only nontriviality, but also (negation) consistency. To date, semantical modellings forA have been unintuitive. One task of this paper is to give a more intuitive modelling forA in consistent logics. In addition, while inconsistent (...) but nontrivial theories, and inconsistent nontrivial logics employing prepositional constants (for which the rule of uniform substitution US fails), have both been studied extensively within the paraconsistent programme, inconsistent nontrivial logics (closed under US) do not seem to have been. This paper gives sufficient conditions for a logic containingA to be inconsistent, and then shows that there is a class of inconsistent nontrivial logics all containingA. A second semantical modelling forA in such logics is given. Finally, some informal remarks about the kind of modellingA seems to require are made. (shrink)

This book was the winner of the International Committee of Architectural Critics 2017 Bruno Zevi Book Award by unanimous decision of the international jury. In his wide-ranging study of architecture and cultural evolution, Chris Abel argues that, despite progress in sustainable development and design, resistance to changing personal and social identities shaped by a technology-based and energy-hungry culture is impeding efforts to avert drastic climate change. The book traces the roots of that culture to the coevolution of Homo sapiens (...) and technology, from the first use of tools as artificial extensions of the human body to the motorized cities spreading around the world, whose uncontrolled effects are fast changing the planet itself. Advancing a new concept of the meme, called the 'technical meme', as the primary agent of cognitive extension and technical embodiment, Abel proposes a theory of the 'extended self' as a complex and diffuse outcome of that coevolution. Challenging conventional ideas of the self as a separate and autonomous being, the extended self, he explains, encompasses material and spatial as well as psychological and social elements, including the built environment and artifacts, and now reaches out into the virtual world of cyberspace. Drawing upon research into extended cognition and embodied minds from philosophy, psychology and the neurosciences, the book presents a new approach to environmental and cultural studies. N.B. This book was the winner of the International Committee of Architectural Critics 2017 Bruno Zevi Book Award by unanimous decision of the international jury. (shrink)

We introduce multifunction algebras B i τ where τ is a set of 0 or 1-ary terms used to bound recursion lengths. We show that if for all ℓ ∈ τ we have ℓ ∈ O then B i τ = FP Σ i−1 p , those multifunctions computable in polynomial time with at most O )) queries to a Σ i−1 p witness oracle for ℓ ∈ τ and p a polynomial. We use our algebras to obtain independence results (...) in bounded arithmetic. In particular, we show if S 2 i proves Σ j b = PH for some j⩾i then S 2 i ≼ B S 2 . This implies if P NP ≠ P NP then S 2 1 does not prove the polynomial hierarchy collapses. We then consider a subtheory, Z , of the well-studied bounded arithmetic theory S 2 = ∪ i S 2 i . Using our algebras we establish the following properties of this theory: Z cannot prove the polynomial hierarchy collapses. In fact, even Z+ Π ̂ 0 b -consequences of S 2 cannot prove the hierarchy collapses. If Z ⊆ S 2 i for any i then the polynomial hierarchy collapses. If Z proves the polynomial hierarchy is infinite then for all i , S 2 i ⊢ Σ i p ≠ Π i p. (shrink)

Background: Although nurses worldwide are confronted with euthanasia requests from patients, the views of palliative care nurses on their involvement in euthanasia remain unclear.Objectives: In depth exploration of the views of palliative care nurses on their involvement in the entire care process surrounding euthanasia.Design: A qualitative Grounded Theory strategy was used.Setting and participants: In anticipation of new Belgian legislation on euthanasia, we conducted semistructured interviews with 12 nurses working in a palliative care setting in the province of Vlaams-Brabant.Results: Palliative care (...) nurses believed unanimously that they have an important role in the process of caring for a patient who requests euthanasia, a role that is not limited to assisting the physician when he is administering life terminating drugs. Nurses’ involvement starts when the patient requests euthanasia and ends with supporting the patient’s relatives and healthcare colleagues after the potential life terminating act. Nurses stressed the importance of having an open mind and of using palliative techniques, also offering a contextual understanding of the patient’s request in the decision making process. Concerning the actual act of performing euthanasia, palliative care nurses saw their role primarily as assisting the patient, the patient’s family, and the physician by being present, even if they could not reconcile themselves with actually performing euthanasia.Conclusions: Based on their professional nursing expertise and unique relationship with the patient, nurses participating as full members of the interdisciplinary expert team are in a key position to provide valuable care to patients requesting euthanasia. (shrink)

The bounded arithmetic theories R2i, S2i, and T2i are closely connected with complexity theory. This paper is motivated by the questions: what are the Σi+1b-definable multifunctions of R2i? and when is one theory conservative over another? To answer these questions we consider theories , and where induction is restricted to prenex formulas. We also define which has induction up to the 0 or 1-ary L2-terms in the set τ. We show and and for . We show that the -multifunctions of (...) are FPΣip and that those of are FPΣip. For -definability we get FPΣi+k+1p for all these theories. Write for the set of terms 2min,t) where ℓ is a finite product of terms in τ and tL2. We prove and we show - INDτ provided τO2. This gives a proof theoretic proof that S2iΔi+1b-LIND and -LLIND solving an open problem. For τO2, we define using weak replacement axioms and show . We show if or if or if where τ′ has an unbounded term then PH=B. We separate PΣip from PΣip for behaved ℓ and deduce theory separations. We lastly introduce a notion of a model separating two theories and derive some consequences. (shrink)

‘Organisational failure’ is central to medical ethics. In the National Health Service (NHS), we usually examine failures at hospital level. We have had around 100 hospital inquiries since the first in 1969, into Ely Hospital, Cardiff. This year, we had the Ockenden Report into Shrewsbury and Telford Hospital. Last year, we had the Outram Inquiry into West Suffolk Hospital. In 2020, the James Inquiry into Ian Paterson. And, before that, Morecombe Bay, Gosport War Memorial, Mid Staffordshire, Liverpool Community Health, Winterbourne (...) View, Anthony Ledward, Stoke Mandeville, Bristol Royal Infirmary and so on. As Taylor says, these reports teach us clinical failure usually has an institutional setting and that blaming individuals overlooks working ‘culture’. They have also led to: (a) new regulatory bodies to manage, investigate and improve NHS standards, (b) new codes of conduct to mandate reporting of serious accidents—backed up by the Whistle-blower’s Act and explicit statutory duties of disclosure, (c) root cause analysis to encourage consistent investigations so we can learn from reliable data and (d) new ‘Speaking Up Guardians’ and a Patient Safety Commissioner to encourage informal discussion about patient safety. What is so surprising is how little these inquiries and reforms have achieved on the larger scale. Of course, we must …. (shrink)

Human vision supports social perception by efficiently detecting agents and extracting rich information about their actions, goals, and intentions. Here, we explore the cognitive architecture of perceived animacy by constructing Bayesian models that integrate domain‐specific hypotheses of social agency with domain‐general cognitive constraints on sensory, memory, and attentional processing. Our model posits that perceived animacy combines a bottom–up, feature‐based, parallel search for goal‐directed movements with a top–down selection process for intent inference. The interaction of these architecturally distinct processes makes perceived (...) animacy fast, flexible, and yet cognitively efficient. In the context of chasing, in which a predator (the “wolf”) pursues a prey (the “sheep”), our model addresses the computational challenge of identifying target agents among varying numbers of distractor objects, despite a quadratic increase in the number of possible interactions as more objects appear in a scene. By comparing modeling results with human psychophysics in several studies, we show that the effectiveness and efficiency of human perceived animacy can be explained by a Bayesian ideal observer model with realistic cognitive constraints. These results provide an understanding of perceived animacy at the algorithmic level—how it is achieved by cognitive mechanisms such as attention and working memory, and how it can be integrated with higher‐level reasoning about social agency. (shrink)

In the past decade, numerous ethical frameworks have been developed to support public health decision‐making in challenging areas. Before the COVID‐19 pandemic began, members of the authorship team were involved in research programmes, in which the development of ethical frameworks was planned, to guide (a) the use of new technologies for emerging infectious disease surveillance; and (b) the allocation of scarce supplies of pandemic influenza vaccine. However, as the pandemic evolved, significant practical challenges emerged that led to our questioning the (...) value of these frameworks. We now believe that a normative instrument, such as a framework, cannot adequately or reliably provide the ethical guidance that needs to be incorporated into public health decision‐making during natural disasters or infectious disease emergencies. Recently it has been suggested that there are potentially more dynamic, flexible, and effective ways to navigate decisions involving complex considerations entailed in policies and practices during a public health emergency. In this paper, we first outline the key functions of a public health ethics framework, before describing why we believe it would not be fit for purpose during a crisis. We end by considering whether proposed alternative methods to promote ethical public health decision‐making goals have the potential to meet these objectives. (shrink)

The Mohist Canons are a set of brief statements on a variety of philosophical and other topics by anonymous members of the Mohist school , an influential philosophical, social, and religious movement of China's Warring States period (479-221 B.C.). [1] Written and compiled most likely between the late 4th and mid 3rd century B.C., the Canons are often referred to as the “later Mohist” or “Neo-Mohist” canons, since they seem chronologically later than the bulk of the Mohist writings, most of (...) which are probably from the mid-5th to the late 4th century. The.. (shrink)

We investigated people's ability to infer others’ mental states from their emotional reactions, manipulating whether agents wanted, expected, and caused an outcome. Participants recovered agents’ desires throughout. When the agent observed, but did not cause the outcome, participants’ ability to recover the agent's beliefs depended on the evidence they got. When the agent caused the event, participants’ judgments also depended on the probability of the action ; when actions were improbable given the mental states, people failed to recover the agent's (...) beliefs even when they saw her react to both the anticipated and actual outcomes. A Bayesian model captured human performance throughout, consistent with the proposal that people rationally integrate information about others’ actions and emotional reactions to infer their unobservable mental states. (shrink)

Following Birkhoff and von Neumann, quantum logic has traditionally been based on the lattice of closed linear subspaces of some Hubert space, or, more generally, on the lattice of projections in a von Neumann algebra A. Unfortunately, the logical interpretation of these lattices is impaired by their nondistributivity and by various other problems. We show that a possible resolution of these difficulties, suggested by the ideas of Bohr, emerges if instead of single projections one considers elementary propositions to be families (...) of projections indexed by a partially ordered set C(A) of appropriate commutative subalgebras of A. In fact, to achieve both maximal generality and ease of use within topos theory, we assume that A is a so-called Rickart C*-algebra and that C(A) consists of all unital commutative Rickart C*-subalgebras of A. Such families of projections form a Hey ting algebra in a natural way, so that the associated propositional logic is intuitionistic: distributivity is recovered at the expense of the law of the excluded middle. Subsequently, generalizing an earlier computation for n x n matrices, we prove that the Heyting algebra thus associated to A arises as a basis for the internal Gelfand spectrum (in the sense of Banaschewski-Mulvey) of the "Bohrification" A̱ of A, which is a commutative Rickart C*-algebra in the topos of functors from C(A) to the category of sets. We explain the relationship of this construction to partial Boolean algebras and Bruns-Lakser completions. Finally, we establish a connection between probability measures on the lattice of projections on a Hubert space H and probability valuations on the internal Gelfand spectrum of A̱ for A = B(H). (shrink)

In this paper I borrow from Maria Lugones’ work on playful “world-traveling” and W.E.B. Du Bois’ notion of “double consciousness” to make the case that humor can facilitate an openness and cooperative attitude among an otherwise closed, even adversarial audience. I focus on what I call “subversive” humor, that which is employed by or on behalf of those who have been continually marginalized. When effectively used, such humor can foster the inclination and even desire to listen to others and, if (...) only for brief moments, adopt their point of view. To be able to see oneself as others see you can also be a desirable capacity, because along with such multidimensional seeing comes an epistemic advantage lacking in those who have no need nor desire to see as others do, especially if the vision of the others happens to be from below where one perceives that the promises of our explicit ideals are constantly being implicitly broken. Such humor is aesthetic, pleasurable in and of itself, and not amenable to scientific dissection. But it is also a skill that can be honed into a powerful tool of persuasion in circumstances where straightforward arguments are less effective. It can raise consciousness about the lived experiences of those suffering under systemic oppression and foster world travelling. Subversive humor encourages audiences, especially those who contribute to what Jean Harvey calls “civilized oppression”, to playfully travel across worlds and “tarry along” with the perspectives of the marginalized. (shrink)

Steels & Belpaeme (S&B) describe the role of genetic evolution in linguistic category sharing among a population of agents. We consider their methodology and conclude that, although it is plausible that genetic evolution is sufficient for such tasks, there is a bias in the presented work for such a conclusion to be reached. We suggest ways to eliminate this bias and make the model more convincingly relevant to the cognitive sciences.

Caring for children with life-shortening illnesses is a humbling task. While some decisions are simple and safe, the emotionally-charged choices regarding how to best care for these children often...

Some of Dave Chappelle’s uses of storytelling about seemingly mundane events, like his experiences with his “white friend Chip” and the police, are examples of what W.E.B. Du Bois calls “Positive Propaganda.” This is in contrast to “Demagoguery,” the sort of propaganda described by Jason Stanley that obstructs empathic recognition of others, and undermines reasonable debate among citizens regarding policies that matter: the justice system, welfare, inequality, and race, for example. Some of Chappelle’s humor, especially in his most recent Netflix (...) specials, but also in his earlier standup performances and his series The Chappelle Show, is akin to art that appeals to emotion in the ways suggested by Du Bois in “Criteria of Negro Art” (1926). Beauty is essential to art, but, “I do not care a damn for any art that is not used for propaganda. But I do care when propaganda is confined to one side while the other is stripped and silent” (p. 22). The “one side” is that which appears to extoll American ideals, but in reality undermines them, perpetuating the subordinate status of “the other”--black citizens. Replace “beauty” with “humor” or “funny”, and we see striking parallels between Chappelle’s socio-political performances and Du Bois’ call for positive propaganda, each of which constitute “civic rhetoric” broadly construed. We no longer live in Du Bois’ America of explicit denial of rights. In many ways our situation is worse, as the mechanisms of exclusion are implicit, difficult to dislodge, because they are invisible. Chappelles’ humor draws attention to subtle undermining-propaganda in our liberal democracy, transforming it through his counter-propaganda into the spectacle that it should be; ubiquitous democracy-denying propaganda should be as obvious to whites as it is to minorities. In his words, we should all see that “that shit is fucking incredible” (Killin’ Them Softly). (shrink)

This note responds to an interpretation of Mohist Canon and Explanation B 671 published by John Makeham some years ago. Makeham’s interpretation makes significant contributions to our understanding of this passage, especially in calling attention to problems with two influential previous interpretations, those of A. C. Graham and Chad Hansen.3 Yet his reading presents difficulties of its own, which I will attempt to rectify here.

The “School of Names” ming jia ) is the traditional Chinese label for a diverse group of Warring States (479-221 B.C.) thinkers who shared an interest in language, disputation, and metaphysics. They were notorious for logic-chopping, purportedly idle conceptual puzzles, and paradoxes such as “Today go to Yue but arrive yesterday” and “A white horse is not a horse.” Because reflection on language in ancient China centered on “names”.

Supererogatory acts are, in some sense, morally better their non-supererogatory alternatives. In this sense, what is it for one option A to be better than an alternative B? I argue for three main conclusions. First, relative rankings are a type of all-in action guidance. If A is better than B, then morality recommends that you A rather than B. Such all-in guidance is useful when acts have the same deontic status. Second, I argue that Right > Wrong: permissible acts are (...) always better than their impermissible alternatives. If Right > Wrong were false, then morality’s deontic verdicts would sometimes conflict with its relative rankings. Such conflict would undermine the thought that morality is a coherent, authoritative guide to action. Third, the All or Nothing Problem is not a counterexample to Right > Wrong as is commonly thought. Instead, it involves an interesting ranking reversal: whether A > B can depend on whether a certain alternative is added as a third option. (shrink)

Some understand Stein’s “Yes, but…” as an entry in the realism—instrumentalism debate (RID) itself, albeit one dissatisfied with then-extant positions. In this paper, however, I argue the opposite: Stein’s conception of science and his approach to its history and philosophy actually preclude the RID. First, I characterize Stein as persistently attending to his own historical and philosophical methods. I then describe his conception of science as both a dialectic and an enterprise, and I draw from this conception several conclusions about (...) the relations between science and its history and philosophy. Finally, I provide a reading of “Yes, but…” that follows from Stein’s conception of science. On this reading, the RID is either irrelevant to or wrong of science and, moreover, distracts from a legitimate inquiry. I conclude by interpreting Stein’s remark that there is ``no difference that makes a difference’’ between a cogent and enlightened realism and a sophisticated instrumentalism. (shrink)

In this paper, we continue investigations into the asymptotic behavior of solutions of differential equations over o-minimal structures.Let ℜ be an expansion of the real field (ℝ, +, ·).A differentiable mapF= (F1,…,F1): (a, b) → ℝiisℜ-Pfaffianif there existsG: ℝ1+l→ ℝldefinable in ℜ such thatF′(t) =G(t, F(t)) for allt∈ (a, b) and each component functionGi: ℝ1+l→ ℝ is independent of the lastl−ivariables (i= 1, …,l). If ℜ is o-minimal andF: (a, b) → ℝlis ℜ-Pfaffian, then (ℜ,F) is o-minimal (Proposition 7). We (...) say thatF: ℝ → ℝlis ultimately ℜ-Pfaffian if there existsr∈ ℝ such that the restrictionF↾(r, ∞) is ℜ-Pfaffian. (In general,ultimatelyabbreviates “for all sufficiently large positive arguments”.)The structure ℜ isclosed under asymptotic integrationif for each ultimately non-zero unary (that is, ℝ → ℝ) functionfdefinable in ℜ there is an ultimately differentiable unary functiongdefinable in ℜ such that limt→+∞[g′(t)/f(t)] = 1- If ℜ is closed under asymptotic integration, then ℜ is o-minimal and definesex: ℝ → ℝ (Proposition 2).Note that the above definitions make sense for expansions of arbitrary ordered fields. (shrink)